Design of accelerated life test sampling plans for lognormal and weibull distributions

Abstract

This thesis is concerned with the optimal design of life-test sampling plans based on accelerated life tests (ALTs) under failure-censoring or time-censoring. The lifetime distribution of products is assumed to be lognormal or Weibull with a location parameter of the log lifetime distribution that is a linear function of a (possibly transformed) stress. Two levels of stress higher than the use condition stress, high and low, are used. Optimum ALT sampling plans which satisfy the producer``s and consumer``s risk requirements are obtained. The properties of the proposed ALT sampling plans are investigated. This thesis is divided into the following four parts. (i) Optimal design of failure-censored ALT sampling plans (FALTSPs) is considered. It is assumed that the high and low stress levels are prespecified. Minimization of the generalized asymptotic variance of the maximum likelihood estimators (MLEs) of the model parameters is used as an optimality criterion. The optimum total sample size, sample proportion allocated to each stress level, and the lot acceptability constant are determined. (ii) Optimum design of FALTSPs under equal expected that time constraint is considered. It is assumed that only the high stress level is prespecified. Minimization of the asymptotic variance of the test statistic for deciding the lot acceptability is used as an optimality cirterion. The optimum total sample size, sample proportion allocated to each stress level, lot acceptability constant, and additionally low stress level are determined under equal expected test time constraint. (iii) Optimal design of time-censored ALT sampling plans are considered. Minimization of the asymptotic variance of the test statistic for deciding the lot acceptability is used as an optimality criterion. The optimum total sample size, low stress level, sample proportion allocated to each stress level, and lot acceptability constant are determined. (iv) Two alternative optimization criteria are consid...