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This is because certain CR data necessitates constructing CR models that are based on hazard rate (HR) patterns associated with cause\u2010specific failure times. To circumvent this obstacle, this study proposes an easy\u2010to\u2010handle methodology that involves constructing a minimum variable following Weibull or Dhillon failures. The model is called the Weibull\u2013Dhillon competing risk (WDCR) model. Compared to many existing literature, the proposed WDCR model can analyze failure times that exhibit increasing and bathtub HRs and effectively characterize failure times linked to inverted bathtub and modified bathtub HRs. We examined several reliability characteristics and demonstrated the relationship between the model's mean residual life and HR function. Due to its complicated joint posterior distribution, the Hamiltonian Monte Carlo (HMC) procedure is employed for Bayesian inference of WDCR model parameters and reliability features. We provide two illustrations to illustrate the proposed model's practical value. The outcomes were better than those of the other contenders, indicating a valuable approach to modeling different CR data, particularly in the context of reliability analyses or other quantitative\u00a0studies.<\/jats:p>","DOI":"10.1002\/qre.3803","type":"journal-article","created":{"date-parts":[[2025,5,12]],"date-time":"2025-05-12T14:54:38Z","timestamp":1747061678000},"page":"2624-2646","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Bayesian Study of a Weibull\u2013Dhillon Competing Risk Model and Its Reliability Implications via HMC Sampling Methodology"],"prefix":"10.1002","volume":"41","author":[{"given":"Badamasi","family":"Abba","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics Central South University Changsha China"}]},{"given":"Mustapha","family":"Muhammad","sequence":"additional","affiliation":[{"name":"Department of Mathematics Guangdong University of Petrochemical Technology Maoming China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8608-1977","authenticated-orcid":false,"given":"Jinbiao","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics Central South University Changsha China"}]}],"member":"311","published-online":{"date-parts":[[2025,5,12]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/qre.2387"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.1080\/16843703.2023.2193771"},{"key":"e_1_2_10_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2023.3276904"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2019.03.014"},{"key":"e_1_2_10_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.probengmech.2023.103523"},{"key":"e_1_2_10_7_1","doi-asserted-by":"publisher","DOI":"10.1108\/BEPAM\u201011\u20102011\u20100027"},{"key":"e_1_2_10_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/qre.2214"},{"key":"e_1_2_10_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.compchemeng.2020.106876"},{"key":"e_1_2_10_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2013.05.019"},{"key":"e_1_2_10_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2012.10.013"},{"key":"e_1_2_10_12_1","doi-asserted-by":"publisher","DOI":"10.1080\/16843703.2022.2071526"},{"key":"e_1_2_10_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2023.109121"},{"key":"e_1_2_10_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0951-8320(02)00022-4"},{"key":"e_1_2_10_15_1","doi-asserted-by":"publisher","DOI":"10.1109\/24.229504"},{"key":"e_1_2_10_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0951-8320(00)00066-1"},{"key":"e_1_2_10_17_1","volume-title":"Statistical Methods for Reliability Data","author":"Meeker W. 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