{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T14:17:39Z","timestamp":1769264259617,"version":"3.49.0"},"reference-count":27,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T00:00:00Z","timestamp":1701388800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002713","name":"Deputyship for Research &amp; Innovation, Ministry of Education in Saudi Arabia","doi-asserted-by":"publisher","award":["IFP-IMSIU-2023120"],"award-info":[{"award-number":["IFP-IMSIU-2023120"]}],"id":[{"id":"10.13039\/501100002713","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University (IMSIU)","award":["IFP-IMSIU-2023120"],"award-info":[{"award-number":["IFP-IMSIU-2023120"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Recently, a newly improved Type-II adaptive progressive censoring plan was devised, which can successfully ensure that the test length will not surpass a particular threshold period. In this study, we explore the statistical inference of the alpha power exponential distribution in the context of improved adaptive progressive Type-II censored data. The parameters, reliability, and hazard functions were estimated from both classical and Bayesian viewpoints using this censoring plan. To begin, we applied the maximum likelihood estimation approach to obtain parameter, reliability, and hazard function estimators. Following that, the approximate confidence intervals for the aforementioned metrics were derived, assuming the asymptotic normality traits of the maximum likelihood estimators. Additionally, by employing the Bayesian method via the Markov chain Monte Carlo technique, the point estimators and highest posterior density intervals of various parameters were created based on the symmetric squared error loss. A simulation study that incorporates numerous scenarios was used to assess the effectiveness of various estimation methodologies. The optimal progressive censorship plans are then discussed based on a set of criteria. Finally, three applications from the engineering and medical domains have been offered as examples.<\/jats:p>","DOI":"10.3390\/sym15122137","type":"journal-article","created":{"date-parts":[[2023,12,1]],"date-time":"2023-12-01T03:58:02Z","timestamp":1701403082000},"page":"2137","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Reliability Analysis and Its Applications for a Newly Improved Type-II Adaptive Progressive Alpha Power Exponential Censored Sample"],"prefix":"10.3390","volume":"15","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":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6353-2245","authenticated-orcid":false,"given":"Mazen","family":"Nassar","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"},{"name":"Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig 44519, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lamiaa Sabry Gad","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":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9916-259X","authenticated-orcid":false,"given":"Ahmed","family":"Elshahhat","sequence":"additional","affiliation":[{"name":"Faculty of Technology and Development, Zagazig University, Zagazig 44519, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1198\/004017004000000482","article-title":"Optimal progressive censoring plans for the Weibull distribution","volume":"46","author":"Ng","year":"2004","journal-title":"Technometrics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1198\/004017008000000217","article-title":"Bayesian inference and life testing plan for the Weibull distribution in presence of progressive censoring","volume":"50","author":"Kundu","year":"2008","journal-title":"Technometrics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1285","DOI":"10.1016\/j.csda.2010.09.017","article-title":"Progressively Type-II censored competing risks data from Lomax distributions","volume":"55","author":"Cramer","year":"2011","journal-title":"Comput. 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