Nonparametric estimation for accelerated life tests under intermittent inspection

Abstract

This thesis is concerned with nonparametric estimation of lifetime distribution at use condition stress based on grouped data from constant, step, and progressive stress accelerated life tests(ALTs) under intermittent inspection in which test items are inspected only at specified points in time. It is assumed that the time transformation function (TTF) between lifetime and stress is a version of inverse power law and the cumulative exposure(CE) model for step and progressive stress holds. This thesis consists of the following three parts. (i) Nonparametric estimation of lifetime distribution at use condition for constant stress ALTs under intermittent inspection is considered. Under the assumption that all failures in the inspection interval occur at the midpoint of that interval, a nonparametric estimator of the lifetime distribution at use condition stress is proposed. The estimation method is also extended to the cases of other TTFs and progressive censoring. Numerical comparisons with the estimators based on the maximum likelihood(ML) and existing nonparametric methods for continuous inspection are made when the true lifetime distribution is Weibull. (ii) Nonparametric estimation for step stress ALTs under intermittent inspection is considered. Under the assumption that a CE model holds for the effects of changing stress, three methods of estimating the lifetime distribution at use condition stress are proposed for the cases where all failures in the inspection interval occur at the midpoint of that interval or occur uniformly within that interval. The estimation method is also extended to the case of progressive censoring. The proposed and ML estimators are numerically compared when the true lifetime distribution is Weibull. (iii) Nonparametric estimation for ramp stress tests under intermittent inspection is considered. Under the assumption of the CE model, two methods of estimating the lifetime distribution at use condition stress are proposed for the c...