A sequential constant-stress accelerated life testing scheme and its Bayesian inference

Abstract

In the analysis of accelerated life testing (ALT) data, some stress-life model is typically used to relate results obtained at stressed conditions to those at use condition. For example, the Arrhenius model has been widely used for accelerated testing involving high temperature. Motivated by the fact that some prior knowledge of particular model parameters is usually available, this paper proposes a sequential constant-stress ALT scheme and its Bayesian inference. Under this scheme, test at the highest stress is firstly conducted to quickly generate failures. Then, using the proposed Bayesian inference method, information obtained at the highest stress is used to construct prior distributions for data analysis at lower stress levels. In this paper, two frameworks of the Bayesian inference method are presented, namely, the all-at-one prior distribution construction and the full sequential prior distribution construction. Assuming Weibull failure times, we (1) derive the closed-form expression for estimating the smallest extreme value location parameter at each stress level, (2) compare the performance of the proposed Bayesian inference with that of MLE by simulations, and (3) assess the risk of including empirical engineering knowledge into ALT data analysis under the proposed framework. Step-by-step illustrations of both frameworks are presented using a real-life ALT data set. Copyright © 2008 John Wiley & Sons, Ltd.