A Two-Stage Latent Variable Estimation Procedure for Time-Censored Accelerated Degradation Tests

Abstract

Parallel constant-stress accelerated degradation testing (PCSADT) is widely used to assess the reliability of highly reliable products in a timely manner when the products’ degradation can be measured. Under a time-censored PCSADT, several groups of units are tested simultaneously, but under different stress levels, until a prespecified censoring time is reached. At this time, degradation values from the censored units, and failure times of the failed units are obtained. When the degradation follows a Wiener process where the parameters depend on the stress level through a life-stress model containing an unknown nuisance parameter, estimating this parameter often biases the maximum likelihood and least-squares estimators of the lifetime parameters. In this paper, we propose a two-stage procedure to address this problem. In the first stage, we transform the data under the different stress levels of a PCSADT so that the resulting data can be considered to have been obtained under normal stress. In the second stage, we introduce a latent variable for the unobserved degradation after the failure time for each failed unit to obtain a pseudodegradation value at the censoring time. We then use all degradation values (pseudo or observed) at the censoring time to develop latent variable estimators for all model parameters. Unlike other existing estimators, the proposed estimators are shown to be s-consistent, have closed-form expressions, and are easy to interpret. We use a real example of light-emitting diodes to illustrate the proposed method. In addition to proving s-consistencies, we conduct a simulation study to demonstrate that the proposed estimators also perform well in finite samples.