Bayesian optimum accelerated life test plans based on quantile regression

Abstract

Quantile regression has emerged as a significant extension of traditional linear models, and its appealing features, such as robustness, efficiency in the presence of censoring and flexibility of modeling stress-life relationship, have recently been recognized for analyzing accelerated life test data. Based on these merits, we present a method for planning accelerated life test in the quantile regression framework for better analysis of the ALT data. Bayesian D-optimality criterion based on accuracy of model parameters on a whole is used to find optimum test plans. We apply the criterion to accelerated life test planning for estimating a distribution quantile, and there is uncertainty as to which model best describes the lifetime distribution. Further, the proposed method is able to handle non-constant scale parameter models. General equivalence theorem is used to verify the global optimality of the numerically optimized ALT plan.