{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:06:13Z","timestamp":1760148373319,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T00:00:00Z","timestamp":1682294400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Yunnan Fundamental Research Project","award":["202101AT070103"],"award-info":[{"award-number":["202101AT070103"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The analysis of the constant-stress partially accelerated life test was considered under progressive Type-II censoring when the lifetime of the products follows a two-parameter bathtub-shaped distribution. The maximum likelihood estimates of the unknown parameters were established, where the expectation\u2013maximization iterative solution is proposed for the estimation. The approximate confidence intervals were also constructed based on asymptotic theory via the Fisher information matrix. For comparison purposes, the bootstrap (i.e., Studentized-t and percentile) confidence intervals of the unknown parameters were also obtained. Finally, simulation studies and a real-life data example are presented to examine the performance of the different results.<\/jats:p>","DOI":"10.3390\/axioms12050417","type":"journal-article","created":{"date-parts":[[2023,4,25]],"date-time":"2023-04-25T01:37:01Z","timestamp":1682386621000},"page":"417","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Inference for Partially Accelerated Life Test from a Bathtub-Shaped Lifetime Distribution with Progressive Censoring"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4736-8334","authenticated-orcid":false,"given":"Yingzi","family":"Niu","sequence":"first","affiliation":[{"name":"School of Mathematics, Yunnan Normal University, Kunming 650500, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2600-5112","authenticated-orcid":false,"given":"Liang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Yunnan Normal University, Kunming 650500, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9687-6036","authenticated-orcid":false,"given":"Yogesh Mani","family":"Tripathi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Patna, Bihta 800013, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8395-8895","authenticated-orcid":false,"given":"Jia","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics, Yunnan Normal University, Kunming 650500, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1007\/s00184-006-0106-3","article-title":"Progressive stress accelerated life tests under finite mixture models","volume":"66","year":"2007","journal-title":"Metrika"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1080\/00224065.2007.11917671","article-title":"Point and interval estimation for a simple step-stress model with Type-II censoring","volume":"39","author":"Balakrishnan","year":"2007","journal-title":"J. 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