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To relieve this problem, we introduce a new failure time model designed to describe and predict time\u2010to\u2010failure data in a complex system, which may involve subjects with either single or double\u2010independent failure modes. The resultant methodology is a hybrid of the Chen and exponential power models, yielding the so\u2010called additive Chen\u2010exponential power (ACEP) model. Its failure rate function can be monotone and bathtub curve with or without a long flat (useful) region. Parameter inference is carried out using both classical and Bayesian approaches. In Bayesian approach, Hamiltonian Monte Carlo (HMC) technique is chosen for its insensitivity to correlated parameters and robust parameter estimation. A comprehensive simulation study employing Markov chain Monte Carlo (MCMC) demonstrates the ACEP estimator's consistent and reliable performance at distinct parameter values. The ACEP model's flexibility is demonstrated through its applications to two non\u2010monotone reliability datasets, which exhibit bathtub failure and one monotone data with increasing failure pattern. We found that the model demonstrates high accuracy in analyzing and describing failure behavior of the study datasets, outperforming the competing candidates and could serve as their reliable alternative.<\/jats:p>","DOI":"10.1002\/qre.3821","type":"journal-article","created":{"date-parts":[[2025,6,12]],"date-time":"2025-06-12T13:59:46Z","timestamp":1749736786000},"page":"2974-2996","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Robust Failure Time Model With Bayesian Inference and Its Application to Reliability Analysis"],"prefix":"10.1002","volume":"41","author":[{"given":"Usman Aliyu","family":"Abdullahi","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics Central South University Changsha China"},{"name":"Department of Statistics Aliko Dangote University of Science and Technology Wudil Nigeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8209-3439","authenticated-orcid":false,"given":"Yuanyuan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics Central South University Changsha China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yimo","family":"Qin","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics Central South University Changsha China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,6,12]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1177\/1748006X20929972"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/TR.2024.3448289"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ress.2011.12.013"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1177\/1748006X20952575"},{"key":"e_1_2_8_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/TR.1987.5222310"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/TR.2001.874943"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1002\/qre.3255"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610926.2014.997357"},{"key":"e_1_2_8_10_1","first-page":"16","article-title":"Survival Analysis: Techniques for Censored and Truncated Data","volume":"1230","author":"Klein J. 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