Bayesian Reliability Analysis Under Uncertain Environments

There are two schools(Bayes school and classical school) in the internationalstatistics. The difference between statistics thoughts of the two schools is whether touse prior information or not. In the traditional Bayesian method, the parameter wasregarded as a random variable, and we can get the posterior distribution ofparameter by combining prior information and sample information. But when thereis not enough data for statistics. the parameter will be regard as uncertain randomset rather than random variable. This paper researches Bayesian estimation underuncertainty theory, and we defines the uncertain parameter as uncertain random setwhich has uncertain prior distribution, then created the uncertain Bayes pointestimator of system reliability. The main contents are as follows,The first part givesthe conception of uncertain real number set, and then discuss the approach touncertain estimation of uncertain parameter and uncertain Bayes point estimator.Thesecond part introduces a method to get the uncertain Bayes point estimator ofsystem reliability under uncertain environment.The third part we also provide thecomputational procedures to evaluate the membershipdegree of any Bayes pointestimate of system reliability.