Equivalent step-stress accelerated life tests with log-location-scale lifetime distributions under Type-I censoring

Abstract

Accelerated Life Testing (ALT) is used to provide timely estimates of a product's lifetime distribution. Step-Stress ALT (SSALT) is one of the most widely adopted stress loadings and the optimum design of a SSALT plan has been extensively studied. However, few research efforts have been devoted to establishing the theoretical rationale for using SSALT in lieu of other types of stress loadings. This article proves the existence of statistically equivalent SSALT plans that can provide equally precise estimates to those derived from any continuous stress loading for the log-location-scale lifetime distributions with Type-I censoring. That is, for any optimization criterion based on the Fisher information matrix, SSALT is identical in comparison to other continuous stress loadings. The Weibull and lognormal distributions are introduced as special cases. For these two distributions, the relationship among statistical equivalencies is investigated and it is shown that two equivalent ALT plans must be equivalent in terms of the strongest version of equivalency for many objective functions. A numerical example for a ramp-stress ALT, using data from an existing study on miniature lamps, is used to illustrate equivalent SSALT plans. Results show that SSALT is not only equivalent to the existing ramp-stress test plans but also more cost-effective in terms of the total test cost.