Bayesian planning of optimal step-stress accelerated life test

Abstract

This study develops a Bayesian method for planning optimal step-stress accelerated life testing. The planning of optimal accelerated life testing has been the subjects of numerous studies. Most existing methods develop plans that reduce or minimize the asymptotic variance of the maximum likelihood estimator of a reliability measure of interest, e.g., a specified low percentile of the lifetime distribution at the normal operating condition. The maximum likelihood method requires knowledge of the precise values of the unknown model parameters, called “planning values.” In practice, un certainty in the “planning values” may exist, which makes the Bayesian approach an attractive alternative to the ma ximum likelihood method for designing optimal accelerated life testing plans. Based on experience with similar products, design specifications, and engineering judgment, a joint prior distribution for the model parameters is formulated to describe the uncertainty in the values of the model parameters. The optimal plan minimizes the preposterior Bayes variance of a specified low percentile of the lifetime distribution at the normal stress condition. Monte Carlo simulation algorithm involving Gibbs sampling is developed to find the optimal plan. This study applies the proposed method to design a simple step-stress accelerated life test with Type-I censoring and the Weibull life distribution. The Bayesian optimal plans are compared with the plan obtained by maximum likelihood method. Influence of sample size and prior distribution on the optimal plan is also investigated. Results indicate that the Bayesian approach has promising potential in the planning of reliability life testing when there is uncertainty in the precise values of the model parameters.