Degradation in Common Dynamic Environments

Degradation studies are often used to assess reliability of products subject to degradation-induced soft failures. Because of limited test resources, several test subjects may have to share a test rig and have their degradation measured by the same operator. The common environments experienced by subjects in the same group introduce significant interindividual correlations in their degradation, which is known as the block effect. In the present article, the Wiener process is used to model product degradation, and the group-specific random environments are captured using a stochastic time scale. Both semiparametric and parametric estimation procedures are developed for the model. Maximum likelihood estimations of the model parameters for both the semiparametric and parametric models are obtained with the help of the EM algorithm. Performance of the maximum likelihood estimators is validated through large sample asymptotics and small sample simulations. The proposed models are illustrated by an application to lumen maintenance data of blue light-emitting diodes. Supplementary materials for this article are available online.

退化分析常被用于评估受退化诱发软失效影响的产品可靠性。由于试验资源有限，多个试验样品往往需共享一套试验台，并由同一操作人员完成退化量测量。同组试验样品所共有的试验环境，会在其退化过程中引入显著的个体间相关性，该效应被称为区组效应（block effect）。
本文采用维纳过程（Wiener process）对产品退化过程进行建模，并通过随机时间尺度刻画组特异性随机环境。针对该模型，本文分别推导了半参数与参数化两类估计流程。借助期望最大化（EM, Expectation-Maximization）算法，可求得半参数模型与参数化模型的模型参数极大似然估计量。通过大样本渐近性分析与小样本模拟试验，验证了极大似然估计量的统计性能。本文以蓝光发光二极管（blue light-emitting diodes, LEDs）的光通量维持率数据为例，对所提出的模型进行了演示说明。本文的补充材料可在线获取。