无失效数据的一类迭代Bayes分析

A Kind of Iterative Bayes Analysis for Zero-Failure Data

对无失效数据分析中(0,ti]时间段上的失效概率pi(i=1,…,m),提出一种用m-1个pi的近似分布的混合分布修正pi先验分布的新方法,给出了一类失效概率的单层Bayes迭代估计和多层Bayes迭代估计.两种迭代方法被应用于液压泵数据分析.依照极大似然原则讨论了λm值的选取.对两种迭代方法的比较结果显示,在按似然原则对λm值选取的稳健性方面,多层Bayes迭代法优于单层Bayes迭代法,但多层Bayes迭代法需要更大的计算量.

As for the failure probabilities pi （i= 1, …, m） falling in （0, ti] in zero-failure data analysis, the paper presents a new method of amending the prior distribution of pi by using the hybrid distribution of m-1 approximate distributions of pi. One kind of monolayer Bayes iterative estimators and hierarchical Bayes iterative estimators for failure probabilities are given. The two iterative methods are applied to hydraulic pump data analysis. According to the maximum likelihood principle, the choice of λm values is discussed. By comparing the two iterative methods, the conclusion is obtained that the hierarchical Bayes iterative method is superior to the monolayer Bayes iterative method in terms of the robustness in the choices of λm value, but the hierarchical Bayes iterative method requires more calculations.