Design of step-stress accelerated life tests for exponential and weibull distributions

Abstract

This thesis is concerned with the problem of optimally designing step-stress accelerated life tests (ALTs) for exponential and Weibull distributions. It consists of the following four parts. (i) The optimum simple step-stress ALTs are developed for Weibull distribution and Type I censoring. It is assumed that a log-linear relation exists between Weibull scale parameter and the stress, that Weibull shape parameter is constant and is independent of the stress, and that a certain cumulative exposure (CE) model holds for the effect of changing streass. The optimum test plan - low stress and stress change time - is obtained which minimizes the asymptotic variance of maximum likelihood estimator (MLE) of a stated percentile at design stress. For selected values of the design parameters, nomographs useful for finding the optimum plan are constructed, and the effects of errors in preestimates of the parameters and the behaviors of variance are investigated. (ii) The optimum simple step-stress ALTs for Weibull deitribution are compared with the corresponding constant stress ALTs in terms of relative efficiency, effects of design parameters, and robustness to preestimates of design parameters. (iii) Two compromise test plans using three stress levels are proposed as alternatives to the simple step-stress ALTs. One is the "best compromise plan" and the other is the "($\omega_1$ : $\omega_m$ : $\omega_2$) allocation plan". The best compromise plan uses the result of optimum simple step-stress ALT, and is determined by the proportion of test time allocated at middle stress. In a ($\omega_1$ : $\omega_m$ : $\omega_2$) appocation plan, the allocation scheme of test time at each stress level is prespecified, and low stress level which minimizes the asymptotic variance of MLE of a stated percentile at design stress is determined. Some practical guidelines useful for the compromise plans are given, and these plans are compared with the optimum simple step-stress test. (iv) The o...