Objective Bayesian analysis for competing risks model with Wiener degradation phenomena and catastrophic failures

• Published in: Applied Mathematical Modelling Vol. 74; pp. 422 - 440
• Main Authors: Guan, Qiang, Tang, Yincai, Xu, Ancha
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.10.2019; Elsevier BV
• Subjects: Algorithms; Bayesian analysis; Catastrophic failure analysis; Competing risks model; Computer simulation; Degradation; Monte Carlo simulation; Objective Bayesian; Reference prior; Reliability; Statistical inference; Weibull distribution; Wiener degradation process; Objective Bayesian; Wiener degradation process; Competing risks model; Reliability; Reference prior
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2019.04.063

•Noninformative priors (Jefferys prior and two reference priors) for competing degradation failure model are proposed.•The noninformative priors are shown to have proper posterior distributions and probability matching properties.•Gibbs sampling algorithms for the Jeffreys prior and reference priors are proposed.•The advantages of our model have been illustrated by simulation and real data examples. In this paper, the objective Bayesian method is applied to investigate the competing risks model involving both catastrophic and degradation failures. By modeling soft failure as the Wiener degradation process, and hard failures as a Weibull distribution, we obtain the noninformative priors (Jefferys prior and two reference priors) for the parameters. Moreover, we show that their posterior distributions have good properties and we propose Gibbs sampling algorithms for the Bayesian inference based on the Jefferys prior and two reference priors. Some simulation studies are conducted to illustrate the superiority of objective Bayesian method. Finally, we apply our methods to two real data examples and compare the objective Bayesian estimates with the other estimates.