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

作　　者：管强 汤银才[2] GUAN Qiang;TANG Yincai(Institute of Information Engineering,Sanming University,Sanming,365004,China;School of Statistics,East China Normal University,Shanghai,200062,China)

机构地区：[1]三明学院信息工程学院,三明365004 [2]华东师范大学统计学院,上海200062

出　　处：《应用概率统计》2018年第6期613-629,共17页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金青年项目(批准号:11401341);国家自然科学基金项目(批准号:11271136;81530086);高等学校学科创新引智计划(批准号:B14019);福建省自然科学基金项目(批准号:2015J05014;2016J01681);2015福建省高校杰出青年科研人才培育计划;2016福建省高校新世纪优秀人才项目(闽教科:[2016]23号);福建省科技厅项目(批准号:2017N0029);福建省教育厅项目(批准号:JK2014046);工业大数据分析及应用福建省高校重点实验室;数字福建工业能源大数据研究所;福建省农业物联网应用重点实验室和物联网应用福建省高校工程研究中心资助

摘　　要：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.

关 键 词：客观贝叶斯 步进应力加速退化试验 维纳过程 Reference先验 GIBBS抽样 

分 类 号：O213.2[理学—概率论与数理统计]