Robust Designs of Step-Stress Accelerated Life Testing Experiments for Reliability

Abstract

In this article, we discuss the optimal and robust designs for accelerated life testing (ALT) when a step-stress plan is performed. It is assumed that time to failure of a product has a Weibull distribution with a log-linear life-stress relationship. We adopt a generalized Khamis-Higgins model for the effect of changing stress levels. Taking into account that the assumed life-stress relationship is possibly misspecified, we have derived the optimal stress changing time of the simple step-stress plans in order to minimize the asymptotic mean squared error of the maximum likelihood estimator for the reliability of a product at the normal use stress level and at a pre-specified time. The optimal 3-stepstress plans with minimum asymptotic squared bias are also discussed. Keywords: Two-step-stress Plans; Three-step-stress Plans; Fisher Information; Asymptotic Bias; Extrapolation; Model Misspecification; Reliability Estimation. 2010 Mathematics Subject Classification: 62K05; 62F35; 62J12