An adaptive two-stage Bayesian model averaging approach to planning and analyzing accelerated life tests under model uncertainty

Abstract

Accelerated life testing (ALT) is commonly used to predict the lifetime of a product at its use stress by subjecting test units to elevated stress conditions that accelerate the occurrence of failures. For new products, the selection of an acceleration model for planning optimal ALT plans is challenging due to the absence of historical lifetime data. The misspecification of an ALT model can lead to considerable errors when it is used to predict the product’s life quantiles. This article proposes a two-stage Bayesian approach to constructing ALT plans and predicting lifetime quantiles. At the first stage, the ALT plan is optimized based on the prior information of candidate models under a modified V-optimality criterion that incorporates both asymptotic prediction variance and squared bias. A Bayesian model averaging (BMA) framework is used to derive the posterior model and the posterior distribution for the life quantile of interest under use stress. If the obtained test data cannot provide satisfactory model selection results, an adaptive second-stage test is conducted based on the posterior information from the first stage. A revisited numerical example demonstrates the efficiency and robustness of the resulting Bayesian ALT plans by comparing with the plans derived from previous methods.