Optimizing the Simple Step Stress Accelerated Life Test with Type I Censored Fréchet Data

Abstract

In this paper, we propose an optimization for the simple step stress accelerated life test for the Fr´echet distribution under type I censoring. The extreme value distribution has recently become increasingly important in engineering statistics as a suitable model to represent phenomena with extreme observations. One probability distribution, that is used to model the maximum extreme events, is the Fr´echet (extreme value type II) distribution. A log-linear relationship between the Fr´echet scale parameter and the stress are assumed. Furthermore, we model the effects of changing stress as a cumulative exposure function. The maximum likelihood estimators of the model parameters are derived. By minimizing the asymptotic variance of the desired life estimate and the reliability estimate, we obtain the optimal simple step stress accelerated life test. Finally, the simulation results are discussed to illustrate the effect of the initial estimates on the optimal values.