{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T23:10:07Z","timestamp":1780960207180,"version":"3.54.1"},"reference-count":57,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,11,15]],"date-time":"2023-11-15T00:00:00Z","timestamp":1700006400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002713","name":"Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University","doi-asserted-by":"publisher","award":["IMSIU-RP23009"],"award-info":[{"award-number":["IMSIU-RP23009"]}],"id":[{"id":"10.13039\/501100002713","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In the statistical literature, one of the most important subjects that is commonly used is stress\u2013strength reliability, which is defined as \u03b4=PW&lt;V, where V and W are the strength and stress random variables, respectively, and \u03b4 is reliability parameter. Type-II progressive censoring with binomial removal is used in this study to examine the inference of \u03b4=PW&lt;V for a component with strength V and being subjected to stress W. We suppose that V and W are independent random variables taken from the Burr XII distribution and the Burr III distribution, respectively, with a common shape parameter. The maximum likelihood estimator of \u03b4 is derived. The Bayes estimator of \u03b4 under the assumption of independent gamma priors is derived. To determine the Bayes estimates for squared error and linear exponential loss functions in the lack of explicit forms, the Metropolis\u2013Hastings method was provided. Utilizing comprehensive simulations and two metrics (average of estimates and root mean squared errors), we compare these estimators. Further, an analysis is performed on two actual data sets based on breakdown times for insulating fluid between electrodes recorded under varying voltages.<\/jats:p>","DOI":"10.3390\/axioms12111054","type":"journal-article","created":{"date-parts":[[2023,11,16]],"date-time":"2023-11-16T01:56:29Z","timestamp":1700099789000},"page":"1054","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Stress\u2013Strength Reliability Analysis for Different Distributions Using Progressive Type-II Censoring with Binomial Removal"],"prefix":"10.3390","volume":"12","author":[{"given":"Ibrahim","family":"Elbatal","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4442-8458","authenticated-orcid":false,"given":"Amal S.","family":"Hassan","sequence":"additional","affiliation":[{"name":"Faculty of Graduate Studies for Statistical Research, Cairo University, 5 Dr. Ahmed Zewail Street, Giza 12613, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"L. S.","family":"Diab","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5501-327X","authenticated-orcid":false,"given":"Anis","family":"Ben Ghorbal","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1333-3862","authenticated-orcid":false,"given":"Mohammed","family":"Elgarhy","sequence":"additional","affiliation":[{"name":"Mathematics and Computer Science Department, Faculty of Science, Beni-Suef University, Beni-Suef 62521, Egypt"},{"name":"Department of Basic Sciences, Higher Institute of Administrative Sciences, Belbeis 44621, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ahmed R.","family":"El-Saeed","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, Obour High Institute for Management & Informatics, Obour 11828, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,11,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kotz, S., and Pensky, M. 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