{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T17:16:40Z","timestamp":1774631800578,"version":"3.50.1"},"reference-count":48,"publisher":"Wiley","issue":"7","license":[{"start":{"date-parts":[[2025,6,16]],"date-time":"2025-06-16T00:00:00Z","timestamp":1750032000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Quality &amp; Reliability Eng"],"published-print":{"date-parts":[[2025,11]]},"abstract":"<jats:title>ABSTRACT<\/jats:title><jats:p>Many real\u2010world systems have performance degradation when operating in extreme environments. While previous research often focuses on system failures under specific stress conditions, there remain critical gaps in understanding and minimizing risks associated with systems operating in a wide range of extreme conditions. This paper addresses this critical need by examining the reliability of systems subjected to multiple stresses, where both stress and strength are independent random variables that follow the Burr III distribution. They have different first\u2010shape parameters but the same second\u2010shape parameter. To improve the efficiency and cost\u2010effectiveness of reliability assessment, we use a progressive Type\u2010II censoring scheme. This study is the first to estimate the multi\u2013stress\u2013strength reliability using this scheme, employing both Bayesian and frequentist statistical methods. We derive the system reliability estimators and use different loss functions to obtain Bayesian estimates with gamma priors. Additionally, we construct asymptotic confidence intervals based on the Fisher information matrix and generate credible intervals with the highest posterior density. Comprehensive Monte Carlo simulations are used to evaluate the performance of the proposed approaches, and real data sets are used for validation. Overall, the simulation experiments show that Bayesian approaches provide better point and interval estimates than conventional approaches under all censoring conditions, which is evaluated using accuracy metrics. Our results provide useful insights for improving the design, performance, and maintenance of systems operating in challenging environments.<\/jats:p>","DOI":"10.1002\/qre.70002","type":"journal-article","created":{"date-parts":[[2025,6,16]],"date-time":"2025-06-16T14:25:16Z","timestamp":1750083916000},"page":"2997-3014","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Enhancing System Reliability Under Extremes: A Multi\u2013Stress\u2013Strength Analysis Using Frequentist and Bayesian Approaches"],"prefix":"10.1002","volume":"41","author":[{"given":"Amal S.","family":"Hassan","sequence":"first","affiliation":[{"name":"Faculty of Graduate Studies for Statistical Research Cairo University  Giza Egypt"}]},{"given":"Najwan","family":"Alsadat","sequence":"additional","affiliation":[{"name":"Department of Quantitative Analysis College of Business Administration King Saud University  Riyadh Saudi Arabia"}]},{"given":"Mohammed","family":"Elgarhy","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences Higher Institute of Administrative Sciences  Belbeis, AlSharkia Egypt"}]},{"given":"Arne","family":"Johannssen","sequence":"additional","affiliation":[{"name":"Faculty of Business Studies Harz University of Applied Sciences  Wernigerode Germany"}]},{"given":"Ehab M.","family":"Almetwally","sequence":"additional","affiliation":[{"name":"Faculty of Business Administration Delta University for Science and Technology  Gamasa Egypt"}]}],"member":"311","published-online":{"date-parts":[[2025,6,16]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/s001840400345"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610918608812514"},{"issue":"2","key":"e_1_2_10_4_1","first-page":"103","article-title":"Stress\u2013strength Reliability of Weibull Distribution Based on Progressively Censored Samples","volume":"35","author":"Akbar A.","year":"2011","journal-title":"Statistics and Operations Research Transactions"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s40745-015-0033-0"},{"key":"e_1_2_10_6_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610926.2013.821485"},{"key":"e_1_2_10_7_1","doi-asserted-by":"publisher","DOI":"10.1080\/21681015.2017.1421590"},{"key":"e_1_2_10_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/qre.2117"},{"key":"e_1_2_10_9_1","doi-asserted-by":"publisher","DOI":"10.1142\/5015"},{"key":"e_1_2_10_10_1","doi-asserted-by":"publisher","DOI":"10.3390\/math11020318"},{"key":"e_1_2_10_11_1","doi-asserted-by":"publisher","DOI":"10.3390\/axioms12121097"},{"key":"e_1_2_10_12_1","doi-asserted-by":"publisher","DOI":"10.1002\/nav.3800220104"},{"key":"e_1_2_10_13_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610928008827982"},{"key":"e_1_2_10_14_1","first-page":"1728","article-title":"On the Estimation of for Weibull Distribution in the Presence of k Outliers","volume":"3","author":"Hassan A. 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