逐步区间删失Weibull分布的Bayesian稳健设计

Bayesian Robust Design for the Weibull Distribution in the Presence of Progressive Interval Censoring

逐步区间删失是获取高可靠性产品相关信息的一种重要方法.文章研究了产品寿命服从Weibull分布,带有随机移除逐步区间删失寿命试验的最优设计问题.采用极大似然方法获取模型参数的估计及其信息矩阵.利用Bayesian方法处理模型参数未知情况下设计准则对模型参数的依赖问题,获得了模型参数估计的Bayesian稳健设计准则.在考虑试验费用有限制的条件下,给出了获得最优稳健设计非线性混合整数算法.同时对先验选取及约束参数设定的敏感性做了分析.数值结果表明文章提出的方法是有效可行的.

Progressive interval censoring is an important method in life testing to obtain information of the products with high reliability.In this paper,we investigate the optimal design problem for the Weibull distribution in the presence of progressive interval censoring with random removals.We use the method of maximum likelihood to derive the estimates of the unknown parameters and the Fisher information matrix.A Bayesian method is adopted to deal with the dependence of the design criteria on the unknown parameters in the model.Then Bayesian design criteria with cost constraint are given to derive the optimal test plan.An algorithm based on nonlinear mixed-integer programming is provided to the Bayesian optimal solution.The sensitivity of the optimal solution to changes of the given conditions is studied.Numerical results demonstrate the feasibility and efficiency of our proposed method.