Abstract

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.

摘要

在可靠性工程中，研究可靠性参数估计的风险估计是一个重要问题。本文研究了不同先验分布下失效概率的E-贝叶斯估计及其E-后验风险。此外，分别得到了不同超参数先验分布下E-后验风险的解析表达式。进行蒙特卡罗模拟以比较所提出的估计方法的性能，结果在 E-后验风险和 MSE（均方误差）的基础上进行比较。最后，分别采用E-Bayesian估计法和MCMC法（同样采用OpenBUGS），结合航空发动机问题进行了计算分析。当考虑在超参数的不同先验分布下评估 E-贝叶斯估计时，