An Integrated Procedure for Bayesian Reliability Inference Using MCMC

The recent proliferation of Markov chain Monte Carlo (MCMC) approaches has led to the use of the Bayesian inference in a wide variety of fields. To facilitateMCMC applications, this paper proposes an integrated procedure for Bayesian inference usingMCMC methods, from a reliability perspective.The goal is to build a framework for related academic research and engineering applications to implementmodern computational-basedBayesian approaches, especially for reliability inferences.Theprocedure developed here is a continuous improvement process with four stages (Plan, Do, Study, and Action) and 11 steps, including: (1) data preparation; (2) prior inspection and integration; (3) prior selection; (4)model selection; (5) posterior sampling; (6)MCMCconvergence diagnostic; (7) Monte Carlo error diagnostic; (8) model improvement; (9) model comparison; (10) inference making; (11) data updating and inference improvement. The paper illustrates the proposed procedure using a case study.