Optimum step-stress accelerated life test plans for log-location-scale distributions

This article presents new tools and methods for finding optimum step-stress accelerated life test plans. First, we present an approach to calculate the large-sample approximate variance of the maximum likelihood estimator of a quantile of the failure time distribution at use conditions from a step-stress accelerated life test. The approach allows for multistep stress changes and censoring for general log-location-scale distributions based on a cumulative exposure model. As an application of this approach, the optimum variance is studied as a function of shape parameter for both Weibull and lognormal distributions. Graphical comparisons among test plans using step-up, step-down, and constant-stress patterns are also presented. The results show that depending on the values of the model parameters and quantile of interest, each of the three test plans can be preferable in terms of optimum variance.