双应力恒加寿命试验下相依竞争失效模型的统计分析  

Statistical analysis of the dependent competing risks model under the double constant-stress accelerated life test

作　　者：王燕[1,2] 师义民[1] WANG Yan;SHI Yimin(School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710072, China;School of Science, Xi’an Polytechnic University, Xi’an 710048, China)

机构地区：[1]西北工业大学数学与统计学院,陕西西安710072 [2]西安工程大学理学院,陕西西安710048

出　　处：《系统工程与电子技术》2020年第11期2644-2653,共10页Systems Engineering and Electronics

基　　金：国家自然科学基金(71571144,71401134)资助课题。

摘　　要：针对传统加速寿命试验仅考虑单一应力且假定产品各失效机理之间独立的问题,首先结合自适应逐步Ⅱ型混合截尾(adaptive type-Ⅱ progressively hybrid censored scheme,AT-Ⅱ PHCS)寿命试验,建立AT-Ⅱ PHCS双应力恒加寿命试验。其次,利用Marshall-Olkin二维Gompertz (Marshall-Olkin bivariate Gompertz,MOBG)分布构建产品失效机理间相依关系。然后,基于AT-Ⅱ PHCS双应力加速寿命试验下相依竞争失效数据,利用极大似然理论,计算了参数的极大似然估计(maximum likelihood estimation,MLE),采用渐近似然理论和Bootstrap抽样方法构建参数的置信区间(confidence interval,CI)。最后,结合一个实例对构建的相依竞争失效模型进行了算例验证,结果表明其具有很好的统计推断性能。To solve problem that traditional accelerated life test only considers a single stress and assumes the competing risks indenpendce,firstly,the double constant-stress accelerated life test under adaptive Type-Ⅱ progressively hybrid censored scheme(AT-Ⅱ PHCS)is established.Secondly,the Marshall-Olkin bivariate Gompertz(MOBG)distribution is used to construct the dependence of the competing risks.Based on the dependent competing data under AT-Ⅱ PHCS double-stress accelerated life test,the maximum likelihood estimation(MLE)of the unknown parameters is obtained.The asymptotic likelihood theory and the Bootstrap sampling method are used to construct the confidence interval(CI)of the unknown parameters.Finally,an example is used to verify the constructed dependent competing risks model,and the results show that it has good statistical inference performance.

关 键 词：双应力恒加寿命试验 相依竞争失效模型 Marshall-Olkin二维Gompertz分布 极大似然估计 BOOTSTRAP方法 

分 类 号：O213.2[理学—概率论与数理统计]