无失效数据下失效概率的多层Bayes和E Bayes估计的性质  

Properties of Hierarchical Bayesian and E Bayesian Estimations of the Failure Probability in Zero-failure Data

作　　者：王建华[1,2] 袁力[2] 

机构地区：[1]华中科技大学数学与统计学院,武汉430074 [2]武汉理工大学理学院数学系,武汉430070

出　　处：《工程数学学报》2010年第1期78-84,共7页Chinese Journal of Engineering Mathematics

摘　　要：高可靠性产品的可靠性试验很难获得样品失效的数据,可靠性参数估计涉及无失效数据分析,Bayes方法是处理无失效数据分析的有力方法。多层Bayes参数估计涉及到Beta函数比的积分。利用Gamma函数比不等式,导出Beta函数比不等式及Beta函数比的积分不等式,证明了无失效数据下失效概率的EBayes估计与多层Bayes估计渐近相等,且给出多层Bayes估计值小于EBayes估计值的一个充分条件。It is difficult to get the samples of the failure in a experiment for higher reliability productions, and its reliability parameter estimation involves the zero-failure data analysis. The Bayesian method is powerful for solving this problem. As we know, the hierarchical Bayesian estimation of a reliability parameter is an integral of Beta functions ratio. In this paper, an inequality about Beta functions ratio is induced, and an integral inequality of Beta functions ratio is established. We prove that the E Bayesian estimation of failure probability is asymptotic equal to its hierarchical Bayesian estimation in the zero-failure data, and give a sufficient condition on which the hierarchical Bayesian estimation of failure probability is less than the E Bayesian estimation.

关 键 词：失效概率 E BAYES估计 多层BAYES估计 不等式 

分 类 号：O212.8[理学—概率论与数理统计]