A Tool for Evaluating Time-Varying-Stress Accelerated Life Test Plans With Log-Location-Scale Distributions

Abstract

Accelerated life tests (ALTs) are often used to make timely assessments of the lifetime distribution of materials and components. The goal of many ALTs is the estimation of a quantile of a log-location-scale failure time distribution. Much of the previous work on planning accelerated life tests has focused on deriving test-planning methods under a specific log-location-scale distribution. This paper presents a new approach for computing approximate large-sample variances of maximum likelihood estimators of a quantile of a general log-location-scale distribution with censoring, and time-varying stress. The approach is based on a cumulative exposure model. Using sample data from a published paper describing optimum ramp-stress test plans, we show that our approach and the one used in the previous work give the same variance-covariance matrix of the quantile estimator from the two different approaches. Then, as an application of this approach, we extend the previous work to a new optimum ramp-stress test plan obtained by simultaneously adjusting the ramp rate with the lower start level of stress. We find that the new optimum test plan can have a smaller variance than that of the optimum ramp-stress test plan previously obtained by adjusting only the ramp rate. We compare optimum ramp-stress test plans with the more commonly used constant-stress accelerated life test plans. We also conduct simulations to provide insight, and to check the adequacy of the large-sample approximate results obtained by the approach.