{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T14:01:45Z","timestamp":1774620105988,"version":"3.50.1"},"reference-count":52,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T00:00:00Z","timestamp":1679616000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Princess Nourah bint Abdulrahman University","award":["FRP-1443-19"],"award-info":[{"award-number":["FRP-1443-19"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In reliability and survival analysis, the time-to-failure data play an important role in the development of the reliability and life characteristics of the products. In some cases, these kinds of data are modeled using a competing risks model. The problem of conducting comparative life testing under a competing risks model when the units come from different lines of production has recently been addressed. In this paper, we address this problem when the life of the unit is distributed using the Gompertz distribution, noting that the units come from two lines of production and two independent causes of failure are activated. The data are collected under a joint generalized type-II hybrid censoring scheme. Maximum likelihood estimators of the unknown parameters are derived, along with the corresponding asymptotic confidence intervals. We also adopt two bootstrap confidence intervals. Using independent gamma priors, the Bayes estimators relative to squared error loss function are obtained with credible intervals. The properties and quality of estimators are measured by performing a Monte Carlo simulation study. Finally, a real-life data set is analyzed to discuss the applicability of the proposed methods to real phenomena. The optimal plan with respect to comments on the numerical results is discussed in the conclusion.<\/jats:p>","DOI":"10.3390\/axioms12040322","type":"journal-article","created":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T06:34:07Z","timestamp":1679639647000},"page":"322","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Comparative Study with Applications for Gompertz Models under Competing Risks and Generalized Hybrid Censoring Schemes"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2788-8946","authenticated-orcid":false,"given":"Laila A.","family":"Al-Essa","sequence":"first","affiliation":[{"name":"Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5630-0203","authenticated-orcid":false,"given":"Ahmed A.","family":"Soliman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3511-3326","authenticated-orcid":false,"given":"Gamal A.","family":"Abd-Elmougod","sequence":"additional","affiliation":[{"name":"Mathematics Department, Faculty of Science, Damanhour University, Damanhour 22511, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5154-7477","authenticated-orcid":false,"given":"Huda M.","family":"Alshanbari","sequence":"additional","affiliation":[{"name":"Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/BF02530502","article-title":"Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution","volume":"2","author":"Childs","year":"2003","journal-title":"Ann. Inst. Stat. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2509","DOI":"10.1016\/j.csda.2005.05.002","article-title":"Analysis of type-II progressively hybrid censored data","volume":"50","author":"Kundu","year":"2006","journal-title":"Comput. Stat. 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