Bootstrap-based confidence intervals in partially accelerated life testing

Accelerated life testing (ALT) is utilized to estimate the underlying failure distribution and related parameters of interest in situations where the components under study are designed for long life and therefore will not yield failure data within a reasonable test period. In ALT, life testing is carried out under two or more higher than normal stress levels, with the resulting acceleration of the failure process yielding a sufficient amount of un-censored life-span data within a practical test duration. Usually one (or more) parameters of the life distribution is linked to the stress level through a suitably selected model based on a well-understood relationship. The estimate of this model is then utilized to determine the life distribution of the components under normal use (design use) conditions. Partially accelerated life testing (PALT) is preferable over accelerated life testing (ALT) in situations where such a model linking the stress to the distribution parameters is unavailable. In this study, parametric and nonparametric bootstrap based methods for obtaining confidence intervals for the parameters of the life distribution as well as a the lower confidence bound for the mean life under normal conditions are developed for both the Weibull and Generalized exponential life distributions under Type I censoring. Monte-Carlo simulation studies are carried out to study the performance of the confidence intervals based on the proposed methods against those of intervals obtained using the traditional delta method. Results show that the bootstrap-based methods performs as well as or better than asymptotic distribution-based methods in most cases --Abstract, page iii