Robust Bayesian Analysis, And System Reliability Evaluation

In the assessment of system reliability, Bayesian analysis is one of very important and effective method. Researches attracted more and more attention to the robustness of Bayesian analysis in the research of Bayes method. In this paper, we mainly discuss the robustness of Bayesian analysis and application of robust Bayes method in the assessment of system reliability.Firstly, by using the theory of the likelihood ratio test, a method of likelihood ratio test for choosing prior distributions and classes of prior distribution is given. We discuss several situations of simple hypothesis and complex ones. The simulate example indicates that the priors and classes chosen by this method are robust.Secondly, by comparing the distribution's tail behavior of prior distributions and likelihood distribution, a robust fusion method about priors is given when prior information comes from different sources. The paper also discusses the posterior robustness of the fusion prior distribution based on this method.Thirdly, under the Type- II censoring Life Test, problems of the Optimal robust Bayes estimation of Scale-Parameter for the Two-parameter Weibull distribution are discussed using the Γ-posterior expected loss as the criterion. When the shape-parameter β is known and unknown, the optimal robust point estimation and interval of 6 are obtained. Then, we discuss the robust Bayes estimation of dynamic parameters when the ML- II prior is given.Finally, we evaluate the reliability of serial-parallel system by using robust bayes method. The robust estimation— posterior Γ -minimax regret estimation of reliability index is given. The Γ -minimax regret rule is compatible with specified prior information, and it is usually robust over Γ.