E-Bayesian estimations of the reliability and its E-posterior risk under different loss functions

This paper studies the E-Bayesian estimations of the reliability and their E-posterior risk under different loss functions (including: squared error loss, weighted squared error loss, precautionary loss and K-loss) were derived under condition of binomial distribution. In the case of the one hyper parameter in order to measure the estimated risk, the definition of E-posterior risk (expected posterior risk)is proposed based on the definition of E-Bayesian estimation, and the formulas of E-Bayesian estimation and the formulas of E-posterior risk are developed, respectively. And an simulation example was given by using the Monte Carlo method. Finally, two practical problems were also performed to compare under different E-posterior risks (also using OpenBUGS). The results show that the proposed method is feasible and convenient for application.