{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T17:16:09Z","timestamp":1774631769208,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,1]],"date-time":"2023-06-01T00:00:00Z","timestamp":1685577600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Based on independent progressive type-II censored samples from two-parameter Burr-type XII distributions, various point and interval estimators of \u03b4=P(Y&lt;X) were proposed when the strength variable was subjected to the step\u2013stress partially accelerated life test. The point estimators computed were maximum likelihood and Bayesian under various symmetric and asymmetric loss functions. The interval estimations constructed were approximate, bootstrap-P, and bootstrap-T confidence intervals, and a Bayesian credible interval. A Markov Chain Monte Carlo approach using Gibbs sampling was designed to derive the Bayesian estimate of \u03b4. Based on the mean square error, bias, confidence interval length, and coverage probability, the results of the numerical analysis of the performance of the maximum likelihood and Bayesian estimates using Monte Carlo simulations were quite satisfactory. To support the theoretical component, an empirical investigation based on two actual data sets was carried out.<\/jats:p>","DOI":"10.3390\/sym15061183","type":"journal-article","created":{"date-parts":[[2023,6,2]],"date-time":"2023-06-02T01:33:54Z","timestamp":1685669634000},"page":"1183","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Simulation Techniques for Strength Component Partially Accelerated to Analyze Stress\u2013Strength Model"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9579-6694","authenticated-orcid":false,"given":"Manal M.","family":"Yousef","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, New Valley University, EL-Khargah 72511, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8994-933X","authenticated-orcid":false,"given":"Aisha","family":"Fayomi","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3888-1275","authenticated-orcid":false,"given":"Ehab M.","family":"Almetwally","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Business Administration, Delta University for Science and Technology, Gamasa City 11152, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,1]]},"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","doi-asserted-by":"crossref","first-page":"558","DOI":"10.1214\/aoms\/1177706631","article-title":"A Distribution-Free Upper Confidence Bound for Pr{Y<X}, Based on Independent Samples of X and Y","volume":"29","author":"Birnbaum","year":"1958","journal-title":"Ann. 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