幂函数模型下恒加寿命试验的非参数贝叶斯分析  

Nonparametric Bayesian Analysis of the Constant Stress Accelerated Life Test with Power Function Model

作　　者：刘斌[1,2] 师义民[1] 蔡静[1] 王瑞兵[1] 

机构地区：[1]西北工业大学应用数学系,西安710129 [2]太原科技大学应用科学学院,太原030024

出　　处：《应用概率统计》2016年第6期617-631,共15页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金(71571144;71401134;71171164;70471057);陕西省自然科学基础研究计划项目(2015JM1003);陕西省国际科技合作与交流计划项目(2016KW-033)资助

摘　　要：线性加速模型常用于恒定应力加速寿命试验的统计分析,这与实际不完全相符.本文建立幂函数加速模型,给出了不同恒定加速应力水平间寿命分位数的关系,利用最小二乘法估计了加速模型的参数及特征标系数向量,从而实现不同应力水平间寿命数据的相互转换.采用Dirichlet过程先验,分别在完全数据情形和截尾数据情形下,得到可靠度函数的后验分布与非参数贝叶斯估计,并证明了后验估计的一致性.最后,通过一个金属氧化物半导体电容寿命实例说明了所建模型的效果.The linear accelerated model is often used to the statistical analysis of constant stress accelerated life test, whereas it does not relate well with the facts. By adopting the power functional accelerated model, the relationship of sample quantiles among different constant stress levels is obtained, which can lead to the estimations of the parameters in accelerated model and the characteristic coefficient vectors by virtue of the least square method, then the life-time data transformation between different stress levels can be operated. For complete data and censoring data, a Dirichlet process prior is introduced to gain the posterior distribution and the nonparametric Bayesian estimation of the reliability function, meanwhile, the consistency of the posterior estimators is proved. Finally, a real life example of Metal-Oxide-Semiconductor capacitors is analyzed to illustrate the effect of our model.

关 键 词：恒加试验 幂函数 非参数贝叶斯 Dirichlet过程 截尾数据 

分 类 号：O212.8[理学—概率论与数理统计]