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

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.