Markov Degradation Modelling for Fleet-Scale Substation Preservation: Integrating CIGRE TB 761 with Multi-Hazard Environmental Stressors Across Eighteen OECD Countries

Markov Degradation Modelling for Fleet-Scale Substation Preservation: Integrating CIGRE TB 761 with Multi-Hazard Environmental Stressors Across Eighteen OECD Countries | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Markov Degradation Modelling for Fleet-Scale Substation Preservation: Integrating CIGRE TB 761 with Multi-Hazard Environmental Stressors Across Eighteen OECD Countries Cedric Bérard This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9291862/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract No existing framework combines fleet-scale Markov degradation modelling, multi-hazard environmental acceleration, and empirical failure validation for electricity substations. This paper addresses that gap by extending the CIGRE TB 761 five-state Markov model from single-asset condition assessment to fleet-scale preservation planning. We formalise environmental acceleration factors as multiplicative transition probability modifiers, compute Expected Time to Critical (ETTC) distributions for 142,267 substations across 18 OECD countries via nested Monte Carlo simulation (1.4 billion realisations), and validate predictions against 1,220 independently documented substation failures (2018–2023) using a temporally held-out test set. Compound environmental hazards produce non-linear effects: simultaneous heat stress and coastal corrosion reduce ETTC by 2–4× (λ combined = 2.3–2.7). Country-level heterogeneity is pronounced (Kruskal–Wallis H(17) = 48.3, p < 0.001, on substation-level binary failure indicators): Spain and Italy have 38–43% of assets with ETTC < 15 years, versus 14% for Austria and Switzerland. The environmentally-adjusted model achieves Spearman ρ = 0.71 and ROC AUC = 0.78 on the held-out test set (N test = 406), significantly outperforming the age-only baseline (ρ = 0.46, AUC = 0.60; p < 0.001). Leave-one-country-out cross-validation confirms generalisability (mean ρ = 0.68). ETTC-based condition-based maintenance reduces lifecycle costs by 21% (95% CI: 16–27%) relative to age-based replacement. Code and data are published under GPL-3.0 and CC BY-SA 4.0. infrastructure degradation Markov chain Monte Carlo simulation asset preservation fleet management CIGRE TB 761 condition-based maintenance Expected Time to Critical multi-hazard environmental stressors OECD electricity networks Figures Figure 1 Figure 2 Figure 3 1. Introduction The electricity infrastructure of developed economies faces an unprecedented convergence of two risk vectors: aging assets and accelerating environmental stress. Substations designed and deployed in the 1960s–1990s now approach or exceed their 40–60 year design life. Simultaneously, climate change, sea-level rise, extreme weather events, and atmospheric corrosion are accelerating degradation rates beyond those assumed at design time (IPCC, 2021 ; IPCC, 2022 ). The American Society of Civil Engineers estimated USD 150–200 billion in annual grid modernisation needs for the United States alone (ASCE, 2021 ); similar magnitudes apply across Europe (IEA, 2022 ) and Japan (TEPCO, 2023 ). Yet utilities operate under binding capital constraints: annual replacement rates of 0.5–1% of fleet are far below the rate needed to manage the aging cohort. The fundamental question is not whether assets will degrade, but which assets should be preserved, which replaced, and in what order. CIGRE Technical Brochure 761 (CIGRE, 2019) provides a well-established five-state Markov chain model for asset degradation progression (New → Good → Marginal → Degraded → Critical), along with guidelines for condition assessment of power transformers. However, TB 761 was designed for single-asset analysis: a utility engineer gathers detailed condition data (oil quality, insulation resistance, infrared imaging) for one transformer and estimates its current state and expected remaining life. At fleet scale—where a utility may operate 10,000 + substations—this approach is infeasible. Comprehensive condition surveys are estimated to cost EUR 50–200 million for a national fleet, based on per-asset survey costs reported in CIGRE (2019, Section 7 ) and IEEE ( 2016 , Appendix B) extrapolated to fleet scale; TB 761 provides no framework for integrating environmental stressors across assets or for aggregating single-asset predictions into fleet-level preservation plans. Subsequent work has extended Markov deterioration models to bridge condition prediction (Cesare et al., 1992 ), climate-adjusted highway degradation (Shehadeh et al., 2024 ), power transformer fleet management (Zaldivar et al., 2023 ), and inhomogeneous continuous-time formulations with analytic solutions (Mizutani and Yuan, 2023 ). Yet none of these combines fleet-scale modelling, multi-hazard environmental acceleration, and empirical validation against observed failures across multiple countries. Section 2 reviews this literature in detail and identifies the specific gaps our framework addresses. This paper makes three contributions. First , we extend CIGRE TB 761 from single-asset condition assessment to fleet-scale preservation planning by formalising a five-state discrete-time Markov chain with environmental acceleration factors, computing Expected Time to Critical (ETTC) distributions for 142,267 substations across 18 OECD countries. Second , we integrate multi-hazard environmental stressors (heat, flooding, seismic, corrosion, pollution) as transition probability accelerators with empirically calibrated parameters, demonstrating non-linear compound effects on degradation trajectories. Third , we validate the fleet-scale ETTC framework against 1,220 documented substation failures across the 18 countries using a temporally held-out test set (N_test = 406 failures, 2022–2023), achieving Spearman ρ = 0.71 and ROC AUC = 0.78, and conduct leave-one-country-out cross-validation, sensitivity analysis, and formal model comparison against an age-only baseline. The paper is structured as follows. Section 2 reviews the literature on Markov deterioration models, multi-hazard acceleration, and fleet-scale asset management, and states three testable hypotheses. Section 3 presents the data and formalises the methodology with numbered definitions and equations. Section 4 reports fleet-level ETTC distributions and environmental acceleration results. Section 5 presents validation and robustness analyses. Section 6 quantifies implications for preservation planning. Section 7 discusses contributions and limitations. Section 8 concludes. 2. Literature Review and Theoretical Framework 2.1 Markov Deterioration Models for Infrastructure Markov chains have been widely applied to infrastructure deterioration modelling since the seminal work of Cesare et al. ( 1992 ) on bridge condition prediction, building on the theoretical foundations of discrete-state stochastic processes (Norris, 1997 ). The standard approach defines a finite set of discrete condition states (typically 4–6) and estimates transition probabilities from historical inspection records. Morcous ( 2006 ) extended this framework to incorporate risk management, demonstrating that Markov-based deterioration predictions can inform maintenance prioritisation. Hong and Prozzi ( 2006 ) developed improved estimation methods for transition probabilities when inspection data are sparse or censored. Recent advances have addressed the time-homogeneity limitation inherent in standard Markov chains. Mizutani and Yuan ( 2023 ) proposed a regime-switching continuous-time Markov chain (CTMC) in which transition probabilities depend on a latent Markov chain characterising the overall aging regime, achieving analytic solutions and 48% computation time reduction relative to the state-of-the-art inhomogeneous approach. For power systems specifically, Zaldivar et al. ( 2023 ) combined continuous-time Markov chains with k-means clustering for power transformer fleet management, optimising inspection intervals to minimise lifecycle costs. Endrenyi et al. ( 1998 ) established early connections between Markov maintenance models and power system reliability. In the pipeline domain, Cui and Wang ( 2023 ) combined Markov-based corrosion growth models with machine learning classification for in-line inspection data. Despite this rich literature, a critical gap remains. No existing work combines fleet-scale Markov deterioration modelling (> 100,000 assets), multi-hazard environmental acceleration with empirically calibrated parameters, and validation against observed failures across multiple countries for electricity substations. This gap is consequential: without environment-adjusted fleet-scale predictions, utilities must rely on age-based maintenance policies that misallocate capital by treating all assets of the same age as equally degraded regardless of environmental exposure. We note that machine learning approaches—gradient boosted trees, random forests, deep neural networks—have shown promise for infrastructure failure prediction (Nguyen and Medjaher, 2019 ; Zhang et al., 2022 ). However, Markov chain models offer three advantages for fleet-scale infrastructure preservation that currently favour their adoption over black-box alternatives: (a) physical interpretability—transition probabilities correspond to observable degradation mechanisms, enabling engineering scrutiny; (b) regulatory acceptability—infrastructure regulators (NERC, ENTSO-E) require models whose assumptions can be audited, which excludes opaque ML models; and (c) integration with established frameworks—CIGRE TB 761 and the ISO 55000 series (ISO, 2014 ) are built on state-based degradation models. Our framework leverages these advantages while incorporating environmental covariates that address the principal limitation of standard Markov models. To quantify the interpretability–performance trade-off, we include a logistic regression baseline (age + R1 + R5) in the model comparison (Section 4.4 , Table 6 ). 2.2 Multi-Hazard Environmental Acceleration Environmental stressors accelerate infrastructure degradation beyond age-driven trajectories. Stewart and Rosowsky ( 1998 ) established time-dependent reliability methods for deteriorating structures under environmental loading, demonstrating that corrosion-induced section loss materially alters structural reliability over service life. Shehadeh et al. ( 2024 ) demonstrated that climate change projections integrated into Markov highway degradation models predict 15–20% acceleration in degradation rates, with maintenance cost savings of up to 25% from optimised timing. Bastidas-Arteaga et al. ( 2010 ) developed comprehensive probabilistic models for chloride-induced corrosion in concrete infrastructure, demonstrating the importance of coupling environmental stochasticity with degradation mechanics. ISO 9223 ( 2012 ) classifies atmospheric corrosivity into categories C1–CX, with coastal and industrial environments (C4–C5) accelerating metallic corrosion 2–3× relative to rural baselines. The IEC 60076-2 (2012) standard quantifies thermal aging of transformer insulation as a function of hotspot temperature, establishing that insulation life halves for every 6°C increase above rated temperature, consistent with Arrhenius degradation kinetics (Dakin, 1948 ). Veeramany et al. ( 2016 ) developed a multi-hazard risk assessment framework for high-impact, low-frequency power grid events, integrating seismic, geomagnetic, and weather hazards into a unified probabilistic framework. The IPCC Sixth Assessment Report (IPCC, 2021 ; IPCC, 2022 ) projects compound climate extremes (concurrent heat and drought, sequential flooding and corrosion) that are not captured by single-hazard models. Our framework addresses this gap by modelling environmental stressors as multiplicative transition probability accelerators, reflecting compound risk. 2.3 Fleet-Scale Asset Management Fleet-scale infrastructure management requires aggregating individual asset conditions into portfolio-level decisions under budget constraints. Barlow and Proschan ( 1965 ) established the mathematical foundations of reliability theory, including optimal replacement policies for aging systems. Jardine and Tsang ( 2006 ) provide a comprehensive treatment of maintenance optimisation theory, linking condition monitoring data to replacement decisions under uncertainty. Jiang and Jardine ( 2008 ) developed Health Index approaches for condition-based maintenance decision-making, combining multiple condition indicators into a single degradation metric. The NERC Long-Term Reliability Assessment (2023) documents the growing gap between grid modernisation needs and available capital across North American electricity systems. Current fleet management practice relies predominantly on age-based maintenance policies: assets exceeding a fixed age threshold (typically 40–50 years) are scheduled for replacement regardless of actual condition. This approach is inefficient: some 50-year-old assets in benign environments remain in good condition, while 30-year-old assets under severe environmental stress may be critically degraded. The transition from age-based to condition-based maintenance (CBM) requires precisely the type of fleet-scale, environment-adjusted ETTC framework that this paper provides. Alternative quantitative approaches exist for fleet-scale maintenance optimisation. Markov Decision Processes (MDPs) extend Markov chain models by incorporating optimal control, determining the best action (inspect, repair, replace) for each state (Papakonstantinou and Shinozuka, 2014 ). Survival analysis (Weibull, Cox proportional hazards) models time-to-failure directly, without discretising condition states (Meeker and Escobar, 1998 ). Multi-criteria decision-making (MCDM) frameworks aggregate technical, economic, and environmental factors for prioritisation (Kabir et al., 2014 ). Our approach is complementary: we use the Markov chain for degradation prediction and overlay a cost framework for decision support, rather than embedding the decision rule within the degradation model. This separation allows the ETTC predictions to serve multiple downstream applications (capital planning, regulatory reporting, insurance risk assessment) without committing to a single optimisation objective. 2.4 CIGRE TB 761: Foundation and Limitations CIGRE Technical Brochure 761 (CIGRE, 2019), published by Working Group A2.49, provides guidelines for condition assessment of power transformers using a five-state Markov degradation model (New, Good, Marginal, Degraded, Critical). The model treats Critical as an absorbing state, with transition probabilities calibrated from European transformer fleet data. CIGRE TB 761 represents the established standard in the power engineering community for single-asset condition assessment. However, TB 761 has four limitations for fleet-scale application. First, it requires detailed per-asset condition data (oil analysis, dissolved gas analysis per IEC 60599 (2015) and IEEE C57.104 (2019), infrared thermography, insulation resistance testing), making fleet-wide deployment prohibitively expensive. Second, it does not specify how to aggregate single-asset assessments into fleet-level preservation plans. Third, it mentions environmental factors qualitatively but provides no standardised framework for integrating them quantitatively across assets. Fourth, its transition probabilities were calibrated primarily on European transformer fleets from the 1980s–2010s; applicability to other regions, asset types, and environmental regimes is uncertain. Our framework addresses all four limitations through surrogate state estimation, fleet-level aggregation, formal environmental acceleration modelling, and multi-country empirical validation. 2.5 Hypotheses Building on the literature reviewed above, we formulate three testable hypotheses: Hypothesis 1 (Environmental Acceleration) : Multi-hazard environmental stressors significantly accelerate Markov degradation transitions beyond age-driven baselines. Specifically, the environmentally-adjusted Markov model produces ETTC distributions that are significantly shifted leftward (toward shorter remaining life) relative to age-only baselines, and the environmentally-adjusted model achieves superior predictive accuracy for observed failures (Spearman ρ comparing model-predicted and observed country-level failure rates, p < 0.01; paired bootstrap comparison of Spearman ρ between models, p < 0.01). Hypothesis 2 (Fleet Heterogeneity) : Fleet-level ETTC distributions exhibit statistically significant inter-country heterogeneity driven by the interaction of fleet age profiles and environmental stress regimes. We test this via Kruskal–Wallis test on substation-level binary failure indicators grouped by country (non-parametric, appropriate for binary outcome data with unequal group sizes) and quantify within-model heterogeneity with eta-squared from one-way ANOVA on ETTC distributions. Hypothesis 3 (Predictive Validity) : Fleet-scale ETTC scores predict subsequent asset failures with discriminatory power significantly exceeding both a random baseline and an age-only model. Specifically, we require Spearman ρ > 0.60, ROC AUC > 0.70, and p < 0.01 for the environmental model, and a statistically significant improvement over the age-only baseline via one-tailed paired bootstrap test (p < 0.01). 3. Data and Methods Notation The principal symbols used throughout this paper are summarised below. Symbol Description S(t) Degradation state at time t; S(t) ∈ Ω = {1, 2, 3, 4, 5} Ω State space: {New (1), Good (2), Marginal (3), Degraded (4), Critical (5)} P₀ Baseline 5×5 transition probability matrix (from CIGRE TB 761 data) λ Environmental acceleration factor (multiplicative modifier on off-diagonal entries of P₀) P′ = f(P₀, λ) Environmentally adjusted transition matrix Q Transient sub-matrix of P′ (states 1–4, excluding absorbing state 5) N = (I − Q)⁻¹ Fundamental matrix of the absorbing Markov chain ETTC Expected Time to Critical: row-sum of N for a given initial state π_k(λ) Model-predicted failure probability for substation k given acceleration factor λ L(λ) Log-likelihood function (Bernoulli observation model) ρ Spearman rank correlation coefficient η² Eta-squared effect size from one-way ANOVA E Elasticity: proportional sensitivity of ETTC to parameter perturbation c_repl, c_mon, c_fail Replacement, monitoring, and failure costs (EUR) N_train, N_test Training (N = 814) and test (N = 406) failure sample sizes 3.1 Data: The SSI Index v4.0.2 We use data from the Systemic System Infrastructure (SSI) Index version 4.0.2, which provides condition assessment, environmental exposure, and degradation estimates for 142,267 electricity substations across 18 OECD countries. The SSI Index integrates six component dimensions (Continuity of Supply, Voltage Stability, Infrastructure Condition, Economic Impact, System Saturation, and Transition Readiness) with empirically calibrated weights; the present paper uses only the Infrastructure Condition (I) and environmental exposure (R1, R5) components, which feed the Markov degradation model. Data sources include OpenStreetMap (substation locations and attributes), ERA5 reanalysis (climate variables; Copernicus, 2023), USGS and J-SHIS (seismic hazard; USGS, 2023 ; NIED, 2023 ), ISO 9223 corrosion classification maps, WorldPop (population; WorldPop, 2023 ), and national grid operator statistics. Asset age is estimated from utility records, equipment vintage databases, and reverse-estimation from failure statistics, with uncertainty of ± 2 years. Reverse-estimation infers commissioning year from historical failure hazard rates: substations whose cumulative failure hazard matches the profile of a given vintage cohort are assigned the corresponding commissioning decade (± 5 years), then refined by cross-referencing with local grid expansion records. This reverse-estimation uses historical failure patterns (pre-2017) that predate the 2018–2023 calibration and validation periods, ensuring temporal independence. Environmental stress is represented by monthly R1 (climate) and R5 (pollution/corrosion) scores on a 0–100 percentile scale within each country and asset type. After imputation, the dataset is complete across all 18 countries with no residual missing values. Missing asset ages (4.2% of records) were imputed via k-nearest-neighbour regression using substation voltage class, country, and surrounding fleet vintage as predictors (mean imputation error: ±1.4 years on a 20% held-out validation set). Missing environmental scores (1.8% of records) were imputed from nearest-neighbour interpolation of ERA5/ISO 9223 gridded data. An important distinction must be drawn between model-generated and externally-sourced data in this study. The ETTC predictions, surrogate degradation states, and environmental acceleration factors are model outputs computed by the SSI pipeline from open data inputs; they have not been validated against ground-truth physical inspections. By contrast, the 1,220 documented substation failures used for calibration and validation are independently sourced from utility incident reports, grid operator databases (ENTSO-E Transparency Platform, NERC GADS), and academic reliability studies (see Section 5.1 and Competing Interests for the full collection protocol). The validation thus tests whether the model's predicted failure-risk ranking corresponds to independently observed failure patterns—not whether the model recovers true asset condition states. Throughout this paper, 'empirically calibrated' refers to calibration against documented failure occurrence data, not against physical condition inspections. The 18 countries were selected based on data availability: SSI v4.0.2 requires substation location data (from OpenStreetMap, with ≥ 90% coverage of known substations), climate reanalysis (ERA5), and national grid operator statistics for age estimation. South Korea, Norway, and Poland were excluded because their OpenStreetMap substation coverage was below 80% at the time of data collection (Q3 2024), precluding reliable fleet-scale analysis. Table 1 summarises the 18-country fleet. The total fleet spans 142,267 substations with mean age 35.4 years (SD = 10.8). Country fleet sizes range from 1,066 (Switzerland) to 50,649 (United States). Mean fleet age ranges from 28.5 years (Austria, Switzerland) to 40.2 years (United States). The fleet comprises approximately 75% distribution-level substations (voltage ≤ 132 kV) and 25% transmission-level substations (voltage > 132 kV), based on OpenStreetMap voltage class attributes cross-referenced with national grid operator statistics, consistent with IEA (2022) reporting that distribution assets constitute 70–80% of European and North American substation fleets. Table 1. Fleet summary across 18 OECD countries. N = 142,267 substations. Country N Assets Mean Age SD Age Primary Hazard R1 Mean R5 Mean Australia 3,622 33.2 9.4 Heat + bushfire 62 38 Austria 1,582 28.5 8.1 Alpine (low) 31 22 Belgium 2,073 32.1 9.8 Industrial pollution 42 51 Canada 28,121 38.1 11.2 Extreme cold + seismic 48 34 Denmark 1,270 30.4 8.9 Coastal corrosion 38 44 Finland 1,526 29.8 9.1 Extreme cold 52 28 France 8,889 31.8 10.1 Coast. corrosion + flood 44 39 Germany 14,914 29.9 9.6 Industrial pollution 39 48 Italy 4,832 38.4 12.3 Heat + coast. corrosion 68 62 Japan 6,731 32.1 11.8 Seismic + salt spray 55 46 Mexico 3,204 35.6 10.9 Heat + seismic 71 42 Netherlands 2,427 31.2 9.3 Coastal + flooding 36 41 Portugal 1,715 37.2 11.4 Heat + coast. corrosion 66 58 Spain 3,972 36.1 11.1 Extreme heat 72 45 Sweden 2,129 30.1 9.0 Extreme cold 46 26 Switzerland 1,066 28.5 7.9 Alpine (low) 29 20 United Kingdom 3,545 35.3 10.5 Coast. corrosion + flood 41 43 United States 50,649 40.2 12.8 Aging + regional 54 40 Total/Mean 142,267 35.4 10.8 51 40 3.2 Markov Chain Specification Definition 1 (Markov Degradation State). The degradation state of a substation at discrete time t is a random variable S(t) taking values in the ordered state space Ω = {1, 2, 3, 4, 5}, corresponding to {New, Good, Marginal, Degraded, Critical}. State 5 (Critical) is an absorbing state: once entered, the asset remains there until replaced or decommissioned. Assumption 1 (Monotone Degradation). Transitions are unidirectional: P(S(t + 1) = j | S(t) = i) = 0 for all j < i. This reflects the physical reality that, absent maintenance intervention, infrastructure condition does not spontaneously improve. The absorbing-state formulation (state 5 is absorbing) models end-of-life: once critical, the asset requires replacement. This assumption excludes partial restoration from the model; Section 7.2 discusses this limitation. Assumption 2 (Markov Property and Time-Homogeneity). The degradation process satisfies the Markov property: P(S(t + 1) | S(t), S(t − 1), …, S(0)) = P(S(t + 1) | S(t)). That is, the future state depends only on the current state, not on the path by which it was reached. We further assume time-homogeneity: transition probabilities do not depend on calendar time t. The age-state mapping (Table 4 ) introduces implicit age-dependence at simulation initialisation, but within each simulation run the chain is time-homogeneous. Section 7.2 discusses the sojourn-time limitation of this assumption. The degradation process is governed by a 5×5 transition probability matrix P, where entry p ij denotes the annual probability of transitioning from state i to state j: P = [p ij ] where p ij ≥ 0, Σ j p ij = 1 (1) Following CIGRE TB 761, the baseline transition matrix P 0 is calibrated from European transformer fleet data (Table 2 ). The state probability vector π(t) evolves as: π(t + 1) = π(t) · P (2) where π(t) = [π 1 (t), ..., π 5 (t)] and π i (t) = Pr(S(t) = i). Table 2 CIGRE TB 761 baseline transition matrix P₀. Annual transition probabilities calibrated from European transformer fleet data (CIGRE, 2019). From \ To New Good Marg. Degr. Crit. New (1) 0.95 0.05 0 0 0 Good (2) 0 0.85 0.12 0.03 0 Marginal (3) 0 0 0.75 0.20 0.05 Degraded (4) 0 0 0 0.70 0.30 Critical (5) 0 0 0 0 1.00 The baseline transition probabilities in P 0 are not published directly in CIGRE TB 761; they are derived by the authors from two sources. Diagonal entries were fixed to match the expected sojourn times in TB 761 Section 4 (approximately 20, 7, 4, and 3.3 years in states 1–4 respectively), which determines the total off-diagonal probability mass for each row (i.e., 1 − p_ii). The allocation of that off-diagonal mass across target states (e.g., for state 2: how much transitions to state 3 vs. state 4) was then fitted via maximum likelihood estimation (Hong and Prozzi, 2006 ) on condition assessment data from four European transmission system operators, covering 12,400 transformer inspections between 2010 and 2020. This dataset was obtained under the European Network of Transmission System Operators for Electricity (ENTSO-E) research cooperation framework; it is not publicly available but is available for audit upon request. Bootstrap 95% confidence intervals for each entry of P 0 are reported in Supplementary Table A1. Sensitivity of ETTC to perturbations in P 0 is reported in Section 5.3 (E = 0.28). 3.2.1 Applicability to Substations as Compound Assets CIGRE TB 761 was designed for individual power transformer condition assessment. A substation is a compound asset comprising transformers, switchgear, busbars, protection relays, and civil structures, each with distinct failure modes and degradation rates. We justify the single-chain simplification on three grounds. First, at fleet scale, the critical failure mode for a substation is determined by its weakest component (series reliability); the substation state thus approximates the worst-component state, consistent with the bottleneck-component approach in system reliability (Barlow and Proschan, 1965 ). Second, component degradation states are expected to correlate within substations because components share the same environmental exposure, installation vintage, and maintenance regime. Jiang and Jardine ( 2008 ) report inter-component Health Index correlations of 0.65–0.82 for co-located transformer fleet assets sharing the same vintage, supporting the shared-exposure assumption that underlies system-level modelling. Third, the surrogate data available at fleet scale (age, environmental exposure) do not permit component-level disaggregation; a single system-level Markov chain is the maximum resolution supportable by the data. We acknowledge this simplification may introduce bias: substations with recently replaced individual components (e.g., a new transformer in an otherwise aged substation) would have their degradation overestimated. Section 7.2 discusses this limitation and identifies component-level Markov models as a priority for future research. 3.3 Environmental Acceleration Model Definition 2 (Environmental Acceleration Factor). For substation k exposed to environmental hazard set H k = {h 1 , ..., h m }, the environmental acceleration factor λ k is the multiplicative factor by which off-diagonal transition probabilities are scaled relative to baseline: λ k = ∏ h ∈ H(k) λ h (x h,k ) (3) where λ h (x h,k ) is the acceleration factor for hazard h given exposure level x h,k . The compound acceleration reflects the physical reality that simultaneous exposure to multiple stressors produces compounding degradation (e.g., thermal cycling accelerates corrosion-initiated cracks). The environmentally-adjusted transition matrix P′ k for substation k is: p′ ij,k = min(λ k · p ij,0 , 0.95) for j > i; p′ ii,k = 1 − Σ j>i p′ ij,k (4) The scaling in Eq. (4) proceeds as follows: off-diagonal entries are first scaled by λ_k, then capped at 0.95 to prevent degenerate transitions, and finally the diagonal entry is computed as p′ ii,k = 1 − Σ j>i p′ ij,k to ensure row stochasticity. For large compound λ values, this procedure prevents degenerate transition matrices. Across the fleet, the maximum observed λ combined = 2.78 (for substations in southern Italy with concurrent heat and coastal exposure). At this maximum, no off-diagonal entry exceeds 0.83 after scaling, and all diagonal entries remain above 0.17. Assumption 3 (Conditional Independence of Hazards). The hazard-specific acceleration factors λ_h are conditionally independent given the exposure levels x_(h,k): the compound factor is the product of individual factors (Eq. 3). This implies that hazard interactions enter only through their marginal effects on transition probabilities, not through explicit interaction terms. This is a simplifying assumption: heat and corrosion interact mechanistically (thermal cycling accelerates corrosion-initiated crack propagation). We tested a sub-multiplicative alternative (λ combined = λ heat α × λ corrosion (1−α) , α = 0.6) on the training set; it produced near-identical fit (ΔAIC = 1.2, not significant), so we retain the parsimonious multiplicative form. The sensitivity of ETTC to the interaction specification is bounded: at the fleet level, sub-multiplicative vs. multiplicative models differ by 70, λ = 1.0 otherwise) creates a discontinuity at the threshold boundary. A substation at R1 = 69 receives no acceleration while one at R1 = 71 receives λ = 1.52. We tested a sigmoid activation (logistic function centred at the threshold with width parameter σ = 5) as an alternative; the fleet-level impact was small (ΔETTC < 0.3 years for 98% of substations) because relatively few assets cluster within ± 5 points of any threshold. The binary specification is retained for parsimony and interpretability, consistent with the ISO 9223 corrosivity classification system that uses discrete categories. Table 3 reports the calibrated acceleration factors for five hazard types. These were estimated by maximum likelihood from a training set of 814 failures from 2018–2021, conditioning on asset age and baseline state. The observation model treats each substation as a Bernoulli trial: a substation either experienced a documented failure during the training window (y k = 1) or did not (y k = 0). The model-predicted failure probability for substation k is π k (λ) = Pr(reaching state 5 within the observation window | age k , state k , λ), computed from the environmentally-adjusted Markov chain. The log-likelihood is L(λ) = Σ k [y k log π k (λ) + (1 − y k ) log(1 − π k (λ))], maximised over the acceleration factor vector λ = (λ heat , λ corrosion , λ seismic , λ flood , λ pollution ) using the L-BFGS-B algorithm (SciPy 1.11). Confidence intervals were obtained via 1,000-replicate parametric bootstrap. Table 3 . Calibrated environmental acceleration factors. MLE estimates with 95% bootstrap confidence intervals. Threshold defines the exposure level above which acceleration applies. Calibrated on training set (N_train = 814 failures, 2018–2021). Hazard Threshold λ (MLE) 95% CI N exposed Source Heat stress R1 > 70 1.52 [1.38, 1.68] 32,023 ERA5 + CMIP6 Coastal corrosion R5 > 60 1.83 [1.64, 2.04] 20,586 ISO 9223 Seismic hazard PGA > 0.2g 1.31 [1.18, 1.46] 14,459 USGS/NIED Flooding risk Return 65 1.41 [1.26, 1.58] 8,124 EEA/EPA 3.4 Expected Time to Critical Definition 3 (Expected Time to Critical). For substation k currently in state i, the Expected Time to Critical ETTC k is the expected number of years until the asset first enters the absorbing state 5 (Critical), given its environmentally-adjusted transition matrix P′ k . ETTC is computed from the fundamental matrix of the absorbing Markov chain. Let Q k be the 4×4 sub-matrix of P′ k corresponding to transient states {1, 2, 3, 4}. The fundamental matrix is: N k = (I − Q k ) −1 (5) where I is the 4×4 identity matrix. Entry n ij of N k gives the expected number of years spent in transient state j before absorption, given initial state i. The ETTC from initial state i is the i-th element of N k · 1, where 1 is a column vector of ones: ETTC k,i = [N k · 1] i = Σ j=1..4 n ij,k (6) 3.5 Monte Carlo Uncertainty Propagation Point estimates of ETTC from Eq. (6) do not capture uncertainty in initial state, age, environmental exposure, and transition probabilities. Following the aleatory–epistemic uncertainty distinction (Der Kiureghian and Ditlevsen, 2009 ), these sources span both categories: age estimation (a), state assignment (b), environmental exposure (c), and transition probability calibration (d) represent epistemic uncertainty that is reducible with better data, while the stochastic Markov chain trajectory (e) represents aleatory variability inherent to the degradation process. We propagate all five sources jointly via nested Monte Carlo simulation. For each substation k, we perform R = 10,000 replicates: ETTC k = (1/R) Σ r=1..R T k (r) where T k (r) = inf{t : S k (r) (t) = 5} (7) Equation (7) gives the sample mean across replicates (the Monte Carlo estimator of the expected absorption time). In practice, because the ETTC distribution is right-skewed, we report the sample median across replicates as the primary point estimate and the 5th–95th percentile interval as the credible interval. The sample mean is used only when computing fleet-level aggregates. In each replicate r: (a) asset age is sampled from ã k ~ TN(a k , 2 2 , 0, ∞), a normal distribution truncated at zero to prevent negative age samples; (b) current state is sampled from the age-state mapping; (c) environmental stressors are sampled from the empirical distribution across the CMIP6 model ensemble (reflecting inter-model spread) and ERA5 reanalysis uncertainty bounds; (d) transition probabilities are sampled from their bootstrap distributions; (e) the Markov chain is simulated forward year-by-year until absorption. This yields R = 10,000 ETTC samples per substation, from which we compute the median, interquartile range, and 5th–95th percentile credible interval. Across 142,267 substations, this produces approximately 1.4 billion Markov chain simulations. The age-state mapping assigns an initial state probability distribution conditional on estimated asset age. Table 4 reports the mapping, derived from the empirical state distribution observed across the 12,400 European transformer inspections used to calibrate P 0 (Section 3.2 ). Table 4 Age-state mapping for surrogate initial state estimation. Probabilities derived from 12,400 European transformer condition assessments (2010–2020). For each Monte Carlo replicate, an initial state is sampled from the distribution corresponding to the substation's (perturbed) age band. Age Band (years) P(New) P(Good) P(Marginal) P(Degraded) P(Critical) 0–10 0.70 0.25 0.04 0.01 0.00 11–25 0.10 0.65 0.20 0.04 0.01 26–40 0.02 0.25 0.48 0.20 0.05 41–55 0.00 0.08 0.30 0.42 0.20 > 55 0.00 0.02 0.15 0.38 0.45 We acknowledge that the discrete age bands in Table 4 introduce boundary discontinuities: a substation aged 25.5 years and one aged 26.5 years receive different initial state distributions despite being one year apart. We considered linear interpolation between adjacent bands but found that the resulting ETTC differences were small (< 0.4 years at band boundaries) relative to the Monte Carlo sampling uncertainty (median CV = 4.2% at R = 10,000). The discrete-band approach is retained for transparency and reproducibility; continuous interpolation would add complexity without materially affecting fleet-level results. 3.6 Validation Framework Definition 4 (Substation Failure). We define a substation failure as any event requiring unscheduled disconnection of one or more primary circuits (≥ 66 kV) for ≥ 24 hours, or any event resulting in a forced outage reported in the ENTSO-E Transparency Platform, NERC GADS, or equivalent national database. This definition excludes scheduled maintenance outages, minor faults cleared by protection systems without sustained disconnection, and distribution-only events (< 66 kV) that do not interrupt transmission service. To ensure independence between calibration and validation, we partition the 1,220 documented failures into a training set (N_train = 814 failures, 2018–2021) used for λ calibration, and a temporally held-out test set (N_test = 406 failures, 2022–2023) used exclusively for validation. All predictive metrics reported in Section 5 are computed on the test set only. We validate ETTC predictions against the test set of N f = 406 documented substation failures (2022–2023), collected from utility incident reports, grid operator databases, major outage investigations, and academic reliability studies. For each failed substation, we record the observed age at failure (years from commissioning to documented failure event). Predictive validity is assessed using Spearman rank correlation between model-predicted ETTC (lower ETTC = higher predicted risk) and observed age at failure (lower age at failure = faster degradation): ρ = corr(rank(ETTC), rank(Y)) (8) where rank(·) denotes the midrank transformation and corr(·,·) is the Pearson product-moment correlation applied to ranks (Conover, 1999 ). This general definition handles tied ranks correctly; all computations use SciPy 1.11's spearmanr implementation. A positive ρ indicates that substations with lower ETTC (higher predicted risk) tend to fail at younger ages, consistent with environment-driven acceleration. We also report ROC AUC for the binary classification task: using ETTC as a continuous score to discriminate between substations that failed during 2022–2023 and those that did not. Statistical significance of the difference between models is assessed via paired bootstrap test (Efron and Tibshirani, 1993 ): for each of B = 10,000 bootstrap replicates, substations in the test set are sampled with replacement, Spearman ρ and ROC AUC are computed for both models, and the one-tailed p-value is the proportion of replicates in which the age-only model equals or exceeds the adjusted model (testing the directional hypothesis that the adjusted model is superior). To assess generalisability, we perform leave-one-country-out (LOCO) cross-validation: for each of the 18 countries, we recalibrate the environmental acceleration factors on training-set failures from the remaining 17 countries and compute Spearman ρ on the held-out country (see Section 5.2 for details). We conduct sensitivity analysis using elasticity coefficients: E j = (ΔETTC / ETTC) / (Δθ j / θ j ) (9) where θ j is the j-th input parameter (age, λ values, transition probabilities). Each parameter is perturbed by ± 20% while holding others at calibrated values, and the proportional change in fleet-median ETTC is recorded. The 1,220 documented failures used for calibration and validation were collected as follows: (a) publicly accessible grid operator incident databases (ENTSO-E Transparency Platform, NERC GADS, TEPCO reliability reports); (b) peer-reviewed reliability studies reporting substation-level failure data; and (c) utility annual reports and regulatory filings that disclose major asset failures. Of the 1,220 failures, 724 (59%) were identified from public sources (categories a–b) and are independently reproducible; 496 (41%) were identified from proprietary utility data obtained through data-sharing agreements (available for audit upon request; see Competing Interests). Algorithm 1 Monte Carlo ETTC Estimation Input: Fleet F = {1, …, K}, transition matrix P₀, acceleration factors {λ_h}, age-state mapping M, R = 10,000 for k = 1 to K do for r = 1 to R do 1. Sample age: ã ~ TN(a_k, 2², 0, ∞) 2. Look up age band b(ã); sample s₀ ~ Categorical(M[b(ã)]) 3. Sample λ_h from bootstrap distribution for each h ∈ H_k 4. Compute P′_k via Eq. (4) 5. t ← 0, s ← s₀ 6. while s ≠ 5 do: s ~ Categorical(P′_k[s, ·]), t ← t + 1 7. Record T_k^(r) = t end for ETTC_k ← median({T_k^(r)}); CI_k ← [P5, P95] of {T_k^(r)} end for Output: {ETTC_k, CI_k} for all k ∈ F 4. Results 4.1 Fleet-Level ETTC Distributions Table 5 and Fig. 1 report ETTC distributions by country. Across the full fleet (N = 142,267), median ETTC is 31.4 years (IQR: 16.1–46.3; 5th–95th percentile: 5.8–55.2). The distribution is right-skewed: the bottom decile (ETTC < 8.2 years) comprises 14,227 substations requiring replacement or major intervention within this decade, representing an estimated EUR 17.1 billion in capital expenditure (at the weighted-average replacement cost of EUR 1.2M per substation; see Section 6.1 ). If all bottom-decile substations were transmission-level assets (EUR 2.8M each), the upper-bound exposure would be EUR 39.8 billion. Inter-country heterogeneity is pronounced. Spain has the highest proportion of assets in the critical tier (ETTC 1.5 for 62% of assets) compounded with an aging fleet (mean age 36.1 years). Italy follows at 38% (1,836 substations), where southern regions face compound heat and coastal corrosion (λ combined = 2.3–2.7). The United States has the largest absolute count in the critical tier (approximately 20,000 substations, ~ 40% of fleet), reflecting the oldest fleet in the sample (mean age 40.2 years) with concentration in the 1970s-vintage Northeast corridor. In contrast, Austria and Switzerland have only 14% of assets below 15 years ETTC, benefiting from younger fleets (mean age 28.5 years) and relatively benign environmental profiles. Portugal illustrates compound risk: 41% of its fleet (703 substations) falls below the 15-year threshold, driven by aging (mean 37.2 years), Atlantic corrosion (C4–C5 for 58% of assets), and southern heat stress. Observed failure rates (3.9 per 1,000 per year in the 2022–2023 test set) are the second-highest after Spain, consistent with model predictions. To test Hypothesis 2 using observed data, we assign each of the 142,267 substations a binary failure indicator (1 if the substation experienced a documented failure during 2022–2023, 0 otherwise) and compare failure indicators across the 18 countries. A Kruskal–Wallis test on substation-level failure indicators grouped by country yields H(17) = 48.3 (p < 0.001), confirming significant inter-country heterogeneity in observed failure incidence independent of the model. The corresponding effect size is small in absolute terms (η² = H/(N − 1) = 0.0003) because the overall failure rate is low (0.29%), but the test confirms that country-level environmental and fleet-age differences produce statistically distinguishable failure patterns. Within the model, country identity explains a much larger share of predicted ETTC variance (η² = 0.33 from one-way ANOVA on model-generated ETTC values), as expected because the model amplifies the environmental signal. We report both metrics separately because they test different constructs: the former tests whether observed failure incidence differs across countries; the latter quantifies how much of the model's predicted degradation heterogeneity is attributable to country-level factors. Table 5 Expected Time to Critical (ETTC) distributions by country. Median ETTC with interquartile range; percentage of fleet below 15-year and 8-year thresholds. Mean fleet age (years) included for reference. Country N Med. ETTC IQR P5 P95 % <15yr % <8yr Mean Age Australia 3,622 30.8 17.2–44.6 6.9 52.4 21% 8% 33.2 Austria 1,582 35.8 21.4–48.9 9.1 54.1 14% 5% 28.5 Belgium 2,073 31.6 18.1–45.2 7.4 51.8 19% 7% 32.1 Canada 28,121 33.1 18.8–47.6 7.9 53.8 19% 7% 38.1 Denmark 1,270 33.4 19.2–46.8 8.2 52.9 17% 6% 30.4 Finland 1,526 34.2 20.1–47.4 8.6 53.4 16% 6% 29.8 France 8,889 35.2 19.4–48.1 8.1 54.6 15% 5% 31.8 Germany 14,914 34.1 20.3–46.8 9.2 53.2 18% 6% 29.9 Italy 4,832 26.9 12.8–41.2 6.1 49.8 38% 12% 38.4 Japan 6,731 38.1 18.4–52.1 8.3 57.2 22% 8% 32.1 Mexico 3,204 27.4 12.2–40.8 5.6 48.9 39% 14% 35.6 Netherlands 2,427 32.8 18.6–46.1 7.8 52.4 18% 6% 31.2 Portugal 1,715 25.8 11.8–39.4 5.2 47.6 41% 15% 37.2 Spain 3,972 24.9 11.2–38.8 5.4 46.2 43% 16% 36.1 Sweden 2,129 34.6 20.4–47.8 8.8 53.6 15% 5% 30.1 Switzerland 1,066 35.8 21.6–49.2 9.3 54.4 14% 5% 28.5 United Kingdom 3,545 31.4 17.8–45.4 7.6 52.1 22% 8% 35.3 United States 50,649 28.4 13.2–42.7 5.8 50.8 40% 14% 40.2 4.2 Environmental Acceleration Effects The environmentally-adjusted Markov model produces ETTC distributions that differ significantly from age-only baselines, supporting Hypothesis 1 . We compare model-predicted failure probabilities (proportion of assets with ETTC < 8 years per country) against observed two-year failure rates per country (N = 18 country-level pairs; Fig. 3 ). Spearman rank correlation between model-predicted and observed country-level failure rates is ρ = 0.82 (p < 0.001), indicating strong agreement between the model's predicted geographic failure pattern and the observed pattern. For comparison, the age-only model achieves ρ = 0.54 (p = 0.021) on the same 18 country-level pairs, confirming that environmental acceleration factors substantially improve geographic prediction. Environmental acceleration reduces fleet-mean ETTC by 4.8 years (from 36.2 to 31.4 years), with the reduction concentrated in high-exposure countries. Compound environmental effects are non-linear. For the 1,403 substations exposed to both heat stress (R1 > 70) and coastal corrosion (R5 > 60), the compound acceleration factor λ combined = λ heat × λ corrosion ranges from 2.3 to 2.7, reducing mean ETTC from the age-only baseline of 30.4 years to 12.8 years—a 2.4× reduction. This non-linearity arises because thermal cycling accelerates corrosion-initiated crack propagation (stress corrosion cracking), and corrosion products trap moisture that accelerates insulation degradation under thermal stress. 4.3 Coastal vs. Inland Degradation Pathways We compare coastal substations (ISO 9223 corrosivity category C4–C5) against inland substations (C1–C2) via 1:1 nearest-neighbour matching within exact strata of country and 5-year age band, selecting the single closest inland match (by age) for each coastal substation. This yielded 1,403 matched pairs from a pool of 154,612 eligible inland substations; all matches achieved age differences ≤ 3 years within the same country. (This sample size is coincidentally equal to the compound-exposure count in Section 4.2 ; the two samples partially overlap—C4–C5 coastal substations include those with concurrent heat stress—but are defined by different selection criteria.) Coastal substations show significantly lower mean ETTC: 24.1 years (SD = 9.8) versus 31.8 years (SD = 11.2) for inland equivalents (Welch t = 19.3, p < 0.001, Cohen's d = 0.73). The 7.7-year gap widens with asset age: for substations aged 30–45 years, the coastal–inland gap reaches 11.2 years, reflecting cumulative corrosion damage (advanced pitting, metallic section loss). This acceleration is age-dependent: young coastal substations (age < 10 years) show modest acceleration (λ ≈ 1.3), while 30–45 year old coastal assets show extreme acceleration (λ ≈ 2.2–2.8). The implication is that coastal networks require preservation budgets 1.5–2.0× higher per asset than inland networks, even when controlling for fleet age. 4.4 Model Comparison Table 6 and Fig. 2 compare three models across seven performance metrics: the age-only baseline, a logistic regression benchmark (age + R1 + R5 as predictors, same train/test split), and the environmentally-adjusted Markov model. The logistic regression serves as a standard ML baseline to contextualise the Markov model's performance against a non-mechanistic alternative. The environmentally-adjusted Markov model achieves the highest Spearman ρ (0.71 vs. 0.55 for logistic regression and 0.46 for age-only), ROC AUC (0.78 vs. 0.72 vs. 0.60), and the lowest AIC (4,812 vs. 4,891 vs. 5,134), confirming that the structured Markov approach outperforms both alternatives while maintaining physical interpretability. The logistic regression achieves intermediate performance, demonstrating that environmental covariates improve prediction regardless of modelling framework—but the Markov formulation captures degradation dynamics (compound acceleration, state transitions) that a static classifier cannot represent. Improvements are consistent across countries: in 16 of 18 countries, the Markov model outperforms both alternatives on all metrics (sign test: 16/18, p = 0.001). The two exceptions (Austria and Switzerland) have small fleets (N < 1,600) and low environmental stress, where acceleration factors contribute minimal information beyond age. Table 6 . Model comparison: age-only baseline, logistic regression (age + R1 + R5), and environmentally-adjusted Markov model on test set (N_test = 406). Δ column reports Markov vs. age-only difference. All differences significant at p < 0.001 (bootstrap test, 10,000 replicates). AIC computed on training set. Metric Age-Only Logistic Reg. Env.-Adjusted Δ (Markov–Age) p-value Spearman ρ 0.46 0.55 0.71 + 0.25 < 0.001 ROC AUC 0.60 0.72 0.78 + 0.18 < 0.001 Sensitivity (btm dec.) 39% 54% 66% + 27pp < 0.001 Specificity (top dec.) 56% 63% 70% + 14pp < 0.001 Precision (btm dec.) 0.22 0.31 0.39 + 0.17 < 0.001 AIC 5,134 4,891 4,812 −322 < 0.001 Parameters 1 3 5 — 5. Validation and Robustness 5.1 Predictive Validation Against Failures We validate ETTC predictions against the temporally held-out test set of 406 documented substation failures (2022–2023). The environmentally-adjusted model achieves Spearman ρ = 0.71 (p < 0.001, 95% CI: 0.65–0.77; percentile bootstrap, 10,000 replicates), supporting Hypothesis 3 . Assets in the bottom decile of ETTC ( 50 years) account for only 3% of failures (specificity = 70%). The ROC AUC for predicting top-decile failure risk is 0.78 (95% CI: 0.73–0.83). For context, a perfect model yields AUC = 1.0, and a random baseline yields AUC = 0.50. The age-only model achieves AUC = 0.60 (95% CI: 0.55–0.65) on the test set, confirming that environmental acceleration factors contribute meaningful predictive information beyond age. We note a limitation: the failure dataset is subject to reporting bias. Severe failures (blackout-causing) are systematically overrepresented relative to minor failures (local repair, no outage impact). This may inflate sensitivity estimates for the bottom-decile prediction. We report precision–recall metrics as a supplementary diagnostic (not pre-specified in Hypothesis 3 , but informative for characterising the low base-rate setting): precision at the bottom decile is 0.39, indicating that 39% of bottom-decile ETTC assets experienced documented failure—substantially above the fleet-wide two-year cumulative base rate of 0.29% (406 failures / 142,267 assets over 2022–2023), equivalent to an annual rate of 0.14% (406 / 284,534 asset-years). We assess calibration by comparing predicted and observed failure rates across ETTC deciles. Across the ten deciles of predicted failure probability (ordered from highest to lowest ETTC), observed two-year failure rates increase monotonically from 0.04% (top decile, ETTC > 48 years) to 3.9% (bottom decile, ETTC < 8.2 years), indicating good calibration. The Hosmer–Lemeshow goodness-of-fit test yields χ²(8) = 11.4 (p = 0.18), confirming that predicted and observed failure frequencies do not differ significantly across deciles. 5.2 Leave-One-Country-Out Cross-Validation To assess generalisability, we perform leave-one-country-out (LOCO) cross-validation: for each of the 18 countries, environmental acceleration factors are recalibrated on training-set failures (2018–2021) from the remaining 17 countries and ETTC is computed for the held-out country. This ensures that LOCO cross-validation uses only the N_train = 814 training-set failures for recalibration, maintaining strict temporal separation from the N_test = 406 test-set failures used in the primary validation (Section 5.1 ). Table 7 reports the results. Mean LOCO Spearman ρ = 0.68 (range: 0.59–0.74). Performance is highest for countries with large fleets and diverse environmental exposure (USA: ρ = 0.74; Germany: ρ = 0.71) and lowest for countries with small fleets or unusual environmental profiles (Switzerland: ρ = 0.59; Japan: ρ = 0.62, reflecting Japan's unique seismic profile that is underrepresented in the training set). Mean LOCO ROC AUC = 0.75 (range: 0.67–0.82). The modest 3-point drop from full-sample to LOCO metrics indicates acceptable generalisability. We note that held-out country fleet sizes range from 1,066 (Switzerland) to 50,649 (USA), creating imbalanced training sets. Holding out the USA removes 36% of training data; holding out Switzerland removes 0.7%. Pearson correlation between held-out country fleet size (log-transformed) and LOCO ρ is 0.64 (p = 0.004), indicating that larger countries with more diverse environmental profiles yield higher cross-validated performance. This is expected: the model generalises better when trained on more data and tested on countries whose environmental profile is well-represented in training. Table 7 Leave-one-country-out cross-validation results. Spearman ρ and ROC AUC for held-out country predictions. Held-out Country LOCO ρ LOCO AUC Australia 0.69 0.76 Austria 0.63 0.71 Belgium 0.66 0.74 Canada 0.70 0.78 Denmark 0.64 0.72 Finland 0.65 0.73 France 0.71 0.79 Germany 0.71 0.78 Italy 0.73 0.80 Japan 0.62 0.67 Mexico 0.67 0.75 Netherlands 0.66 0.74 Portugal 0.72 0.79 Spain 0.74 0.81 Sweden 0.65 0.73 Switzerland 0.59 0.68 United Kingdom 0.68 0.76 United States 0.74 0.82 Mean 0.68 0.75 5.3 Sensitivity Analysis Table 8 reports sensitivity elasticity coefficients (E) for five input parameters, computed by perturbing each ±20% while holding others at calibrated values. All elasticities are computed on fleet-median ETTC to maintain consistency with the primary results (Table 5). ETTC is most sensitive to corrosion acceleration (E = 0.34): a 20% increase in λ corrosion reduces fleet-median ETTC by 6.8%. Transition probability uncertainty ranks second (E = 0.28), followed by heat acceleration (E = 0.21) and seismic acceleration (E = 0.14). Age estimation error has the lowest elasticity (E = 0.09), indicating that the ±2-year age uncertainty contributes minimally to ETTC uncertainty relative to environmental factors. These results reinforce the importance of accurate corrosion classification (ISO 9223) and climate projection data (CMIP6) for fleet-scale degradation modelling. Table 8 . Sensitivity elasticity coefficients. Each parameter perturbed ± 20%; proportional change in fleet-median ETTC recorded. Parameter E (elasticity) ΔETTC at + 20% ΔETTC at − 20% Interpretation λ_corrosion 0.34 −6.8% + 7.2% Most sensitive Transition probs. 0.28 −5.6% + 5.9% High sensitivity λ_heat 0.21 −4.2% + 4.5% Moderate λ_seismic 0.14 −2.8% + 3.0% Moderate Age estimation 0.09 −1.8% + 1.9% Low sensitivity We note that the one-at-a-time perturbation approach does not capture interaction effects between parameters. As a partial check, we simultaneously perturbed λ_corrosion and λ_heat by + 20% each: the resulting fleet-median ETTC reduction was 12.1%, compared with 11.0% from the sum of individual effects (6.8% + 4.2%), indicating a modest positive interaction (synergy factor ≈ 1.10). Full variance decomposition using Sobol' indices (Saltelli et al., 2008 ) would require approximately 10× the computational budget (≈ 14 billion additional simulations) and is identified as a priority for future work. 5.4 Monte Carlo Convergence We verify convergence of the Monte Carlo ETTC estimator by computing the running coefficient of variation (CV) of fleet-mean ETTC as a function of replicate count R. At R = 1,000, CV = 0.8%; at R = 5,000, CV = 0.3%; at R = 10,000, CV = 0.15%. We further assess convergence by comparing four independent Monte Carlo runs initialised with different random seeds: the between-run variance in fleet-mean ETTC is 0.04 years² versus within-run variance of 2.31 years², yielding a between-to-within variance ratio of 0.017, analogous to an intraclass correlation coefficient. Values below 0.05 indicate that between-run variability is negligible relative to within-run stochastic variation. Individual substation ETTCs exhibit wider CV (median 4.2% at R = 10,000), reflecting inherent stochastic variability. We report 5th–95th percentile credible intervals for all ETTC estimates to transparently convey this uncertainty. All simulations were implemented in Python 3.11 using NumPy 1.25 for vectorised Markov chain transitions and SciPy 1.11 for statistical tests. The 1.4 billion Monte Carlo realisations required approximately 18 hours on a 64-core server (AMD EPYC 7763, 256 GB RAM) with parallelisation across countries. 6. Implications for Preservation Planning 6.1 ETTC-Based Capital Prioritisation The fleet-scale ETTC framework enables formal preservation capital optimisation. We define the expected lifecycle cost for substation k under maintenance policy m as: C k (m) = Σ t=1..T [c repl · Pr(S k (t) = 5|m) + c mon · f(ETTC k ) + c fail · Pr(failure_k,t | m)] · (1 + r) −t (10) We parameterise Eq. (10) as follows, drawing on European utility benchmarks (IEA, 2022 ; National Grid ESO, 2023 ) and industry cost data. Replacement cost c repl = EUR 1.2M (weighted average across voltage classes: EUR 600k for distribution substations, EUR 2.8M for transmission, weighted 75%/25% by fleet composition). Annual monitoring cost c mon = EUR 2,500 per asset at baseline, scaled by ETTC-derived monitoring intensity: f(ETTC) = max(1, 15/ETTC), such that assets with ETTC < 15 years receive enhanced monitoring at 1.5–3× baseline cost. Expected failure cost c fail = EUR 4.8M per event (comprising emergency repair EUR 1.8M, outage damage EUR 2.2M, regulatory penalty EUR 0.8M), based on analysis of 247 major substation failure events across European TSOs (2015–2023), compiled from ENTSO-E Transparency Platform incident reports and utility annual reports. This cost dataset is independent of the 1,220-failure validation dataset: the cost dataset records financial impact of failures, whereas the validation dataset records failure occurrence and timing. Of the 247 cost events, 89 overlap with the validation dataset; the remaining 158 predate the validation period or involve utilities not included in the SSI fleet. Discount rate r = 3.5% (consistent with the European Commission Guide to Cost-Benefit Analysis; European Commission, 2014 ). Under these parameters, ETTC-based CBM reduces net present lifecycle cost by 21% (95% CI: 16–27%) relative to age-based replacement over a 20-year horizon, assuming a fleet-wide annual replacement budget of EUR 1.4 billion. 6.2 Condition-Based vs. Age-Based Maintenance We compare ETTC-based condition-based maintenance (CBM) against traditional age-based maintenance across the 142,267-substation fleet using a 20-year simulation horizon. Under age-based maintenance (replace all assets exceeding 50 years), 22,814 substations (16%) are flagged for replacement, including 8,412 assets with ETTC > 30 years (i.e., in good condition despite age). Under ETTC-based CBM (prioritise by lowest ETTC), the same capital budget addresses 14,227 assets in the bottom ETTC decile—assets with the highest actual failure risk. In this simulation, the ETTC-based approach reduces projected 20-year failure events by 21% relative to age-based replacement (bootstrap 95% CI: 14–29%), while requiring the same capital expenditure. Equivalently, ETTC-based CBM achieves the same reliability target at 21% lower lifecycle cost. (This failure-reduction figure of 21% is numerically coincident with the lifecycle cost reduction reported in Section 6.1 , which has a tighter confidence interval of 16–27%; the two metrics measure different quantities but converge because failure prevention is the dominant cost driver in the lifecycle model.) We emphasise that this estimate is based on simulated deployment of the ETTC framework, not observed field implementation; real-world savings will depend on utility-specific operational constraints. This aligns with the 25% cost savings reported by Shehadeh et al. ( 2024 ) for climate-adjusted highway maintenance. 6.3 Regional Heterogeneity and Policy The stark inter-country heterogeneity in model-predicted ETTC distributions (η² = 0.33 from one-way ANOVA on model-predicted ETTC values) has direct implications for regulatory policy. Southern European countries (Italy, Spain, Portugal) require preservation budgets 2–3× higher per asset than Alpine countries (Austria, Switzerland), even after controlling for fleet size. Within countries, regional variation is equally pronounced: Southern Italy (Sicily, Calabria) has mean ETTC of 19.2 years versus 31.1 years for Northern Italy—a 12-year gap driven by compound heat and corrosion. For utilities, this means preservation capital should be allocated by environmental risk profile, not equally distributed across regions. For regulators setting allowable capital expenditure (CAPEX) in tariff reviews, fleet-level ETTC distributions provide an evidence-based benchmark for preservation needs. For the European Union's CSRD (European Commission, 2022 ), SFDR (European Commission, 2019 ), and EU Taxonomy Climate Delegated Act (European Commission, 2021 ) frameworks, substation ETTC provides a quantitative, asset-level indicator of physical climate risk that can complement existing portfolio-level ESG metrics. In particular, the Taxonomy requires disclosure of climate-related physical risks for infrastructure assets; ETTC distributions offer a standardised metric for this purpose. 6.4 Implementation Pathway For a utility seeking to operationalise the ETTC framework, we recommend a four-stage implementation pathway. Stage 1 (Data assembly, 3–6 months) : Map the substation fleet using OpenStreetMap and utility GIS records; assign asset ages from commissioning records or reverse-estimation; extract environmental exposure scores from ERA5 reanalysis and ISO 9223 corrosion maps. Stage 2 (Model calibration, 1–2 months) : Estimate the baseline transition matrix P₀ from available condition inspection records (or adopt the values in Table 2 for European fleets); calibrate environmental acceleration factors λ against historical failure data via the MLE procedure in Section 3.3 . Stage 3 (Fleet scoring, 1 month) : Run the Monte Carlo simulation pipeline (10,000 replicates per asset) to compute ETTC distributions; rank assets by median ETTC and classify into preservation tiers (e.g., ETTC 30 = monitor). Stage 4 (Integration with CAPEX planning, ongoing) : Embed ETTC rankings into the annual capital allocation cycle; update environmental scores annually and re-run Monte Carlo each planning period. The marginal data-acquisition cost of subsequent cycles is near-zero once the pipeline is established, as all data inputs are open-source (computational cost is approximately 18 hours per cycle on a 64-core server; see Section 5.4 ). Code and data are available under GPL-3.0 and CC BY-SA 4.0 (see Availability of Data and Materials). 7. Discussion 7.1 Contributions This paper contributes to three literatures. To the Markov deterioration literature (Cesare et al., 1992 ; Mizutani and Yuan, 2023 ), we contribute the largest-scale application to date: 142,267 assets across 18 countries, with formal environmental acceleration and empirical validation. To the multi-hazard infrastructure literature (Veeramany et al., 2016 ; Shehadeh et al., 2024 ), we contribute a multiplicative compound acceleration framework calibrated against observed failures, demonstrating that compound hazards reduce ETTC by 2–4×. To the fleet management literature (Zaldivar et al., 2023 ; Jiang and Jardine, 2008 ), we contribute a scalable surrogate approach that enables fleet-scale ETTC computation without per-asset condition surveys, reducing the marginal data-acquisition cost from EUR 50–200M (full condition survey) to near-zero per assessment cycle, once the SSI pipeline is established (using open data inputs and automated computation). 7.2 Limitations Several limitations warrant acknowledgment. First, the CIGRE TB 761 Markov model was designed for power transformers, not substations as compound assets (transformers + switchgear + busbars + control systems). Our model treats each substation as an integrated system with a single degradation trajectory—a simplification that may obscure component-level heterogeneity. Second, surrogate state estimation using age and environmental proxies introduces systematic uncertainty: assets may be in better or worse condition than their age suggests, and we cannot observe true condition without physical inspection. Third, the discrete-time Markov chain assumption (annual transitions) is a simplification; continuous-time formulations (Mizutani and Yuan, 2023 ; Zaldivar et al., 2023 ) better capture within-year dynamics. While Mizutani and Yuan ( 2023 ) achieve computational gains via analytic CTMC solutions, their approach assumes a standard generator matrix; our environmental acceleration parameterisation (Eq. 4), which caps scaled off-diagonal entries and recomputes diagonals per asset, does not admit a closed-form continuous-time analogue, precluding direct adoption of their efficient framework at our scale. Fourth, the 1,220-failure validation dataset represents only 0.86% of the fleet, with reporting bias toward severe failures. Fifth, environmental acceleration factors are calibrated cross-sectionally; they may not capture temporal dynamics (e.g., accelerating climate change shifting λ values over decades). Sixth, the framework currently treats transitions as unidirectional; in practice, maintenance interventions can restore assets to better states, which would require a semi-Markov or Markov decision process formulation. Three further limitations merit acknowledgment. Seventh, the 18-country sample comprises exclusively OECD economies; applicability to developing countries remains untested and would require adaptation to sparser data environments. Eighth, the Markov property (Assumption 2 ) assumes memorylessness: within-simulation sojourn-time effects are not captured, despite Arrhenius kinetics (Dakin, 1948 ) predicting duration-dependent insulation degradation. The age-state mapping (Table 4 ) introduces implicit duration dependence at initialisation, but semi-Markov formulations (Mizutani and Yuan, 2023 ) would address this more formally. We did not conduct a formal statistical test of the Markov property (e.g., chi-squared test of independence between successive transitions conditional on current state) on the calibration dataset; such a test is a priority for future work and may reveal systematic departures that motivate semi-Markov extensions. Ninth, ETTC predictions are validated against failure occurrence (binary), not ground-truth condition inspections; a utility partner study comparing model-predicted states against physical inspection results is a high priority for future work. Tenth, the lifecycle cost model (Eq. 10) assumes independent failures; in practice, spatially correlated failures during extreme events (e.g., heatwaves, flooding) can produce cascading grid effects whose costs exceed the sum of individual failure costs. Modelling correlated failure scenarios would strengthen the economic case for preservation. Future research should address five priorities: (1) panel data analysis using repeated SSI assessments to estimate time-varying transition probabilities; (2) component-level Markov models disaggregating substation-level degradation into transformer, switchgear, and control system trajectories; (3) extension to non-OECD electricity networks where aging and environmental stress are acute but data availability is limited; (4) semi-Markov formulations incorporating sojourn-time dependence for improved within-state dynamics, informed by formal Markov property testing on the calibration dataset; and (5) correlated-failure scenario modelling to capture cascading grid effects during spatially concentrated extreme events. 8. Conclusion Infrastructure preservation is the defining challenge for OECD electricity networks. This paper extends the CIGRE TB 761 Markov degradation model from single-asset condition assessment to fleet-scale preservation planning, demonstrating its application across 142,267 substations in 18 OECD countries using a temporally held-out validation approach. Table 9 summarises the hypothesis testing results; three principal findings emerge. Table 9 Summary of hypothesis testing results. Hypothesis Test Result Verdict H1: Environmental acceleration Spearman ρ (country-level); paired bootstrap ρ_country = 0.82, p < 0.001; Δρ = +0.25 Supported H2: Fleet heterogeneity Kruskal–Wallis; ANOVA η² H(17) = 48.3, p < 0.001; η² = 0.33 Supported H3: Predictive validity Spearman ρ; ROC AUC ρ = 0.71, AUC = 0.78; LOCO ρ = 0.68 Supported First, multi-hazard environmental stressors significantly accelerate degradation beyond age-driven baselines (Hypothesis 1 supported). The environmentally-adjusted model outperforms the age-only baseline by 0.25 points on Spearman ρ (0.71 vs. 0.46, a 54% relative improvement) and 30% on ROC AUC (0.78 vs. 0.60), with strong country-level agreement between predicted and observed failure patterns (ρ = 0.82). Compound environmental effects are non-linear: simultaneous heat and corrosion reduce ETTC by 2–4×. Second, fleet-level ETTC distributions exhibit pronounced inter-country heterogeneity (η² = 0.33; Hypothesis 2 supported). Spain and Italy have 38–43% of assets with ETTC below 15 years, driven by the interaction of aging fleets and severe environmental stress. The United States has the largest absolute at-risk cohort (approximately 20,000 substations) reflecting its vintage 1970s fleet. Austria and Switzerland have only 14% of assets in the critical tier. Third, fleet-scale ETTC predictions have strong predictive validity against documented failures (Hypothesis 3 supported), with LOCO cross-validation confirming generalisability (mean ρ = 0.68 across 18 held-out countries). ETTC-based condition-based maintenance reduces lifecycle costs by 21% (95% CI: 16–27%) relative to age-based replacement at equivalent reliability over a 20-year horizon. For utilities, the framework enables evidence-based preservation capital allocation. For regulators, fleet-level ETTC distributions provide quantitative benchmarks for tariff-setting and infrastructure resilience assessment. For the research community, we demonstrate that Markov deterioration models can be operationalised at fleet scale using open data and surrogate estimation, without requiring prohibitively expensive per-asset condition surveys. The SSI Index v4.0.2 methodology, code (GPL-3.0), and calibration datasets (CC BY-SA 4.0) are published at https://ikengassiindex.github.io/index.html and https://github.com/ikengassiindex/ikengassiindex.github.io to enable independent replication, extension, and regulatory integration. Abbreviations AIC: Akaike Information Criterion; ANOVA: Analysis of Variance; ASCE: American Society of Civil Engineers; AUC: Area Under the Curve; CAPEX: Capital Expenditure; CBM: Condition-Based Maintenance; CI: Confidence Interval; CIGRE: Conseil International des Grands Réseaux Électriques; CMIP6: Coupled Model Intercomparison Project Phase 6; CSRD: Corporate Sustainability Reporting Directive; CTMC: Continuous-Time Markov Chain; CV: Coefficient of Variation; EEA: European Environment Agency; ENTSO-E: European Network of Transmission System Operators for Electricity; EPA: Environmental Protection Agency; ERA5: ECMWF Reanalysis v5; ESG: Environmental, Social and Governance; ETTC: Expected Time to Critical; GADS: Generating Availability Data System; GIS: Geographic Information System; IEA: International Energy Agency; IEC: International Electrotechnical Commission; IEEE: Institute of Electrical and Electronics Engineers; IPCC: Intergovernmental Panel on Climate Change; IQR: Interquartile Range; ISO: International Organization for Standardization; J-SHIS: Japan Seismic Hazard Information Station; KW: Kruskal–Wallis; LR: Logistic Regression; L-BFGS-B: Limited-memory Broyden–Fletcher–Goldfarb–Shanno Bounded; LOCO: Leave-One-Country-Out; MDP: Markov Decision Process; MCDM: Multi-Criteria Decision-Making; ML: Machine Learning; MLE: Maximum Likelihood Estimation; NERC: North American Electric Reliability Corporation; NIED: National Research Institute for Earth Science and Disaster Resilience; OECD: Organisation for Economic Co-operation and Development; PGA: Peak Ground Acceleration; pp: Percentage Points; ROC: Receiver Operating Characteristic; SD: Standard Deviation; SFDR: Sustainable Finance Disclosure Regulation; SIAE: Società Italiana degli Autori ed Editori; SSI: Systemic System Infrastructure; TB: Technical Brochure; TEPCO: Tokyo Electric Power Company; TSO: Transmission System Operator; USCO: United States Copyright Office; USGS: United States Geological Survey Declarations Ethics Approval and Consent to Participate Not applicable. This study uses publicly available infrastructure data and aggregated fleet statistics. No human participants, human material, or human data were involved. Consent for Publication Not applicable. Competing Interests The author is an employee of Ikenga, an employee-owned company that develops and maintains the SSI Index. This manuscript was prepared independently; Ikenga's commercial operations had no input into research design, analysis, or conclusions. We note that: (a) the paper's claims concern Markov degradation methodology and environmental acceleration effects, not SSI Index validity per se; (b) all methods are standard in reliability engineering; (c) full replication data and code are published under open licences (GPL-3.0 and CC BY-SA 4.0); and (d) the Limitations section (7.2) explicitly acknowledges that surrogate degradation states have not been independently validated by physical inspection. The failure data collection protocol is documented in Section 3.6 . Independent replication is invited using the published SSI code and any alternative failure dataset. Funding This research was funded in its entirety by Ikenga (employee-owned, no external investors) as part of ongoing SSI development since v1.0 (2020). All code and data are published under open-source and open-data licences respectively. Author Contribution C. Bérard: Conceptualisation, Methodology, Software, Formal Analysis, Data Curation, Validation, Visualisation, Investigation, Writing—Original Draft, Writing—Review & Editing. Single author; sole responsibility for all aspects of the work. Acknowledgements The author gratefully acknowledges the European Network of Transmission System Operators for Electricity (ENTSO-E) for facilitating data access under the research cooperation framework, and the anonymous grid operators whose condition assessment records informed the calibration of P₀. Data Availability SSI Index v4.0.2 (https://ikengassiindex.github.io) degradation assessment data (ETTC distributions, Markov transition parameters, environmental acceleration factors) are publicly available at https://ikengassiindex.github.io/index.html under CC BY-SA 4.0. Raw substation age proxies, condition estimates, and country-level fleet statistics are published in CSV and GeoJSON formats, updated monthly. Monte Carlo simulation outputs (1.4 billion iterations aggregated to summary statistics) are available upon request. The SSI Index methodology, software, and calibration datasets are protected by copyright registrations with the United States Copyright Office (USCO) and the Italian Society of Authors and Publishers (SIAE). Copyright registration protects authorship attribution and does not restrict access; all data remain freely available under the stated open licence (CC BY-SA 4.0). We encourage independent teams to replicate the analysis using alternative failure data sources; the SSI code accepts any failure dataset in the documented CSV format. Code Availability Python code for Markov simulation, ETTC computation, and Monte Carlo uncertainty propagation is available at https://github.com/ikengassiindex/ikengassiindex.github.io under GPL-3.0. The repository includes the full simulation pipeline (NumPy 1.25, SciPy 1.11), validation scripts, and documentation for reproducing all results reported in this paper. References ASCE (2021) 2021 Infrastructure Report Card: A Comprehensive Assessment of America's Infrastructure. American Society of Civil Engineers, Washington, DC Barlow RE, Proschan F (1965) Mathematical Theory of Reliability. Wiley, New York Bastidas-Arteaga E, Chateauneuf A, Sanchez-Silva M, Bressolette P, Schoefs F (2010) Comprehensive probabilistic model of chloride ingress in unsaturated concrete. Eng Struct 32(8):2291–2299 Cesare MA, Thompson PD, Hyman W (1992) Modeling bridge deterioration with Markov chains. J Transp Eng 118(6):820–833 CIGRE Working Group A2.49 (2019) Condition Assessment of Power Transformers. Technical Brochure 761. CIGRE, Paris Conover WJ (1999) Practical Nonparametric Statistics, 3rd edition. John Wiley & Sons, New York Copernicus Climate Change Service (2023) ERA5 Reanalysis Dataset. ECMWF. https://cds.climate.copernicus.eu Cui B, Wang H (2023) Analysis and prediction of pipeline corrosion defects based on data analytics of in-line inspection. J Infrastructure Preservation Resil 4:14 Dakin TW (1948) Electrical insulation deterioration treated as a chemical rate phenomenon. AIEE Trans 67(1):113–122 Der Kiureghian A, Ditlevsen O (2009) Aleatory or epistemic? Does it matter? Structural Safety, 31(2), 105–112 Efron B, Tibshirani RJ (1993) An Introduction to the Bootstrap. Chapman and Hall/CRC, New York Endrenyi J, George GH, Ross RJ, Roustum S (1998) The present status of maintenance strategies and the impact of maintenance on reliability. IEEE Trans Power Syst 13(3):1–7 European Commission (2014) Guide to Cost-Benefit Analysis of Investment Projects: Economic Appraisal Tool for Cohesion Policy 2014–2020. Publications Office of the European Union, Luxembourg European Commission (2019) Regulation (EU) 2019/2088 on sustainability-related disclosures in the financial services sector (SFDR) European Commission (2021) Delegated Regulation (EU) 2021/2139 (EU Taxonomy Climate Delegated Act) European Commission (2022) Directive (EU) 2022/2464 amending the Corporate Sustainability Reporting Directive (CSRD) Hong T, Prozzi JA (2006) Estimation of infrastructure transition probabilities from condition rating data. J Infrastruct Syst 12(2):91–97 IEA (2022) World Energy Outlook 2022. International Energy Agency, Paris IEC (2012) Power transformers—Part 2: Temperature rise for liquid-immersed transformers. IEC 60076–60072 IEC (2015) Mineral oil-filled electrical equipment in service—Guidance on the interpretation of dissolved and free gases analysis. IEC 60599:2015 IEEE (2016) Guide for the Preservation and Maintenance of Electrical Equipment in Substations. IEEE Std 939–2016 IEEE (2019) Guide for the Interpretation of Gases Generated in Mineral Oil-Immersed Transformers. IEEE Std C57.104-2019. Ikenga (2024) SSI Index v4.0.2: Fleet-Scale Degradation Assessment Framework. https://ikengassiindex.github.io/index.html IPCC (2021) Climate Change 2021: The Physical Science Basis. AR6 Working Group I. Cambridge University Press IPCC (2022) Climate Change 2022: Impacts, Adaptation and Vulnerability. AR6 Working Group II. Cambridge University Press ISO (2012) Corrosion of metals and alloys—Corrosivity of atmospheres—Classification, determination and estimation. ISO 9223:2012 ISO (2014) Asset management—Overview, principles and terminology. ISO 55000:2014 Jardine AKS, Tsang AHC (2006) Maintenance, Replacement, and Reliability: Theory and Applications. CRC, Boca Raton Jiang R, Jardine AKS (2008) Health state evaluation of an item: A general framework and graphical representation. Reliab Eng Syst Saf 93(1):89–99 Kabir G, Sadiq R, Tesfamariam S (2014) A review of multi-criteria decision-making methods for infrastructure management. Struct Infrastruct Eng 10(9):1176–1210 Meeker WQ, Escobar LA (1998) Statistical Methods for Reliability Data. Wiley, New York Mizutani D, Yuan X-X (2023) Infrastructure deterioration modeling with an inhomogeneous continuous time Markov chain: A latent state approach with analytic transition probabilities. Computer-Aided Civ Infrastruct Eng 38(13):1730–1748 Morcous G (2006) Performance prediction of bridge deck systems using Markov chains. J Perform Constr Facil 20(2):146–155 National Grid ESO (2023) Future Energy Scenarios. London NERC (2023) 2023 Long-Term Reliability Assessment. North American Electric Reliability Corporation Nguyen KTP, Medjaher K (2019) A new dynamic predictive maintenance framework using deep learning for failure prognostics. Reliab Eng Syst Saf 188:251–262 NIED (2023) Japan Seismic Hazard Information Station (J-SHIS). https://www.j-shis.bosai.go.jp Norris JR (1997) Markov Chains. Cambridge University Press, Cambridge OpenStreetMap C (2024) https://www.openstreetmap.org Papakonstantinou KG, Shinozuka M (2014) Optimum inspection and maintenance policies for corroded structures using partially observable Markov decision processes and stochastic, physically based models. Probab Eng Mech 37:93–108 Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global Sensitivity Analysis: The Primer. Wiley, Chichester Shehadeh A, Alshboul O, Tamimi M (2024) Integrating climate change predictions into infrastructure degradation modelling using advanced Markovian frameworks to enhanced resilience. J Environ Manage 368:122234 Stewart MG, Rosowsky DV (1998) Time-dependent reliability of deteriorating reinforced concrete bridge decks. Struct Saf 20(1):91–109 TEPCO (2023) Annual Report on Electricity Supply Reliability. Tokyo Electric Power Company Holdings, Tokyo USGS (2023) Unified Hazard Tool: Probabilistic Seismic Hazard Analysis. https://earthquake.usgs.gov Veeramany A, Jarman KD, Varley RW, Lindberg SE (2016) Framework for modeling high-impact, low-frequency power grid events to support risk-informed decisions. Int J Disaster Risk Reduct 18:197–213 WorldPop (2023) Global High Resolution Population Dataset. https://www.worldpop.org Zaldivar DA, Sanchez AM, Romero AA (2023) A comprehensive methodology for the optimization of condition-based maintenance in power transformer fleets. Electr Power Syst Res 220:109374 Zhang Y, Aslani F, Lehman DE (2022) Deep learning for infrastructure condition assessment: A comprehensive review. Autom Constr 141:104424 Additional Declarations No competing interests reported. Supplementary Files SSIPaperJIPRSupplementary.docx GraphicalAbstract.docx Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 07 May, 2026 Reviewers invited by journal 15 Apr, 2026 Editor assigned by journal 14 Apr, 2026 Submission checks completed at journal 14 Apr, 2026 First submitted to journal 01 Apr, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Countries are ranked by median ETTC (left axis, years); bar colour indicates the proportion of fleet with ETTC \u0026lt; 15 years (red \u0026gt; 35%, amber 20–35%, green \u0026lt; 20%). Error bars show interquartile range. The dashed vertical line at ETTC = 15 years marks the critical intervention threshold.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-9291862/v1/93b52b93a2a753972aea5a09.png"},{"id":107705741,"identity":"8bbe5c16-0000-4d9d-b6fe-48d694959055","added_by":"auto","created_at":"2026-04-24 09:14:56","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":234617,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eReceiver Operating Characteristic (ROC) curves for the environmentally-adjusted Markov model (AUC = 0.78) and age-only baseline (AUC = 0.60) on the temporally held-out test set (N_test = 406). The diagonal dashed line represents random classification (AUC = 0.50).\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-9291862/v1/e74c6f8192f8a7aaa00e95d1.png"},{"id":107600302,"identity":"c19f413f-8d73-44ee-8ae1-02429e1db47b","added_by":"auto","created_at":"2026-04-23 06:32:20","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":203552,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eModel-predicted failure probability (% of fleet with ETTC \u0026lt; 8 years) against observed failure rate (per 1,000 substations per year) for 18 OECD countries (Spearman ρ = 0.82, p \u0026lt; 0.001). Dashed line shows linear trend. Country codes follow ISO 3166-1 alpha-3.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-9291862/v1/5a4964856934eed674896493.png"},{"id":107708985,"identity":"414bd045-1c02-478f-827c-bc9acb478220","added_by":"auto","created_at":"2026-04-24 09:33:59","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1377468,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9291862/v1/aae9c2d5-9dfe-465c-a2dc-8f09c1216b23.pdf"},{"id":107600299,"identity":"1db57d04-fb90-42fe-a741-80e65613f02a","added_by":"auto","created_at":"2026-04-23 06:32:20","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":10306,"visible":true,"origin":"","legend":"","description":"","filename":"SSIPaperJIPRSupplementary.docx","url":"https://assets-eu.researchsquare.com/files/rs-9291862/v1/aa4dab89585df9d07b47b64a.docx"},{"id":107706508,"identity":"2b29d6d5-5604-43b2-9b2d-4030b80c0fa4","added_by":"auto","created_at":"2026-04-24 09:18:13","extension":"docx","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":173680,"visible":true,"origin":"","legend":"","description":"","filename":"GraphicalAbstract.docx","url":"https://assets-eu.researchsquare.com/files/rs-9291862/v1/4d13e0ca920c955bbae8b9d5.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Markov Degradation Modelling for Fleet-Scale Substation Preservation: Integrating CIGRE TB 761 with Multi-Hazard Environmental Stressors Across Eighteen OECD Countries","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe electricity infrastructure of developed economies faces an unprecedented convergence of two risk vectors: aging assets and accelerating environmental stress. Substations designed and deployed in the 1960s\u0026ndash;1990s now approach or exceed their 40\u0026ndash;60 year design life. Simultaneously, climate change, sea-level rise, extreme weather events, and atmospheric corrosion are accelerating degradation rates beyond those assumed at design time (IPCC, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; IPCC, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). The American Society of Civil Engineers estimated USD 150\u0026ndash;200 billion in annual grid modernisation needs for the United States alone (ASCE, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2021\u003c/span\u003e); similar magnitudes apply across Europe (IEA, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) and Japan (TEPCO, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Yet utilities operate under binding capital constraints: annual replacement rates of 0.5\u0026ndash;1% of fleet are far below the rate needed to manage the aging cohort. The fundamental question is not whether assets will degrade, but which assets should be preserved, which replaced, and in what order.\u003c/p\u003e\n\u003cp\u003eCIGRE Technical Brochure 761 (CIGRE, 2019) provides a well-established five-state Markov chain model for asset degradation progression (New \u0026rarr; Good \u0026rarr; Marginal \u0026rarr; Degraded \u0026rarr; Critical), along with guidelines for condition assessment of power transformers. However, TB 761 was designed for single-asset analysis: a utility engineer gathers detailed condition data (oil quality, insulation resistance, infrared imaging) for one transformer and estimates its current state and expected remaining life. At fleet scale\u0026mdash;where a utility may operate 10,000\u0026thinsp;+\u0026thinsp;substations\u0026mdash;this approach is infeasible. Comprehensive condition surveys are estimated to cost EUR 50\u0026ndash;200\u0026nbsp;million for a national fleet, based on per-asset survey costs reported in CIGRE (2019, Section \u003cspan refid=\"Sec31\" class=\"InternalRef\"\u003e7\u003c/span\u003e) and IEEE (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2016\u003c/span\u003e, Appendix B) extrapolated to fleet scale; TB 761 provides no framework for integrating environmental stressors across assets or for aggregating single-asset predictions into fleet-level preservation plans.\u003c/p\u003e\n\u003cp\u003eSubsequent work has extended Markov deterioration models to bridge condition prediction (Cesare et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e1992\u003c/span\u003e), climate-adjusted highway degradation (Shehadeh et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), power transformer fleet management (Zaldivar et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), and inhomogeneous continuous-time formulations with analytic solutions (Mizutani and Yuan, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Yet none of these combines fleet-scale modelling, multi-hazard environmental acceleration, and empirical validation against observed failures across multiple countries. Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e reviews this literature in detail and identifies the specific gaps our framework addresses.\u003c/p\u003e\n\u003cp\u003eThis paper makes three contributions. \u003cstrong\u003eFirst\u003c/strong\u003e, we extend CIGRE TB 761 from single-asset condition assessment to fleet-scale preservation planning by formalising a five-state discrete-time Markov chain with environmental acceleration factors, computing Expected Time to Critical (ETTC) distributions for 142,267 substations across 18 OECD countries. \u003cstrong\u003eSecond\u003c/strong\u003e, we integrate multi-hazard environmental stressors (heat, flooding, seismic, corrosion, pollution) as transition probability accelerators with empirically calibrated parameters, demonstrating non-linear compound effects on degradation trajectories. \u003cstrong\u003eThird\u003c/strong\u003e, we validate the fleet-scale ETTC framework against 1,220 documented substation failures across the 18 countries using a temporally held-out test set (N_test\u0026thinsp;=\u0026thinsp;406 failures, 2022\u0026ndash;2023), achieving Spearman \u0026rho;\u0026thinsp;=\u0026thinsp;0.71 and ROC AUC\u0026thinsp;=\u0026thinsp;0.78, and conduct leave-one-country-out cross-validation, sensitivity analysis, and formal model comparison against an age-only baseline.\u003c/p\u003e\n\u003cp\u003eThe paper is structured as follows. Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e reviews the literature on Markov deterioration models, multi-hazard acceleration, and fleet-scale asset management, and states three testable hypotheses. Section \u003cspan refid=\"Sec8\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents the data and formalises the methodology with numbered definitions and equations. Section \u003cspan refid=\"Sec16\" class=\"InternalRef\"\u003e4\u003c/span\u003e reports fleet-level ETTC distributions and environmental acceleration results. Section \u003cspan refid=\"Sec21\" class=\"InternalRef\"\u003e5\u003c/span\u003e presents validation and robustness analyses. Section \u003cspan refid=\"Sec26\" class=\"InternalRef\"\u003e6\u003c/span\u003e quantifies implications for preservation planning. Section \u003cspan refid=\"Sec31\" class=\"InternalRef\"\u003e7\u003c/span\u003e discusses contributions and limitations. Section \u003cspan refid=\"Sec34\" class=\"InternalRef\"\u003e8\u003c/span\u003e concludes.\u003c/p\u003e"},{"header":"2. Literature Review and Theoretical Framework","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Markov Deterioration Models for Infrastructure\u003c/h2\u003e \u003cp\u003eMarkov chains have been widely applied to infrastructure deterioration modelling since the seminal work of Cesare et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e1992\u003c/span\u003e) on bridge condition prediction, building on the theoretical foundations of discrete-state stochastic processes (Norris, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e1997\u003c/span\u003e). The standard approach defines a finite set of discrete condition states (typically 4\u0026ndash;6) and estimates transition probabilities from historical inspection records. Morcous (\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) extended this framework to incorporate risk management, demonstrating that Markov-based deterioration predictions can inform maintenance prioritisation. Hong and Prozzi (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) developed improved estimation methods for transition probabilities when inspection data are sparse or censored.\u003c/p\u003e \u003cp\u003eRecent advances have addressed the time-homogeneity limitation inherent in standard Markov chains. Mizutani and Yuan (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) proposed a regime-switching continuous-time Markov chain (CTMC) in which transition probabilities depend on a latent Markov chain characterising the overall aging regime, achieving analytic solutions and 48% computation time reduction relative to the state-of-the-art inhomogeneous approach. For power systems specifically, Zaldivar et al. (\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) combined continuous-time Markov chains with k-means clustering for power transformer fleet management, optimising inspection intervals to minimise lifecycle costs. Endrenyi et al. (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e1998\u003c/span\u003e) established early connections between Markov maintenance models and power system reliability. In the pipeline domain, Cui and Wang (\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) combined Markov-based corrosion growth models with machine learning classification for in-line inspection data.\u003c/p\u003e \u003cp\u003eDespite this rich literature, a critical gap remains. No existing work combines fleet-scale Markov deterioration modelling (\u0026gt;\u0026thinsp;100,000 assets), multi-hazard environmental acceleration with empirically calibrated parameters, and validation against observed failures across multiple countries for electricity substations. This gap is consequential: without environment-adjusted fleet-scale predictions, utilities must rely on age-based maintenance policies that misallocate capital by treating all assets of the same age as equally degraded regardless of environmental exposure.\u003c/p\u003e \u003cp\u003eWe note that machine learning approaches\u0026mdash;gradient boosted trees, random forests, deep neural networks\u0026mdash;have shown promise for infrastructure failure prediction (Nguyen and Medjaher, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Zhang et al., \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). However, Markov chain models offer three advantages for fleet-scale infrastructure preservation that currently favour their adoption over black-box alternatives: (a) physical interpretability\u0026mdash;transition probabilities correspond to observable degradation mechanisms, enabling engineering scrutiny; (b) regulatory acceptability\u0026mdash;infrastructure regulators (NERC, ENTSO-E) require models whose assumptions can be audited, which excludes opaque ML models; and (c) integration with established frameworks\u0026mdash;CIGRE TB 761 and the ISO 55000 series (ISO, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) are built on state-based degradation models. Our framework leverages these advantages while incorporating environmental covariates that address the principal limitation of standard Markov models. To quantify the interpretability\u0026ndash;performance trade-off, we include a logistic regression baseline (age\u0026thinsp;+\u0026thinsp;R1\u0026thinsp;+\u0026thinsp;R5) in the model comparison (Section \u003cspan refid=\"Sec20\" class=\"InternalRef\"\u003e4.4\u003c/span\u003e, Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Multi-Hazard Environmental Acceleration\u003c/h2\u003e \u003cp\u003eEnvironmental stressors accelerate infrastructure degradation beyond age-driven trajectories. Stewart and Rosowsky (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e1998\u003c/span\u003e) established time-dependent reliability methods for deteriorating structures under environmental loading, demonstrating that corrosion-induced section loss materially alters structural reliability over service life. Shehadeh et al. (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) demonstrated that climate change projections integrated into Markov highway degradation models predict 15\u0026ndash;20% acceleration in degradation rates, with maintenance cost savings of up to 25% from optimised timing. Bastidas-Arteaga et al. (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) developed comprehensive probabilistic models for chloride-induced corrosion in concrete infrastructure, demonstrating the importance of coupling environmental stochasticity with degradation mechanics. ISO 9223 (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) classifies atmospheric corrosivity into categories C1\u0026ndash;CX, with coastal and industrial environments (C4\u0026ndash;C5) accelerating metallic corrosion 2\u0026ndash;3\u0026times; relative to rural baselines. The IEC 60076-2 (2012) standard quantifies thermal aging of transformer insulation as a function of hotspot temperature, establishing that insulation life halves for every 6\u0026deg;C increase above rated temperature, consistent with Arrhenius degradation kinetics (Dakin, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e1948\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eVeeramany et al. (\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) developed a multi-hazard risk assessment framework for high-impact, low-frequency power grid events, integrating seismic, geomagnetic, and weather hazards into a unified probabilistic framework. The IPCC Sixth Assessment Report (IPCC, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; IPCC, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) projects compound climate extremes (concurrent heat and drought, sequential flooding and corrosion) that are not captured by single-hazard models. Our framework addresses this gap by modelling environmental stressors as multiplicative transition probability accelerators, reflecting compound risk.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Fleet-Scale Asset Management\u003c/h2\u003e \u003cp\u003eFleet-scale infrastructure management requires aggregating individual asset conditions into portfolio-level decisions under budget constraints. Barlow and Proschan (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1965\u003c/span\u003e) established the mathematical foundations of reliability theory, including optimal replacement policies for aging systems. Jardine and Tsang (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) provide a comprehensive treatment of maintenance optimisation theory, linking condition monitoring data to replacement decisions under uncertainty. Jiang and Jardine (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) developed Health Index approaches for condition-based maintenance decision-making, combining multiple condition indicators into a single degradation metric. The NERC Long-Term Reliability Assessment (2023) documents the growing gap between grid modernisation needs and available capital across North American electricity systems.\u003c/p\u003e \u003cp\u003eCurrent fleet management practice relies predominantly on age-based maintenance policies: assets exceeding a fixed age threshold (typically 40\u0026ndash;50 years) are scheduled for replacement regardless of actual condition. This approach is inefficient: some 50-year-old assets in benign environments remain in good condition, while 30-year-old assets under severe environmental stress may be critically degraded. The transition from age-based to condition-based maintenance (CBM) requires precisely the type of fleet-scale, environment-adjusted ETTC framework that this paper provides.\u003c/p\u003e \u003cp\u003eAlternative quantitative approaches exist for fleet-scale maintenance optimisation. Markov Decision Processes (MDPs) extend Markov chain models by incorporating optimal control, determining the best action (inspect, repair, replace) for each state (Papakonstantinou and Shinozuka, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Survival analysis (Weibull, Cox proportional hazards) models time-to-failure directly, without discretising condition states (Meeker and Escobar, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e1998\u003c/span\u003e). Multi-criteria decision-making (MCDM) frameworks aggregate technical, economic, and environmental factors for prioritisation (Kabir et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Our approach is complementary: we use the Markov chain for degradation prediction and overlay a cost framework for decision support, rather than embedding the decision rule within the degradation model. This separation allows the ETTC predictions to serve multiple downstream applications (capital planning, regulatory reporting, insurance risk assessment) without committing to a single optimisation objective.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 CIGRE TB 761: Foundation and Limitations\u003c/h2\u003e \u003cp\u003eCIGRE Technical Brochure 761 (CIGRE, 2019), published by Working Group A2.49, provides guidelines for condition assessment of power transformers using a five-state Markov degradation model (New, Good, Marginal, Degraded, Critical). The model treats Critical as an absorbing state, with transition probabilities calibrated from European transformer fleet data. CIGRE TB 761 represents the established standard in the power engineering community for single-asset condition assessment.\u003c/p\u003e \u003cp\u003eHowever, TB 761 has four limitations for fleet-scale application. First, it requires detailed per-asset condition data (oil analysis, dissolved gas analysis per IEC 60599 (2015) and IEEE C57.104 (2019), infrared thermography, insulation resistance testing), making fleet-wide deployment prohibitively expensive. Second, it does not specify how to aggregate single-asset assessments into fleet-level preservation plans. Third, it mentions environmental factors qualitatively but provides no standardised framework for integrating them quantitatively across assets. Fourth, its transition probabilities were calibrated primarily on European transformer fleets from the 1980s\u0026ndash;2010s; applicability to other regions, asset types, and environmental regimes is uncertain. Our framework addresses all four limitations through surrogate state estimation, fleet-level aggregation, formal environmental acceleration modelling, and multi-country empirical validation.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Hypotheses\u003c/h2\u003e \u003cp\u003eBuilding on the literature reviewed above, we formulate three testable hypotheses:\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eHypothesis 1\u003c/strong\u003e \u003cp\u003e \u003cb\u003e(Environmental Acceleration)\u003c/b\u003e: Multi-hazard environmental stressors significantly accelerate Markov degradation transitions beyond age-driven baselines. Specifically, the environmentally-adjusted Markov model produces ETTC distributions that are significantly shifted leftward (toward shorter remaining life) relative to age-only baselines, and the environmentally-adjusted model achieves superior predictive accuracy for observed failures (Spearman ρ comparing model-predicted and observed country-level failure rates, p\u0026thinsp;\u0026lt;\u0026thinsp;0.01; paired bootstrap comparison of Spearman ρ between models, p\u0026thinsp;\u0026lt;\u0026thinsp;0.01).\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eHypothesis 2\u003c/strong\u003e \u003cp\u003e \u003cb\u003e(Fleet Heterogeneity)\u003c/b\u003e: Fleet-level ETTC distributions exhibit statistically significant inter-country heterogeneity driven by the interaction of fleet age profiles and environmental stress regimes. We test this via Kruskal\u0026ndash;Wallis test on substation-level binary failure indicators grouped by country (non-parametric, appropriate for binary outcome data with unequal group sizes) and quantify within-model heterogeneity with eta-squared from one-way ANOVA on ETTC distributions.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eHypothesis 3\u003c/strong\u003e \u003cp\u003e \u003cb\u003e(Predictive Validity)\u003c/b\u003e: Fleet-scale ETTC scores predict subsequent asset failures with discriminatory power significantly exceeding both a random baseline and an age-only model. Specifically, we require Spearman ρ\u0026thinsp;\u0026gt;\u0026thinsp;0.60, ROC AUC\u0026thinsp;\u0026gt;\u0026thinsp;0.70, and p\u0026thinsp;\u0026lt;\u0026thinsp;0.01 for the environmental model, and a statistically significant improvement over the age-only baseline via one-tailed paired bootstrap test (p\u0026thinsp;\u0026lt;\u0026thinsp;0.01).\u003c/p\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3. Data and Methods","content":"\u003cp\u003e\u003cstrong\u003eNotation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe principal symbols used throughout this paper are summarised below.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eSymbol\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eDescription\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eS(t)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eDegradation state at time t; S(t) \u0026isin; Ω = {1, 2, 3, 4, 5}\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eΩ\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eState space: {New (1), Good (2), Marginal (3), Degraded (4), Critical (5)}\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eP₀\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eBaseline 5\u0026times;5 transition probability matrix (from CIGRE TB 761 data)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026lambda;\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eEnvironmental acceleration factor (multiplicative modifier on off-diagonal entries of P₀)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eP\u0026prime; = f(P₀, \u0026lambda;)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eEnvironmentally adjusted transition matrix\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eQ\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eTransient sub-matrix of P\u0026prime; (states 1\u0026ndash;4, excluding absorbing state 5)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eN = (I\u0026thinsp;\u0026minus;\u0026thinsp;Q)⁻\u0026sup1;\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eFundamental matrix of the absorbing Markov chain\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eETTC\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eExpected Time to Critical: row-sum of N for a given initial state\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026pi;_k(\u0026lambda;)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eModel-predicted failure probability for substation k given acceleration factor \u0026lambda;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eL(\u0026lambda;)\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eLog-likelihood function (Bernoulli observation model)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026rho;\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eSpearman rank correlation coefficient\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003e\u0026eta;\u0026sup2;\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eEta-squared effect size from one-way ANOVA\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eE\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eElasticity: proportional sensitivity of ETTC to parameter perturbation\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003ec_repl, c_mon, c_fail\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eReplacement, monitoring, and failure costs (EUR)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cem\u003eN_train, N_test\u003c/em\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eTraining (N\u0026thinsp;=\u0026thinsp;814) and test (N\u0026thinsp;=\u0026thinsp;406) failure sample sizes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1 Data: The SSI Index v4.0.2\u003c/h2\u003e\n \u003cp\u003eWe use data from the Systemic System Infrastructure (SSI) Index version 4.0.2, which provides condition assessment, environmental exposure, and degradation estimates for 142,267 electricity substations across 18 OECD countries. The SSI Index integrates six component dimensions (Continuity of Supply, Voltage Stability, Infrastructure Condition, Economic Impact, System Saturation, and Transition Readiness) with empirically calibrated weights; the present paper uses only the Infrastructure Condition (I) and environmental exposure (R1, R5) components, which feed the Markov degradation model. Data sources include OpenStreetMap (substation locations and attributes), ERA5 reanalysis (climate variables; Copernicus, 2023), USGS and J-SHIS (seismic hazard; USGS, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; NIED, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), ISO 9223 corrosion classification maps, WorldPop (population; WorldPop, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), and national grid operator statistics.\u003c/p\u003e\n \u003cp\u003eAsset age is estimated from utility records, equipment vintage databases, and reverse-estimation from failure statistics, with uncertainty of \u0026plusmn;\u0026thinsp;2 years. Reverse-estimation infers commissioning year from historical failure hazard rates: substations whose cumulative failure hazard matches the profile of a given vintage cohort are assigned the corresponding commissioning decade (\u0026plusmn;\u0026thinsp;5 years), then refined by cross-referencing with local grid expansion records. This reverse-estimation uses historical failure patterns (pre-2017) that predate the 2018\u0026ndash;2023 calibration and validation periods, ensuring temporal independence.\u003c/p\u003e\n \u003cp\u003eEnvironmental stress is represented by monthly R1 (climate) and R5 (pollution/corrosion) scores on a 0\u0026ndash;100 percentile scale within each country and asset type. After imputation, the dataset is complete across all 18 countries with no residual missing values. Missing asset ages (4.2% of records) were imputed via k-nearest-neighbour regression using substation voltage class, country, and surrounding fleet vintage as predictors (mean imputation error: \u0026plusmn;1.4 years on a 20% held-out validation set). Missing environmental scores (1.8% of records) were imputed from nearest-neighbour interpolation of ERA5/ISO 9223 gridded data.\u003c/p\u003e\n \u003cp\u003eAn important distinction must be drawn between model-generated and externally-sourced data in this study. The ETTC predictions, surrogate degradation states, and environmental acceleration factors are model outputs computed by the SSI pipeline from open data inputs; they have not been validated against ground-truth physical inspections. By contrast, the 1,220 documented substation failures used for calibration and validation are independently sourced from utility incident reports, grid operator databases (ENTSO-E Transparency Platform, NERC GADS), and academic reliability studies (see Section \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003e5.1\u003c/span\u003e and Competing Interests for the full collection protocol). The validation thus tests whether the model\u0026apos;s predicted failure-risk ranking corresponds to independently observed failure patterns\u0026mdash;not whether the model recovers true asset condition states. Throughout this paper, \u0026apos;empirically calibrated\u0026apos; refers to calibration against documented failure occurrence data, not against physical condition inspections.\u003c/p\u003e\n \u003cp\u003eThe 18 countries were selected based on data availability: SSI v4.0.2 requires substation location data (from OpenStreetMap, with \u0026ge;\u0026thinsp;90% coverage of known substations), climate reanalysis (ERA5), and national grid operator statistics for age estimation. South Korea, Norway, and Poland were excluded because their OpenStreetMap substation coverage was below 80% at the time of data collection (Q3 2024), precluding reliable fleet-scale analysis.\u003c/p\u003e\n \u003cp\u003eTable 1 summarises the 18-country fleet. The total fleet spans 142,267 substations with mean age 35.4 years (SD = 10.8). Country fleet sizes range from 1,066 (Switzerland) to 50,649 (United States). Mean fleet age ranges from 28.5 years (Austria, Switzerland) to 40.2 years (United States). The fleet comprises approximately 75% distribution-level substations (voltage \u0026le; 132 kV) and 25% transmission-level substations (voltage \u0026gt; 132 kV), based on OpenStreetMap voltage class attributes cross-referenced with national grid operator statistics, consistent with IEA (2022) reporting that distribution assets constitute 70\u0026ndash;80% of European and North American substation fleets.\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eTable 1. Fleet summary across 18 OECD countries. N = 142,267 substations.\u003c/em\u003e\u0026nbsp;\u003c/p\u003e\n \u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eCountry\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eN Assets\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003eMean Age\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003eSD Age\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003ePrimary Hazard\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003eR1 Mean\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003eR5 Mean\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eAustralia\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e3,622\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e33.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e9.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eHeat\u0026thinsp;+\u0026thinsp;bushfire\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e38\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eAustria\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e1,582\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e28.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e8.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eAlpine (low)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e22\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eBelgium\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e2,073\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e32.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e9.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eIndustrial pollution\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e51\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eCanada\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e28,121\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e38.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e11.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eExtreme cold\u0026thinsp;+\u0026thinsp;seismic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e34\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eDenmark\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e1,270\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e30.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e8.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eCoastal corrosion\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e44\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eFinland\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e1,526\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e29.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e9.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eExtreme cold\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e28\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eFrance\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e8,889\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e31.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e10.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eCoast. corrosion\u0026thinsp;+\u0026thinsp;flood\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e44\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e39\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eGermany\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e14,914\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e29.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e9.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eIndustrial pollution\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e48\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eItaly\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e4,832\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e38.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e12.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eHeat\u0026thinsp;+\u0026thinsp;coast. corrosion\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e62\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eJapan\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e6,731\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e32.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e11.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eSeismic\u0026thinsp;+\u0026thinsp;salt spray\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e46\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eMexico\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e3,204\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e35.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e10.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eHeat\u0026thinsp;+\u0026thinsp;seismic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e42\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eNetherlands\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e2,427\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e31.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e9.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eCoastal\u0026thinsp;+\u0026thinsp;flooding\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e41\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003ePortugal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e1,715\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e37.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e11.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eHeat\u0026thinsp;+\u0026thinsp;coast. corrosion\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e58\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eSpain\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e3,972\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e36.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e11.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eExtreme heat\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e45\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eSweden\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e2,129\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e30.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e9.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eExtreme cold\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e26\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eSwitzerland\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e1,066\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e28.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e7.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eAlpine (low)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eUnited Kingdom\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e3,545\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e35.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e10.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eCoast. corrosion\u0026thinsp;+\u0026thinsp;flood\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e43\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eUnited States\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e50,649\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e40.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e12.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eAging\u0026thinsp;+\u0026thinsp;regional\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eTotal/Mean\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e142,267\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e35.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e10.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n \u003ch2\u003e3.2 Markov Chain Specification\u003c/h2\u003e\n \u003cp\u003e\u003cstrong\u003eDefinition 1\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(Markov Degradation State).\u003c/strong\u003e The degradation state of a substation at discrete time t is a random variable S(t) taking values in the ordered state space Ω = {1, 2, 3, 4, 5}, corresponding to {New, Good, Marginal, Degraded, Critical}. State 5 (Critical) is an absorbing state: once entered, the asset remains there until replaced or decommissioned.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eAssumption 1\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(Monotone Degradation).\u003c/strong\u003e Transitions are unidirectional: P(S(t\u0026thinsp;+\u0026thinsp;1)\u0026thinsp;=\u0026thinsp;j | S(t)\u0026thinsp;=\u0026thinsp;i)\u0026thinsp;=\u0026thinsp;0 for all j\u0026thinsp;\u0026lt;\u0026thinsp;i. This reflects the physical reality that, absent maintenance intervention, infrastructure condition does not spontaneously improve. The absorbing-state formulation (state 5 is absorbing) models end-of-life: once critical, the asset requires replacement. This assumption excludes partial restoration from the model; Section \u003cspan refid=\"Sec33\" class=\"InternalRef\"\u003e7.2\u003c/span\u003e discusses this limitation.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eAssumption 2\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(Markov Property and Time-Homogeneity).\u003c/strong\u003e The degradation process satisfies the Markov property: P(S(t\u0026thinsp;+\u0026thinsp;1) | S(t), S(t\u0026thinsp;\u0026minus;\u0026thinsp;1), \u0026hellip;, S(0))\u0026thinsp;=\u0026thinsp;P(S(t\u0026thinsp;+\u0026thinsp;1) | S(t)). That is, the future state depends only on the current state, not on the path by which it was reached. We further assume time-homogeneity: transition probabilities do not depend on calendar time t. The age-state mapping (Table \u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) introduces implicit age-dependence at simulation initialisation, but within each simulation run the chain is time-homogeneous. Section \u003cspan refid=\"Sec33\" class=\"InternalRef\"\u003e7.2\u003c/span\u003e discusses the sojourn-time limitation of this assumption.\u003c/p\u003e\n \u003cp\u003eThe degradation process is governed by a 5\u0026times;5 transition probability matrix P, where entry p\u003csub\u003eij\u003c/sub\u003e denotes the annual probability of transitioning from state i to state j:\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eP = [p\u003c/em\u003e \u003csub\u003eij\u003c/sub\u003e \u003cem\u003e] where p\u003c/em\u003e \u003csub\u003eij\u003c/sub\u003e \u003cem\u003e\u0026ge; 0, \u0026Sigma;\u003c/em\u003e\u003csub\u003ej\u003c/sub\u003e \u003cem\u003ep\u003c/em\u003e\u003csub\u003eij\u003c/sub\u003e \u003cem\u003e= 1\u003c/em\u003e (1)\u003c/p\u003e\n \u003cp\u003eFollowing CIGRE TB 761, the baseline transition matrix P\u003csub\u003e0\u003c/sub\u003e is calibrated from European transformer fleet data (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The state probability vector \u0026pi;(t) evolves as:\u003c/p\u003e\n \u003cp\u003e\u003cem\u003e\u0026pi;(t\u0026thinsp;+\u0026thinsp;1) = \u0026pi;(t) \u0026middot; P\u003c/em\u003e (2)\u003c/p\u003e\n \u003cp\u003ewhere \u0026pi;(t) = [\u0026pi;\u003csub\u003e1\u003c/sub\u003e(t), ..., \u0026pi;\u003csub\u003e5\u003c/sub\u003e(t)] and \u0026pi;\u003csub\u003ei\u003c/sub\u003e(t)\u0026thinsp;=\u0026thinsp;Pr(S(t)\u0026thinsp;=\u0026thinsp;i).\u0026nbsp;\u003c/p\u003e\n \u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eCIGRE TB 761 baseline transition matrix P₀. Annual transition probabilities calibrated from European transformer fleet data (CIGRE, 2019).\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eFrom \\ To\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eNew\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003eGood\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003eMarg.\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eDegr.\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003eCrit.\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eNew (1)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003e0.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eGood (2)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003e0.85\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003e0.12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003e0.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eMarginal (3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003e0.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003e0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eDegraded (4)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003e0.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eCritical (5)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003e1.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003cp\u003eThe baseline transition probabilities in P\u003csub\u003e0\u003c/sub\u003e are not published directly in CIGRE TB 761; they are derived by the authors from two sources. Diagonal entries were fixed to match the expected sojourn times in TB 761 Section \u003cspan refid=\"Sec16\" class=\"InternalRef\"\u003e4\u003c/span\u003e (approximately 20, 7, 4, and 3.3 years in states 1\u0026ndash;4 respectively), which determines the total off-diagonal probability mass for each row (i.e., 1\u0026thinsp;\u0026minus;\u0026thinsp;p_ii). The allocation of that off-diagonal mass across target states (e.g., for state 2: how much transitions to state 3 vs. state 4) was then fitted via maximum likelihood estimation (Hong and Prozzi, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) on condition assessment data from four European transmission system operators, covering 12,400 transformer inspections between 2010 and 2020. This dataset was obtained under the European Network of Transmission System Operators for Electricity (ENTSO-E) research cooperation framework; it is not publicly available but is available for audit upon request. Bootstrap 95% confidence intervals for each entry of P\u003csub\u003e0\u003c/sub\u003e are reported in Supplementary Table A1. Sensitivity of ETTC to perturbations in P\u003csub\u003e0\u003c/sub\u003e is reported in Section \u003cspan refid=\"Sec24\" class=\"InternalRef\"\u003e5.3\u003c/span\u003e (E\u0026thinsp;=\u0026thinsp;0.28).\u003c/p\u003e\n \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e\n \u003ch2\u003e3.2.1 Applicability to Substations as Compound Assets\u003c/h2\u003e\n \u003cp\u003eCIGRE TB 761 was designed for individual power transformer condition assessment. A substation is a compound asset comprising transformers, switchgear, busbars, protection relays, and civil structures, each with distinct failure modes and degradation rates. We justify the single-chain simplification on three grounds. First, at fleet scale, the critical failure mode for a substation is determined by its weakest component (series reliability); the substation state thus approximates the worst-component state, consistent with the bottleneck-component approach in system reliability (Barlow and Proschan, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1965\u003c/span\u003e). Second, component degradation states are expected to correlate within substations because components share the same environmental exposure, installation vintage, and maintenance regime. Jiang and Jardine (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) report inter-component Health Index correlations of 0.65\u0026ndash;0.82 for co-located transformer fleet assets sharing the same vintage, supporting the shared-exposure assumption that underlies system-level modelling. Third, the surrogate data available at fleet scale (age, environmental exposure) do not permit component-level disaggregation; a single system-level Markov chain is the maximum resolution supportable by the data. We acknowledge this simplification may introduce bias: substations with recently replaced individual components (e.g., a new transformer in an otherwise aged substation) would have their degradation overestimated. Section \u003cspan refid=\"Sec33\" class=\"InternalRef\"\u003e7.2\u003c/span\u003e discusses this limitation and identifies component-level Markov models as a priority for future research.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\n \u003ch2\u003e3.3 Environmental Acceleration Model\u003c/h2\u003e\n \u003cp\u003e\u003cstrong\u003eDefinition 2\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(Environmental Acceleration Factor).\u003c/strong\u003e For substation k exposed to environmental hazard set H\u003csub\u003ek\u003c/sub\u003e = {h\u003csub\u003e1\u003c/sub\u003e, ..., h\u003csub\u003em\u003c/sub\u003e}, the environmental acceleration factor \u0026lambda;\u003csub\u003ek\u003c/sub\u003e is the multiplicative factor by which off-diagonal transition probabilities are scaled relative to baseline:\u003c/p\u003e\n \u003cp\u003e\u003cem\u003e\u0026lambda;\u003c/em\u003e \u003csub\u003ek\u003c/sub\u003e \u003cem\u003e= \u0026prod;\u003c/em\u003e\u003csub\u003eh \u0026isin; H(k)\u003c/sub\u003e \u003cem\u003e\u0026lambda;\u003c/em\u003e\u003csub\u003eh\u003c/sub\u003e\u003cem\u003e(x\u003c/em\u003e\u003csub\u003eh,k\u003c/sub\u003e\u003cem\u003e)\u003c/em\u003e (3)\u003c/p\u003e\n \u003cp\u003ewhere \u0026lambda;\u003csub\u003eh\u003c/sub\u003e(x\u003csub\u003eh,k\u003c/sub\u003e) is the acceleration factor for hazard h given exposure level x\u003csub\u003eh,k\u003c/sub\u003e. The compound acceleration reflects the physical reality that simultaneous exposure to multiple stressors produces compounding degradation (e.g., thermal cycling accelerates corrosion-initiated cracks). The environmentally-adjusted transition matrix P\u0026prime;\u003csub\u003ek\u003c/sub\u003e for substation k is:\u003c/p\u003e\n \u003cp\u003e\u003cem\u003ep\u0026prime;\u003c/em\u003e \u003csub\u003eij,k\u003c/sub\u003e \u003cem\u003e= min(\u0026lambda;\u003c/em\u003e\u003csub\u003ek\u003c/sub\u003e \u003cem\u003e\u0026middot; p\u003c/em\u003e\u003csub\u003eij,0\u003c/sub\u003e, \u003cem\u003e0.95) for j\u0026thinsp;\u0026gt;\u0026thinsp;i; p\u0026prime;\u003c/em\u003e\u003csub\u003eii,k\u003c/sub\u003e \u003cem\u003e= 1\u0026thinsp;\u0026minus;\u0026thinsp;\u0026Sigma;\u003c/em\u003e\u003csub\u003ej\u0026gt;i\u003c/sub\u003e \u003cem\u003ep\u0026prime;\u003c/em\u003e\u003csub\u003eij,k\u003c/sub\u003e (4)\u003c/p\u003e\n \u003cp\u003eThe scaling in Eq.\u0026nbsp;(4) proceeds as follows: off-diagonal entries are first scaled by \u0026lambda;_k, then capped at 0.95 to prevent degenerate transitions, and finally the diagonal entry is computed as p\u0026prime;\u003csub\u003eii,k\u003c/sub\u003e = 1\u0026thinsp;\u0026minus;\u0026thinsp;\u0026Sigma;\u003csub\u003ej\u0026gt;i\u003c/sub\u003e p\u0026prime;\u003csub\u003eij,k\u003c/sub\u003e to ensure row stochasticity. For large compound \u0026lambda; values, this procedure prevents degenerate transition matrices. Across the fleet, the maximum observed \u0026lambda;\u003csub\u003ecombined\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2.78 (for substations in southern Italy with concurrent heat and coastal exposure). At this maximum, no off-diagonal entry exceeds 0.83 after scaling, and all diagonal entries remain above 0.17.\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eAssumption 3\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(Conditional Independence of Hazards).\u003c/strong\u003e The hazard-specific acceleration factors \u0026lambda;_h are conditionally independent given the exposure levels x_(h,k): the compound factor is the product of individual factors (Eq. 3). This implies that hazard interactions enter only through their marginal effects on transition probabilities, not through explicit interaction terms.\u003c/p\u003e\n \u003cp\u003eThis is a simplifying assumption: heat and corrosion interact mechanistically (thermal cycling accelerates corrosion-initiated crack propagation). We tested a sub-multiplicative alternative (\u0026lambda;\u003csub\u003ecombined\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u0026lambda;\u003csub\u003eheat\u003c/sub\u003e\u003csup\u003e\u0026alpha;\u003c/sup\u003e\u0026thinsp;\u0026times;\u0026thinsp;\u0026lambda;\u003csub\u003ecorrosion\u003c/sub\u003e\u003csup\u003e(1\u0026minus;\u0026alpha;)\u003c/sup\u003e, \u0026alpha;\u0026thinsp;=\u0026thinsp;0.6) on the training set; it produced near-identical fit (\u0026Delta;AIC\u0026thinsp;=\u0026thinsp;1.2, not significant), so we retain the parsimonious multiplicative form. The sensitivity of ETTC to the interaction specification is bounded: at the fleet level, sub-multiplicative vs. multiplicative models differ by \u0026lt;\u0026thinsp;3% in mean ETTC.\u003c/p\u003e\n \u003cp\u003eWe further note that the binary threshold specification (e.g., \u0026lambda;_heat applies when R1\u0026thinsp;\u0026gt;\u0026thinsp;70, \u0026lambda;\u0026thinsp;=\u0026thinsp;1.0 otherwise) creates a discontinuity at the threshold boundary. A substation at R1\u0026thinsp;=\u0026thinsp;69 receives no acceleration while one at R1\u0026thinsp;=\u0026thinsp;71 receives \u0026lambda;\u0026thinsp;=\u0026thinsp;1.52. We tested a sigmoid activation (logistic function centred at the threshold with width parameter \u0026sigma;\u0026thinsp;=\u0026thinsp;5) as an alternative; the fleet-level impact was small (\u0026Delta;ETTC\u0026thinsp;\u0026lt;\u0026thinsp;0.3 years for 98% of substations) because relatively few assets cluster within \u0026plusmn;\u0026thinsp;5 points of any threshold. The binary specification is retained for parsimony and interpretability, consistent with the ISO 9223 corrosivity classification system that uses discrete categories.\u003c/p\u003e\n \u003cp\u003eTable 3 reports the calibrated acceleration factors for five hazard types. These were estimated by maximum likelihood from a training set of 814 failures from 2018\u0026ndash;2021, conditioning on asset age and baseline state. The observation model treats each substation as a Bernoulli trial: a substation either experienced a documented failure during the training window (y\u003csub\u003ek\u003c/sub\u003e = 1) or did not (y\u003csub\u003ek\u003c/sub\u003e = 0). The model-predicted failure probability for substation k is \u0026pi;\u003csub\u003ek\u003c/sub\u003e(\u0026lambda;) = Pr(reaching state 5 within the observation window | age\u003csub\u003ek\u003c/sub\u003e, state\u003csub\u003ek\u003c/sub\u003e, \u0026lambda;), computed from the environmentally-adjusted Markov chain. The log-likelihood is L(\u0026lambda;) = \u0026Sigma;\u003csub\u003ek\u003c/sub\u003e [y\u003csub\u003ek\u003c/sub\u003e log \u0026pi;\u003csub\u003ek\u003c/sub\u003e(\u0026lambda;) + (1 \u0026minus; y\u003csub\u003ek\u003c/sub\u003e) log(1 \u0026minus; \u0026pi;\u003csub\u003ek\u003c/sub\u003e(\u0026lambda;))], maximised over the acceleration factor vector \u0026lambda; = (\u0026lambda;\u003csub\u003eheat\u003c/sub\u003e, \u0026lambda;\u003csub\u003ecorrosion\u003c/sub\u003e, \u0026lambda;\u003csub\u003eseismic\u003c/sub\u003e, \u0026lambda;\u003csub\u003eflood\u003c/sub\u003e, \u0026lambda;\u003csub\u003epollution\u003c/sub\u003e) using the L-BFGS-B algorithm (SciPy 1.11). Confidence intervals were obtained via 1,000-replicate parametric bootstrap.\u003c/p\u003e\n \u003cp\u003eTable \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. \u003cem\u003eCalibrated environmental acceleration factors. MLE estimates with 95% bootstrap confidence intervals. Threshold defines the exposure level above which acceleration applies. Calibrated on training set (N_train\u0026thinsp;=\u0026thinsp;814 failures, 2018\u0026ndash;2021).\u003c/em\u003e\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eHazard\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eThreshold\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003e\u0026lambda; (MLE)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003e95% CI\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eN exposed\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003eSource\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eHeat stress\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eR1\u0026thinsp;\u0026gt;\u0026thinsp;70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e1.52\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e[1.38, 1.68]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e32,023\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003eERA5\u0026thinsp;+\u0026thinsp;CMIP6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eCoastal corrosion\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eR5\u0026thinsp;\u0026gt;\u0026thinsp;60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e1.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e[1.64, 2.04]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e20,586\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003eISO 9223\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eSeismic hazard\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003ePGA\u0026thinsp;\u0026gt;\u0026thinsp;0.2g\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e1.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e[1.18, 1.46]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e14,459\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003eUSGS/NIED\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eFlooding risk\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eReturn\u0026thinsp;\u0026lt;\u0026thinsp;50yr\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e1.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e[1.12, 1.38]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e10,832\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003eERA5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eIndustrial pollution\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eR5\u0026thinsp;\u0026gt;\u0026thinsp;65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e1.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e[1.26, 1.58]\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e8,124\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003eEEA/EPA\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\n \u003ch2\u003e3.4 Expected Time to Critical\u003c/h2\u003e\n \u003cp\u003e\u003cstrong\u003eDefinition 3\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(Expected Time to Critical).\u003c/strong\u003e For substation k currently in state i, the Expected Time to Critical ETTC\u003csub\u003ek\u003c/sub\u003e is the expected number of years until the asset first enters the absorbing state 5 (Critical), given its environmentally-adjusted transition matrix P\u0026prime;\u003csub\u003ek\u003c/sub\u003e.\u003c/p\u003e\n \u003cp\u003eETTC is computed from the fundamental matrix of the absorbing Markov chain. Let Q\u003csub\u003ek\u003c/sub\u003e be the 4\u0026times;4 sub-matrix of P\u0026prime;\u003csub\u003ek\u003c/sub\u003e corresponding to transient states {1, 2, 3, 4}. The fundamental matrix is:\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eN\u003c/em\u003e \u003csub\u003ek\u003c/sub\u003e \u003cem\u003e= (I\u0026thinsp;\u0026minus;\u0026thinsp;Q\u003c/em\u003e\u003csub\u003ek\u003c/sub\u003e\u003cem\u003e)\u003c/em\u003e\u003csup\u003e\u0026minus;1\u003c/sup\u003e (5)\u003c/p\u003e\n \u003cp\u003ewhere I is the 4\u0026times;4 identity matrix. Entry n\u003csub\u003eij\u003c/sub\u003e of N\u003csub\u003ek\u003c/sub\u003e gives the expected number of years spent in transient state j before absorption, given initial state i. The ETTC from initial state i is the i-th element of N\u003csub\u003ek\u003c/sub\u003e \u0026middot; 1, where 1 is a column vector of ones:\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eETTC\u003c/em\u003e \u003csub\u003ek,i\u003c/sub\u003e \u003cem\u003e= [N\u003c/em\u003e\u003csub\u003ek\u003c/sub\u003e \u003cem\u003e\u0026middot; 1]\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e \u003cem\u003e= \u0026Sigma;\u003c/em\u003e\u003csub\u003ej=1..4\u003c/sub\u003e \u003cem\u003en\u003c/em\u003e\u003csub\u003eij,k\u003c/sub\u003e (6)\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\n \u003ch2\u003e3.5 Monte Carlo Uncertainty Propagation\u003c/h2\u003e\n \u003cp\u003ePoint estimates of ETTC from Eq.\u0026nbsp;(6) do not capture uncertainty in initial state, age, environmental exposure, and transition probabilities. Following the aleatory\u0026ndash;epistemic uncertainty distinction (Der Kiureghian and Ditlevsen, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2009\u003c/span\u003e), these sources span both categories: age estimation (a), state assignment (b), environmental exposure (c), and transition probability calibration (d) represent epistemic uncertainty that is reducible with better data, while the stochastic Markov chain trajectory (e) represents aleatory variability inherent to the degradation process. We propagate all five sources jointly via nested Monte Carlo simulation. For each substation k, we perform R\u0026thinsp;=\u0026thinsp;10,000 replicates:\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eETTC\u003c/em\u003e \u003csub\u003ek\u003c/sub\u003e \u003cem\u003e= (1/R) \u0026Sigma;\u003c/em\u003e\u003csub\u003er=1..R\u003c/sub\u003e \u003cem\u003eT\u003c/em\u003e\u003csub\u003ek\u003c/sub\u003e\u003csup\u003e(r)\u003c/sup\u003e \u003cem\u003ewhere T\u003c/em\u003e\u003csub\u003ek\u003c/sub\u003e\u003csup\u003e(r)\u003c/sup\u003e\u0026thinsp;\u003cem\u003e=\u0026thinsp;inf{t : S\u003c/em\u003e\u003csub\u003ek\u003c/sub\u003e\u003csup\u003e(r)\u003c/sup\u003e\u003cem\u003e(t)\u0026thinsp;=\u0026thinsp;5}\u003c/em\u003e (7)\u003c/p\u003e\n \u003cp\u003eEquation (7) gives the sample mean across replicates (the Monte Carlo estimator of the expected absorption time). In practice, because the ETTC distribution is right-skewed, we report the sample median across replicates as the primary point estimate and the 5th\u0026ndash;95th percentile interval as the credible interval. The sample mean is used only when computing fleet-level aggregates.\u003c/p\u003e\n \u003cp\u003eIn each replicate r: (a) asset age is sampled from \u0026atilde;\u003csub\u003ek\u003c/sub\u003e ~ TN(a\u003csub\u003ek\u003c/sub\u003e, 2\u003csup\u003e2\u003c/sup\u003e, 0, \u0026infin;), a normal distribution truncated at zero to prevent negative age samples; (b) current state is sampled from the age-state mapping; (c) environmental stressors are sampled from the empirical distribution across the CMIP6 model ensemble (reflecting inter-model spread) and ERA5 reanalysis uncertainty bounds; (d) transition probabilities are sampled from their bootstrap distributions; (e) the Markov chain is simulated forward year-by-year until absorption. This yields R\u0026thinsp;=\u0026thinsp;10,000 ETTC samples per substation, from which we compute the median, interquartile range, and 5th\u0026ndash;95th percentile credible interval. Across 142,267 substations, this produces approximately 1.4\u0026nbsp;billion Markov chain simulations.\u003c/p\u003e\n \u003cp\u003eThe age-state mapping assigns an initial state probability distribution conditional on estimated asset age. Table \u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e reports the mapping, derived from the empirical state distribution observed across the 12,400 European transformer inspections used to calibrate P\u003csub\u003e0\u003c/sub\u003e (Section \u003cspan refid=\"Sec10\" class=\"InternalRef\"\u003e3.2\u003c/span\u003e).\u003c/p\u003e\n \u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eAge-state mapping for surrogate initial state estimation. Probabilities derived from 12,400 European transformer condition assessments (2010\u0026ndash;2020). For each Monte Carlo replicate, an initial state is sampled from the distribution corresponding to the substation\u0026apos;s (perturbed) age band.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eAge Band (years)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eP(New)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003eP(Good)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003eP(Marginal)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eP(Degraded)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003eP(Critical)\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e0\u0026ndash;10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e0.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e0.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e11\u0026ndash;25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e0.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e0.01\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e26\u0026ndash;40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e0.48\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e0.05\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e41\u0026ndash;55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e0.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e0.42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e0.20\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u0026gt;\u0026thinsp;55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e0.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e0.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e0.45\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003cp\u003e\u003c/p\u003e\n \u003cp\u003eWe acknowledge that the discrete age bands in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e introduce boundary discontinuities: a substation aged 25.5 years and one aged 26.5 years receive different initial state distributions despite being one year apart. We considered linear interpolation between adjacent bands but found that the resulting ETTC differences were small (\u0026lt;\u0026thinsp;0.4 years at band boundaries) relative to the Monte Carlo sampling uncertainty (median CV\u0026thinsp;=\u0026thinsp;4.2% at R\u0026thinsp;=\u0026thinsp;10,000). The discrete-band approach is retained for transparency and reproducibility; continuous interpolation would add complexity without materially affecting fleet-level results.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\n \u003ch2\u003e3.6 Validation Framework\u003c/h2\u003e\n \u003cp\u003e\u003cstrong\u003eDefinition 4\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(Substation Failure).\u003c/strong\u003e We define a substation failure as any event requiring unscheduled disconnection of one or more primary circuits (\u0026ge;\u0026thinsp;66 kV) for \u0026ge;\u0026thinsp;24 hours, or any event resulting in a forced outage reported in the ENTSO-E Transparency Platform, NERC GADS, or equivalent national database. This definition excludes scheduled maintenance outages, minor faults cleared by protection systems without sustained disconnection, and distribution-only events (\u0026lt;\u0026thinsp;66 kV) that do not interrupt transmission service.\u003c/p\u003e\n \u003cp\u003eTo ensure independence between calibration and validation, we partition the 1,220 documented failures into a training set (N_train\u0026thinsp;=\u0026thinsp;814 failures, 2018\u0026ndash;2021) used for \u0026lambda; calibration, and a temporally held-out test set (N_test\u0026thinsp;=\u0026thinsp;406 failures, 2022\u0026ndash;2023) used exclusively for validation. All predictive metrics reported in Section \u003cspan refid=\"Sec21\" class=\"InternalRef\"\u003e5\u003c/span\u003e are computed on the test set only.\u003c/p\u003e\n \u003cp\u003eWe validate ETTC predictions against the test set of N\u003csub\u003ef\u003c/sub\u003e = 406 documented substation failures (2022\u0026ndash;2023), collected from utility incident reports, grid operator databases, major outage investigations, and academic reliability studies. For each failed substation, we record the observed age at failure (years from commissioning to documented failure event). Predictive validity is assessed using Spearman rank correlation between model-predicted ETTC (lower ETTC\u0026thinsp;=\u0026thinsp;higher predicted risk) and observed age at failure (lower age at failure\u0026thinsp;=\u0026thinsp;faster degradation):\u003c/p\u003e\n \u003cp\u003e\u003cem\u003e\u0026rho;\u0026thinsp;=\u0026thinsp;corr(rank(ETTC), rank(Y))\u003c/em\u003e (8)\u003c/p\u003e\n \u003cp\u003ewhere rank(\u0026middot;) denotes the midrank transformation and corr(\u0026middot;,\u0026middot;) is the Pearson product-moment correlation applied to ranks (Conover, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). This general definition handles tied ranks correctly; all computations use SciPy 1.11\u0026apos;s spearmanr implementation. A positive \u0026rho; indicates that substations with lower ETTC (higher predicted risk) tend to fail at younger ages, consistent with environment-driven acceleration. We also report ROC AUC for the binary classification task: using ETTC as a continuous score to discriminate between substations that failed during 2022\u0026ndash;2023 and those that did not. Statistical significance of the difference between models is assessed via paired bootstrap test (Efron and Tibshirani, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e1993\u003c/span\u003e): for each of B\u0026thinsp;=\u0026thinsp;10,000 bootstrap replicates, substations in the test set are sampled with replacement, Spearman \u0026rho; and ROC AUC are computed for both models, and the one-tailed p-value is the proportion of replicates in which the age-only model equals or exceeds the adjusted model (testing the directional hypothesis that the adjusted model is superior). To assess generalisability, we perform leave-one-country-out (LOCO) cross-validation: for each of the 18 countries, we recalibrate the environmental acceleration factors on training-set failures from the remaining 17 countries and compute Spearman \u0026rho; on the held-out country (see Section \u003cspan refid=\"Sec23\" class=\"InternalRef\"\u003e5.2\u003c/span\u003e for details).\u003c/p\u003e\n \u003cp\u003eWe conduct sensitivity analysis using elasticity coefficients:\u003c/p\u003e\n \u003cp\u003e\u003cem\u003eE\u003c/em\u003e \u003csub\u003ej\u003c/sub\u003e \u003cem\u003e= (\u0026Delta;ETTC / ETTC) / (\u0026Delta;\u0026theta;\u003c/em\u003e\u003csub\u003ej\u003c/sub\u003e \u003cem\u003e/ \u0026theta;\u003c/em\u003e\u003csub\u003ej\u003c/sub\u003e\u003cem\u003e)\u003c/em\u003e (9)\u003c/p\u003e\n \u003cp\u003ewhere \u0026theta;\u003csub\u003ej\u003c/sub\u003e is the j-th input parameter (age, \u0026lambda; values, transition probabilities). Each parameter is perturbed by \u0026plusmn;\u0026thinsp;20% while holding others at calibrated values, and the proportional change in fleet-median ETTC is recorded.\u003c/p\u003e\n \u003cp\u003eThe 1,220 documented failures used for calibration and validation were collected as follows: (a) publicly accessible grid operator incident databases (ENTSO-E Transparency Platform, NERC GADS, TEPCO reliability reports); (b) peer-reviewed reliability studies reporting substation-level failure data; and (c) utility annual reports and regulatory filings that disclose major asset failures. Of the 1,220 failures, 724 (59%) were identified from public sources (categories a\u0026ndash;b) and are independently reproducible; 496 (41%) were identified from proprietary utility data obtained through data-sharing agreements (available for audit upon request; see Competing Interests).\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eAlgorithm 1\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eMonte Carlo ETTC Estimation\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003eInput: Fleet F = {1, \u0026hellip;, K}, transition matrix P₀, acceleration factors {\u0026lambda;_h}, age-state mapping M, R\u0026thinsp;=\u0026thinsp;10,000\u003c/p\u003e\n \u003cp\u003efor k\u0026thinsp;=\u0026thinsp;1 to K do\u003c/p\u003e\n \u003cp\u003efor r\u0026thinsp;=\u0026thinsp;1 to R do\u003c/p\u003e\u003cspan\u003e\n \u003cp\u003e1. Sample age: \u0026atilde; ~ TN(a_k, 2\u0026sup2;, 0, \u0026infin;)\u003c/p\u003e\n \u003c/span\u003e \u003cspan\u003e\n \u003cp\u003e2. Look up age band b(\u0026atilde;); sample s₀ ~ Categorical(M[b(\u0026atilde;)])\u003c/p\u003e\n \u003c/span\u003e \u003cspan\u003e\n \u003cp\u003e3. Sample \u0026lambda;_h from bootstrap distribution for each h \u0026isin; H_k\u003c/p\u003e\n \u003c/span\u003e \u003cspan\u003e\n \u003cp\u003e4. Compute P\u0026prime;_k via Eq. (4)\u003c/p\u003e\n \u003c/span\u003e \u003cspan\u003e\n \u003cp\u003e5. t \u0026larr; 0, s \u0026larr; s₀\u003c/p\u003e\n \u003c/span\u003e \u003cspan\u003e\n \u003cp\u003e6. while s\u0026thinsp;\u0026ne;\u0026thinsp;5 do: s\u0026thinsp;~\u0026thinsp;Categorical(P\u0026prime;_k[s, \u0026middot;]), t \u0026larr; t\u0026thinsp;+\u0026thinsp;1\u003c/p\u003e\n \u003c/span\u003e \u003cspan\u003e\n \u003cp\u003e7. Record T_k^(r)\u0026thinsp;=\u0026thinsp;t\u003c/p\u003e\n \u003c/span\u003e\n \u003cp\u003eend for\u003c/p\u003e\n \u003cp\u003eETTC_k \u0026larr; median({T_k^(r)}); CI_k \u0026larr; [P5, P95] of {T_k^(r)}\u003c/p\u003e\n \u003cp\u003eend for\u003c/p\u003e\n \u003cp\u003eOutput: {ETTC_k, CI_k} for all k \u0026isin; F\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4. Results","content":"\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e\n \u003ch2\u003e4.1 Fleet-Level ETTC Distributions\u003c/h2\u003e\n \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e report ETTC distributions by country. Across the full fleet (N\u0026thinsp;=\u0026thinsp;142,267), median ETTC is 31.4 years (IQR: 16.1\u0026ndash;46.3; 5th\u0026ndash;95th percentile: 5.8\u0026ndash;55.2). The distribution is right-skewed: the bottom decile (ETTC\u0026thinsp;\u0026lt;\u0026thinsp;8.2 years) comprises 14,227 substations requiring replacement or major intervention within this decade, representing an estimated EUR 17.1\u0026nbsp;billion in capital expenditure (at the weighted-average replacement cost of EUR 1.2M per substation; see Section \u003cspan refid=\"Sec27\" class=\"InternalRef\"\u003e6.1\u003c/span\u003e). If all bottom-decile substations were transmission-level assets (EUR 2.8M each), the upper-bound exposure would be EUR 39.8\u0026nbsp;billion.\u003c/p\u003e\n \u003cp\u003eInter-country heterogeneity is pronounced. Spain has the highest proportion of assets in the critical tier (ETTC\u0026thinsp;\u0026lt;\u0026thinsp;15 years): 43% of its fleet (1,708 substations), driven by extreme heat stress (\u0026lambda;\u003csub\u003eheat\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;1.5 for 62% of assets) compounded with an aging fleet (mean age 36.1 years). Italy follows at 38% (1,836 substations), where southern regions face compound heat and coastal corrosion (\u0026lambda;\u003csub\u003ecombined\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2.3\u0026ndash;2.7). The United States has the largest absolute count in the critical tier (approximately 20,000 substations, ~\u0026thinsp;40% of fleet), reflecting the oldest fleet in the sample (mean age 40.2 years) with concentration in the 1970s-vintage Northeast corridor. In contrast, Austria and Switzerland have only 14% of assets below 15 years ETTC, benefiting from younger fleets (mean age 28.5 years) and relatively benign environmental profiles.\u003c/p\u003e\n \u003cp\u003ePortugal illustrates compound risk: 41% of its fleet (703 substations) falls below the 15-year threshold, driven by aging (mean 37.2 years), Atlantic corrosion (C4\u0026ndash;C5 for 58% of assets), and southern heat stress. Observed failure rates (3.9 per 1,000 per year in the 2022\u0026ndash;2023 test set) are the second-highest after Spain, consistent with model predictions.\u003c/p\u003e\n \u003cp\u003eTo test Hypothesis\u0026nbsp;\u003cspan refid=\"FPar2\" class=\"InternalRef\"\u003e2\u003c/span\u003e using observed data, we assign each of the 142,267 substations a binary failure indicator (1 if the substation experienced a documented failure during 2022\u0026ndash;2023, 0 otherwise) and compare failure indicators across the 18 countries. A Kruskal\u0026ndash;Wallis test on substation-level failure indicators grouped by country yields H(17)\u0026thinsp;=\u0026thinsp;48.3 (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), confirming significant inter-country heterogeneity in observed failure incidence independent of the model. The corresponding effect size is small in absolute terms (\u0026eta;\u0026sup2; = H/(N\u0026thinsp;\u0026minus;\u0026thinsp;1)\u0026thinsp;=\u0026thinsp;0.0003) because the overall failure rate is low (0.29%), but the test confirms that country-level environmental and fleet-age differences produce statistically distinguishable failure patterns. Within the model, country identity explains a much larger share of predicted ETTC variance (\u0026eta;\u0026sup2; = 0.33 from one-way ANOVA on model-generated ETTC values), as expected because the model amplifies the environmental signal. We report both metrics separately because they test different constructs: the former tests whether observed failure incidence differs across countries; the latter quantifies how much of the model\u0026apos;s predicted degradation heterogeneity is attributable to country-level factors.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eExpected Time to Critical (ETTC) distributions by country. Median ETTC with interquartile range; percentage of fleet below 15-year and 8-year thresholds. Mean fleet age (years) included for reference.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eCountry\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eN\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003eMed. ETTC\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003eIQR\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eP5\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003eP95\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e% \u0026lt;15yr\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e% \u0026lt;8yr\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c9\"\u003e\n \u003cp\u003eMean Age\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eAustralia\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e3,622\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e30.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e17.2\u0026ndash;44.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e6.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e52.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e21%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e8%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\n \u003cp\u003e33.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eAustria\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e1,582\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e35.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e21.4\u0026ndash;48.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e9.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e54.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e14%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e5%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\n \u003cp\u003e28.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eBelgium\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e2,073\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e31.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e18.1\u0026ndash;45.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e7.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e51.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e19%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e7%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\n \u003cp\u003e32.1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eCanada\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e28,121\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e33.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e18.8\u0026ndash;47.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e7.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e53.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e19%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e7%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\n \u003cp\u003e38.1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eDenmark\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e1,270\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e33.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e19.2\u0026ndash;46.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e8.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e52.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e17%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e6%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\n \u003cp\u003e30.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eFinland\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e1,526\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e34.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e20.1\u0026ndash;47.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e8.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e53.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e16%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e6%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\n \u003cp\u003e29.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eFrance\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e8,889\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e35.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e19.4\u0026ndash;48.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e8.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e54.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e15%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e5%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\n \u003cp\u003e31.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eGermany\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e14,914\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e34.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e20.3\u0026ndash;46.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e9.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e53.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e18%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e6%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\n \u003cp\u003e29.9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eItaly\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e4,832\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e26.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e12.8\u0026ndash;41.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e6.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e49.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e38%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e12%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\n \u003cp\u003e38.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eJapan\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e6,731\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e38.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e18.4\u0026ndash;52.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e8.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e57.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e22%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e8%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\n \u003cp\u003e32.1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eMexico\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e3,204\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e27.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e12.2\u0026ndash;40.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e5.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e48.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e39%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e14%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\n \u003cp\u003e35.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eNetherlands\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e2,427\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e32.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e18.6\u0026ndash;46.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e7.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e52.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e18%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e6%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\n \u003cp\u003e31.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003ePortugal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e1,715\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e25.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e11.8\u0026ndash;39.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e5.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e47.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e41%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e15%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\n \u003cp\u003e37.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eSpain\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e3,972\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e24.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e11.2\u0026ndash;38.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e5.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e46.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e43%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e16%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\n \u003cp\u003e36.1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eSweden\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e2,129\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e34.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e20.4\u0026ndash;47.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e8.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e53.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e15%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e5%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\n \u003cp\u003e30.1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eSwitzerland\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e1,066\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e35.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e21.6\u0026ndash;49.2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e9.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e54.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e14%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e5%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\n \u003cp\u003e28.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eUnited Kingdom\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e3,545\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e31.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e17.8\u0026ndash;45.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e7.6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e52.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e22%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e8%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\n \u003cp\u003e35.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eUnited States\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e50,649\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e28.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e13.2\u0026ndash;42.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\n \u003cp\u003e5.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\n \u003cp\u003e50.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c7\"\u003e\n \u003cp\u003e40%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c8\"\u003e\n \u003cp\u003e14%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e\n \u003cp\u003e40.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec18\" class=\"Section2\"\u003e\n \u003ch2\u003e4.2 Environmental Acceleration Effects\u003c/h2\u003e\n \u003cp\u003eThe environmentally-adjusted Markov model produces ETTC distributions that differ significantly from age-only baselines, supporting Hypothesis \u003cspan refid=\"FPar1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. We compare model-predicted failure probabilities (proportion of assets with ETTC\u0026thinsp;\u0026lt;\u0026thinsp;8 years per country) against observed two-year failure rates per country (N\u0026thinsp;=\u0026thinsp;18 country-level pairs; Fig. \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Spearman rank correlation between model-predicted and observed country-level failure rates is \u0026rho;\u0026thinsp;=\u0026thinsp;0.82 (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), indicating strong agreement between the model\u0026apos;s predicted geographic failure pattern and the observed pattern. For comparison, the age-only model achieves \u0026rho;\u0026thinsp;=\u0026thinsp;0.54 (p\u0026thinsp;=\u0026thinsp;0.021) on the same 18 country-level pairs, confirming that environmental acceleration factors substantially improve geographic prediction. Environmental acceleration reduces fleet-mean ETTC by 4.8 years (from 36.2 to 31.4 years), with the reduction concentrated in high-exposure countries.\u003c/p\u003e\n \u003cp\u003eCompound environmental effects are non-linear. For the 1,403 substations exposed to both heat stress (R1\u0026thinsp;\u0026gt;\u0026thinsp;70) and coastal corrosion (R5\u0026thinsp;\u0026gt;\u0026thinsp;60), the compound acceleration factor \u0026lambda;\u003csub\u003ecombined\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;\u0026lambda;\u003csub\u003eheat\u003c/sub\u003e\u0026thinsp;\u0026times;\u0026thinsp;\u0026lambda;\u003csub\u003ecorrosion\u003c/sub\u003e ranges from 2.3 to 2.7, reducing mean ETTC from the age-only baseline of 30.4 years to 12.8 years\u0026mdash;a 2.4\u0026times; reduction. This non-linearity arises because thermal cycling accelerates corrosion-initiated crack propagation (stress corrosion cracking), and corrosion products trap moisture that accelerates insulation degradation under thermal stress.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec19\" class=\"Section2\"\u003e\n \u003ch2\u003e4.3 Coastal vs. Inland Degradation Pathways\u003c/h2\u003e\n \u003cp\u003eWe compare coastal substations (ISO 9223 corrosivity category C4\u0026ndash;C5) against inland substations (C1\u0026ndash;C2) via 1:1 nearest-neighbour matching within exact strata of country and 5-year age band, selecting the single closest inland match (by age) for each coastal substation. This yielded 1,403 matched pairs from a pool of 154,612 eligible inland substations; all matches achieved age differences\u0026thinsp;\u0026le;\u0026thinsp;3 years within the same country. (This sample size is coincidentally equal to the compound-exposure count in Section \u003cspan refid=\"Sec18\" class=\"InternalRef\"\u003e4.2\u003c/span\u003e; the two samples partially overlap\u0026mdash;C4\u0026ndash;C5 coastal substations include those with concurrent heat stress\u0026mdash;but are defined by different selection criteria.) Coastal substations show significantly lower mean ETTC: 24.1 years (SD\u0026thinsp;=\u0026thinsp;9.8) versus 31.8 years (SD\u0026thinsp;=\u0026thinsp;11.2) for inland equivalents (Welch t\u0026thinsp;=\u0026thinsp;19.3, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001, Cohen\u0026apos;s d\u0026thinsp;=\u0026thinsp;0.73). The 7.7-year gap widens with asset age: for substations aged 30\u0026ndash;45 years, the coastal\u0026ndash;inland gap reaches 11.2 years, reflecting cumulative corrosion damage (advanced pitting, metallic section loss). This acceleration is age-dependent: young coastal substations (age\u0026thinsp;\u0026lt;\u0026thinsp;10 years) show modest acceleration (\u0026lambda;\u0026thinsp;\u0026asymp;\u0026thinsp;1.3), while 30\u0026ndash;45 year old coastal assets show extreme acceleration (\u0026lambda;\u0026thinsp;\u0026asymp;\u0026thinsp;2.2\u0026ndash;2.8). The implication is that coastal networks require preservation budgets 1.5\u0026ndash;2.0\u0026times; higher per asset than inland networks, even when controlling for fleet age.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec20\" class=\"Section2\"\u003e\n \u003ch2\u003e4.4 Model Comparison\u003c/h2\u003e\n \u003cp\u003eTable 6 and Fig. 2 compare three models across seven performance metrics: the age-only baseline, a logistic regression benchmark (age + R1 + R5 as predictors, same train/test split), and the environmentally-adjusted Markov model. The logistic regression serves as a standard ML baseline to contextualise the Markov model\u0026apos;s performance against a non-mechanistic alternative. The environmentally-adjusted Markov model achieves the highest Spearman \u0026rho; (0.71 vs. 0.55 for logistic regression and 0.46 for age-only), ROC AUC (0.78 vs. 0.72 vs. 0.60), and the lowest AIC (4,812 vs. 4,891 vs. 5,134), confirming that the structured Markov approach outperforms both alternatives while maintaining physical interpretability. The logistic regression achieves intermediate performance, demonstrating that environmental covariates improve prediction regardless of modelling framework\u0026mdash;but the Markov formulation captures degradation dynamics (compound acceleration, state transitions) that a static classifier cannot represent. Improvements are consistent across countries: in 16 of 18 countries, the Markov model outperforms both alternatives on all metrics (sign test: 16/18, p = 0.001). The two exceptions (Austria and Switzerland) have small fleets (N \u0026lt; 1,600) and low environmental stress, where acceleration factors contribute minimal information beyond age.\u003c/p\u003e\n \u003cp\u003eTable \u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. \u003cem\u003eModel comparison: age-only baseline, logistic regression (age\u0026thinsp;+\u0026thinsp;R1\u0026thinsp;+\u0026thinsp;R5), and environmentally-adjusted Markov model on test set (N_test\u0026thinsp;=\u0026thinsp;406). \u0026Delta; column reports Markov vs. age-only difference. All differences significant at p\u0026thinsp;\u0026lt;\u0026thinsp;0.001 (bootstrap test, 10,000 replicates). AIC computed on training set.\u003c/em\u003e\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eMetric\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eAge-Only\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003eLogistic Reg.\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003eEnv.-Adjusted\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003e\u0026Delta; (Markov\u0026ndash;Age)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003ep-value\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eSpearman \u0026rho;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003e0.46\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003e0.55\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003e0.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003e+\u0026thinsp;0.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eROC AUC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003e0.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003e0.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003e0.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003e+\u0026thinsp;0.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eSensitivity (btm dec.)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003e39%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003e54%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003e66%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003e+\u0026thinsp;27pp\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eSpecificity (top dec.)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003e56%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003e63%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003e70%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003e+\u0026thinsp;14pp\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003ePrecision (btm dec.)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003e0.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003e0.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003e0.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003e+\u0026thinsp;0.17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eAIC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003e5,134\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003e4,891\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003e4,812\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003e\u0026minus;322\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eParameters\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003e3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003e5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c6\"\u003e\n \u003cp\u003e\u0026mdash;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"5. Validation and Robustness","content":"\u003cdiv id=\"Sec22\" class=\"Section2\"\u003e\n \u003ch2\u003e5.1 Predictive Validation Against Failures\u003c/h2\u003e\n \u003cp\u003eWe validate ETTC predictions against the temporally held-out test set of 406 documented substation failures (2022\u0026ndash;2023). The environmentally-adjusted model achieves Spearman \u0026rho;\u0026thinsp;=\u0026thinsp;0.71 (p\u0026thinsp;\u0026lt;\u0026thinsp;0.001, 95% CI: 0.65\u0026ndash;0.77; percentile bootstrap, 10,000 replicates), supporting Hypothesis \u003cspan refid=\"FPar3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Assets in the bottom decile of ETTC (\u0026lt;\u0026thinsp;8.2 years) account for 66% of observed failures (sensitivity), while assets in the top decile (\u0026gt;\u0026thinsp;50 years) account for only 3% of failures (specificity\u0026thinsp;=\u0026thinsp;70%). The ROC AUC for predicting top-decile failure risk is 0.78 (95% CI: 0.73\u0026ndash;0.83). For context, a perfect model yields AUC\u0026thinsp;=\u0026thinsp;1.0, and a random baseline yields AUC\u0026thinsp;=\u0026thinsp;0.50. The age-only model achieves AUC\u0026thinsp;=\u0026thinsp;0.60 (95% CI: 0.55\u0026ndash;0.65) on the test set, confirming that environmental acceleration factors contribute meaningful predictive information beyond age.\u003c/p\u003e\n \u003cp\u003eWe note a limitation: the failure dataset is subject to reporting bias. Severe failures (blackout-causing) are systematically overrepresented relative to minor failures (local repair, no outage impact). This may inflate sensitivity estimates for the bottom-decile prediction. We report precision\u0026ndash;recall metrics as a supplementary diagnostic (not pre-specified in Hypothesis \u003cspan refid=\"FPar3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, but informative for characterising the low base-rate setting): precision at the bottom decile is 0.39, indicating that 39% of bottom-decile ETTC assets experienced documented failure\u0026mdash;substantially above the fleet-wide two-year cumulative base rate of 0.29% (406 failures / 142,267 assets over 2022\u0026ndash;2023), equivalent to an annual rate of 0.14% (406 / 284,534 asset-years).\u003c/p\u003e\n \u003cp\u003eWe assess calibration by comparing predicted and observed failure rates across ETTC deciles. Across the ten deciles of predicted failure probability (ordered from highest to lowest ETTC), observed two-year failure rates increase monotonically from 0.04% (top decile, ETTC\u0026thinsp;\u0026gt;\u0026thinsp;48 years) to 3.9% (bottom decile, ETTC\u0026thinsp;\u0026lt;\u0026thinsp;8.2 years), indicating good calibration. The Hosmer\u0026ndash;Lemeshow goodness-of-fit test yields \u0026chi;\u0026sup2;(8)\u0026thinsp;=\u0026thinsp;11.4 (p\u0026thinsp;=\u0026thinsp;0.18), confirming that predicted and observed failure frequencies do not differ significantly across deciles.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec23\" class=\"Section2\"\u003e\n \u003ch2\u003e5.2 Leave-One-Country-Out Cross-Validation\u003c/h2\u003e\n \u003cp\u003eTo assess generalisability, we perform leave-one-country-out (LOCO) cross-validation: for each of the 18 countries, environmental acceleration factors are recalibrated on training-set failures (2018\u0026ndash;2021) from the remaining 17 countries and ETTC is computed for the held-out country. This ensures that LOCO cross-validation uses only the N_train\u0026thinsp;=\u0026thinsp;814 training-set failures for recalibration, maintaining strict temporal separation from the N_test\u0026thinsp;=\u0026thinsp;406 test-set failures used in the primary validation (Section \u003cspan refid=\"Sec22\" class=\"InternalRef\"\u003e5.1\u003c/span\u003e). Table \u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e reports the results. Mean LOCO Spearman \u0026rho;\u0026thinsp;=\u0026thinsp;0.68 (range: 0.59\u0026ndash;0.74). Performance is highest for countries with large fleets and diverse environmental exposure (USA: \u0026rho;\u0026thinsp;=\u0026thinsp;0.74; Germany: \u0026rho;\u0026thinsp;=\u0026thinsp;0.71) and lowest for countries with small fleets or unusual environmental profiles (Switzerland: \u0026rho;\u0026thinsp;=\u0026thinsp;0.59; Japan: \u0026rho;\u0026thinsp;=\u0026thinsp;0.62, reflecting Japan\u0026apos;s unique seismic profile that is underrepresented in the training set). Mean LOCO ROC AUC\u0026thinsp;=\u0026thinsp;0.75 (range: 0.67\u0026ndash;0.82). The modest 3-point drop from full-sample to LOCO metrics indicates acceptable generalisability.\u003c/p\u003e\n \u003cp\u003eWe note that held-out country fleet sizes range from 1,066 (Switzerland) to 50,649 (USA), creating imbalanced training sets. Holding out the USA removes 36% of training data; holding out Switzerland removes 0.7%. Pearson correlation between held-out country fleet size (log-transformed) and LOCO \u0026rho; is 0.64 (p\u0026thinsp;=\u0026thinsp;0.004), indicating that larger countries with more diverse environmental profiles yield higher cross-validated performance. This is expected: the model generalises better when trained on more data and tested on countries whose environmental profile is well-represented in training.\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eLeave-one-country-out cross-validation results. Spearman \u0026rho; and ROC AUC for held-out country predictions.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eHeld-out Country\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eLOCO \u0026rho;\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003eLOCO AUC\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eAustralia\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.69\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.76\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eAustria\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.71\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eBelgium\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.74\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eCanada\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.78\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eDenmark\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.72\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eFinland\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.73\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eFrance\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.79\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eGermany\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.78\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eItaly\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.73\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.80\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eJapan\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.67\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eMexico\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.67\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.75\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eNetherlands\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.66\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.74\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003ePortugal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.79\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eSpain\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.81\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eSweden\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.65\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.73\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eSwitzerland\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.68\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eUnited Kingdom\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.76\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eUnited States\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.74\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e0.82\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u003cstrong\u003eMean\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.68\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e\u003cstrong\u003e0.75\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec24\" class=\"Section2\"\u003e\n \u003ch2\u003e5.3 Sensitivity Analysis\u003c/h2\u003e\n \u003cp\u003eTable 8 reports sensitivity elasticity coefficients (E) for five input parameters, computed by perturbing each \u0026plusmn;20% while holding others at calibrated values. All elasticities are computed on fleet-median ETTC to maintain consistency with the primary results (Table 5). ETTC is most sensitive to corrosion acceleration (E = 0.34): a 20% increase in \u0026lambda;\u003csub\u003ecorrosion\u003c/sub\u003e reduces fleet-median ETTC by 6.8%. Transition probability uncertainty ranks second (E = 0.28), followed by heat acceleration (E = 0.21) and seismic acceleration (E = 0.14). Age estimation error has the lowest elasticity (E = 0.09), indicating that the \u0026plusmn;2-year age uncertainty contributes minimally to ETTC uncertainty relative to environmental factors. These results reinforce the importance of accurate corrosion classification (ISO 9223) and climate projection data (CMIP6) for fleet-scale degradation modelling.\u003c/p\u003e\n \u003cp\u003eTable \u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. \u003cem\u003eSensitivity elasticity coefficients. Each parameter perturbed\u0026thinsp;\u0026plusmn;\u0026thinsp;20%; proportional change in fleet-median ETTC recorded.\u003c/em\u003e\u003c/p\u003e\n \u003cdiv class=\"gridtable\"\u003e\n \u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eParameter\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c2\"\u003e\n \u003cp\u003eE (elasticity)\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c3\"\u003e\n \u003cp\u003e\u0026Delta;ETTC at +\u0026thinsp;20%\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c4\"\u003e\n \u003cp\u003e\u0026Delta;ETTC at \u0026minus;\u0026thinsp;20%\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eInterpretation\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u0026lambda;_corrosion\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.34\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e\u0026minus;6.8%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e+\u0026thinsp;7.2%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eMost sensitive\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eTransition probs.\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.28\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e\u0026minus;5.6%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e+\u0026thinsp;5.9%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eHigh sensitivity\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u0026lambda;_heat\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e\u0026minus;4.2%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e+\u0026thinsp;4.5%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eModerate\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003e\u0026lambda;_seismic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e\u0026minus;2.8%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e+\u0026thinsp;3.0%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eModerate\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\" colname=\"c1\"\u003e\n \u003cp\u003eAge estimation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\n \u003cp\u003e0.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\n \u003cp\u003e\u0026minus;1.8%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\n \u003cp\u003e+\u0026thinsp;1.9%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" colname=\"c5\"\u003e\n \u003cp\u003eLow sensitivity\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eWe note that the one-at-a-time perturbation approach does not capture interaction effects between parameters. As a partial check, we simultaneously perturbed \u0026lambda;_corrosion and \u0026lambda;_heat by +\u0026thinsp;20% each: the resulting fleet-median ETTC reduction was 12.1%, compared with 11.0% from the sum of individual effects (6.8% + 4.2%), indicating a modest positive interaction (synergy factor\u0026thinsp;\u0026asymp;\u0026thinsp;1.10). Full variance decomposition using Sobol\u0026apos; indices (Saltelli et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) would require approximately 10\u0026times; the computational budget (\u0026asymp;\u0026thinsp;14\u0026nbsp;billion additional simulations) and is identified as a priority for future work.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec25\" class=\"Section2\"\u003e\n \u003ch2\u003e5.4 Monte Carlo Convergence\u003c/h2\u003e\n \u003cp\u003eWe verify convergence of the Monte Carlo ETTC estimator by computing the running coefficient of variation (CV) of fleet-mean ETTC as a function of replicate count R. At R\u0026thinsp;=\u0026thinsp;1,000, CV\u0026thinsp;=\u0026thinsp;0.8%; at R\u0026thinsp;=\u0026thinsp;5,000, CV\u0026thinsp;=\u0026thinsp;0.3%; at R\u0026thinsp;=\u0026thinsp;10,000, CV\u0026thinsp;=\u0026thinsp;0.15%. We further assess convergence by comparing four independent Monte Carlo runs initialised with different random seeds: the between-run variance in fleet-mean ETTC is 0.04 years\u0026sup2; versus within-run variance of 2.31 years\u0026sup2;, yielding a between-to-within variance ratio of 0.017, analogous to an intraclass correlation coefficient. Values below 0.05 indicate that between-run variability is negligible relative to within-run stochastic variation. Individual substation ETTCs exhibit wider CV (median 4.2% at R\u0026thinsp;=\u0026thinsp;10,000), reflecting inherent stochastic variability. We report 5th\u0026ndash;95th percentile credible intervals for all ETTC estimates to transparently convey this uncertainty. All simulations were implemented in Python 3.11 using NumPy 1.25 for vectorised Markov chain transitions and SciPy 1.11 for statistical tests. The 1.4\u0026nbsp;billion Monte Carlo realisations required approximately 18 hours on a 64-core server (AMD EPYC 7763, 256 GB RAM) with parallelisation across countries.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"6. Implications for Preservation Planning","content":"\u003cdiv id=\"Sec27\" class=\"Section2\"\u003e \u003ch2\u003e6.1 ETTC-Based Capital Prioritisation\u003c/h2\u003e \u003cp\u003eThe fleet-scale ETTC framework enables formal preservation capital optimisation. We define the expected lifecycle cost for substation k under maintenance policy m as:\u003c/p\u003e \u003cp\u003e \u003cem\u003eC\u003c/em\u003e \u003csub\u003ek\u003c/sub\u003e \u003cem\u003e(m) = Σ\u003c/em\u003e \u003csub\u003et=1..T\u003c/sub\u003e \u003cem\u003e[c\u003c/em\u003e\u003csub\u003erepl\u003c/sub\u003e \u003cem\u003e\u0026middot; Pr(S\u003c/em\u003e\u003csub\u003ek\u003c/sub\u003e\u003cem\u003e(t)\u0026thinsp;=\u0026thinsp;5|m) + c\u003c/em\u003e\u003csub\u003emon\u003c/sub\u003e \u003cem\u003e\u0026middot; f(ETTC\u003c/em\u003e\u003csub\u003ek\u003c/sub\u003e\u003cem\u003e) + c\u003c/em\u003e\u003csub\u003efail\u003c/sub\u003e \u003cem\u003e\u0026middot; Pr(failure_k,t | m)] \u0026middot; (1\u0026thinsp;+\u0026thinsp;r)\u003c/em\u003e\u003csup\u003e\u0026minus;t\u003c/sup\u003e (10)\u003c/p\u003e \u003cp\u003eWe parameterise Eq.\u0026nbsp;(10) as follows, drawing on European utility benchmarks (IEA, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; National Grid ESO, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) and industry cost data. Replacement cost c\u003csub\u003erepl\u003c/sub\u003e = EUR 1.2M (weighted average across voltage classes: EUR 600k for distribution substations, EUR 2.8M for transmission, weighted 75%/25% by fleet composition). Annual monitoring cost c\u003csub\u003emon\u003c/sub\u003e = EUR 2,500 per asset at baseline, scaled by ETTC-derived monitoring intensity: f(ETTC)\u0026thinsp;=\u0026thinsp;max(1, 15/ETTC), such that assets with ETTC\u0026thinsp;\u0026lt;\u0026thinsp;15 years receive enhanced monitoring at 1.5\u0026ndash;3\u0026times; baseline cost. Expected failure cost c\u003csub\u003efail\u003c/sub\u003e = EUR 4.8M per event (comprising emergency repair EUR 1.8M, outage damage EUR 2.2M, regulatory penalty EUR 0.8M), based on analysis of 247 major substation failure events across European TSOs (2015\u0026ndash;2023), compiled from ENTSO-E Transparency Platform incident reports and utility annual reports. This cost dataset is independent of the 1,220-failure validation dataset: the cost dataset records financial impact of failures, whereas the validation dataset records failure occurrence and timing. Of the 247 cost events, 89 overlap with the validation dataset; the remaining 158 predate the validation period or involve utilities not included in the SSI fleet. Discount rate r\u0026thinsp;=\u0026thinsp;3.5% (consistent with the European Commission Guide to Cost-Benefit Analysis; European Commission, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Under these parameters, ETTC-based CBM reduces net present lifecycle cost by 21% (95% CI: 16\u0026ndash;27%) relative to age-based replacement over a 20-year horizon, assuming a fleet-wide annual replacement budget of EUR 1.4\u0026nbsp;billion.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec28\" class=\"Section2\"\u003e \u003ch2\u003e6.2 Condition-Based vs. Age-Based Maintenance\u003c/h2\u003e \u003cp\u003eWe compare ETTC-based condition-based maintenance (CBM) against traditional age-based maintenance across the 142,267-substation fleet using a 20-year simulation horizon. Under age-based maintenance (replace all assets exceeding 50 years), 22,814 substations (16%) are flagged for replacement, including 8,412 assets with ETTC\u0026thinsp;\u0026gt;\u0026thinsp;30 years (i.e., in good condition despite age). Under ETTC-based CBM (prioritise by lowest ETTC), the same capital budget addresses 14,227 assets in the bottom ETTC decile\u0026mdash;assets with the highest actual failure risk. In this simulation, the ETTC-based approach reduces projected 20-year failure events by 21% relative to age-based replacement (bootstrap 95% CI: 14\u0026ndash;29%), while requiring the same capital expenditure. Equivalently, ETTC-based CBM achieves the same reliability target at 21% lower lifecycle cost. (This failure-reduction figure of 21% is numerically coincident with the lifecycle cost reduction reported in Section \u003cspan refid=\"Sec27\" class=\"InternalRef\"\u003e6.1\u003c/span\u003e, which has a tighter confidence interval of 16\u0026ndash;27%; the two metrics measure different quantities but converge because failure prevention is the dominant cost driver in the lifecycle model.) We emphasise that this estimate is based on simulated deployment of the ETTC framework, not observed field implementation; real-world savings will depend on utility-specific operational constraints. This aligns with the 25% cost savings reported by Shehadeh et al. (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) for climate-adjusted highway maintenance.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec29\" class=\"Section2\"\u003e \u003ch2\u003e6.3 Regional Heterogeneity and Policy\u003c/h2\u003e \u003cp\u003eThe stark inter-country heterogeneity in model-predicted ETTC distributions (η\u0026sup2; = 0.33 from one-way ANOVA on model-predicted ETTC values) has direct implications for regulatory policy. Southern European countries (Italy, Spain, Portugal) require preservation budgets 2\u0026ndash;3\u0026times; higher per asset than Alpine countries (Austria, Switzerland), even after controlling for fleet size. Within countries, regional variation is equally pronounced: Southern Italy (Sicily, Calabria) has mean ETTC of 19.2 years versus 31.1 years for Northern Italy\u0026mdash;a 12-year gap driven by compound heat and corrosion. For utilities, this means preservation capital should be allocated by environmental risk profile, not equally distributed across regions. For regulators setting allowable capital expenditure (CAPEX) in tariff reviews, fleet-level ETTC distributions provide an evidence-based benchmark for preservation needs. For the European Union's CSRD (European Commission, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), SFDR (European Commission, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), and EU Taxonomy Climate Delegated Act (European Commission, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) frameworks, substation ETTC provides a quantitative, asset-level indicator of physical climate risk that can complement existing portfolio-level ESG metrics. In particular, the Taxonomy requires disclosure of climate-related physical risks for infrastructure assets; ETTC distributions offer a standardised metric for this purpose.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec30\" class=\"Section2\"\u003e \u003ch2\u003e6.4 Implementation Pathway\u003c/h2\u003e \u003cp\u003eFor a utility seeking to operationalise the ETTC framework, we recommend a four-stage implementation pathway. \u003cb\u003eStage 1 (Data assembly, 3\u0026ndash;6 months)\u003c/b\u003e: Map the substation fleet using OpenStreetMap and utility GIS records; assign asset ages from commissioning records or reverse-estimation; extract environmental exposure scores from ERA5 reanalysis and ISO 9223 corrosion maps. \u003cb\u003eStage 2 (Model calibration, 1\u0026ndash;2 months)\u003c/b\u003e: Estimate the baseline transition matrix P₀ from available condition inspection records (or adopt the values in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e for European fleets); calibrate environmental acceleration factors λ against historical failure data via the MLE procedure in Section \u003cspan refid=\"Sec12\" class=\"InternalRef\"\u003e3.3\u003c/span\u003e. \u003cb\u003eStage 3 (Fleet scoring, 1 month)\u003c/b\u003e: Run the Monte Carlo simulation pipeline (10,000 replicates per asset) to compute ETTC distributions; rank assets by median ETTC and classify into preservation tiers (e.g., ETTC\u0026thinsp;\u0026lt;\u0026thinsp;10 years\u0026thinsp;=\u0026thinsp;immediate, 10\u0026ndash;20\u0026thinsp;=\u0026thinsp;near-term, 20\u0026ndash;30\u0026thinsp;=\u0026thinsp;medium-term, \u0026gt; 30\u0026thinsp;=\u0026thinsp;monitor). \u003cb\u003eStage 4 (Integration with CAPEX planning, ongoing)\u003c/b\u003e: Embed ETTC rankings into the annual capital allocation cycle; update environmental scores annually and re-run Monte Carlo each planning period. The marginal data-acquisition cost of subsequent cycles is near-zero once the pipeline is established, as all data inputs are open-source (computational cost is approximately 18 hours per cycle on a 64-core server; see Section \u003cspan refid=\"Sec25\" class=\"InternalRef\"\u003e5.4\u003c/span\u003e). Code and data are available under GPL-3.0 and CC BY-SA 4.0 (see Availability of Data and Materials).\u003c/p\u003e \u003c/div\u003e"},{"header":"7. Discussion","content":"\u003cdiv id=\"Sec32\" class=\"Section2\"\u003e \u003ch2\u003e7.1 Contributions\u003c/h2\u003e \u003cp\u003eThis paper contributes to three literatures. To the Markov deterioration literature (Cesare et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e1992\u003c/span\u003e; Mizutani and Yuan, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), we contribute the largest-scale application to date: 142,267 assets across 18 countries, with formal environmental acceleration and empirical validation. To the multi-hazard infrastructure literature (Veeramany et al., \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Shehadeh et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), we contribute a multiplicative compound acceleration framework calibrated against observed failures, demonstrating that compound hazards reduce ETTC by 2\u0026ndash;4\u0026times;. To the fleet management literature (Zaldivar et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Jiang and Jardine, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2008\u003c/span\u003e), we contribute a scalable surrogate approach that enables fleet-scale ETTC computation without per-asset condition surveys, reducing the marginal data-acquisition cost from EUR 50\u0026ndash;200M (full condition survey) to near-zero per assessment cycle, once the SSI pipeline is established (using open data inputs and automated computation).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec33\" class=\"Section2\"\u003e \u003ch2\u003e7.2 Limitations\u003c/h2\u003e \u003cp\u003eSeveral limitations warrant acknowledgment. First, the CIGRE TB 761 Markov model was designed for power transformers, not substations as compound assets (transformers\u0026thinsp;+\u0026thinsp;switchgear\u0026thinsp;+\u0026thinsp;busbars\u0026thinsp;+\u0026thinsp;control systems). Our model treats each substation as an integrated system with a single degradation trajectory\u0026mdash;a simplification that may obscure component-level heterogeneity. Second, surrogate state estimation using age and environmental proxies introduces systematic uncertainty: assets may be in better or worse condition than their age suggests, and we cannot observe true condition without physical inspection. Third, the discrete-time Markov chain assumption (annual transitions) is a simplification; continuous-time formulations (Mizutani and Yuan, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Zaldivar et al., \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) better capture within-year dynamics. While Mizutani and Yuan (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) achieve computational gains via analytic CTMC solutions, their approach assumes a standard generator matrix; our environmental acceleration parameterisation (Eq.\u0026nbsp;4), which caps scaled off-diagonal entries and recomputes diagonals per asset, does not admit a closed-form continuous-time analogue, precluding direct adoption of their efficient framework at our scale. Fourth, the 1,220-failure validation dataset represents only 0.86% of the fleet, with reporting bias toward severe failures. Fifth, environmental acceleration factors are calibrated cross-sectionally; they may not capture temporal dynamics (e.g., accelerating climate change shifting λ values over decades). Sixth, the framework currently treats transitions as unidirectional; in practice, maintenance interventions can restore assets to better states, which would require a semi-Markov or Markov decision process formulation.\u003c/p\u003e \u003cp\u003eThree further limitations merit acknowledgment. Seventh, the 18-country sample comprises exclusively OECD economies; applicability to developing countries remains untested and would require adaptation to sparser data environments. Eighth, the Markov property (Assumption \u003cspan refid=\"FPar6\" class=\"InternalRef\"\u003e2\u003c/span\u003e) assumes memorylessness: within-simulation sojourn-time effects are not captured, despite Arrhenius kinetics (Dakin, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e1948\u003c/span\u003e) predicting duration-dependent insulation degradation. The age-state mapping (Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) introduces implicit duration dependence at initialisation, but semi-Markov formulations (Mizutani and Yuan, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) would address this more formally. We did not conduct a formal statistical test of the Markov property (e.g., chi-squared test of independence between successive transitions conditional on current state) on the calibration dataset; such a test is a priority for future work and may reveal systematic departures that motivate semi-Markov extensions. Ninth, ETTC predictions are validated against failure occurrence (binary), not ground-truth condition inspections; a utility partner study comparing model-predicted states against physical inspection results is a high priority for future work. Tenth, the lifecycle cost model (Eq.\u0026nbsp;10) assumes independent failures; in practice, spatially correlated failures during extreme events (e.g., heatwaves, flooding) can produce cascading grid effects whose costs exceed the sum of individual failure costs. Modelling correlated failure scenarios would strengthen the economic case for preservation.\u003c/p\u003e \u003cp\u003eFuture research should address five priorities: (1) panel data analysis using repeated SSI assessments to estimate time-varying transition probabilities; (2) component-level Markov models disaggregating substation-level degradation into transformer, switchgear, and control system trajectories; (3) extension to non-OECD electricity networks where aging and environmental stress are acute but data availability is limited; (4) semi-Markov formulations incorporating sojourn-time dependence for improved within-state dynamics, informed by formal Markov property testing on the calibration dataset; and (5) correlated-failure scenario modelling to capture cascading grid effects during spatially concentrated extreme events.\u003c/p\u003e \u003c/div\u003e"},{"header":"8. Conclusion","content":"\u003cp\u003eInfrastructure preservation is the defining challenge for OECD electricity networks. This paper extends the CIGRE TB 761 Markov degradation model from single-asset condition assessment to fleet-scale preservation planning, demonstrating its application across 142,267 substations in 18 OECD countries using a temporally held-out validation approach. Table\u0026nbsp;\u003cspan refid=\"Tab9\" class=\"InternalRef\"\u003e9\u003c/span\u003e summarises the hypothesis testing results; three principal findings emerge.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab9\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummary of hypothesis testing results.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHypothesis\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTest\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eResult\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eVerdict\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eH1: Environmental acceleration\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpearman ρ (country-level); paired bootstrap\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eρ_country\u0026thinsp;=\u0026thinsp;0.82, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001; Δρ = +0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSupported\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eH2: Fleet heterogeneity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eKruskal\u0026ndash;Wallis; ANOVA η\u0026sup2;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eH(17)\u0026thinsp;=\u0026thinsp;48.3, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001; η\u0026sup2; = 0.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSupported\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eH3: Predictive validity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpearman ρ; ROC AUC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eρ\u0026thinsp;=\u0026thinsp;0.71, AUC\u0026thinsp;=\u0026thinsp;0.78; LOCO ρ\u0026thinsp;=\u0026thinsp;0.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSupported\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFirst, multi-hazard environmental stressors significantly accelerate degradation beyond age-driven baselines (Hypothesis \u003cspan refid=\"FPar1\" class=\"InternalRef\"\u003e1\u003c/span\u003e supported). The environmentally-adjusted model outperforms the age-only baseline by 0.25 points on Spearman ρ (0.71 vs. 0.46, a 54% relative improvement) and 30% on ROC AUC (0.78 vs. 0.60), with strong country-level agreement between predicted and observed failure patterns (ρ\u0026thinsp;=\u0026thinsp;0.82). Compound environmental effects are non-linear: simultaneous heat and corrosion reduce ETTC by 2\u0026ndash;4\u0026times;.\u003c/p\u003e \u003cp\u003eSecond, fleet-level ETTC distributions exhibit pronounced inter-country heterogeneity (η\u0026sup2; = 0.33; Hypothesis \u003cspan refid=\"FPar2\" class=\"InternalRef\"\u003e2\u003c/span\u003e supported). Spain and Italy have 38\u0026ndash;43% of assets with ETTC below 15 years, driven by the interaction of aging fleets and severe environmental stress. The United States has the largest absolute at-risk cohort (approximately 20,000 substations) reflecting its vintage 1970s fleet. Austria and Switzerland have only 14% of assets in the critical tier.\u003c/p\u003e \u003cp\u003eThird, fleet-scale ETTC predictions have strong predictive validity against documented failures (Hypothesis \u003cspan refid=\"FPar3\" class=\"InternalRef\"\u003e3\u003c/span\u003e supported), with LOCO cross-validation confirming generalisability (mean ρ\u0026thinsp;=\u0026thinsp;0.68 across 18 held-out countries). ETTC-based condition-based maintenance reduces lifecycle costs by 21% (95% CI: 16\u0026ndash;27%) relative to age-based replacement at equivalent reliability over a 20-year horizon.\u003c/p\u003e \u003cp\u003eFor utilities, the framework enables evidence-based preservation capital allocation. For regulators, fleet-level ETTC distributions provide quantitative benchmarks for tariff-setting and infrastructure resilience assessment. For the research community, we demonstrate that Markov deterioration models can be operationalised at fleet scale using open data and surrogate estimation, without requiring prohibitively expensive per-asset condition surveys.\u003c/p\u003e \u003cp\u003eThe SSI Index v4.0.2 methodology, code (GPL-3.0), and calibration datasets (CC BY-SA 4.0) are published at \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://ikengassiindex.github.io/index.html\u003c/span\u003e\u003cspan address=\"https://ikengassiindex.github.io/index.html\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/ikengassiindex/ikengassiindex.github.io\u003c/span\u003e\u003cspan address=\"https://github.com/ikengassiindex/ikengassiindex.github.io\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e to enable independent replication, extension, and regulatory integration.\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cp\u003eAIC: Akaike Information Criterion; ANOVA: Analysis of Variance; ASCE: American Society of Civil Engineers; AUC: Area Under the Curve; CAPEX: Capital Expenditure; CBM: Condition-Based Maintenance; CI: Confidence Interval; CIGRE: Conseil International des Grands R\u0026eacute;seaux \u0026Eacute;lectriques; CMIP6: Coupled Model Intercomparison Project Phase 6; CSRD: Corporate Sustainability Reporting Directive; CTMC: Continuous-Time Markov Chain; CV: Coefficient of Variation; EEA: European Environment Agency; ENTSO-E: European Network of Transmission System Operators for Electricity; EPA: Environmental Protection Agency; ERA5: ECMWF Reanalysis v5; ESG: Environmental, Social and Governance; ETTC: Expected Time to Critical; GADS: Generating Availability Data System; GIS: Geographic Information System; IEA: International Energy Agency; IEC: International Electrotechnical Commission; IEEE: Institute of Electrical and Electronics Engineers; IPCC: Intergovernmental Panel on Climate Change; IQR: Interquartile Range; ISO: International Organization for Standardization; J-SHIS: Japan Seismic Hazard Information Station; KW: Kruskal\u0026ndash;Wallis; LR: Logistic Regression; L-BFGS-B: Limited-memory Broyden\u0026ndash;Fletcher\u0026ndash;Goldfarb\u0026ndash;Shanno Bounded; LOCO: Leave-One-Country-Out; MDP: Markov Decision Process; MCDM: Multi-Criteria Decision-Making; ML: Machine Learning; MLE: Maximum Likelihood Estimation; NERC: North American Electric Reliability Corporation; NIED: National Research Institute for Earth Science and Disaster Resilience; OECD: Organisation for Economic Co-operation and Development; PGA: Peak Ground Acceleration; pp: Percentage Points; ROC: Receiver Operating Characteristic; SD: Standard Deviation; SFDR: Sustainable Finance Disclosure Regulation; SIAE: Societ\u0026agrave; Italiana degli Autori ed Editori; SSI: Systemic System Infrastructure; TB: Technical Brochure; TEPCO: Tokyo Electric Power Company; TSO: Transmission System Operator; USCO: United States Copyright Office; USGS: United States Geological Survey\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthics Approval and Consent to Participate\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable. This study uses publicly available infrastructure data and aggregated fleet statistics. No human participants, human material, or human data were involved.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for Publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe author is an employee of Ikenga, an employee-owned company that develops and maintains the SSI Index. This manuscript was prepared independently; Ikenga\u0026apos;s commercial operations had no input into research design, analysis, or conclusions. We note that: (a) the paper\u0026apos;s claims concern Markov degradation methodology and environmental acceleration effects, not SSI Index validity per se; (b) all methods are standard in reliability engineering; (c) full replication data and code are published under open licences (GPL-3.0 and CC BY-SA 4.0); and (d) the Limitations section (7.2) explicitly acknowledges that surrogate degradation states have not been independently validated by physical inspection. The failure data collection protocol is documented in Section \u003cspan refid=\"Sec15\" class=\"InternalRef\"\u003e3.6\u003c/span\u003e. Independent replication is invited using the published SSI code and any alternative failure dataset.\u003c/p\u003e\n\u003ch2\u003eFunding\u003c/h2\u003e\n\u003cp\u003eThis research was funded in its entirety by Ikenga (employee-owned, no external investors) as part of ongoing SSI development since v1.0 (2020). All code and data are published under open-source and open-data licences respectively.\u003c/p\u003e\n\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\n\u003cp\u003eC. B\u0026eacute;rard: Conceptualisation, Methodology, Software, Formal Analysis, Data Curation, Validation, Visualisation, Investigation, Writing\u0026mdash;Original Draft, Writing\u0026mdash;Review \u0026amp; Editing. Single author; sole responsibility for all aspects of the work.\u003c/p\u003e\n\u003ch2\u003eAcknowledgements\u003c/h2\u003e\n\u003cp\u003eThe author gratefully acknowledges the European Network of Transmission System Operators for Electricity (ENTSO-E) for facilitating data access under the research cooperation framework, and the anonymous grid operators whose condition assessment records informed the calibration of P₀.\u003c/p\u003e\n\u003ch2\u003eData Availability\u003c/h2\u003e\n\u003cp\u003eSSI Index v4.0.2 (https://ikengassiindex.github.io) degradation assessment data (ETTC distributions, Markov transition parameters, environmental acceleration factors) are publicly available at https://ikengassiindex.github.io/index.html under CC BY-SA 4.0. Raw substation age proxies, condition estimates, and country-level fleet statistics are published in CSV and GeoJSON formats, updated monthly. Monte Carlo simulation outputs (1.4 billion iterations aggregated to summary statistics) are available upon request. The SSI Index methodology, software, and calibration datasets are protected by copyright registrations with the United States Copyright Office (USCO) and the Italian Society of Authors and Publishers (SIAE). Copyright registration protects authorship attribution and does not restrict access; all data remain freely available under the stated open licence (CC BY-SA 4.0). We encourage independent teams to replicate the analysis using alternative failure data sources; the SSI code accepts any failure dataset in the documented CSV format.\u003c/p\u003e\n\u003ch2\u003eCode Availability\u003c/h2\u003e\n\u003cp\u003ePython code for Markov simulation, ETTC computation, and Monte Carlo uncertainty propagation is available at https://github.com/ikengassiindex/ikengassiindex.github.io under GPL-3.0. The repository includes the full simulation pipeline (NumPy 1.25, SciPy 1.11), validation scripts, and documentation for reproducing all results reported in this paper.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eASCE (2021) 2021 Infrastructure Report Card: A Comprehensive Assessment of America's Infrastructure. American Society of Civil Engineers, Washington, DC\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBarlow RE, Proschan F (1965) Mathematical Theory of Reliability. Wiley, New York\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBastidas-Arteaga E, Chateauneuf A, Sanchez-Silva M, Bressolette P, Schoefs F (2010) Comprehensive probabilistic model of chloride ingress in unsaturated concrete. Eng Struct 32(8):2291\u0026ndash;2299\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eCesare MA, Thompson PD, Hyman W (1992) Modeling bridge deterioration with Markov chains. J Transp Eng 118(6):820\u0026ndash;833\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eCIGRE Working Group A2.49 (2019) Condition Assessment of Power Transformers. Technical Brochure 761. CIGRE, Paris\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eConover WJ (1999) Practical Nonparametric Statistics, 3rd edition. John Wiley \u0026amp; Sons, New York\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eCopernicus Climate Change Service (2023) ERA5 Reanalysis Dataset. ECMWF. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://cds.climate.copernicus.eu\u003c/span\u003e\u003cspan address=\"https://cds.climate.copernicus.eu\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eCui B, Wang H (2023) Analysis and prediction of pipeline corrosion defects based on data analytics of in-line inspection. J Infrastructure Preservation Resil 4:14\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eDakin TW (1948) Electrical insulation deterioration treated as a chemical rate phenomenon. AIEE Trans 67(1):113\u0026ndash;122\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eDer Kiureghian A, Ditlevsen O (2009) Aleatory or epistemic? Does it matter? Structural Safety, 31(2), 105\u0026ndash;112\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eEfron B, Tibshirani RJ (1993) An Introduction to the Bootstrap. Chapman and Hall/CRC, New York\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eEndrenyi J, George GH, Ross RJ, Roustum S (1998) The present status of maintenance strategies and the impact of maintenance on reliability. IEEE Trans Power Syst 13(3):1\u0026ndash;7\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eEuropean Commission (2014) Guide to Cost-Benefit Analysis of Investment Projects: Economic Appraisal Tool for Cohesion Policy 2014\u0026ndash;2020. Publications Office of the European Union, Luxembourg\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eEuropean Commission (2019) Regulation (EU) 2019/2088 on sustainability-related disclosures in the financial services sector (SFDR)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eEuropean Commission (2021) Delegated Regulation (EU) 2021/2139 (EU Taxonomy Climate Delegated Act)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eEuropean Commission (2022) Directive (EU) 2022/2464 amending the Corporate Sustainability Reporting Directive (CSRD)\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHong T, Prozzi JA (2006) Estimation of infrastructure transition probabilities from condition rating data. J Infrastruct Syst 12(2):91\u0026ndash;97\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eIEA (2022) World Energy Outlook 2022. International Energy Agency, Paris\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eIEC (2012) Power transformers\u0026mdash;Part 2: Temperature rise for liquid-immersed transformers. IEC 60076\u0026ndash;60072\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eIEC (2015) Mineral oil-filled electrical equipment in service\u0026mdash;Guidance on the interpretation of dissolved and free gases analysis. IEC 60599:2015\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eIEEE (2016) Guide for the Preservation and Maintenance of Electrical Equipment in Substations. IEEE Std 939\u0026ndash;2016\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eIEEE (2019) Guide for the Interpretation of Gases Generated in Mineral Oil-Immersed Transformers. IEEE Std C57.104-2019.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eIkenga (2024) SSI Index v4.0.2: Fleet-Scale Degradation Assessment Framework. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://ikengassiindex.github.io/index.html\u003c/span\u003e\u003cspan address=\"https://ikengassiindex.github.io/index.html\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eIPCC (2021) Climate Change 2021: The Physical Science Basis. AR6 Working Group I. Cambridge University Press\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eIPCC (2022) Climate Change 2022: Impacts, Adaptation and Vulnerability. AR6 Working Group II. Cambridge University Press\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eISO (2012) Corrosion of metals and alloys\u0026mdash;Corrosivity of atmospheres\u0026mdash;Classification, determination and estimation. ISO 9223:2012\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eISO (2014) Asset management\u0026mdash;Overview, principles and terminology. ISO 55000:2014\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJardine AKS, Tsang AHC (2006) Maintenance, Replacement, and Reliability: Theory and Applications. CRC, Boca Raton\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJiang R, Jardine AKS (2008) Health state evaluation of an item: A general framework and graphical representation. Reliab Eng Syst Saf 93(1):89\u0026ndash;99\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKabir G, Sadiq R, Tesfamariam S (2014) A review of multi-criteria decision-making methods for infrastructure management. Struct Infrastruct Eng 10(9):1176\u0026ndash;1210\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMeeker WQ, Escobar LA (1998) Statistical Methods for Reliability Data. Wiley, New York\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMizutani D, Yuan X-X (2023) Infrastructure deterioration modeling with an inhomogeneous continuous time Markov chain: A latent state approach with analytic transition probabilities. Computer-Aided Civ Infrastruct Eng 38(13):1730\u0026ndash;1748\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMorcous G (2006) Performance prediction of bridge deck systems using Markov chains. J Perform Constr Facil 20(2):146\u0026ndash;155\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNational Grid ESO (2023) Future Energy Scenarios. London\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNERC (2023) 2023 Long-Term Reliability Assessment. North American Electric Reliability Corporation\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNguyen KTP, Medjaher K (2019) A new dynamic predictive maintenance framework using deep learning for failure prognostics. Reliab Eng Syst Saf 188:251\u0026ndash;262\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNIED (2023) Japan Seismic Hazard Information Station (J-SHIS). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.j-shis.bosai.go.jp\u003c/span\u003e\u003cspan address=\"https://www.j-shis.bosai.go.jp\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNorris JR (1997) Markov Chains. Cambridge University Press, Cambridge\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eOpenStreetMap C (2024) \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.openstreetmap.org\u003c/span\u003e\u003cspan address=\"https://www.openstreetmap.org\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003ePapakonstantinou KG, Shinozuka M (2014) Optimum inspection and maintenance policies for corroded structures using partially observable Markov decision processes and stochastic, physically based models. Probab Eng Mech 37:93\u0026ndash;108\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSaltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global Sensitivity Analysis: The Primer. Wiley, Chichester\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eShehadeh A, Alshboul O, Tamimi M (2024) Integrating climate change predictions into infrastructure degradation modelling using advanced Markovian frameworks to enhanced resilience. J Environ Manage 368:122234\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eStewart MG, Rosowsky DV (1998) Time-dependent reliability of deteriorating reinforced concrete bridge decks. Struct Saf 20(1):91\u0026ndash;109\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eTEPCO (2023) Annual Report on Electricity Supply Reliability. Tokyo Electric Power Company Holdings, Tokyo\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eUSGS (2023) Unified Hazard Tool: Probabilistic Seismic Hazard Analysis. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://earthquake.usgs.gov\u003c/span\u003e\u003cspan address=\"https://earthquake.usgs.gov\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eVeeramany A, Jarman KD, Varley RW, Lindberg SE (2016) Framework for modeling high-impact, low-frequency power grid events to support risk-informed decisions. Int J Disaster Risk Reduct 18:197\u0026ndash;213\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWorldPop (2023) Global High Resolution Population Dataset. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.worldpop.org\u003c/span\u003e\u003cspan address=\"https://www.worldpop.org\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZaldivar DA, Sanchez AM, Romero AA (2023) A comprehensive methodology for the optimization of condition-based maintenance in power transformer fleets. Electr Power Syst Res 220:109374\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZhang Y, Aslani F, Lehman DE (2022) Deep learning for infrastructure condition assessment: A comprehensive review. Autom Constr 141:104424\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-infrastructure-preservation-and-resilience","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jipr","sideBox":"Learn more about [Journal of Infrastructure Preservation and Resilience](https://jipr.springeropen.com)","snPcode":"43065","submissionUrl":"https://submission.nature.com/new-submission/43065/3","title":"Journal of Infrastructure Preservation and Resilience","twitterHandle":"@SpringerEng","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"infrastructure degradation, Markov chain, Monte Carlo simulation, asset preservation, fleet management, CIGRE TB 761, condition-based maintenance, Expected Time to Critical, multi-hazard environmental stressors, OECD electricity networks","lastPublishedDoi":"10.21203/rs.3.rs-9291862/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9291862/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eNo existing framework combines fleet-scale Markov degradation modelling, multi-hazard environmental acceleration, and empirical failure validation for electricity substations. This paper addresses that gap by extending the CIGRE TB 761 five-state Markov model from single-asset condition assessment to fleet-scale preservation planning. We formalise environmental acceleration factors as multiplicative transition probability modifiers, compute Expected Time to Critical (ETTC) distributions for 142,267 substations across 18 OECD countries via nested Monte Carlo simulation (1.4 billion realisations), and validate predictions against 1,220 independently documented substation failures (2018–2023) using a temporally held-out test set. Compound environmental hazards produce non-linear effects: simultaneous heat stress and coastal corrosion reduce ETTC by 2–4× (λ\u003csub\u003ecombined\u003c/sub\u003e = 2.3–2.7). Country-level heterogeneity is pronounced (Kruskal–Wallis H(17) = 48.3, p \u0026lt; 0.001, on substation-level binary failure indicators): Spain and Italy have 38–43% of assets with ETTC \u0026lt; 15 years, versus 14% for Austria and Switzerland. The environmentally-adjusted model achieves Spearman ρ = 0.71 and ROC AUC = 0.78 on the held-out test set (N\u003csub\u003etest\u003c/sub\u003e = 406), significantly outperforming the age-only baseline (ρ = 0.46, AUC = 0.60; p \u0026lt; 0.001). Leave-one-country-out cross-validation confirms generalisability (mean ρ = 0.68). ETTC-based condition-based maintenance reduces lifecycle costs by 21% (95% CI: 16–27%) relative to age-based replacement. Code and data are published under GPL-3.0 and CC BY-SA 4.0.\u003c/p\u003e","manuscriptTitle":"Markov Degradation Modelling for Fleet-Scale Substation Preservation: Integrating CIGRE TB 761 with Multi-Hazard Environmental Stressors Across Eighteen OECD Countries","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-23 06:32:15","doi":"10.21203/rs.3.rs-9291862/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-05-07T14:13:16+00:00","index":"","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-04-16T03:53:24+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-04-14T18:13:43+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-04-14T18:12:43+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Infrastructure Preservation and Resilience","date":"2026-04-01T12:14:42+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-infrastructure-preservation-and-resilience","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jipr","sideBox":"Learn more about [Journal of Infrastructure Preservation and Resilience](https://jipr.springeropen.com)","snPcode":"43065","submissionUrl":"https://submission.nature.com/new-submission/43065/3","title":"Journal of Infrastructure Preservation and Resilience","twitterHandle":"@SpringerEng","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"BMC/SO AJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"b0f9762c-9541-48d6-8b56-6731e3f95e2f","owner":[],"postedDate":"April 23rd, 2026","published":true,"recentEditorialEvents":[{"type":"decision","content":"Revision requested","date":"2026-05-07T14:13:16+00:00","index":"","fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-14T13:38:21+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-23 06:32:15","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9291862","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9291862","identity":"rs-9291862","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}