Expected Bayesian Estimation of Failure Rate and Its Character under Entropy Loss Function

The hierarchical Bayesian estimation of failure rate often relies on completed integral,so it's difficult to calculate.In this paper,the expected Bayesian estimation was defined,which is based on the Bayesian estimation.The failure rate is estimated after the prior distribution of super parameters was given.The formulas of the expected Bayesian estimation and the hierarchical Bayesian estimation of failure rate were given in condition of the certain super parameters,which indicates that the expected Bayesian estimation can effectively avoid the completed integral of the hierarchical Bayesian estimation,and the expected Bayesian estimation is more concise and more convenience to calculate.Finally,calculation is performed regarding to practical problem,which shows that the expected Bayesian estimation and the hierarchical Bayesian estimation are not only both steady but also approximate.As a conclusion,we get that the expected Bayesian estimation method is feasible and easier to operate.