Bayesian Survival Analysis Based On MCMC Method And Its Applications In Reliability

Quality is the topic of the day in the 21st century. As one of the pivotal taches for quality assurance, reliability considerations are playing a particularly important role. With the execution of "Integrated Product and Process Design (IPPD)", "6σmethod" and "Maintenance Free Operating Period (MFOP)", reliability considerations today are facing greater challenges than ever. It raises a higher requirement for reliability estimation methods simultaneity because of increased product complexity, increasingly inhospitable environment of operation, as well as the requirements of shortening the manufacturing period and reducing the cost. The goal of this thesis is to combine Bayesian theory and survival analysis with Markov Chain Monte Carlo (MCMC) method, by that the lifetime data in reliability trails will be analyzed.With the background that, nowadays the theory of Bayesian survival analysis was still developing and its application studies at present were mainly limited in clinic trails or biostatistics, firstly, the main logic flow for doing Bayesian reliability analysis with MCMC method was proposed in this thesis by discussing systematically the knowledge such as priors choosing, posterior sampling, convergence diagnosing, MC error, model comparative and the like. And then, with another background that, studies for the moment were mostly utilizing Bayesian analysis or survival analysis separately, the study with MCMC method here were applied to do reliability analysis including parameter models, semi-parameter models, frailty models and other unfamiliar models. What's more, the reliability trails and the environmental trails in which the trials had been done in wide variety of environments were integrated well.From the study perspective, the advantages both of Bayesian analysis and survival analysis for analyzing lifetime data in reliability trails were emerged coinstantaneous by synthetically applying the two methodologies. From the study approach, the difficulties of the high-dimension numerical integral had been resolved better by making use of MCMC with Gibbs sampler. From the study contents, the theory of reliability analysis had been substantiated which had based upon conjoining survival analysis and reliability theory, especially including the study on frailty factors and other unclassical survival models in reliability analysis.The following innovation works were included in this thesis: (1) The logic framework of doing reliability evaluation using Bayesian survival analysis with MCMC method was proposed.(2) The theory of Bayesian survival analysis was introduced to do analysis for lifetime data in reliability trails by the numbers, which had been showed concretely in:◆Several model structures were studied with framework for Bayesian analysis using MCMC method.◆The semi-parameter methods were utilized to decrease the limits for both model priors and hazard functions.◆"Cure rate fraction" for systems was introduced to exposure the existent of comparable "longevity" subsystems in some complex systems.◆The "two-phase hypothesis" for units' failure was proposed. Through that, the signification of "early failure change point" as well as its contribution for non-monotone hazard rate had been displayed.◆Frailty models with frailty factors were applied to describe those unknown and unmeasured random effects in reliability trails.The results were showed that: several problems in reliability analysis such as small sample, incomplete data, and complex running environments had been settled well; The theory of reliability analysis for small sample and for complex system was enriched based on Bayesian survival analysis; Also, the effectiveness and maneuverability had been improved by using MCMC method due to its powerful calculate capability.