Planning Simple Step-Stress Accelerated Life Tests Using Bayesian Methods

Abstract

This study proposes Bayesian methods for planning optimal simple step-stress accelerated life tests. The Bayesian approach is an attractive alternative to the maximum likelihood method when there is uncertainty in the planning values of the model parameters. The uncertainty in the planning values is described by a joint prior distribution of the model parameters. The optimization criterion is defined as minimization of the pre-posterior variance of the logarithm of a quantile life at the normal stress condition. Two optimization algorithms, one based on Monte Carlo integration, and the other based on large-sample approximation, are developed to find the optimal plans. Nonparametric kernel smoothing technique is adopted in both algorithms to reduce the computational time. The proposed Bayesian approach is also extended to the design of three-level step-stress accelerated life tests. Effects of prior and sample size on the optimal plans are also investigated. Results indicate that both the prior, and the sample size affect the optimal Bayesian plans. And under certain conditions, the Bayesian approach, and the maximum likelihood approach provide very similar optimal plans.