Properties of Hierarchical Bayesian and E Bayesian Estimations of the Failure Probability in Zero-failure Data

It is diffcult to get the samples of the failure in a experiment for higher reliability productions,and its reliability parameter estimation involves the zero-failure data analysis.The Bayesian method is powerful for solving this problem.As we know,the hierarchical Bayesian estimation of a reliability parameter is an integral of Beta functions ratio.In this paper,an inequality about Beta functions ratio is induced,and an integral inequality of Beta functions ratio is established.We prove that the E Bayesian estimation of failure probability is asymptotic equal to its hierarchical Bayesian estimation in the zero-failure data,and give a sufficient condition on which the hierarchical Bayesian estimation of failure probability is less than the E Bayesian estimation.