{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:41:47Z","timestamp":1760229707483,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T00:00:00Z","timestamp":1655856000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Modeling competing failure modes is an important problem in engineering and survival analyses. Competing failure modes are partially observed in many applications and often pose a modeling challenge. This study discusses the inference for partially observed failure modes assuming a Burr XII distribution. In particular, we consider two failure modes, and the failure time data are collected under a hybrid type I censoring scheme. The model parameters are estimated using maximum likelihood and Bayesian methods under a symmetric squared error loss function, whereas the intervals estimation is done with three methods: asymptotic and credible confidence intervals. Besides a simulation study, a real-life data set is taken from individuals who live in an environment with several diseases to present the utility of the work. Additionally, a simulation study is constructed to measure and compare different estimation methods.<\/jats:p>","DOI":"10.3390\/sym14071298","type":"journal-article","created":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T23:11:19Z","timestamp":1655939479000},"page":"1298","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Burr XII Distribution for Disease Data Analysis in the Presence of a Partially Observed Failure Mode"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8047-6882","authenticated-orcid":false,"given":"Fatimah E.","family":"Almuhayfith","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, College of Sciences, King Faisal University, Alahsa 31982, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9385-5291","authenticated-orcid":false,"given":"Jumanah Ahmed","family":"Darwish","sequence":"additional","affiliation":[{"name":"Department of Statistics, College of Science, University of Jeddah, Jeddah 21959, Saudi Arabia"}]},{"given":"Randa","family":"Alharbi","sequence":"additional","affiliation":[{"name":"Department of Statistics, Faculty of Science, University of Tabuk, Tabuk 47512, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1552-3763","authenticated-orcid":false,"given":"Marin","family":"Marin","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brasov, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Balakrishnan, N., and Aggarwala, R. 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