Study on the effect of the different prior distributions on E-Bayesian estimation of failure probability and its E-posterior risk

In reliability engineering, study the estimated risk of reliability parameters estimation is an important problem. This paper studies the E-Bayesian estimations and their E-posterior risk of the failure probability under different prior distributions. Moreover, the analytical expressions of E-posterior risk under different prior distributions of hyper parameters are obtained respectively. Monte Carlo simulation is performed to compare the performances of the proposed method of estimation, results are compared on basis of E-posterior risk and MSE (mean square error). Finally, used respectively E-Bayesian estimation method and MCMC method (also using OpenBUGS), combined with the aero engine problem are performed to calculation and analysis. When consider evaluating the E-Bayesian estimations under different prior distributions of hyper parameters, this paper proposed the E-posterior risk as an evaluation standard in reliability engineering.