Design of accelerated life test plans and statistical inferences under competing causes of failure

Abstract

This thesis is concerned with the problems of optimally designing accelerated life tests (ALTs) and making nonparametric inferences on lifetime distribution for products with competing risks. In design of ALTs, Weibull lifetime distribution of each potential failure cause and Type I censoring are considered. This thesis is divided into the following three parts. (i) Optimum simple constant stress ALT plans for products with competing risks are derived under Type I censoring. It is assumed that the lifetime distribution for each potential failure cause is Weibull with a scale parameter that is a log-linear function of a (possibly transformed) stress, that shape parameters of the lifetime distributions for all potential failure causes are independent of stress and are equal, and that the lifetimes for all potential failure causes are statistically independent. The optimum test plan - low stress level and sample proportion allocated to low stress - is obtained which minimizes the sum over all failure causes of the asymptotic variances of the maximum likelihood (ML) estimators of the specified quantile at design stress. For selected values of the design parameters, tables useful for finding optimum test plans are constructed, and the behaviors of optimum plans and the effects of competing risks on optimum plans are investigated. (ii) Optimum simple step stress ALT plans for products with competing risks under Type I censoring are derived. Additional to the assumptions of constant stress cases, a cumulative exposure (CE) model is assumed for the effect of changing stress. The optimum test plan - low stress level and stress changing time - is obtained under the same optimality criterion as constant stress ALT plan. For selected values of design parameters, tables useful for finding optimum plans are constructed, and the behaviors of optimum plans and the effects of competing risks on optimum test plans are investigated. (iii) Nonparametric estimation methods for ramp...