Optimal designs of progressive stress accelerated life tests for exponential and weibull distributions

Abstract

This thesis is concerned with the optimal designs of progressive stress accelerated life tests (ALTs) for items with exponentially and Weibull distributed lives under time and stress censoring. It consists of the following three parts. (i) The optimal designs of progressive stress ALTs under time censoring for items whose lives follow a Weibull distribution are considered. It is assumed that the inverse power law holds between the Weibull scale parameter and stress, and the cumulative exposure (CE) model for the effect of changing stress applies. The optimum plans - low stress rate and proportion of test units allocated to low stress mode - are found which minimize the asymptotic variance of the maximum likelihood estimator (MLE) of the log 100qth percentile at design stress. For selected values of the design parameters these optimum plans are tabulated, and the effect of preestimates is studied. For the case of no censoring optimum plans are obtained analytically. (ii) The optimal designs of progressive stress ALTs under time and stress censoring for items with exponentially distributed lives are considered. It is assumed that the inverse power law holds between mean life and stress. The optimum plans - ramp rate - are found which minimize the asymptotic variance of the MLE of the log mean life at design stress. The optimal plans are developed for the following four cases: 1) without time and stress censoring, 2) with stress censoring only, 3) with time censoring only, and 4) with time and stress censoring. For the first case the optimal ramp rate is obtained analytically. For the second case the optimal ramp rate can be obtained as solution of a nonlinear equation. For cases of 3) and 4) nomographs useful for finding optimum plans are provided. (iii) The progressive stress ALTs under time and stress censoring for items whose lives follow a Weibull distribution are designed. It is assumed that the inverse power law holds between the Weibull scale parameter and...