基于维纳过程步进应力加速退化试验的客观贝叶斯分析

Objective Bayesian Analysis for Step-Stress Accelerated Degradation Test Based on Wiener Process Models

高可靠性产品在加速寿命试验中其失效数据经常比较少,利用步进应力加速退化试验来评估产品寿命分布是一种非常好的方法.本文基于维纳过程的步进应力加速退化试验模型利用客观贝叶斯方法获得了其模型参数的无信息先验(Jefferys先验和Reference先验).并证明了对应的后验分布都是正常的.对于Jefferys先验和Reference先验下的后验提出相应的Gibbs抽样算法.最后,我们模拟对比了客观贝叶斯估计、贝叶斯估计和极大似然估计,模拟结果揭示了客观贝叶斯方法的优良性.

Step-stress accelerated degradation test(SSADT) is a useful tool for assessing the lifetime distribution of highly reliable products when the available test items are very few.In this paper,we discuss multiple-steps step-stress accelerated degradation models based on Wiener process,and we apply the objective Bayesian method for such analytically intractable models to obtain the noninformative priors(Jefferys prior and two Reference priors).Moreover,we show that their posterior distributions are proper,and we propose Gibbs sampling algorithms for the Bayesian inference based on the Jefferys prior and two Reference priors.Finally,we present some simulation studies to compare the objective Bayesian estimates with the other Bayesian estimate and the maximum likelihood estimates(MLEs).Simulation results demonstrate the superiority of objective Bayesian analysis method.