竞争失效产品部分加速寿命试验的统计分析  

Statistical Analysis for Partially Accelerated Life Tests with Competing Causes of Failure

作　　者：师义民[1] 师小琳[2] Shi Yimin Shi Xiaolin(School of Nature and Applied Sciences, Northwestern Polytechnical University, Xi＇an 710072, China School of Electronic Engineering, Xi＇an University of Posts and Telecommunications, Xi＇an 710121, China)

机构地区：[1]西北工业大学理学院,陕西西安710072 [2]西安邮电大学电子工程学院,陕西西安710121

出　　处：《西北工业大学学报》2017年第1期109-115,共7页Journal of Northwestern Polytechnical University

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

摘　　要：基于加速寿命试验的失效数据对产品的寿命特征进行统计分析时,需要利用产品寿命和应力水平之间的关系即加速模型。但在工程实际中,加速模型不一定总是已知的,例如新研制的产品。针对这个问题,提出了一种利用部分加速寿命试验研究竞争失效产品寿命特征的统计分析方法。在逐步Ⅰ型混合截尾下,讨论Pareto分布竞争失效产品恒定应力部分加速寿命试验的统计分析问题。文中给出了未知参数和加速因子的极大估计(MLE)和贝叶斯估计(BE)。利用Bootstrap方法及贝叶斯理论分别获得了参数和加速因子的Bootstrap置信区间(Stud-t)、最高后验概率密度置信区间(HPD)。最后运用Monte Carlo方法对各种估计的平均相对误差(ARE)、均方误差(MSE)及参数的置信区间进行了模拟计算,并讨论了样本量和分配比例对估计精度的影响。结果表明:参数的MLE和BE的ARE和MSE均随样本量增大而减小;而参数BE的ARE和MSE均小于MLE的ARE和MSE;样本分配比例和2种估计所对应的ARE和MSE呈负相关关系;在相同的置信度下,参数的HPD置信区间的长度小于Stud-t置信区间的长度。Based on the failure data of accelerated life test to analyze the life characteristics of product, we need to use the relationship between product life and stress levels, that acceleration model. But in engineering practice, the accelerated model is not always known, such as the newly developed products. In order to solve this problem, a sta- tistical analysis method is proposed to research the product llfe characteristics of competing failure based on the par- tially accelerated life test. Under Type-I progressive hybrid censoring, we discuss the statistical analysis for constant-stress partially accelerated life tests with competing failure modes and Pareto life data. The maximum like- lihood estimation and Bayesian estimation of unknown parameters and acceleration factor are obtained. By using the Bootstrap and Bayes method, the Bootstrap confidence interval （Stud-t） and the highest posterior probability confi- dence interval （HPD） are presented. Finally, we use the Monte Carlo method to carry out the calculation of the av- erage relative error（ARE） and the mean square error（MES） of various estimations and confidence interval of the unknown parameters. We analyze the influence of different sample sizes and distribution proportion on the accuracy of different estimation results. The calculation results, given in Table 1-Table 5, and their analysis show prelimina- rily that： （ 1 ） the AREs and the MESs of various estimations decrease with the samples size increase ; （2） the AR-Es and the MESs of the BE are less than that of the MLE ; （3） There is a negative correlation between the proportion of the sample distribution and the AREs and MSEs of two kinds estimates respectively; （4） at the same confi- dence level, the length of the HPD confidence interval for parameters less than that of the Stud-t confidence intervals.

关 键 词：竞争失效 PARETO分布 恒定应力部分加速寿命试验 统计分析 蒙特卡罗方法 平均相对误差 均方误差 极大似然估计 BAYES估计 平方损失函数 置信区间 

分 类 号：O213[理学—概率论与数理统计]