E-Bayesian estimation and E-posterior risk of failure probability under different loss functions and its applications in reliability analysis

This paper, based on the E-Bayesian estimation (expected Bayesian estimation), introduced the definition of E-posterior risk (expected posterior risk); we will derive the expressions of E-Bayesian estimation and their E-posterior risk for failure probability under the compound symmetric LINEX loss function, and will compare the results with the corresponding results under the square loss function. Monte Carlo simulations compared the performances of the proposed the estimation method, and compared the results on the basis of E-posterior risk. Finally, combined with the life testing data from a type of aero engine, the calculation and reliability analysis are performed, with E-Bayesian estimation and hierarchical Bayesian estimation, respectively (also using the MCMC method). When considering evaluating the E-Bayesian estimations under different loss functions, in this paper the E-posterior risk as an the evaluation standard is proposed.