失效概率的E-Bayes估计和E-MSE及其应用  

E-Bayesian Estimation and E-MSE of Failure Probability and Its Applications

作　　者：韩明[1] Han Ming(School of Science,Ningbo University of Technology,Zhejiang Ningbo 315211)

机构地区：[1]宁波工程学院理学院,浙江宁波315211

出　　处：《数学物理学报（A辑）》2022年第6期1790-1801,共12页Acta Mathematica Scientia

基　　金：宁波市自然科学基金(2019A610041)。

摘　　要：为了度量估计误差,该文在E-Bayes估计(expected Bayesian estimation)的基础上引入了E-MSE(expected mean square error)的定义,并推导不同损失函数(包括平方损失函数和LINEX损失函数)下失效概率的E-Bayes估计及其E-MSE的表达式.通过MonteCarlo模拟比较了所提出估计方法的性能(比较基于E-MSE).最后,分别采用E-Bayes方法和MCMC方法,结合发动机可靠性问题进行了计算和分析.在考虑评价不同损失函数下参数的E-Bayes估计时,该文提出用E-MSE作为评价标准.In order to measure the estimated error,this paper based on the E-Bayesian estimation(expected Bayesian estimation)introduced the definition of E-MSE(expected mean square error),and derive the expressions of E-Bayesian estimation of failure probability and their the E-MSE under different loss functions(including:squared error loss function and LINEX loss function).By Monte Carlo simulations compared with the performances of the proposed the estimation method(the comparison of the results is based on the E-MSE).Finally,combined with the engine reliability problem,used respectively E-Bayesian estimation method and the MCMC method the calculation and analysis are performed.When considering evaluating the E-Bayesian estimations under different loss functions,this paper proposed the E-posterior risk as an evaluation standard.

关 键 词：E-BAYES估计 E-MSE 失效概率 MONTE CARLO模拟 MCMC方法 

分 类 号：O213.2[理学—概率论与数理统计]