{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T09:12:52Z","timestamp":1768813972494,"version":"3.49.0"},"reference-count":35,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,5,21]],"date-time":"2021-05-21T00:00:00Z","timestamp":1621555200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, the Weibull extension distribution parameters are estimated under a progressive type-II censoring scheme with random removal. The parameters of the model are estimated using the maximum likelihood method, maximum product spacing, and Bayesian estimation methods. In classical estimation (maximum likelihood method and maximum product spacing), we did use the Newton\u2013Raphson algorithm. The Bayesian estimation is done using the Metropolis\u2013Hastings algorithm based on the square error loss function. The proposed estimation methods are compared using Monte Carlo simulations under a progressive type-II censoring scheme. An empirical study using a real data set of transformer insulation and a simulation study is performed to validate the introduced methods of inference. Based on the result of our study, it can be concluded that the Bayesian method outperforms the maximum likelihood and maximum product-spacing methods for estimating the Weibull extension parameters under a progressive type-II censoring scheme in both simulation and empirical studies.<\/jats:p>","DOI":"10.3390\/axioms10020100","type":"journal-article","created":{"date-parts":[[2021,5,23]],"date-time":"2021-05-23T23:58:05Z","timestamp":1621814285000},"page":"100","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["Applying Transformer Insulation Using Weibull Extended Distribution Based on Progressive Censoring Scheme"],"prefix":"10.3390","volume":"10","author":[{"given":"Hisham M.","family":"Almongy","sequence":"first","affiliation":[{"name":"Applied Statistics and Insurance Department, Faculty of Commerce, Mansoura University, Mansoura 35511, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7765-1616","authenticated-orcid":false,"given":"Fatma Y.","family":"Alshenawy","sequence":"additional","affiliation":[{"name":"Applied Statistics and Insurance Department, Faculty of Commerce, Mansoura University, Mansoura 35511, Egypt"}],"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":"Statistics Department, Faculty of Business Administration, Delta University of Science and Technology, Mansoura 35511, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Doaa A.","family":"Abdo","sequence":"additional","affiliation":[{"name":"Applied Statistics and Insurance Department, Faculty of Commerce, Mansoura University, Mansoura 35511, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Balakrishnan, N., and Aggarwala, R. 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