双超参数无失效数据的E-Bayes可靠性分析

E-Bayes reliability analysis of double hyperparameters zero failure data

讨论了双超参数情形无失效数据问题.利用构造先验分布为含有双超参数的Beta分布情形的减函数,给出了2个超参数情形下失效概率pi=P(T<ti)的E-Bayes估计,并在此基础上考查了其可靠性指标.最后,利用最值定理与介值定理证明了其可靠性指标的合理性.结果表明:当si→∞时,E-Bayes估计方法与用多层Bayes方法所得可靠性指标趋于相等,计算较为简便.

The problem of double hyperparameters under zero failure data is studied.The prior distribution is constructed as a decreasing Beta function which contains double hyperparameters.Giving E-Bayes estimation of its failure probability pi=P（Tti）,we examine its reliability target.At last,the theorem of maximum and minimum value and intermediate value theorem are used for theoretical justification.The result indicates that as si→∞,reliability target is almost equivalent with this method and the hierarchical Bayes estimation method.The result shows that the method adopted here is feasible,reasonable and superior.