{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T12:47:01Z","timestamp":1773060421487,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,16]],"date-time":"2022-04-16T00:00:00Z","timestamp":1650067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004242","name":"Princess Nourah bint Abdulrahman University","doi-asserted-by":"publisher","award":["PNURSP2022R50"],"award-info":[{"award-number":["PNURSP2022R50"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We consider an optimization design for the alpha power exponential (APE) distribution as asymmetrical probability distributions under progressive type-I censoring for a step-stress accelerated life test. In this study, two stress variables are taken into account. To save the time and cost of lifetime testing, progressive censoring and accelerated life testing are utilized. The test units\u2019 lifespans are supposed to follow an APE distribution. A cumulative exposure model is used to study the impact of varying stress levels. A log-linear relationship between the APE distribution\u2019s scale parameter and stress is postulated. The maximum likelihood estimators, Bayesian estimators of the model parameters based on the symmetric loss function, approximate confidence intervals (CIs) and credible intervals are provided. Under normal operating conditions, an ideal test plan is designed by minimizing the asymptotic variance of the percentile life.<\/jats:p>","DOI":"10.3390\/sym14040830","type":"journal-article","created":{"date-parts":[[2022,4,20]],"date-time":"2022-04-20T00:22:43Z","timestamp":1650414163000},"page":"830","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Optimal Design for a Bivariate Step-Stress Accelerated Life Test with Alpha Power Exponential Distribution Based on Type-I Progressive Censored Samples"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9449-7489","authenticated-orcid":false,"given":"Refah","family":"Alotaibi","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"given":"Aned Al","family":"Mutairi","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3888-1275","authenticated-orcid":false,"given":"Ehab M.","family":"Almetwally","sequence":"additional","affiliation":[{"name":"Department of Mathematical Statistical, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt"},{"name":"Department of Statistical, Faculty of Business Administration, Delta University for Science and Technology, Gamasa, Mansoura 11152, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2208-3498","authenticated-orcid":false,"given":"Chanseok","family":"Park","sequence":"additional","affiliation":[{"name":"Applied Statistics Laboratory, Department of Industrial Engineering, Pusan National University, Busan 46241, Korea"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7501-7232","authenticated-orcid":false,"given":"Hoda","family":"Rezk","sequence":"additional","affiliation":[{"name":"Department of Statistics, Al-Azhar University, Cairo 11651, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,16]]},"reference":[{"key":"ref_1","unstructured":"Meeker, W.Q., and Escobar, L.A. 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