Design of accelerated and partially accelerated life tests under exponential and lognormal lifetime distributions

Abstract

This thesis is concerned with optimal designs of partially accelerated life tests (PALT) and accelerated life tests (ALT) for exponential and lognormal lifetime distributions under Type I censoring. This thesis is divided into the following four parts. (i) For items having exponentially distributed lives, optimal designs of two PALTs in which test items are run at both accelerated and use conditions until a predetermined time are considered. One is the step PALT which allows the test to be changed from use to accelerated condition at a specified time, and the other is the constant PALT where each test item is run at either use or accelerated condition only. Maximum likelihood estimators (MLEs) of the hazard rate at use condition and the acceleration factor which is the ratio of the hazard rate at accelerated condition to that at use condition are obtained. The change time for the step PALT or the proportion of sample allocated to accelerated condition for the contant PALT is determined to minimize either the generalized asymptotic variance of MLEs of the acceleration factor and the hazard rate at use condition or the asymptotic variance of MLE of the acceleration factor. (ii) For items with lognormally distributed lives, optimal designs of step PALTs are considered. MLEs of the location and scale parameters of the lifetime distribution at use condition, and the acceleration factor which is the ratio of the mean life at use condition to that at accelerated condition are obtained. The change time is determined to minimize either the asymptotic variance of MLE of the acceleration factor or the generalized asymptotic variance of MLEs of the model parameters. (iii) Optimal designs are considered for simple constant stress ALTs in which two levels, low and high, of stress are constantly applied and the failed items are replaced with new items. For exponential distribution with mean life of a log-linear function of stress, MLE of the log mean life at design stress is ...