{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T21:14:10Z","timestamp":1783458850128,"version":"3.55.0"},"reference-count":46,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010754","name":"Zhejiang Gongshang University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100010754","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271480"],"award-info":[{"award-number":["12271480"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Reliability Engineering &amp; System Safety"],"published-print":{"date-parts":[[2027,1]]},"DOI":"10.1016\/j.ress.2026.113088","type":"journal-article","created":{"date-parts":[[2026,7,2]],"date-time":"2026-07-02T07:01:05Z","timestamp":1782975665000},"page":"113088","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"P2","title":["A new bivariate gamma degradation model and its reliability assessment, with application to the analysis of polymeric coating data"],"prefix":"10.1016","volume":"277","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-1363-1338","authenticated-orcid":false,"given":"Hao","family":"Qian","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bing Xing","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5842-8892","authenticated-orcid":false,"given":"Narayanaswamy","family":"Balakrishnan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"3","key":"10.1016\/j.ress.2026.113088_b1","doi-asserted-by":"crossref","first-page":"2295","DOI":"10.2298\/TSCI2403295S","article-title":"Bivariate and two-phase degradation modeling and reliability analysis with random effects","volume":"28","author":"Sun","year":"2024","journal-title":"Therm Sci"},{"issue":"1","key":"10.1016\/j.ress.2026.113088_b2","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1109\/TR.2022.3172416","article-title":"Reliability analysis based on a bivariate degradation model considering random initial state and its correlation with degradation rate","volume":"72","author":"Zheng","year":"2023","journal-title":"IEEE Trans Reliab"},{"issue":"4","key":"10.1016\/j.ress.2026.113088_b3","doi-asserted-by":"crossref","first-page":"971","DOI":"10.23919\/JSEE.2021.000083","article-title":"Reliability modeling of the bivariate deteriorating product with both monotonic and non-monotonic degradation paths","volume":"32","author":"Sun","year":"2021","journal-title":"J Syst Eng Electron"},{"issue":"6","key":"10.1016\/j.ress.2026.113088_b4","doi-asserted-by":"crossref","first-page":"784","DOI":"10.1007\/s12204-018-1984-z","article-title":"Bivariate constant-stress accelerated degradation model and inference based on the inverse Gaussian process","volume":"23","author":"Duan","year":"2018","journal-title":"J Shanghai Jiaotong Univ (Sci)"},{"issue":"2","key":"10.1016\/j.ress.2026.113088_b5","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1007\/s11771-018-3747-2","article-title":"Bayesian framework for satellite rechargeable lithium battery synthesizing bivariate degradation and lifetime data","volume":"25","author":"Zhang","year":"2018","journal-title":"J Central South Univ"},{"issue":"2","key":"10.1016\/j.ress.2026.113088_b6","doi-asserted-by":"crossref","first-page":"624","DOI":"10.1109\/TR.2015.2513038","article-title":"Bivariate analysis of incomplete degradation observations based on inverse Gaussian processes and copulas","volume":"65","author":"Peng","year":"2016","journal-title":"IEEE Trans Reliab"},{"issue":"3","key":"10.1016\/j.ress.2026.113088_b7","doi-asserted-by":"crossref","first-page":"897","DOI":"10.1109\/TR.2018.2791616","article-title":"On modeling bivariate Wiener degradation process","volume":"67","author":"Xu","year":"2018","journal-title":"IEEE Trans Reliab"},{"key":"10.1016\/j.ress.2026.113088_b8","series-title":"Service life prediction of polymeric materials: Global perspectives","first-page":"241","author":"Martin","year":"2009"},{"key":"10.1016\/j.ress.2026.113088_b9","doi-asserted-by":"crossref","DOI":"10.1016\/j.cie.2021.107450","article-title":"On multivariate copula modeling of dependent degradation processes","volume":"159","author":"Fang","year":"2021","journal-title":"Comput Ind Eng"},{"issue":"3","key":"10.1016\/j.ress.2026.113088_b10","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1080\/00401706.2020.1796814","article-title":"General path models for degradation data with multiple characteristics and covariates","volume":"63","author":"Lu","year":"2021","journal-title":"Technometrics"},{"issue":"3","key":"10.1016\/j.ress.2026.113088_b11","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1080\/00401706.2022.2157881","article-title":"A multivariate stochastic degradation model for dependent performance characteristics","volume":"65","author":"Zhai","year":"2023","journal-title":"Technometrics"},{"issue":"2","key":"10.1016\/j.ress.2026.113088_b12","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1080\/00401706.1993.10485038","article-title":"Using degradation measures to estimate a time-to-failure distribution","volume":"35","author":"Lu","year":"1993","journal-title":"Technometrics"},{"issue":"5","key":"10.1016\/j.ress.2026.113088_b13","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1016\/j.ress.2006.02.002","article-title":"Degradation models and implied lifetime distributions","volume":"92","author":"Bae","year":"2007","journal-title":"Reliab Eng Syst Saf"},{"issue":"2","key":"10.1016\/j.ress.2026.113088_b14","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1109\/TDMR.2012.2190415","article-title":"Lifetime estimation of high-power white LED using degradation-data-driven method","volume":"12","author":"Fan","year":"2012","journal-title":"IEEE Trans Device Mater Reliab"},{"issue":"3","key":"10.1016\/j.ress.2026.113088_b15","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1016\/j.ejor.2018.02.033","article-title":"Degradation data analysis and remaining useful life estimation: A review on Wiener-process-based methods","volume":"271","author":"Zhang","year":"2018","journal-title":"European J Oper Res"},{"key":"10.1016\/j.ress.2026.113088_b16","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1023\/B:LIDA.0000036389.14073.dd","article-title":"Covariates and random effects in a Gamma process model with application to degradation and failure","volume":"10","author":"Lawless","year":"2004","journal-title":"Lifetime Data Anal."},{"issue":"3","key":"10.1016\/j.ress.2026.113088_b17","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1080\/00401706.2013.830074","article-title":"The inverse Gaussian process as a degradation model","volume":"56","author":"Ye","year":"2014","journal-title":"Technometrics"},{"issue":"2","key":"10.1016\/j.ress.2026.113088_b18","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1080\/00401706.2019.1630008","article-title":"Student-t processes for degradation analysis","volume":"62","author":"Peng","year":"2020","journal-title":"Technometrics"},{"issue":"1","key":"10.1016\/j.ress.2026.113088_b19","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1109\/TR.2014.2299151","article-title":"Estimating remaining useful life with three-source variability in degradation modeling","volume":"63","author":"Si","year":"2014","journal-title":"IEEE Trans Reliab"},{"key":"10.1016\/j.ress.2026.113088_b20","unstructured":"Wang P, Coit D. Reliability prediction based on degradation modeling for systems with multiple degradation measures. In: Annual symposium reliability and maintainability, 2004 - RAMS. 2004, p. 302\u20137."},{"issue":"7","key":"10.1016\/j.ress.2026.113088_b21","doi-asserted-by":"crossref","first-page":"1316","DOI":"10.1080\/00949655.2012.658805","article-title":"Bivariate degradation analysis of products based on Wiener processes and copulas","volume":"83","author":"Pan","year":"2013","journal-title":"J Stat Comput Simul"},{"issue":"1","key":"10.1016\/j.ress.2026.113088_b22","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1080\/03610918.2017.1280162","article-title":"Inverse Gaussian process models for bivariate degradation analysis: A Bayesian perspective","volume":"47","author":"Duan","year":"2018","journal-title":"Comm Statist Simulation Comput"},{"key":"10.1016\/j.ress.2026.113088_b23","first-page":"8","article-title":"Reliability assessment for systems with two performance characteristics based on gamma processes with marginal heterogeneous random effects","volume":"19","author":"Luis","year":"2017","journal-title":"Eksploat I Niezawodn - Maint Reliab"},{"issue":"3","key":"10.1016\/j.ress.2026.113088_b24","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1080\/08982112.2020.1757704","article-title":"Multi-dimensional L\u00e9vy processes with L\u00e9vy copulas for multiple dependent degradation processes in lifetime analysis","volume":"32","author":"Shi","year":"2020","journal-title":"Qual Eng"},{"issue":"8","key":"10.1016\/j.ress.2026.113088_b25","doi-asserted-by":"crossref","first-page":"3203","DOI":"10.1002\/qre.3105","article-title":"Correlation-driven multivariate degradation modeling and RUL prediction based on Wiener process model","volume":"39","author":"Yan","year":"2023","journal-title":"Qual Reliab Eng Int"},{"issue":"2","key":"10.1016\/j.ress.2026.113088_b26","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1080\/00401706.2023.2242413","article-title":"A class of hierarchical multivariate Wiener processes for modeling dependent degradation data","volume":"66","author":"Fang","year":"2024","journal-title":"Technometrics"},{"key":"10.1016\/j.ress.2026.113088_b27","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2021.108200","article-title":"A common random effect induced bivariate gamma degradation process with application to remaining useful life prediction","volume":"219","author":"Song","year":"2022","journal-title":"Reliab Eng Syst Saf"},{"key":"10.1016\/j.ress.2026.113088_b28","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2023.109722","article-title":"Flexible modelling of a bivariate degradation process with a shared frailty and an application to fatigue crack data","volume":"242","author":"Barui","year":"2024","journal-title":"Reliab Eng Syst Saf"},{"issue":"1","key":"10.1016\/j.ress.2026.113088_b29","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1080\/00224065.2024.2402850","article-title":"Multivariate reparameterized inverse Gaussian processes with common effects for degradation-based reliability prediction","volume":"57","author":"Zhuang","year":"2025","journal-title":"J Qual Technol"},{"issue":"9","key":"10.1016\/j.ress.2026.113088_b30","doi-asserted-by":"crossref","first-page":"1924","DOI":"10.1080\/03610926.2012.677300","article-title":"A bivariate Gamma model for a latent degradation process","volume":"43","author":"Shemehsavar","year":"2014","journal-title":"Comm Statist Theory Methods"},{"issue":"9","key":"10.1016\/j.ress.2026.113088_b31","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1080\/24725854.2024.2389538","article-title":"A multivariate student-t process model for dependent tail-weighted degradation data","volume":"57","author":"Xu","year":"2025","journal-title":"IISE Trans"},{"key":"10.1016\/j.ress.2026.113088_b32","doi-asserted-by":"crossref","DOI":"10.1016\/j.ymssp.2020.106899","article-title":"A two-stage method based on extreme learning machine for predicting the remaining useful life of rolling-element bearings","volume":"144","author":"Pan","year":"2020","journal-title":"Mech Syst Signal Process"},{"key":"10.1016\/j.ress.2026.113088_b33","doi-asserted-by":"crossref","unstructured":"Fang G, Pan R, Hong Y. A copula-based multivariate degradation analysis for reliability prediction. In: 2018 annual reliability and maintainability symposium. RAMS, 2018, p. 1\u20137.","DOI":"10.1109\/RAM.2018.8463026"},{"issue":"3","key":"10.1016\/j.ress.2026.113088_b34","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1007\/s13253-018-0326-9","article-title":"Environmental risk assessment of emerging contaminants using degradation data","volume":"23","author":"Hong","year":"2018","journal-title":"J Agric Biol. Environ Stat"},{"key":"10.1016\/j.ress.2026.113088_b35","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1016\/j.apm.2019.07.045","article-title":"Statistical analysis for the doubly accelerated degradation Wiener model: An objective Bayesian approach","volume":"77","author":"He","year":"2020","journal-title":"Appl Math Model"},{"issue":"1","key":"10.1016\/j.ress.2026.113088_b36","doi-asserted-by":"crossref","first-page":"2107","DOI":"10.1109\/TR.2024.3381072","article-title":"Bayesian reliability assessment of permanent magnet brake under small sample size","volume":"74","author":"Xu","year":"2025","journal-title":"IEEE Trans Reliab"},{"key":"10.1016\/j.ress.2026.113088_b37","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/BF00048672","article-title":"A form of multivariate gamma distribution","volume":"44","author":"Mathai","year":"1992","journal-title":"Ann Inst Statist Math"},{"issue":"1","key":"10.1016\/j.ress.2026.113088_b38","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1080\/02331888.2023.2168004","article-title":"New closed form estimators for a bivariate gamma distribution","volume":"57","author":"Nawa","year":"2023","journal-title":"Statistics"},{"key":"10.1016\/j.ress.2026.113088_b39","series-title":"Statistical modeling for degradation data","first-page":"171","article-title":"Gamma degradation models: Inference and optimal design","author":"Balakrishnan","year":"2017"},{"issue":"7","key":"10.1016\/j.ress.2026.113088_b40","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1080\/02664760500079613","article-title":"On some reliability measures and their stochastic orderings for the Topp-Leone distribution","volume":"32","author":"Ghitany","year":"2005","journal-title":"J Appl Stat"},{"issue":"2","key":"10.1016\/j.ress.2026.113088_b41","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1080\/00401706.2017.1328377","article-title":"Inference on the Gamma distribution","volume":"60","author":"Wang","year":"2018","journal-title":"Technometrics"},{"key":"10.1016\/j.ress.2026.113088_b42","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.apm.2018.10.017","article-title":"Inference for constant-stress accelerated degradation test based on Gamma process","volume":"67","author":"Jiang","year":"2019","journal-title":"Appl Math Model"},{"issue":"3","key":"10.1016\/j.ress.2026.113088_b43","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1016\/j.ejor.2020.11.036","article-title":"Degradation data analysis based on gamma process with random effects","volume":"292","author":"Wang","year":"2021","journal-title":"European J Oper Res"},{"key":"10.1016\/j.ress.2026.113088_b44","series-title":"Generalized inference in repeated measures: Exact methods in MANOVA and mixed models","author":"Weerahandi","year":"2004"},{"key":"10.1016\/j.ress.2026.113088_b45","first-page":"1","article-title":"Asymptotic ANOVA and simultaneous confidence intervals for beta distributions via generalized fiducial approach","author":"Yan","year":"2025","journal-title":"Comm Statist Simulation Comput"},{"issue":"1\u20132","key":"10.1016\/j.ress.2026.113088_b46","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1093\/biomet\/47.1-2.173","article-title":"On normalizing the incomplete beta-function for fitting to dose-response curves","volume":"47","author":"Wise","year":"1960","journal-title":"Biometrika"}],"container-title":["Reliability Engineering &amp; System Safety"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0951832026008975?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0951832026008975?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T20:22:07Z","timestamp":1783455727000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0951832026008975"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2027,1]]},"references-count":46,"alternative-id":["S0951832026008975"],"URL":"https:\/\/doi.org\/10.1016\/j.ress.2026.113088","relation":{},"ISSN":["0951-8320"],"issn-type":[{"value":"0951-8320","type":"print"}],"subject":[],"published":{"date-parts":[[2027,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A new bivariate gamma degradation model and its reliability assessment, with application to the analysis of polymeric coating data","name":"articletitle","label":"Article Title"},{"value":"Reliability Engineering & System Safety","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.ress.2026.113088","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"113088"}}