Failure Behavior and Reliability analysis of Diesel Particulate Filters based on After-sales Maintenance Data

Failure Behavior and Reliability analysis of Diesel Particulate Filters based on After-sales Maintenance Data | 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 Failure Behavior and Reliability analysis of Diesel Particulate Filters based on After-sales Maintenance Data Shirin Ahmadbeigi, Mohammad Ali Ehteram, Abbas Naeimi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3826365/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 26 Jul, 2024 Read the published version in Emission Control Science and Technology → Version 1 posted 7 You are reading this latest preprint version Abstract Diesel particulate filters (DPFs) are essential tools for controlling pollution emissions. However, some DPFs may encounter failures during operation, thereby posing risks to both the diesel vehicle engine and emission control. Low-quality diesel fuel, due to its higher sulfur content, raises the risk of DPF becoming inactive. This paper examines the reliability of DPFs from a leading national vehicle manufacturer, utilizing after-sales maintenance data. Statistical analysis has been conducted on 10,833 vehicles over the years 2018 to 2022. In addition, the records of failures, the root causes of malfunctions, and the factors influencing the failures of these filters have also been investigated. The results indicate that the highest percentage of failures is associated with urban buses, and the least reliable are mini-buses. In such a way that, it can be stated that the DPFs of all mini-buses malfunction at least once after 17,000 kilometers, which is significantly lower than the defined threshold of 100,000 kilometers. The main causes of damage to the DPF substrate are leaks in the fuel and lubrication systems. Additionally, laboratory analysis of a silicon carbide DPF sample, using scanning electron microscopy (SEM) and X-ray diffraction (XRD), revealed corrosion within the DPF substrate. The chemical compounds obtained from laboratory studies indicate a high percentage of sulfur (2.28% by weight) in diesel fuel and oil leakage into the DPF. Chemical compounds obtained from laboratory studies indicate a high percentage of sulfur (2.28% by weight) in diesel fuel and oil leakage to the DPF. This study accurately demonstrates the alignment of results obtained from simulation, reliability assessment, failure root cause analysis, and laboratory analysis. Diesel particulate filter (DPF) Silicon carbide Reliability analysis After-sales maintenance (service) data failure root cause Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 1-Introduction The diesel engine stands out as the most efficient internal combustion engine globally, prized for its low fuel consumption, minimal maintenance needs, and durability compared to petrol engines. However, concerns loom over the emissions of primary pollutants such as carbon monoxide (CO), unburned hydrocarbons (HCs), particulate matters (PMs), nitrogen oxides (NOx), and sulfur dioxide (SO2) from diesel engines [ 1 , 2 ]. Particles, specifically soot with a diameter less than 1 µm, emitted from diesel exhaust, pose health risks and contribute to environmental degradation [ 3 , 4 ]. Recognizing these hazards, the International Agency for Research on Cancer (IARC) classifies diesel engine exhaust gases as a Group 1 carcinogen [ 5 ]. To mitigate diesel particulate matter (PM), two approaches are prominent: PM filters and NOx abatement [ 1 ]. Wall flow DPFs, are effective in removing PM, achieving over 90% efficiency [ 6 , 7 ]. Nevertheless, the accumulation of soot in DPFs necessitates periodic regeneration to maintain efficiency [ 8 ]. However, regeneration produces ash that, over time, affects filter performance [ 9 , 10 ]. Ash, stemming from various sources including lubricating oil additives and engine erosion, is compounded by low-quality diesel with high sulfur content [ 3 ]. This poses challenges to DPF deactivation, increasing pollutant emissions [ 13 , 14 , and 15 ]. Understanding the interaction between ash and DPF substrate materials is crucial, as existing hypotheses propose the corrosion of substrates due to alkaline compounds [ 12 , 14 , 15 , and 16 ]. Therefore, studying the reliability of DPFs plays a crucial role in identifying weaknesses in these filters, followed by investigating the root causes of filter failures. This has a fundamental impact on the automotive industry to minimize engine malfunctions resulting from filter failures and on the environment to control pollutant emissions. Reliability is a pivotal factor in product quality, garnering increased attention from companies. DPF reliability directly impacts engine service life, operational costs, and market competitiveness. Investigating the causes of DPF failure and understanding weak points are foundational for design development and effective repair and maintenance management [ 17 ]. Researchers like Merkel et al. [ 18 ] noted that significant iron oxide presence intensifies the ash reaction with cordierite filter materials. Yang et al. [ 9 ] investigated cordierite DPF failures in 2016, linking substrate issues to chemical compounds in PM particles and physical changes in cordierite substrate. Millo et al. [ 13 ] explored high sulfur fuel effects on Diesel Oxidation Catalyst (DOC) and DPF toxicity, with a successful after Desulfation procedure. Ehteram et al. [ 19 ] examined sulfur content impact on emissions, finding a 99.9% filtering efficiency, and a decrease in particle removal with higher sulfur diesel. In 2018, they studied substrate/cake soot mass ratio and soot porosity effects on DPF emissions and back pressure during loading and regeneration. DPF failures can elevate particulate absorption, directly affecting engine performance [ 9 ]. While extensive studies have been conducted on vehicle reliability and its components [ 20 – 34 ], limited attention has been given to DPF reliability. This paper aims to fill this gap by analyzing the reliability of DPF systems in diesel vehicles through after-sales service data and conducting laboratory analysis on a sample filter to understand failure mechanisms and ash compositions. The research involves statistical analysis using after-sales service data from a major vehicle-manufacturing company covering a four-year period from 2018 to 2021, involving 10,833 examined vehicles. The reliability of DPFs is assessed using the Weibull analytical model. Additionally, laboratory analysis of a DPF sample is conducted to investigate failure and determine the composition of ash sediment. By correlating failure records with laboratory findings, this study seeks to enhance our understanding of DPF reliability and contribute valuable insights to the automotive industry and environmental protection. 2. Materials and methods 2.1. Reliability of DPF In this section, we describe the statistical methods of investigating DPF failure. 2.1.1. Failure data Failure data are the most effective tools for reliability analysis. In this research study, thousands of after-sales service data for diesel vehicles was collected from the certified representatives of an after-sales service company throughout the country in four years (from March 2018 to March 2022) (Fig. 1 ). Among all the company's products, only Euro-4 and above are equipped with DPF. For data analysis, all the company's products were categorized into four groups during this period, based on mileage, the type of vehicle usage, and the type of used filter. These groups include trucks, minibuses, pickup trucks, and buses. During the categorization of failure data, the following principles have been considered: The entire range of warranty-covered vehicles is not equipped with DPFs. Therefore, among all products, only those vehicles equipped with DPFs are included in the statistical population. For analysis purposes, it is necessary to categorize vehicles into two groups: faulty and functional. The functional group pertains to vehicles whose DPF is not damaged; so, for recording the mileage of this group, the last mileage number (that the vehicles have referred to After sales service company for the initial service, the secondary service, the periodic services, recall executions, or a non-filter-related failure) has been considered as the functional (without-failure) mileage. For the 'faulty mileage' as well, the first mileage at which a vehicle has visited the representative due to DPF malfunction has been considered as the faulty mileage. 2.1.2. Failure analysis process and modelling of reliability To analyze the downtime, it is needed to classify the data and prepare them for modeling. The total products of the company are characterized according to common characteristics such as the type of car used, operational kilometers, the work environment, etc. They are divided into four general categories of buses, trucks, minibuses and pickup trucks. Modeling of the corrupted data is then done. The details of the modeling steps are explained below: The list of all products from March 2018 to March 2022; Separation of failure data; Determination of failure (faulty) mileage and (functional) without-failure mileage; A vehicle can refer to the after-sales services company several times during the examined period for receiving various services; therefore, the repetitive vehicles have to be excluded, and the failure or without-failure data of each vehicle should be recorded just for one time. For this purpose, the visit time and the failure type were examined; and regarding the DPF failure, the first visiting time due to filter failure is registered as the failure mileage for that particular vehicle. For the vehicles experiencing DPF failure, it is necessary to examine the failure record, the initial visit, and subsequent visits until the DPF failure to determine the mechanism of the filter failure. In this way, by examining the visits record, it is possible to identify failures in other components of the vehicle that may lead to the filter failure. The results are presented in Table 1 . Table 1 The production and failure statistics of the company in the examined period Total products Percentage Products equipped with DPF percentage DPF failures Percentage Total number of vehicles produced 100 Total number of vehicles equipped with DPF 82.1 Total number of DPF failures 12 Total number of city buses 6.8 Total number of buses equipped with DPF 96.7 Total number of buses DPF failures 30.3 Total number of minibuses 4.3 Total number of minibuses equipped with DPF 64.4 Total number of minibuses DPF failures 29.4 Total number of photon pickup truck 8.5 Total number of photon pickup truck equipped with DPF 100 Total number of pickup trucks DPF failures 7.5 Total number of trucks 63.5 Total number of trucks equipped with DPF 92.1 Total number of trucks DPF failures 10.4 Total number of Camionettes 5.5 Total number of Camionettes equipped with DPF 95.5 Total number of Camionettes DPF failures 4.6 d) Data analysis For data analysis, Weibull + + 6 (a statistical software) was used. This software provides the ability to select an appropriate life distribution for modeling the data. This software is capable of selecting a suitable lifetime distribution for data modelling. There are 9 distributions and 3 specific analytical methods available for selection. Each distribution can be utilized for the analysis of a dataset. However, if the distribution does not agree with the failure rate behavior expected by the data, the prediction precision is decreased. Here, the preferred distribution for fitting the data is the Weibull distribution. Failure analysis and investigation of suitable models, considering the Weibull equations, can provide valuable and useful data about the failure root causes. For example, a beta coefficient larger than 1 signifies failure due to depreciation (erosion), while a beta coefficient smaller than 1 indicates premature failure due to improper assembly, design and use of equipment. Furthermore, the type of employed Weibull model (single-equation or double-equation) can indicate whether the failure-causing factor has a single root or is situated in two parallel roots [ 20 ]. 2.1.3. Weibull distribution The Weibull distribution is widely used in reliability analysis. This distribution covers a wide variety of shapes. Owing to its flexibility in describing hazard rates, the Weibull distribution can represent all three regions of the bathtub curve. It can be demonstrated that the Weibull distribution is suitable for describing a system or composite components composed of several elements or other sections. The failure of this complex system or components occurs through the most severe flaw or damage to its elements or sections (weakest-link model). Weibull distribution can be utilized for the data with fixed, decreasing, and increasing failure rates. Similar to the normal logarithm distribution, Weibull is also a two-parameter distribution whose estimation is not a straightforward task even in cases where we have a complete set of data (uncensored) [39]. The probability density distribution function for the Weibull distribution is in the form of Eq. 1 : $$\text{f}\left(\text{t}\right)=\frac{{{\beta }\left(\text{t}\right)}^{{\beta }-1}}{{{\alpha }}^{{\beta }}}\text{exp}\left[-{\left(\frac{\text{t}}{{\alpha }}\right)}^{{\beta }}\right]. {\alpha }.{\beta }>0 . \text{t}>0$$ 1 The \({\alpha }\) and \({\beta }\) parameters in the Weibull distribution are called size and shape parameters, respectively. If, in Eq. 2, \(0<{\beta }<1\) , the Weibull distribution will be in the form of a distribution with a decreasing failure rate in which ca be used for describing the premature failure area in the bathtub curve. For \({\beta }=1\) , the Weibull distribution is an exponential distribution. If \({\beta }>1\) , the Weibull distribution can be used for modelling the erosion area of the bathtub curve because the failure rate follows a decreasing trend [ 35 ]. The reliability model of the Weibull distribution of DPF is as Eq. 3 , for each group of the company’s guaranteed vehicles: $$R\left(\text{t}\right)=\text{e}\text{x}\text{p}\left[-{\left(\frac{\text{t}}{{\alpha }}\right)}^{{\beta }}\right]$$ 2 In Weibull + + 6 software, for the Weibull distribution, several models are defined based on the number of parameters; the mixed Weibull model agrees with our failure data. 1.1.1 Mixed Weibull The Mixed Weibull analysis is used for analyzing the data sets that reflect different trends of failure behavior. This method is useful in case of failure cases that cannot be considered independent (it means that the occurrence of a failure case affects the probability of another case occurrence) or when recognizing the failure case responsible for any unique point is impossible [ 36 ]. The hypotheses of this distribution are: The reference population comprises two groups of items (weak and strong) with the unknown mix ratio of \(\rho\) . Each sub-population is determined by a unique failure case (for instance, premature or erosion failures). The cases belonging to one sub-population may fail exclusively due to that failure case. The items are exposed to various operational conditions in the reference population, which can be determined by the engine and vehicle types described by a known vector of auxiliary variables \(x=({x}_{1},{x}_{2})\) . Even after the failure occurrence, it is unknown whether the item sub-population belongs there because the manufacturers and the after-sales maintenance agents do not have to do a failure analysis to recognize the real failure case. The lifetime function of the items in every sub-population is a two-parameter Weibull regression model. This model shows that auxiliary variables exclusively act upon the scale parameter and leave the shape parameter unchanged, see reference [ 37 ]. According to the above hypotheses, the lifetime function is stated as Eq. 3 : $$R(t\left|x)=\sum _{i=1}^{2}{\rho }_{i}\text{exp}\left[{-\left(\frac{t}{{\alpha }_{i}\left(x\right)}\right)}^{{\beta }_{i}}\right]\right.$$ 3 Where, \({\rho }_{2}=1-{\rho }_{1}\) and the scale parameters of \({\alpha }_{i}\left(x\right)\) (i=1,2) are functions of x which generally include unknown regression parameters. Equation 3 could be rewritten as Eq. 4 [ 29 ]: $$R(t\left|x)=\sum _{i=1}^{2}{\rho }_{i}\text{exp}[-{\left(\frac{t}{{\alpha }_{i0} exp\left(x{\delta }_{i}\right)}\right)}^{{\beta }_{i}}]\right.$$ 4 The variables in Eq. 4 are as follows: mixed parameter: \({\rho }={{\rho }}_{1}\) ; shape parameters: \({{\beta }}_{\text{i}}(\text{i}=\text{1,2});\) scale parameters: \({{\alpha }}_{\text{i}0}(\text{i}=\text{1,2})\) ; regression coefficients \({{\delta }}_{\text{i}\text{j}}\left(\text{i}=\text{1,2} ;\text{j}=\text{1,2}\right).\) 1.2 Analysis of a DPF sample In this section, a DPF sample has been tested in a laboratory. In addition to the statistical analysis of the failure behavior of soot filters, to investigate the microscopic root causes of these failures, a damaged sample of a DPF, as shown in Fig. 2 a, was sectioned for analysis using SEM and subjected to XRF and XRD tests. The DPF used in this research belongs to a minibus with a mileage of 10,400 kilometers. It was referenced due to the illumination of the yellow DPF monitor light. The yellow light turning on in this type means a pressure increase inside the filter up to 200kPa. Based on the fabric and thickness of the shell, the DPF shell was cut to take the substrate out of the shell without damaging it. The cutting process was done alongside the filter from two sides. The results are shown in Fig. 2 b, 2 c and 2 d. According to Fig. 2 c and 2 d; the dark-colored soot has accumulated (as sediment) at the inlet of the DPF. 2.2.1. Cutting and failure the filter substrate for analysis A section of 5 cm width along the length of the filter at the inlet was cut, and then the cut section was subjected to laboratory analysis. The results are illustrated in Fig. 3 . Figure 3 a shows a view of the DPF substrate and the specified area for cutting. Figure 3 b and 3 c, also shows cut sections at the inlet side of filter, which are divided into smaller pieces for various examinations. 2.2.2. SEM testing A SEM, VEGA3 model manufactured by TESCAN in Czech, was used to investigate any failure such as corrosion, crack, hole, and fracture. For this purpose, a 950 \(℃\) furnace was utilized. The sample was put inside the 600 \(℃\) furnace for 8 hours. After 8 hours and the combustion of soot, a sample was removed from the furnace, and using a Silver blower model GTP03A10, all the ash inside the pores was removed. Following washing with deionized water and allowing 24 hours for drying, the sample was prepared for examination using an electron microscope. 2.2.3. XRF and XRD analysis of the sample Another piece of the DPF sample was cut for XRF and XRD tests. The XRF test was conducted using the ARL 8410 model XRF device. In this test, the sample was ground up to 100 grams, and then, for research purposes, a tablet was prepared and analyzed using the XRF device. The XRF test was conducted in accordance with the ASTM E1621-21 reference standard, with environmental conditions set at a temperature of 22°C and a humidity of 39%. The test was done in the range of the standard certificate domain of ISO/IEC17025 in a semi-quantitative manner. Also, carbon was measured by the sulfur-analyzer carbon device in accordance with the ASTM E 1915 standard. The XRD (X-ray Diffraction) method is used to determine the chemical composition, and the XRD device used is the XPERT PRO MPD model manufactured by PANalytical. In this test, a fraction of a few tenths of a gram of the substance is separated, and the separated sample is finely ground into a fine powder. As a result, the extra pressure (the surface energy) is minimized, and displacement of the peak is prevented. Powders with sizes smaller than 10 micrometers are suitable. Now, the prepared sample is uniformly placed on the sample holder, and then radiation is directed towards it. The test reference standard is BS EN 13925-1 2008. The environmental conditions included 22 \(℃\) temperature and 39% wetness. The conducted test was within the scope of the ISO/IEC 17025 standard certification. 3. Results 3.1. Modeling the reliability of DPF This section offers the results and diagrams attained by modelling the vehicle's reliability. For analyzing the DPF reliability, a suitable distribution with failure data is required. Figure 4 shows the results of reliability modeling for each group of cars using the Weibull + + 6 software. Based on calculations performed by software, the result showed that each group's failure data agreed with one Weibull distribution model. The best Weibull distribution for data analysis in buses is the mixed Weibull with two sub-populations, while minibuses' failure data agree with the two-parameter Weibull distribution. The best Weibull distribution is the Mix Weibull failure data with two sub-populations for trucks and pickup trucks. The failure data are collected by registering the times when the vehicles were taken to company representatives throughout the country in various periods. The obtained reliability diagrams, fitting the failure data of each group of vehicles, are shown in Fig. 4. Table 2 illustrates the Weibull parameters obtained for each group of vehicles. According to the curve in Fig. 4 and the results in Table 2 , it could be asserted that the weakest reliability among the different groups classified is related to the minibuses. In minibuses, reliability reaches zero after about a 17000-kilometre mileage; it means that, after a 17000-kilometre mileage, the DPF of all minibuses fail at once least. In buses and pickup trucks, respectively, reliability reaches zero after a 48000-kilometre and a 72000-kilometre mileage. Among the groups classified, trucks have higher reliability; their DPF reliability reaches zero after a 72000-kilometre mileage. However, in typical situations and based on universal standards, the filters should remain functional after a 100000-kilometre mileage. The critical condition of the minibuses DPFs used in urban areas shows the significance of failure more vividly. In Fig. 4, the straight lines are the predictions of the Weibull model. Table 2 The data related to DPF reliability modeling in the classified vehicle. Vehicle type Mileage at 80% reliability Mileage at 50% reliability Mileage at zero reliability Beta values Eta values Values of each population in mix Weibull Bus 8000 12000 48000 3.9357 1.0507E + 4 0.4359 2.4511 2.2966E + 4 0.5641 Truck 11000 26000 160000 1.1577 3.5760E + 4 0.9012 11.5196 2.5740E + 4 0.0988 Minibus 6300 8000 17000 3.0815 9813.4269 - Pickup Truck 10000 20000 72000 9.0496 2.2721 0.2113 1.5687 2.3444E + 4 0.7887 To investigate the root causes of failure, the reasons for the visits of vehicles with smoke filter issues, along with the history of other malfunctions of those vehicles, have been carefully examined. Figure 5 illustrates the results of studying the root causes of DPF failure in each group of vehicles by studying their failure records. In minibuses, pickups, and trucks, the most common cause of DPF failure is related to engine malfunctions, accounting for 90%, 77%, and 61% of diesel particle filter failures in minibuses, pickups, and trucks, respectively. Examining the engine defects shows that problems (such as burning of cylinder-head gasket, oil filter failure, valve gasket failure, injector pump, fuel pipes, radial-shaft seal failure of fuel input pipe) can lead to fuel leakage, oil leakage, and substrate poisoning which in turn might lead to immature DPF failure. As described in the results of laboratory experiments analyzing the DPF sample, oil leakage and its entry into the DPF lead to the DPF failure. This is because the oil poisons all precious metals inside the soot filter, and on the other hand, fuel leakage causes excessive heating of the filter and the creation of peak temperatures in the substrate and causes the sedimentation of sulfur in the filter. After the engine faults, the exhaust system failure is the second root cause of DPF failure, which can generally cause physical failures such as pipe fractures. Figure 6 shows the resulting populations for each group of vehicles described in Table 2 . A comparison of two Fig. 5 and Fig. 6 shows 'Two Parameters Weibull Model can properly predict two failure root causes and show the contribution of each. The results obtained from failure root causes shown in Fig. 5 are near to those obtained from two parameters Weibull modeling curve, which shows the population of each failure (Fig. 6 ). It seems that in minibuses, the main problem causing DPF failures is related to engine system failures and defects, and the failure of the exhaust system did not lead to the primary failure and only happened next to the main failure due to improper assembly. In fact, by examining the failure records, it can be said that the failure of the DPF caused by the exhaust system is divided into two parts, one part is a physical failure mainly caused by fractures, constituting the majority share, and second part, with a smaller share, is the exhaust system failure resulting from the malfunction of the DPF due to the use of low-quality fuel. 3.2. Results of DPF laboratory analysis Table 3 shows the DPF functional specifications. Table 3 the DPF functional specifications. Vehicle type Mileage Failure details Euro-4 minibus + DPF 10400 Km The monitor yellow light turning on Figure 7 shows some cut sections of the internal surface of the DPF sample. As observed, soot is trapped in the pores and channels of the DPF. Table 4 shows the results of the chemical analysis of the sample obtained by XRF method based on the weight percentage of the elements and the components. Table 4 Analysis results of the sent sample. Oxide Weight percentage \({\text{A}\text{l}}_{2}{\text{O}}_{3}\) 3.98 \({\text{F}\text{e}}_{2}{\text{O}}_{3}\) 1.99 C 91.07 \(\text{S}{\text{O}}_{3}\) 2.28 \(\text{C}\text{a}\text{O}\) 0.20 \({\text{K}}_{2}\text{O}\) 0.48 The DPF ash compounds vary in various vehicles. However, the ash produced by light and heavy vehicles generally contains phosphorus, sulfur, magnesium, Zinc, and calcium oxides from industrial oil and fewer metal oxides from engine erosion [ 9 ]. The overall ash composition found in the DPF substrate is consistent with the ash deposition results reported by other researchers. Considering the distribution, the chemical composition of Al 2 O 3 constitutes the majority of the ash, accounting for a weight percentage of 3.98%. Then, SO 3 , with 2.28%, has the highest weight percentage among the compounds. Other compounds, including Fe 2 O 3 , CaO, and K 2 O, are found in the range of 1.99 to 0.48 weight percent. It is worth noting that the suitable amount of sulfur in fuel for a better filter performance is about 50PPM. It is evident that the existence of 3% of the sulfur oxides in the ash causes severe corrosion. The origin of sulfur can be from the vehicle's fuel or from engine oil (in the case of oil leakage). Detecting Fe 2 O 3 at relatively high concentrations in the shredded substrate of the DPF confirms the results of previous laboratory studies, which indicate the role of iron in enhancing reactions with the DPF substrate [ 9 ]. Figure 8 shows the cut section of the DPF at the inlet, which, as can be seen, has created a rainbow shape on the substrate. According previous research studies, SiO 2 makes the carbide silicon rainbow-shaped. An electron microscope was used to investigate any sign of destruction on the internal surface of the filter substrate. The results are illustrated in Fig. 9 . The images taken by the electron microscope (Fig. 9 ) show a hole in the surface of the filter substrate caused by corrosion and breakage. It is worth noting that the filter has only worked for 10400 kilometers, and the destruction has occurred at such age and without the regeneration process. 4. Conclusions In this research, DPF reliability in a leading vehicle-manufacturing company was evaluated using after-sales maintenance data. The analysis revealed rapid filter erosion across all models, attributed to a beta coefficient greater than 1 in Weibull functions, indicating erosion as the primary failure mechanism. Concurrent engine and exhaust failures were observed, with minibuses exhibiting higher engine failure severity. Investigation into city minibus-related DPF failures identified them as the least reliable products, possibly due to their demanding operational conditions. Soot filter reliability in minibuses dropped to 80% after 6300 kilometers and below 50% after 8000 kilometers, reaching zero in less than 17000 kilometers. Despite manufacturer recommendations for DPF replacement after 2 years or 200,000 kilometers, failures, especially in minibuses, occurred prematurely. The fuel-supplying system played a pivotal role, constituting 100% of failures in minibuses due to filter substrate clogging. Laboratory analysis confirmed engine faults as the primary cause. After-sales service practices often involve furnace regeneration, but laboratory findings emphasized the need to address early clogging issues. The filter substrate failed due to ash-related reactions at high temperatures, reducing efficiency. Adjusting fuel sulfur content and managing engine oil consumption significantly improved filter lifespan, by up to 90%. Reliability simulation, employing 'two-parameters Weibull' function, accurately identified failure root causes and their impact percentages. Comprehensive data gathering is crucial for a thorough analysis of factors influencing reliability. The study emphasizes the need to reevaluate regeneration practices and underscores the significance of fuel and oil management for optimal DPF performance. Declarations Funding (information that explains whether and by whom the research was supported) Not applicable. Conflicts of interest/Competing interests (include appropriate disclosures) The authors certify that they have NO affiliations with or involvement in any organization or entity with any financial interest, or non-financial interest in the subject matter or materials discussed in this manuscript. Ethics approval/declarations (include appropriate approvals or waivers) This study was approved by the Ethics committee of Shahid Beheshti University. Consent to participate: Not applicable. Consent for publication: Not applicable. Availability of data and material/ Data availability: Not applicable. Code availability (software application or custom code): Not applicable. Authors' contributions: Shirin Ahmadbeigi wrote the main manuscript. Mohammad Ali Ehteram assisted doing the statistical analysis. Abbas Naeimi supervised writing and editing the manuscript. 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Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 231(7), 941-951. Attardi, L., Guida, M., & Pulcini, G. (2005). A Mixed-Weibull regression model for the analysis of automotive warranty data. Reliability Engineering & System Safety, 87(2), 265-273. ‏ M. Fonte, P. Duarte, L. Reis, M. Freitas, V. Infante, Failure mode analysis of two crankshafts of a single cylinder diesel engine. Eng. Fail. Anal. 56, 185–193 (2015). Z.W. Yu, X.L. Xu, H.X. Yu, Fatigue failure of electronic unit pumps used in truck diesel engine. J. Fail. Anal. Prev. 16, 902– 911 (2016). Deulgaonkar, V. R., Pawar, K., Kudle, P., Raverkar, A., & Raut, A. (2019). Failure analysis of fuel pumps used for diesel engines in transport utility vehicles. Engineering Failure Analysis, 105, 1262-1272. Muhit, I. B., Masia, M. J., & Stewart, M. G. (2023). Failure Analysis and Structural Reliability of Unreinforced Masonry Veneer Walls: Influence of Wall Tie Corrosion. Engineering Failure Analysis, 107354. Wang, Z., Zhao, L., Kong, Z., Yu, J., & Yan, C. (2022). Development of accelerated reliability test cycle for electric drive system based on vehicle operating data. Engineering Failure Analysis, 141, 106696. Li, J., Zhang, B., Lyu, D., Guo, J., Su, K., & Hu, B. (2022). Fatigue reliability analysis of tunnelling boring machine cutterhead with cracks. Engineering Failure Analysis, 141, 106669. Li, X. Y., Tao, Z., Wu, J. P., & Zhang, W. (2021). Uncertainty theory based reliability modeling for fatigue. Engineering Failure Analysis, 119, 104931. Madavan, R., & Balaraman, S. (2016). Failure analysis of transformer liquid—solid insulation system under selective environmental conditions using Weibull statistics method. Engineering Failure Analysis, 65, 26-38. Ravikumar, A., & Rietz, A. (2021). Leakage and assembly of gasket in truck exhaust aftertreatment systems. Engineering Failure Analysis, 126, 105463. Xu, X. L., & Yu, Z. W. (2015). Fracture failure of oil-pipes of truck diesel engine boost compensator. Journal of Failure Analysis and Prevention, 15, 651-656. ‏ Deulgaonkar, V. R., Pawar, K., Kudle, P., Raverkar, A., & Raut, A. (2019). Failure analysis of fuel pumps used for diesel engines in transport utility vehicles. Engineering Failure Analysis, 105, 1262-1272. ‏ Deulgaonkar, V., Joshi, K., Jawale, P., Bhutada, S., & Fernandes, S. (2021). Failure analysis of timing device piston and supply pump vanes in fuel injection system for transport utility vehicles. Journal of Failure Analysis and Prevention, 21(1), 172-178. ‏ Caldera, M., Massone, J. M., & Martinez, R. A. (2017). Failure analysis of a damaged direct injection diesel engine piston. Journal of Failure Analysis and Prevention, 17, 979-988. Wang, Z., & Wang, Z. Q. (2014). Method for calculating the B10 reliable life of mechanical components of vehicle engine based on the stress-strength interference. Journal of Mechanical Engineering, 50(16), 47. ‏ Modarre, s Mohammad; Kaminskiy, Mark P; Krivtsov, Vasiliy (2016. Reliability Engineering and Risk Analysis a Practical Guide, Third Edition. User’s Guide, Weibull++. Reliasoft Lawless, J. F. (1982). Statistical models and methods for lifetime data Wiley. New York. ‏ Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 26 Jul, 2024 Read the published version in Emission Control Science and Technology → Version 1 posted Editorial decision: Revision requested 12 Feb, 2024 Reviews received at journal 26 Jan, 2024 Reviewers agreed at journal 17 Jan, 2024 Reviewers invited by journal 16 Jan, 2024 Editor assigned by journal 09 Jan, 2024 Submission checks completed at journal 08 Jan, 2024 First submitted to journal 31 Dec, 2023 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. We do this by developing innovative software and high quality services for the global research community. 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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-3826365","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":266194693,"identity":"3e1b363f-96ef-42aa-aba8-a9edd4aa7417","order_by":0,"name":"Shirin Ahmadbeigi","email":"","orcid":"","institution":"Shahid Beheshti University","correspondingAuthor":false,"prefix":"","firstName":"Shirin","middleName":"","lastName":"Ahmadbeigi","suffix":""},{"id":266194694,"identity":"6501a2c5-bea6-478b-9a71-d95a230664fa","order_by":1,"name":"Mohammad Ali Ehteram","email":"","orcid":"","institution":"Shahid Beheshti University","correspondingAuthor":false,"prefix":"","firstName":"Mohammad","middleName":"Ali","lastName":"Ehteram","suffix":""},{"id":266194695,"identity":"59cfaec0-1959-4094-8fd7-72a131881b18","order_by":2,"name":"Abbas Naeimi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxklEQVRIiWNgGAWjYNACAwYefgYeCJuNaC2SDaRpAek6wEOkSv4G3oMfPhRskzE+f/aYBEONHQOf9AH8WiQO8CVLzjC4zWN2Iy9NguFYMgMbXwIBaw7wGEjzgLXwmEkwsB1gYCPkQPkDPMa//wC1GPefAWr5R4QWoK/NpBmAWgwYcswkGNuI0GII1GLZA9QicSMv2SKxL5mHoBY5oMNu/Phz256//+zBGx++2cnJ9xDQwiD/AImTwMBAbOyMglEwCkbBKMAHACs7NYjFs9ZfAAAAAElFTkSuQmCC","orcid":"","institution":"Shahid Beheshti University","correspondingAuthor":true,"prefix":"","firstName":"Abbas","middleName":"","lastName":"Naeimi","suffix":""}],"badges":[],"createdAt":"2023-12-31 18:14:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3826365/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3826365/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s40825-024-00246-3","type":"published","date":"2024-07-26T16:15:41+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":49435956,"identity":"c0e95edd-f996-4af3-b26a-565ed9af5a34","added_by":"auto","created_at":"2024-01-10 20:05:24","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":20105,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCompany's products in percentage during four years based on the product type\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-3826365/v1/05732ab91b31908aa3bb787b.png"},{"id":49435960,"identity":"5ff989a4-b4fe-4c45-b9db-f15e82fcb156","added_by":"auto","created_at":"2024-01-10 20:05:25","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":1083884,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a)The examined DPF, (b) The cut shell of the examined DPF, (c) inlet of DPF, (D) outlet of DPF\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-3826365/v1/b801d57331fc62184801c4ef.png"},{"id":49435961,"identity":"03f2f12b-d81c-49c5-8bdf-6645e8002c82","added_by":"auto","created_at":"2024-01-10 20:05:25","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":414467,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003e(a)The specified direction for cutting the filter substrate, (b) and (d) A sample of the cut sections at the inlet side of filter\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-3826365/v1/8fc11b187ea4951e1ea62a9b.png"},{"id":49436842,"identity":"9a9cb01c-997f-4909-99ce-11d38e50aecc","added_by":"auto","created_at":"2024-01-10 20:13:25","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":58715,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eThe reliability curve obtained for each group of vehicles\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-3826365/v1/3fce9af0ae304b9cc0447149.png"},{"id":49435957,"identity":"5e9a98f4-6a9e-4a99-8a3f-7e5608969fcc","added_by":"auto","created_at":"2024-01-10 20:05:25","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":24112,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComparison of the failure type in DPFs of each group of vehicles in percentage.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-3826365/v1/0ccce6c340acb6e662302b38.png"},{"id":49435959,"identity":"dad2573a-19e5-4209-a6d3-09137c58af9e","added_by":"auto","created_at":"2024-01-10 20:05:25","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":20369,"visible":true,"origin":"","legend":"\u003cp\u003ePopulations in mixed Weibull owned for each group of vehicles.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-3826365/v1/ec93ce3fd85c0a0b1403ae3f.png"},{"id":49436843,"identity":"6b7f12c3-4f77-49ad-a5dc-a7017b45d711","added_by":"auto","created_at":"2024-01-10 20:13:25","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":528677,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eImages related to the internal surface of the cut filter and the accumulated soot\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-3826365/v1/6a9bb7639527c10f1af874ca.png"},{"id":49435964,"identity":"cd6f4871-51ff-4d32-8dee-59a4b2066854","added_by":"auto","created_at":"2024-01-10 20:05:25","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":265723,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eAn image of the internal surface of the cut filter at the inlet\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-3826365/v1/fb32d3e75bdfd04ca7d0c00a.png"},{"id":49435963,"identity":"9d2c2ced-430b-498f-9d71-7c157d55f270","added_by":"auto","created_at":"2024-01-10 20:05:25","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":370248,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSEM images of cut surface of the sample 20 KV at various magnifications\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-3826365/v1/7f2dfa21d0a02cafcbe3e369.png"},{"id":61596226,"identity":"0db8ff93-fabd-4764-9919-324b44229d0f","added_by":"auto","created_at":"2024-08-01 17:25:50","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3412982,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3826365/v1/4ffffd92-116d-4059-a4ad-c1c7ae9fea03.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Failure Behavior and Reliability analysis of Diesel Particulate Filters based on After-sales Maintenance Data","fulltext":[{"header":"1-Introduction","content":"\u003cp\u003eThe diesel engine stands out as the most efficient internal combustion engine globally, prized for its low fuel consumption, minimal maintenance needs, and durability compared to petrol engines. However, concerns loom over the emissions of primary pollutants such as carbon monoxide (CO), unburned hydrocarbons (HCs), particulate matters (PMs), nitrogen oxides (NOx), and sulfur dioxide (SO2) from diesel engines [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Particles, specifically soot with a diameter less than 1 \u0026micro;m, emitted from diesel exhaust, pose health risks and contribute to environmental degradation [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Recognizing these hazards, the International Agency for Research on Cancer (IARC) classifies diesel engine exhaust gases as a Group 1 carcinogen [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. To mitigate diesel particulate matter (PM), two approaches are prominent: PM filters and NOx abatement [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. Wall flow DPFs, are effective in removing PM, achieving over 90% efficiency [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Nevertheless, the accumulation of soot in DPFs necessitates periodic regeneration to maintain efficiency [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. However, regeneration produces ash that, over time, affects filter performance [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Ash, stemming from various sources including lubricating oil additives and engine erosion, is compounded by low-quality diesel with high sulfur content [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. This poses challenges to DPF deactivation, increasing pollutant emissions [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, and \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eUnderstanding the interaction between ash and DPF substrate materials is crucial, as existing hypotheses propose the corrosion of substrates due to alkaline compounds [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, and \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Therefore, studying the reliability of DPFs plays a crucial role in identifying weaknesses in these filters, followed by investigating the root causes of filter failures. This has a fundamental impact on the automotive industry to minimize engine malfunctions resulting from filter failures and on the environment to control pollutant emissions.\u003c/p\u003e \u003cp\u003eReliability is a pivotal factor in product quality, garnering increased attention from companies. DPF reliability directly impacts engine service life, operational costs, and market competitiveness. Investigating the causes of DPF failure and understanding weak points are foundational for design development and effective repair and maintenance management [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eResearchers like Merkel et al. [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] noted that significant iron oxide presence intensifies the ash reaction with cordierite filter materials. Yang et al. [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] investigated cordierite DPF failures in 2016, linking substrate issues to chemical compounds in PM particles and physical changes in cordierite substrate. Millo et al. [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] explored high sulfur fuel effects on Diesel Oxidation Catalyst (DOC) and DPF toxicity, with a successful after Desulfation procedure. Ehteram et al. [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] examined sulfur content impact on emissions, finding a 99.9% filtering efficiency, and a decrease in particle removal with higher sulfur diesel. In 2018, they studied substrate/cake soot mass ratio and soot porosity effects on DPF emissions and back pressure during loading and regeneration. DPF failures can elevate particulate absorption, directly affecting engine performance [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eWhile extensive studies have been conducted on vehicle reliability and its components [\u003cspan additionalcitationids=\"CR21 CR22 CR23 CR24 CR25 CR26 CR27 CR28 CR29 CR30 CR31 CR32 CR33\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e], limited attention has been given to DPF reliability. This paper aims to fill this gap by analyzing the reliability of DPF systems in diesel vehicles through after-sales service data and conducting laboratory analysis on a sample filter to understand failure mechanisms and ash compositions.\u003c/p\u003e \u003cp\u003eThe research involves statistical analysis using after-sales service data from a major vehicle-manufacturing company covering a four-year period from 2018 to 2021, involving 10,833 examined vehicles. The reliability of DPFs is assessed using the Weibull analytical model. Additionally, laboratory analysis of a DPF sample is conducted to investigate failure and determine the composition of ash sediment. By correlating failure records with laboratory findings, this study seeks to enhance our understanding of DPF reliability and contribute valuable insights to the automotive industry and environmental protection.\u003c/p\u003e"},{"header":"2. Materials and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\n \u003ch2\u003e2.1. Reliability of DPF\u003c/h2\u003e\n \u003cp\u003eIn this section, we describe the statistical methods of investigating DPF failure.\u003c/p\u003e\n \u003cdiv id=\"Sec4\" class=\"Section3\"\u003e\n \u003ch2\u003e2.1.1. Failure data\u003c/h2\u003e\n \u003cp\u003eFailure data are the most effective tools for reliability analysis. In this research study, thousands of after-sales service data for diesel vehicles was collected from the certified representatives of an after-sales service company throughout the country in four years (from March 2018 to March 2022) (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e). Among all the company\u0026apos;s products, only Euro-4 and above are equipped with DPF.\u003c/p\u003e\n \u003cp\u003eFor data analysis, all the company\u0026apos;s products were categorized into four groups during this period, based on mileage, the type of vehicle usage, and the type of used filter. These groups include trucks, minibuses, pickup trucks, and buses. During the categorization of failure data, the following principles have been considered:\u003c/p\u003e\n \u003cul\u003e\n \u003cli\u003e\n \u003cp\u003eThe entire range of warranty-covered vehicles is not equipped with DPFs. Therefore, among all products, only those vehicles equipped with DPFs are included in the statistical population.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eFor analysis purposes, it is necessary to categorize vehicles into two groups: faulty and functional.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eThe functional group pertains to vehicles whose DPF is not damaged; so, for recording the mileage of this group, the last mileage number (that the vehicles have referred to After sales service company for the initial service, the secondary service, the periodic services, recall executions, or a non-filter-related failure) has been considered as the functional (without-failure) mileage.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eFor the \u0026apos;faulty mileage\u0026apos; as well, the first mileage at which a vehicle has visited the representative due to DPF malfunction has been considered as the faulty mileage.\u003c/p\u003e\n \u003c/li\u003e\n \u003c/ul\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e\n \u003ch2\u003e2.1.2. Failure analysis process and modelling of reliability\u003c/h2\u003e\n \u003cp\u003eTo analyze the downtime, it is needed to classify the data and prepare them for modeling. The total products of the company are characterized according to common characteristics such as the type of car used, operational kilometers, the work environment, etc. They are divided into four general categories of buses, trucks, minibuses and pickup trucks. Modeling of the corrupted data is then done. The details of the modeling steps are explained below:\u003c/p\u003e\n \u003col start=\"1\" style=\"list-style-type: lower-alpha;\"\u003e\n \u003cli\u003eThe list of all products from March 2018 to March 2022;\u003c/li\u003e\n \u003cli\u003eSeparation of failure data;\u003c/li\u003e\n \u003cli\u003eDetermination of failure (faulty) mileage and (functional) without-failure mileage;\u003c/li\u003e\n \u003c/ol\u003e\n \u003cp\u003eA vehicle can refer to the after-sales services company several times during the examined period for receiving various services; therefore, the repetitive vehicles have to be excluded, and the failure or without-failure data of each vehicle should be recorded just for one time.\u003c/p\u003e\n \u003cp\u003eFor this purpose, the visit time and the failure type were examined; and regarding the DPF failure, the first visiting time due to filter failure is registered as the failure mileage for that particular vehicle. For the vehicles experiencing DPF failure, it is necessary to examine the failure record, the initial visit, and subsequent visits until the DPF failure to determine the mechanism of the filter failure. In this way, by examining the visits record, it is possible to identify failures in other components of the vehicle that may lead to the filter failure. The results are presented in Table \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\n \u003cp\u003e\u003c/p\u003e\u0026nbsp;\u003ctable id=\"Tab1\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eThe production and failure statistics of the company in the examined period\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eTotal products\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePercentage\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eProducts equipped with DPF\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003epercentage\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eDPF failures\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003ePercentage\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\"\u003e\n \u003cp\u003eTotal number of vehicles produced\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal number of vehicles equipped with DPF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e82.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal number of DPF failures\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal number of city buses\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e6.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal number of buses equipped with DPF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e96.7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal number of buses DPF failures\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e30.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal number of minibuses\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal number of minibuses equipped with DPF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e64.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal number of minibuses DPF failures\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e29.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal number of photon pickup truck\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal number of photon pickup truck equipped with DPF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal number of pickup trucks DPF failures\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e7.5\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal number of trucks\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e63.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal number of trucks equipped with DPF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e92.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal number of trucks DPF failures\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e10.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal number of Camionettes\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e5.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal number of Camionettes equipped with DPF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e95.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eTotal number of Camionettes DPF failures\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e4.6\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\u003ed) Data analysis\u003c/p\u003e\n \u003cp\u003eFor data analysis, Weibull\u0026thinsp;+\u0026thinsp;+\u0026thinsp;6 (a statistical software) was used. This software provides the ability to select an appropriate life distribution for modeling the data. This software is capable of selecting a suitable lifetime distribution for data modelling. There are 9 distributions and 3 specific analytical methods available for selection. Each distribution can be utilized for the analysis of a dataset. However, if the distribution does not agree with the failure rate behavior expected by the data, the prediction precision is decreased. Here, the preferred distribution for fitting the data is the Weibull distribution. Failure analysis and investigation of suitable models, considering the Weibull equations, can provide valuable and useful data about the failure root causes.\u003c/p\u003e\n \u003cp\u003eFor example, a beta coefficient larger than 1 signifies failure due to depreciation (erosion), while a beta coefficient smaller than 1 indicates premature failure due to improper assembly, design and use of equipment. Furthermore, the type of employed Weibull model (single-equation or double-equation) can indicate whether the failure-causing factor has a single root or is situated in two parallel roots [\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e\n \u003ch2\u003e2.1.3. Weibull distribution\u003c/h2\u003e\n \u003cp\u003eThe Weibull distribution is widely used in reliability analysis. This distribution covers a wide variety of shapes. Owing to its flexibility in describing hazard rates, the Weibull distribution can represent all three regions of the bathtub curve. It can be demonstrated that the Weibull distribution is suitable for describing a system or composite components composed of several elements or other sections. The failure of this complex system or components occurs through the most severe flaw or damage to its elements or sections (weakest-link model). Weibull distribution can be utilized for the data with fixed, decreasing, and increasing failure rates. Similar to the normal logarithm distribution, Weibull is also a two-parameter distribution whose estimation is not a straightforward task even in cases where we have a complete set of data (uncensored) [39]. The probability density distribution function for the Weibull distribution is in the form of Eq. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e:\u003c/p\u003e\n \u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e$$\\text{f}\\left(\\text{t}\\right)=\\frac{{{\\beta }\\left(\\text{t}\\right)}^{{\\beta }-1}}{{{\\alpha }}^{{\\beta }}}\\text{exp}\\left[-{\\left(\\frac{\\text{t}}{{\\alpha }}\\right)}^{{\\beta }}\\right]. {\\alpha }.{\\beta }\u0026gt;0 . \\text{t}\u0026gt;0$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eThe \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\alpha }\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\beta }\\)\u003c/span\u003e\u003c/span\u003e parameters in the Weibull distribution are called size and shape parameters, respectively. If, in Eq. 2, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(0\u0026lt;{\\beta }\u0026lt;1\\)\u003c/span\u003e\u003c/span\u003e, the Weibull distribution will be in the form of a distribution with a decreasing failure rate in which ca be used for describing the premature failure area in the bathtub curve. For \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\beta }=1\\)\u003c/span\u003e\u003c/span\u003e, the Weibull distribution is an exponential distribution. If \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\beta }\u0026gt;1\\)\u003c/span\u003e\u003c/span\u003e, the Weibull distribution can be used for modelling the erosion area of the bathtub curve because the failure rate follows a decreasing trend [\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eThe reliability model of the Weibull distribution of DPF is as Eq. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e, for each group of the company\u0026rsquo;s guaranteed vehicles:\u003c/p\u003e\n \u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e$$R\\left(\\text{t}\\right)=\\text{e}\\text{x}\\text{p}\\left[-{\\left(\\frac{\\text{t}}{{\\alpha }}\\right)}^{{\\beta }}\\right]$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eIn Weibull\u0026thinsp;+\u0026thinsp;+\u0026thinsp;6 software, for the Weibull distribution, several models are defined based on the number of parameters; the mixed Weibull model agrees with our failure data.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e\n \u003ch2\u003e1.1.1 Mixed Weibull\u003c/h2\u003e\n \u003cp\u003eThe Mixed Weibull analysis is used for analyzing the data sets that reflect different trends of failure behavior. This method is useful in case of failure cases that cannot be considered independent (it means that the occurrence of a failure case affects the probability of another case occurrence) or when recognizing the failure case responsible for any unique point is impossible [\u003cspan class=\"CitationRef\"\u003e36\u003c/span\u003e].\u003c/p\u003e\n \u003cp\u003eThe hypotheses of this distribution are:\u003c/p\u003e\n \u003cul\u003e\n \u003cli\u003e\n \u003cp\u003eThe reference population comprises two groups of items (weak and strong) with the unknown mix ratio of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\rho\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eEach sub-population is determined by a unique failure case (for instance, premature or erosion failures). The cases belonging to one sub-population may fail exclusively due to that failure case.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eThe items are exposed to various operational conditions in the reference population, which can be determined by the engine and vehicle types described by a known vector of auxiliary variables \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(x=({x}_{1},{x}_{2})\\)\u003c/span\u003e\u003c/span\u003e .\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eEven after the failure occurrence, it is unknown whether the item sub-population belongs there because the manufacturers and the after-sales maintenance agents do not have to do a failure analysis to recognize the real failure case.\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eThe lifetime function of the items in every sub-population is a two-parameter Weibull regression model. This model shows that auxiliary variables exclusively act upon the scale parameter and leave the shape parameter unchanged, see reference [\u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e].\u003c/p\u003e\n \u003c/li\u003e\n \u003c/ul\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003cp\u003eAccording to the above hypotheses, the lifetime function is stated as Eq. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e:\u003c/p\u003e\n \u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e$$R(t\\left|x)=\\sum _{i=1}^{2}{\\rho }_{i}\\text{exp}\\left[{-\\left(\\frac{t}{{\\alpha }_{i}\\left(x\\right)}\\right)}^{{\\beta }_{i}}\\right]\\right.$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eWhere, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }_{2}=1-{\\rho }_{1}\\)\u003c/span\u003e\u003c/span\u003e and the scale parameters of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\alpha }_{i}\\left(x\\right)\\)\u003c/span\u003e\u003c/span\u003e (i=1,2) are functions of x which generally include unknown regression parameters.\u003c/p\u003e\n \u003cp\u003eEquation \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e could be rewritten as Eq. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e [\u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e]:\u003c/p\u003e\n \u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e$$R(t\\left|x)=\\sum _{i=1}^{2}{\\rho }_{i}\\text{exp}[-{\\left(\\frac{t}{{\\alpha }_{i0} exp\\left(x{\\delta }_{i}\\right)}\\right)}^{{\\beta }_{i}}]\\right.$$\u003c/div\u003e\n \u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\n \u003c/div\u003e\n \u003cp\u003eThe variables in Eq. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e are as follows:\u003c/p\u003e\n \u003cul\u003e\n \u003cli\u003e\n \u003cp\u003emixed parameter: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\rho }={{\\rho }}_{1}\\)\u003c/span\u003e\u003c/span\u003e;\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eshape parameters:\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\beta }}_{\\text{i}}(\\text{i}=\\text{1,2});\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003escale parameters:\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\alpha }}_{\\text{i}0}(\\text{i}=\\text{1,2})\\)\u003c/span\u003e\u003c/span\u003e;\u003c/p\u003e\n \u003c/li\u003e\n \u003cli\u003e\n \u003cp\u003eregression coefficients\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({{\\delta }}_{\\text{i}\\text{j}}\\left(\\text{i}=\\text{1,2} ;\\text{j}=\\text{1,2}\\right).\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/li\u003e\n \u003c/ul\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n \u003ch2\u003e1.2 Analysis of a DPF sample\u003c/h2\u003e\n \u003cp\u003eIn this section, a DPF sample has been tested in a laboratory.\u003c/p\u003e\n \u003cp\u003eIn addition to the statistical analysis of the failure behavior of soot filters, to investigate the microscopic root causes of these failures, a damaged sample of a DPF, as shown in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea, was sectioned for analysis using SEM and subjected to XRF and XRD tests.\u003c/p\u003e\n \u003cp\u003eThe DPF used in this research belongs to a minibus with a mileage of 10,400 kilometers. It was referenced due to the illumination of the yellow DPF monitor light. The yellow light turning on in this type means a pressure increase inside the filter up to 200kPa. Based on the fabric and thickness of the shell, the DPF shell was cut to take the substrate out of the shell without damaging it. The cutting process was done alongside the filter from two sides. The results are shown in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eb, \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ec and \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ed. According to Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ec and \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ed; the dark-colored soot has accumulated (as sediment) at the inlet of the DPF.\u003c/p\u003e\n \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e\n \u003ch2\u003e2.2.1. Cutting and failure the filter substrate for analysis\u003c/h2\u003e\n \u003cp\u003eA section of 5 cm width along the length of the filter at the inlet was cut, and then the cut section was subjected to laboratory analysis. The results are illustrated in Fig. \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003e. Figure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ea shows a view of the DPF substrate and the specified area for cutting. Figure \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb and \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ec, also shows cut sections at the inlet side of filter, which are divided into smaller pieces for various examinations.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e\n \u003ch2\u003e2.2.2. SEM testing\u003c/h2\u003e\n \u003cp\u003eA SEM, VEGA3 model manufactured by TESCAN in Czech, was used to investigate any failure such as corrosion, crack, hole, and fracture. For this purpose, a 950\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(℃\\)\u003c/span\u003e\u003c/span\u003e furnace was utilized. The sample was put inside the 600\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(℃\\)\u003c/span\u003e\u003c/span\u003e furnace for 8 hours. After 8 hours and the combustion of soot, a sample was removed from the furnace, and using a Silver blower model GTP03A10, all the ash inside the pores was removed. Following washing with deionized water and allowing 24 hours for drying, the sample was prepared for examination using an electron microscope.\u003c/p\u003e\n \u003c/div\u003e\n \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e\n \u003ch2\u003e2.2.3. XRF and XRD analysis of the sample\u003c/h2\u003e\n \u003cp\u003eAnother piece of the DPF sample was cut for XRF and XRD tests. The XRF test was conducted using the ARL 8410 model XRF device. In this test, the sample was ground up to 100 grams, and then, for research purposes, a tablet was prepared and analyzed using the XRF device. The XRF test was conducted in accordance with the ASTM E1621-21 reference standard, with environmental conditions set at a temperature of 22\u0026deg;C and a humidity of 39%. The test was done in the range of the standard certificate domain of ISO/IEC17025 in a semi-quantitative manner. Also, carbon was measured by the sulfur-analyzer carbon device in accordance with the ASTM E 1915 standard. The XRD (X-ray Diffraction) method is used to determine the chemical composition, and the XRD device used is the XPERT PRO MPD model manufactured by PANalytical. In this test, a fraction of a few tenths of a gram of the substance is separated, and the separated sample is finely ground into a fine powder. As a result, the extra pressure (the surface energy) is minimized, and displacement of the peak is prevented. Powders with sizes smaller than 10 micrometers are suitable. Now, the prepared sample is uniformly placed on the sample holder, and then radiation is directed towards it. The test reference standard is BS EN 13925-1 2008. The environmental conditions included 22\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(℃\\)\u003c/span\u003e\u003c/span\u003e temperature and 39% wetness. The conducted test was within the scope of the ISO/IEC 17025 standard certification.\u003c/p\u003e\n \u003c/div\u003e\n\u003c/div\u003e"},{"header":"3. Results","content":"\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Modeling the reliability of DPF\u003c/h2\u003e \u003cp\u003eThis section offers the results and diagrams attained by modelling the vehicle's reliability. For analyzing the DPF reliability, a suitable distribution with failure data is required. Figure\u0026nbsp;4 shows the results of reliability modeling for each group of cars using the Weibull\u0026thinsp;+\u0026thinsp;+\u0026thinsp;6 software. Based on calculations performed by software, the result showed that each group's failure data agreed with one Weibull distribution model. The best Weibull distribution for data analysis in buses is the mixed Weibull with two sub-populations, while minibuses' failure data agree with the two-parameter Weibull distribution. The best Weibull distribution is the Mix Weibull failure data with two sub-populations for trucks and pickup trucks. The failure data are collected by registering the times when the vehicles were taken to company representatives throughout the country in various periods. The obtained reliability diagrams, fitting the failure data of each group of vehicles, are shown in Fig.\u0026nbsp;4. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e illustrates the Weibull parameters obtained for each group of vehicles.\u003c/p\u003e \u003cp\u003eAccording to the curve in Fig.\u0026nbsp;4 and the results in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, it could be asserted that the weakest reliability among the different groups classified is related to the minibuses. In minibuses, reliability reaches zero after about a 17000-kilometre mileage; it means that, after a 17000-kilometre mileage, the DPF of all minibuses fail at once least. In buses and pickup trucks, respectively, reliability reaches zero after a 48000-kilometre and a 72000-kilometre mileage. Among the groups classified, trucks have higher reliability; their DPF reliability reaches zero after a 72000-kilometre mileage. However, in typical situations and based on universal standards, the filters should remain functional after a 100000-kilometre mileage. The critical condition of the minibuses DPFs used in urban areas shows the significance of failure more vividly. In Fig.\u0026nbsp;4, the straight lines are the predictions of the Weibull model.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe data related to DPF reliability modeling in the classified vehicle.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVehicle type\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMileage at 80% reliability\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMileage at 50% reliability\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMileage at zero reliability\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBeta values\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eEta values\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eValues of each population in mix Weibull\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eBus\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e8000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e12000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e48000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.9357\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1.0507E\u0026thinsp;+\u0026thinsp;4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.4359\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.4511\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.2966E\u0026thinsp;+\u0026thinsp;4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.5641\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTruck\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e11000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e26000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e160000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.1577\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e3.5760E\u0026thinsp;+\u0026thinsp;4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.9012\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e11.5196\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.5740E\u0026thinsp;+\u0026thinsp;4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.0988\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMinibus\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e8000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e17000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.0815\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e9813.4269\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003ePickup Truck\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e10000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e20000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e72000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e9.0496\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.2721\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.2113\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.5687\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.3444E\u0026thinsp;+\u0026thinsp;4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.7887\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\u003eTo investigate the root causes of failure, the reasons for the visits of vehicles with smoke filter issues, along with the history of other malfunctions of those vehicles, have been carefully examined. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates the results of studying the root causes of DPF failure in each group of vehicles by studying their failure records. In minibuses, pickups, and trucks, the most common cause of DPF failure is related to engine malfunctions, accounting for 90%, 77%, and 61% of diesel particle filter failures in minibuses, pickups, and trucks, respectively. Examining the engine defects shows that problems (such as burning of cylinder-head gasket, oil filter failure, valve gasket failure, injector pump, fuel pipes, radial-shaft seal failure of fuel input pipe) can lead to fuel leakage, oil leakage, and substrate poisoning which in turn might lead to immature DPF failure.\u003c/p\u003e \u003cp\u003eAs described in the results of laboratory experiments analyzing the DPF sample, oil leakage and its entry into the DPF lead to the DPF failure. This is because the oil poisons all precious metals inside the soot filter, and on the other hand, fuel leakage causes excessive heating of the filter and the creation of peak temperatures in the substrate and causes the sedimentation of sulfur in the filter. After the engine faults, the exhaust system failure is the second root cause of DPF failure, which can generally cause physical failures such as pipe fractures. Figure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the resulting populations for each group of vehicles described in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA comparison of two Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows 'Two Parameters Weibull Model can properly predict two failure root causes and show the contribution of each. The results obtained from failure root causes shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e are near to those obtained from two parameters Weibull modeling curve, which shows the population of each failure (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e). It seems that in minibuses, the main problem causing DPF failures is related to engine system failures and defects, and the failure of the exhaust system did not lead to the primary failure and only happened next to the main failure due to improper assembly. In fact, by examining the failure records, it can be said that the failure of the DPF caused by the exhaust system is divided into two parts, one part is a physical failure mainly caused by fractures, constituting the majority share, and second part, with a smaller share, is the exhaust system failure resulting from the malfunction of the DPF due to the use of low-quality fuel.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Results of DPF laboratory analysis\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the DPF functional specifications.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ethe DPF functional specifications.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\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 \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eVehicle type\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMileage\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFailure details\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEuro-4 minibus\u0026thinsp;+\u0026thinsp;DPF\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10400 Km\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eThe monitor yellow light turning on\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\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows some cut sections of the internal surface of the DPF sample. As observed, soot is trapped in the pores and channels of the DPF. Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the results of the chemical analysis of the sample obtained by XRF method based on the weight percentage of the elements and the components.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAnalysis results of the sent sample.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOxide\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWeight percentage\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{A}\\text{l}}_{2}{\\text{O}}_{3}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{F}\\text{e}}_{2}{\\text{O}}_{3}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.99\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e91.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{S}{\\text{O}}_{3}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.28\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{C}\\text{a}\\text{O}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.20\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{K}}_{2}\\text{O}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.48\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\u003eThe DPF ash compounds vary in various vehicles. However, the ash produced by light and heavy vehicles generally contains phosphorus, sulfur, magnesium, Zinc, and calcium oxides from industrial oil and fewer metal oxides from engine erosion [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe overall ash composition found in the DPF substrate is consistent with the ash deposition results reported by other researchers. Considering the distribution, the chemical composition of Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e constitutes the majority of the ash, accounting for a weight percentage of 3.98%. Then, SO\u003csub\u003e3\u003c/sub\u003e, with 2.28%, has the highest weight percentage among the compounds. Other compounds, including Fe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e, CaO, and K\u003csub\u003e2\u003c/sub\u003eO, are found in the range of 1.99 to 0.48 weight percent. It is worth noting that the suitable amount of sulfur in fuel for a better filter performance is about 50PPM. It is evident that the existence of 3% of the sulfur oxides in the ash causes severe corrosion. The origin of sulfur can be from the vehicle's fuel or from engine oil (in the case of oil leakage). Detecting Fe\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e at relatively high concentrations in the shredded substrate of the DPF confirms the results of previous laboratory studies, which indicate the role of iron in enhancing reactions with the DPF substrate [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e shows the cut section of the DPF at the inlet, which, as can be seen, has created a rainbow shape on the substrate. According previous research studies, SiO\u003csub\u003e2\u003c/sub\u003e makes the carbide silicon rainbow-shaped.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAn electron microscope was used to investigate any sign of destruction on the internal surface of the filter substrate. The results are illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e. The images taken by the electron microscope (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e) show a hole in the surface of the filter substrate caused by corrosion and breakage. It is worth noting that the filter has only worked for 10400 kilometers, and the destruction has occurred at such age and without the regeneration process.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003eIn this research, DPF reliability in a leading vehicle-manufacturing company was evaluated using after-sales maintenance data. The analysis revealed rapid filter erosion across all models, attributed to a beta coefficient greater than 1 in Weibull functions, indicating erosion as the primary failure mechanism. Concurrent engine and exhaust failures were observed, with minibuses exhibiting higher engine failure severity. Investigation into city minibus-related DPF failures identified them as the least reliable products, possibly due to their demanding operational conditions. Soot filter reliability in minibuses dropped to 80% after 6300 kilometers and below 50% after 8000 kilometers, reaching zero in less than 17000 kilometers. Despite manufacturer recommendations for DPF replacement after 2 years or 200,000 kilometers, failures, especially in minibuses, occurred prematurely. The fuel-supplying system played a pivotal role, constituting 100% of failures in minibuses due to filter substrate clogging. Laboratory analysis confirmed engine faults as the primary cause. After-sales service practices often involve furnace regeneration, but laboratory findings emphasized the need to address early clogging issues. The filter substrate failed due to ash-related reactions at high temperatures, reducing efficiency. Adjusting fuel sulfur content and managing engine oil consumption significantly improved filter lifespan, by up to 90%. Reliability simulation, employing 'two-parameters Weibull' function, accurately identified failure root causes and their impact percentages. Comprehensive data gathering is crucial for a thorough analysis of factors influencing reliability. The study emphasizes the need to reevaluate regeneration practices and underscores the significance of fuel and oil management for optimal DPF performance.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cul\u003e\n \u003cli\u003eFunding (information that explains whether and by whom the research was supported) \u0026nbsp;\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eConflicts of interest/Competing interests (include appropriate disclosures) \u0026nbsp;\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThe authors certify that they have NO affiliations with or involvement in any organization or entity with any financial interest, or non-financial interest in the subject matter or materials discussed in this manuscript.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eEthics approval/declarations (include appropriate approvals or waivers) \u0026nbsp;\u0026nbsp;\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eThis study was approved by the Ethics committee of Shahid Beheshti University.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eConsent to participate:\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eConsent for publication:\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eAvailability of data and material/ Data availability:\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eCode availability (software application or custom code): \u0026nbsp;\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eAuthors\u0026apos; contributions:\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003eShirin Ahmadbeigi wrote the main manuscript. Mohammad Ali Ehteram assisted doing the statistical analysis. Abbas Naeimi supervised writing and editing the manuscript. All authors read and approved the final manuscript.\u0026quot;) \u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eAdler, J. (2005). Ceramic diesel particulate filters. International Journal of Applied Ceramic Technology, 2(6), 429-439.\u003cspan dir=\"RTL\"\u003e\u0026nbsp;\u0026rlm;\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003ePrasad, R., \u0026amp; Singh, S. V. (2020). Catalytic abatement of CO, HCs and soot emissions over spinel-based catalysts from diesel engines: an overview.\u0026nbsp;Journal of Environmental Chemical Engineering,\u0026nbsp;8(2), 103627.\u003cspan dir=\"RTL\"\u003e\u0026nbsp;\u0026rlm;\u003c/span\u003e\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eKong, H., \u0026amp; Yamamoto, K. (2019). 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Statistical models and methods for lifetime data Wiley.\u0026nbsp;New York.\u003cspan dir=\"RTL\"\u003e\u0026nbsp;\u0026rlm;\u003c/span\u003e\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"emission-control-science-and-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ecst","sideBox":"Learn more about [Emission Control Science and Technology](http://link.springer.com/journal/40825)","snPcode":"40825","submissionUrl":"https://submission.nature.com/new-submission/40825/3","title":"Emission Control Science and Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Diesel particulate filter (DPF), Silicon carbide, Reliability analysis, After-sales maintenance (service) data, failure root cause","lastPublishedDoi":"10.21203/rs.3.rs-3826365/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3826365/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDiesel particulate filters (DPFs) are essential tools for controlling pollution emissions. However, some DPFs may encounter failures during operation, thereby posing risks to both the diesel vehicle engine and emission control. Low-quality diesel fuel, due to its higher sulfur content, raises the risk of DPF becoming inactive. This paper examines the reliability of DPFs from a leading national vehicle manufacturer, utilizing after-sales maintenance data. Statistical analysis has been conducted on 10,833 vehicles over the years 2018 to 2022. In addition, the records of failures, the root causes of malfunctions, and the factors influencing the failures of these filters have also been investigated. The results indicate that the highest percentage of failures is associated with urban buses, and the least reliable are mini-buses. In such a way that, it can be stated that the DPFs of all mini-buses malfunction at least once after 17,000 kilometers, which is significantly lower than the defined threshold of 100,000 kilometers. The main causes of damage to the DPF substrate are leaks in the fuel and lubrication systems. Additionally, laboratory analysis of a silicon carbide DPF sample, using scanning electron microscopy (SEM) and X-ray diffraction (XRD), revealed corrosion within the DPF substrate. The chemical compounds obtained from laboratory studies indicate a high percentage of sulfur (2.28% by weight) in diesel fuel and oil leakage into the DPF. Chemical compounds obtained from laboratory studies indicate a high percentage of sulfur (2.28% by weight) in diesel fuel and oil leakage to the DPF. This study accurately demonstrates the alignment of results obtained from simulation, reliability assessment, failure root cause analysis, and laboratory analysis.\u003c/p\u003e","manuscriptTitle":"Failure Behavior and Reliability analysis of Diesel Particulate Filters based on After-sales Maintenance Data","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-01-10 20:05:20","doi":"10.21203/rs.3.rs-3826365/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-02-13T01:46:19+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-01-26T17:15:55+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"7bfe02e2-f67d-46ad-9037-f0ee189e0bc0","date":"2024-01-17T16:25:47+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-01-17T02:07:08+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-01-10T00:42:17+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-01-09T04:46:55+00:00","index":"","fulltext":""},{"type":"submitted","content":"Emission Control Science and Technology","date":"2023-12-31T18:03:54+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"emission-control-science-and-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ecst","sideBox":"Learn more about [Emission Control Science and Technology](http://link.springer.com/journal/40825)","snPcode":"40825","submissionUrl":"https://submission.nature.com/new-submission/40825/3","title":"Emission Control Science and Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"92e6fcd3-3c7f-421f-8446-741661253b6d","owner":[],"postedDate":"January 10th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-08-01T17:06:40+00:00","versionOfRecord":{"articleIdentity":"rs-3826365","link":"https://doi.org/10.1007/s40825-024-00246-3","journal":{"identity":"emission-control-science-and-technology","isVorOnly":false,"title":"Emission Control Science and Technology"},"publishedOn":"2024-07-26 16:15:41","publishedOnDateReadable":"July 26th, 2024"},"versionCreatedAt":"2024-01-10 20:05:20","video":"","vorDoi":"10.1007/s40825-024-00246-3","vorDoiUrl":"https://doi.org/10.1007/s40825-024-00246-3","workflowStages":[]},"version":"v1","identity":"rs-3826365","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3826365","identity":"rs-3826365","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}