{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T02:05:05Z","timestamp":1762049105767,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,4,29]],"date-time":"2022-04-29T00:00:00Z","timestamp":1651190400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of China","award":["No.11861049","2020LH01002","2020MS01001","BZ2020035"],"award-info":[{"award-number":["No.11861049","2020LH01002","2020MS01001","BZ2020035"]}]},{"DOI":"10.13039\/501100004763","name":"the Natural Science Foundation of Inner Mongolia","doi-asserted-by":"publisher","award":["No.11861049","2020LH01002","2020MS01001","BZ2020035"],"award-info":[{"award-number":["No.11861049","2020LH01002","2020MS01001","BZ2020035"]}],"id":[{"id":"10.13039\/501100004763","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Inner Mongolia Autonomous Region graduate Scientific research innovation project","award":["No.11861049","2020LH01002","2020MS01001","BZ2020035"],"award-info":[{"award-number":["No.11861049","2020LH01002","2020MS01001","BZ2020035"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The statistical inference of the reliability and parameters of the stress\u2013strength model has received great attention in the field of reliability analysis. When following the generalized progressive hybrid censoring (GPHC) scheme, it is important to discuss the point estimate and interval estimate of the reliability of the multicomponent stress\u2013strength (MSS) model, in which the stress and the strength variables are derived from different distributions by assuming that stress follows the Chen distribution and that strength follows the Gompertz distribution. In the present study, the Newton\u2013Raphson method was adopted to derive the maximum likelihood estimation (MLE) of the model parameters, and the corresponding asymptotic distribution was adopted to construct the asymptotic confidence interval (ACI). Subsequently, the exact confidence interval (ECI) of the parameters was calculated. A hybrid Markov chain Monte Carlo (MCMC) method was adopted to determine the approximate Bayesian estimation (BE) of the unknown parameters and the high posterior density credible interval (HPDCI). A simulation study with the actual dataset was conducted for the BEs with squared error loss function (SELF) and the MLEs of the model parameters and reliability, comparing the bias and mean squares errors (MSE). In addition, the three interval estimates were compared in terms of the average interval length (AIL) and coverage probability (CP).<\/jats:p>","DOI":"10.3390\/e24050619","type":"journal-article","created":{"date-parts":[[2022,4,29]],"date-time":"2022-04-29T16:49:57Z","timestamp":1651250997000},"page":"619","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Multicomponent Stress\u2013Strength Model Based on Generalized Progressive Hybrid Censoring Scheme: A Statistical Analysis"],"prefix":"10.3390","volume":"24","author":[{"given":"Haijing","family":"Ma","sequence":"first","affiliation":[{"name":"College of Science, Inner Mongolia University of Technology, Hohhot 010051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5889-1326","authenticated-orcid":false,"given":"Zaizai","family":"Yan","sequence":"additional","affiliation":[{"name":"College of Science, Inner Mongolia University of Technology, Hohhot 010051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Junmei","family":"Jia","sequence":"additional","affiliation":[{"name":"College of Science, Inner Mongolia University of Technology, Hohhot 010051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,29]]},"reference":[{"key":"ref_1","first-page":"13","article-title":"On a use of the Mann-Whitney statistic","volume":"Volume 1","author":"Birnbaum","year":"1956","journal-title":"Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability"},{"key":"ref_2","first-page":"1","article-title":"The Estimation of Reliability from stress-strength Relationships","volume":"Volume 4","author":"Church","year":"1967","journal-title":"Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1715","DOI":"10.1081\/STA-120037269","article-title":"New Approximate Inferential Methods for the Reliability Parameter in a stress-strength Model: The Normal","volume":"33","author":"Guo","year":"2005","journal-title":"Commun. 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