{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T07:16:20Z","timestamp":1783667780579,"version":"3.55.0"},"reference-count":38,"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\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["G2025203034"],"award-info":[{"award-number":["G2025203034"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2027,1]]},"DOI":"10.1016\/j.cam.2026.117865","type":"journal-article","created":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T23:38:38Z","timestamp":1780443518000},"page":"117865","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Dependence modeling and reliability inference of stress\u2013strength model in multicomponent redundant system based on mixed copula function"],"prefix":"10.1016","volume":"489","author":[{"given":"Xue","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3195-7270","authenticated-orcid":false,"given":"Linmin","family":"Hu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yufei","family":"Gong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Renfang","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaomei","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.cam.2026.117865_bib0001","series-title":"Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability","first-page":"13","article-title":"On a use of the Mann-Whitney statistic","author":"Birnbaum","year":"1956"},{"key":"10.1016\/j.cam.2026.117865_bib0002","series-title":"Statistical Methods for Reliability Data","author":"Meeker","year":"2021"},{"issue":"5","key":"10.1016\/j.cam.2026.117865_bib0003","doi-asserted-by":"crossref","first-page":"1631","DOI":"10.1007\/s00362-017-0889-5","article-title":"Signature-based approach for stress\u2013strength systems","volume":"60","author":"Pakdaman","year":"2019","journal-title":"Stat. Pap."},{"issue":"1","key":"10.1016\/j.cam.2026.117865_bib0004","doi-asserted-by":"crossref","first-page":"2345","DOI":"10.3934\/math.2024116","article-title":"Asset selection based on estimating stress\u2013strength probabilities: the case of returns following three-parameter generalized extreme value distributions","volume":"9","author":"Quintino","year":"2024","journal-title":"AIMS Math."},{"issue":"1","key":"10.1016\/j.cam.2026.117865_bib0005","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1080\/00401706.1970.10488633","article-title":"The estimation of reliability from stress\u2013strength relationships","volume":"12","author":"Church","year":"1970","journal-title":"Technometrics"},{"issue":"17","key":"10.1016\/j.cam.2026.117865_bib0006","doi-asserted-by":"crossref","first-page":"1839","DOI":"10.1016\/j.spl.2009.05.026","article-title":"Estimation of R = P(Y < X) for three-parameter Weibull distribution","volume":"79","author":"Kundu","year":"2009","journal-title":"Stat. Probab. Lett."},{"key":"10.1016\/j.cam.2026.117865_bib0007","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.apm.2017.03.020","article-title":"Bayes estimation of P(Y < X) for the Weibull distribution with arbitrary parameters","volume":"47","author":"Jia","year":"2017","journal-title":"Appl. Math. Model."},{"key":"10.1016\/j.cam.2026.117865_bib0008","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/j.matcom.2024.09.005","article-title":"Estimation of the stress\u2013strength reliability for the exponential-Rayleigh distribution","volume":"228","author":"Kotb","year":"2025","journal-title":"Math. Comput. Simul."},{"key":"10.1016\/j.cam.2026.117865_bib0009","article-title":"Stress\u2013strength reliability under partially accelerated life testing using Weibull model","volume":"20","author":"Sarhan","year":"2023","journal-title":"Sci. Afr."},{"issue":"348","key":"10.1016\/j.cam.2026.117865_bib0010","doi-asserted-by":"crossref","first-page":"966","DOI":"10.1080\/01621459.1974.10480238","article-title":"Estimation of reliability in a multicomponent stress\u2013strength model","volume":"69","author":"Bhattacharyya","year":"1974","journal-title":"J. Am. Stat. Assoc."},{"key":"10.1016\/j.cam.2026.117865_bib0011","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2024.110480","article-title":"Crossover point analysis with Jensen-Shannon divergence lower bound for bi-objective reliability optimization of k-out-of-n system","volume":"252","author":"Maneckshaw","year":"2024","journal-title":"Reliab. Eng. Syst. Saf."},{"key":"10.1016\/j.cam.2026.117865_bib0012","doi-asserted-by":"crossref","DOI":"10.1016\/j.ress.2025.110948","article-title":"Developing k-out-of-n: G multilevel system with mixed redundancy strategy to protect DSP code using simplified swarm optimization","volume":"260","author":"Hsieh","year":"2025","journal-title":"Reliab. Eng. Syst. Saf."},{"issue":"3","key":"10.1016\/j.cam.2026.117865_bib0013","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1080\/24754269.2024.2341982","article-title":"Statistical inference of reliability for a k-out-of-n: G system with switching failure under Poisson shocks","volume":"8","author":"Luo","year":"2024","journal-title":"Stat. Theory Relat. Fields"},{"key":"10.1016\/j.cam.2026.117865_bib0014","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.matcom.2021.07.026","article-title":"Interval estimation of multicomponent stress\u2013strength reliability based on inverse Weibull distribution","volume":"191","author":"Jana","year":"2022","journal-title":"Math. Comput. Simul."},{"issue":"3","key":"10.1016\/j.cam.2026.117865_bib0015","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1080\/03610918.2024.2413911","article-title":"Reliability inference of stress\u2013strength for a k-out-of-n: G mixed standby system with switching failure","volume":"55","author":"Luo","year":"2024","journal-title":"Commun. Stat. Simul. Comput."},{"key":"10.1016\/j.cam.2026.117865_bib0016","doi-asserted-by":"crossref","DOI":"10.1016\/j.apm.2025.116221","article-title":"Inference for stress\u2013strength reliability based on k-out-of-n system with different exponentiated gamma components","volume":"147","author":"Liu","year":"2025","journal-title":"Appl. Math. Model."},{"issue":"4","key":"10.1016\/j.cam.2026.117865_bib0017","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1007\/BF02926000","article-title":"Note on estimation of reliability under bivariate pareto stress\u2013strength model","volume":"38","author":"Hanagal","year":"1997","journal-title":"Stat. Pap."},{"key":"10.1016\/j.cam.2026.117865_bib0018","series-title":"Bayesian inference on P(X>Y) in bivariate Rayleigh model","first-page":"4095","volume":"47","author":"Pak","year":"2018"},{"issue":"7","key":"10.1016\/j.cam.2026.117865_bib0019","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1080\/03081079.2023.2218017","article-title":"On the copula-based reliability of stress\u2013strength model under bivariate stress","volume":"52","author":"Hudaverdi","year":"2023","journal-title":"Int. J. Gen. Syst."},{"issue":"4","key":"10.1016\/j.cam.2026.117865_bib0020","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1080\/03081079.2024.2405687","article-title":"Stress\u2013strength reliability estimation of s-out-of-k multicomponent systems based on copula function for dependent strength elements under progressively censored sample","volume":"54","author":"Hakamipour","year":"2025","journal-title":"Int. J. Gen. Syst."},{"issue":"3","key":"10.1016\/j.cam.2026.117865_bib0021","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/s10260-012-0192-5","article-title":"A stress\u2013strength model with dependent variables to measure household financial fragility","volume":"21","author":"Domma","year":"2012","journal-title":"Stat. Methods Appl."},{"issue":"3","key":"10.1016\/j.cam.2026.117865_bib0022","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1007\/s00362-012-0463-0","article-title":"A copula-based approach to account for dependence in stress\u2013strength models","volume":"54","author":"Domma","year":"2013","journal-title":"Stat. Pap."},{"issue":"10","key":"10.1016\/j.cam.2026.117865_bib0023","doi-asserted-by":"crossref","first-page":"4443","DOI":"10.1007\/s12206-016-0909-8","article-title":"A dependent stress\u2013strength interference model based on mixed copula function","volume":"30","author":"Gao","year":"2016","journal-title":"J. Mech. Sci. Technol."},{"key":"10.1016\/j.cam.2026.117865_bib0024","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.cam.2018.04.066","article-title":"Reliability estimation of multicomponent stress\u2013strength model based on copula function under progressively hybrid censoring","volume":"344","author":"Bai","year":"2018","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.cam.2026.117865_bib0025","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2021.113920","article-title":"Reliability estimation of s-out-of-k system in a multicomponent stress\u2013strength dependent model based on copula function","volume":"404","author":"Zhu","year":"2022","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.cam.2026.117865_bib0026","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2022.114602","article-title":"Inference of reliability in a multicomponent stress\u2013strength model under generalized progressive hybrid censoring","volume":"418","author":"Zhu","year":"2023","journal-title":"J. Comput. Appl. Math."},{"issue":"3","key":"10.1016\/j.cam.2026.117865_bib0027","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1214\/aoms\/1177728723","article-title":"Truncated life tests in the exponential case","volume":"25","author":"Epstein","year":"1954","journal-title":"Ann. Math. Stat."},{"issue":"3","key":"10.1016\/j.cam.2026.117865_bib0028","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1080\/00401706.1963.10490102","article-title":"Progressively censored samples in life testing","volume":"5","author":"Cohen","year":"1963","journal-title":"Technometrics"},{"issue":"17","key":"10.1016\/j.cam.2026.117865_bib0029","doi-asserted-by":"crossref","first-page":"9317","DOI":"10.1007\/s00500-024-09674-3","article-title":"Statistical inference on multicomponent stress\u2013strength reliability with non-identical component strengths using progressively censored data from Kumaraswamy distribution","volume":"28","author":"Saini","year":"2024","journal-title":"Soft Comput."},{"key":"10.1016\/j.cam.2026.117865_bib0030","series-title":"Statistical Models and Methods for Biomedical and Technical Systems","first-page":"319","article-title":"Exact likelihood inference for an exponential parameter under progressive hybrid censoring schemes","author":"Childs","year":"2008"},{"key":"10.1016\/j.cam.2026.117865_bib0031","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.stamet.2014.09.002","article-title":"Exact likelihood inference for an exponential parameter under generalized progressive hybrid censoring scheme","volume":"23","author":"Cho","year":"2015","journal-title":"Stat. Methodol."},{"key":"10.1016\/j.cam.2026.117865_bib0032","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2024.116015","article-title":"Reliability inference for multicomponent stress\u2013strength model under generalized progressive hybrid censoring","volume":"451","author":"Zhu","year":"2024","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.cam.2026.117865_bib0033","series-title":"An Introduction to Copulas","author":"Nelsen","year":"2006"},{"key":"10.1016\/j.cam.2026.117865_bib0034","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1016\/j.cam.2018.05.013","article-title":"Inference of progressively censored competing risks data from Kumaraswamy distributions","volume":"343","author":"Wang","year":"2018","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.cam.2026.117865_bib0035","doi-asserted-by":"crossref","DOI":"10.1016\/j.cam.2019.112345","article-title":"Estimation of the inverted exponentiated Rayleigh distribution based on adaptive type II progressive hybrid censored sample","volume":"364","author":"Panahi","year":"2020","journal-title":"J. Comput. Appl. Math."},{"issue":"282","key":"10.1016\/j.cam.2026.117865_bib0036","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1080\/01621459.1958.10501452","article-title":"Nonparametric estimation from incomplete observations","volume":"53","author":"Kaplan","year":"1958","journal-title":"J. Am. Stat. Assoc."},{"key":"10.1016\/j.cam.2026.117865_bib0037","series-title":"Handbook of Software Reliability Engineering","author":"Lyu","year":"1996"},{"issue":"1","key":"10.1016\/j.cam.2026.117865_bib0038","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1080\/00949655.2021.1935947","article-title":"Stress\u2013strength reliability estimation of a consecutive k-out-of-n system based on proportional hazard rate family","volume":"92","author":"Demiray","year":"2022","journal-title":"J. Stat. Comput. Simul."}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726005078?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726005078?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T06:45:36Z","timestamp":1783665936000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042726005078"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2027,1]]},"references-count":38,"alternative-id":["S0377042726005078"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2026.117865","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2027,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Dependence modeling and reliability inference of stress\u2013strength model in multicomponent redundant system based on mixed copula function","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2026.117865","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"117865"}}