Inference for acceleration transforms in stress testing with applications to models based on reliability kinetics.

Abstract

Life testing is a necessary step to assess life time distributions of materials and products. Since many highly reliable products last too long for laboratory testing, accelerated life testing (ALT) is commonly used to yield failures quickly, i.e., products are tested under stress levels higher than the use level. The traditional accelerated failure time model used in stress testing assumes that the life time distributions at different stress levels belong to a scale family. This model is adequate for some simple failure processes but has been found to be inappropriate in many applications. A more general class of acceleration transform models has been considered recently in the literature. Meeker and LuValle (1995) consider a particular application motivated by reliability kinetics and develop parametric inference for the acceleration transform function. In this research I consider two semiparametric methods, minimum-distance method and M-method, of inference for the acceleration transform and the base-line distribution without making any specific parametric assumptions about the shape of the distribution. Consistency and asymptotic normality of both estimators are studied. Both small-sample and asymptotic efficiencies are investigated for the two estimators under different accelerated life test models. Inference for the acceleration transform and model diagnostics are developed using asymptotic results and bootstrap methods.