Stress-Strength Reliability Inference in Multicomponent Systems Under the Unit-Gamma Gompertz–Weibull Distribution Based on Progressive Type-II Censoring

Stress-Strength Reliability Inference in Multicomponent Systems Under the Unit-Gamma Gompertz–Weibull Distribution Based on Progressive Type-II Censoring | 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 Article Stress-Strength Reliability Inference in Multicomponent Systems Under the Unit-Gamma Gompertz–Weibull Distribution Based on Progressive Type-II Censoring Zohreh Pakdaman, Reza Alizadeh Noughabi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8851105/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 12 You are reading this latest preprint version Abstract Reliable assessment of multicomponent systems operating under uncertain stress is fundamentalto modern engineering, environmental management, and risk analysis. In many practicallife-testing experiments, observations are subject to progressive Type-II censoring, andsystem capacities are naturally bounded, rendering classical stress–strength models inadequatefor capturing complex reliability behaviour. Despite extensive developments in parametric reliabilitymodeling, flexible frameworks capable of jointly accommodating multicomponent systemstructures, bounded distributions, and progressive censoring remain limited. This studydevelops a comprehensive inferential framework for multicomponent stress–strength reliabilityunder progressive Type-II censoring based on the Unit-Gamma Gompertz–Weibull distribution.The proposed model provides substantial flexibility in modeling diverse density andhazard-rate shapes while preserving analytical tractability for reliability formulation. We deriveexplicit expressions for key reliability measures and construct a unified estimation strategythat integrates maximum likelihood estimation, approximate likelihood methods, a Monte Carloexpectation–maximization algorithm, and Bayesian inference via Lindley’s approximation andMetropolis–Hastings sampling. Extensive Monte Carlo simulations demonstrate stable finitesampleperformance across varying censoring intensities and system configurations. Applicationto hydrological capacity data from the Shasta reservoir highlights improved goodness-of-fit andmore robust reliability estimation compared with competing bounded distributions. Sensitivityand influence analyses further confirm the stability of the proposed framework. Overall, themethodology offers a flexible and practically implementable tool for stress–strength reliabilityanalysis in multicomponent systems with censored and bounded observations. AMS 2000 Subject Classification: Primary 62N05; Secondary 62F10. Earth and environmental sciences/Hydrology Physical sciences/Mathematics and computing Unit-Gamma Gompertz–Weibull distribution Progressive Type-II cen- soring Stress–Strength Reliability Maximum likelihood Estimation Monte Carlo Expectation Maximization Algorithm Bayesian Inference Sensitivity Analysis Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 07 Apr, 2026 Reviews received at journal 23 Mar, 2026 Reviews received at journal 20 Mar, 2026 Reviewers agreed at journal 25 Feb, 2026 Reviewers agreed at journal 21 Feb, 2026 Reviewers agreed at journal 20 Feb, 2026 Reviewers agreed at journal 20 Feb, 2026 Reviewers invited by journal 19 Feb, 2026 Editor assigned by journal 19 Feb, 2026 Editor invited by journal 18 Feb, 2026 Submission checks completed at journal 13 Feb, 2026 First submitted to journal 13 Feb, 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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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8851105","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":594944334,"identity":"80f18586-8123-4b29-adf5-ec264864645a","order_by":0,"name":"Zohreh Pakdaman","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABCElEQVRIiWNgGAWjYHACZgYeEMXegyrMQ1gLzxmStUjkEOkq+dnNjw3e1GyTN5d8e/BxZY6Nvbz72QMMP2oYZMwbsGthnHPMOHHOsduGO2fnJRue3ZbGbHgmL4Gx5xgDj8wBHK6SSDA+zMN2m3HD7RwzycZth9kMG3IMGHgbGHgkcDiMTSL982Gef7ftN9w8A9bCY9j/xoDxLx4tPBI5xsm8bbcTN9zgAWuRkJfIMWDGZ4uEzJliw7l9t5M3nMkxNmzclmZgIPHG4LDMMQmcWuRnt2+WePPttu2G42cMHzZuA4ZYf47hwzc1Nva4tDBgSBgcYGA4gEUcjxb5BtyKR8EoGAWjYGQCAIifVbvP7aHGAAAAAElFTkSuQmCC","orcid":"","institution":"Hormozgan University","correspondingAuthor":true,"prefix":"","firstName":"Zohreh","middleName":"","lastName":"Pakdaman","suffix":""},{"id":594944335,"identity":"d0305bcc-1a04-417a-9de5-1c2133e5a8c3","order_by":1,"name":"Reza Alizadeh Noughabi","email":"","orcid":"","institution":"Hormozgan University","correspondingAuthor":false,"prefix":"","firstName":"Reza","middleName":"Alizadeh","lastName":"Noughabi","suffix":""}],"badges":[],"createdAt":"2026-02-11 11:26:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8851105/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8851105/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":103506986,"identity":"9b8a4854-9224-463b-a30b-0834e38353c5","added_by":"auto","created_at":"2026-02-26 13:40:08","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5141128,"visible":true,"origin":"","legend":"","description":"","filename":"StressStrengthReliabilityInferenceinMulticomponent.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8851105/v1_covered_720d04ac-ead0-4b09-91ad-886f96af9c2f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Stress-Strength Reliability Inference in Multicomponent Systems Under the Unit-Gamma Gompertz–Weibull Distribution Based on Progressive Type-II Censoring","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Unit-Gamma Gompertz–Weibull distribution, Progressive Type-II cen- soring, Stress–Strength Reliability, Maximum likelihood Estimation, Monte Carlo Expectation Maximization Algorithm, Bayesian Inference, Sensitivity Analysis","lastPublishedDoi":"10.21203/rs.3.rs-8851105/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8851105/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eReliable assessment of multicomponent systems operating under uncertain stress is fundamentalto modern engineering, environmental management, and risk analysis. In many practicallife-testing experiments, observations are subject to progressive Type-II censoring, andsystem capacities are naturally bounded, rendering classical stress–strength models inadequatefor capturing complex reliability behaviour. Despite extensive developments in parametric reliabilitymodeling, flexible frameworks capable of jointly accommodating multicomponent systemstructures, bounded distributions, and progressive censoring remain limited. This studydevelops a comprehensive inferential framework for multicomponent stress–strength reliabilityunder progressive Type-II censoring based on the Unit-Gamma Gompertz–Weibull distribution.The proposed model provides substantial flexibility in modeling diverse density andhazard-rate shapes while preserving analytical tractability for reliability formulation. 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