The Application Of Bayesian Theory In Reliability Analysis Of The Binomial Distribution

In this paper, when there has few samples or zero-failure data, we discuss the estimation of the binomial unit reliability in multi-sources of prior information with Bayesian, HB (Hierarchical Bayesian) and E Bayesian theories. Then we study the information entropy method for converting units' data into the equivalence test binomial data of system. And study the entropy method converting the varied environment binomial units' data into survival-failure data of system . The results from simulations show that the methods proposed in this paper are effective and reasonable. The main results are as following:Firstly, when prior information comes from different sources, we compare the non-information prior distribution, conjugate prior with mixed Beta prior distribution. And confirm inheritance factor with Kullback information method.Secondly, in the case of few sample and zero-failure data, we estimate unit reliability and confidence limit with the Hierarchical Bayesian estimation, E- Bayesian based on the mixed prior.Thirdly, discuss the entropy method of converting units' data into survival-failure data of system in zero-failure data. And study the entropy method converting the varied environment binomial units' data into survival-failure data of system .