Optimum Accelerated Life Tests with a Nonconstant Scale Parameter

Previous work on planning accelerated life tests has assumed that the scale parameter σ for a location-scale distribution of log lifetime remains constant over all stress levels. This assumption is, however, inappropriate for many applications, including accelerated tests for metal fatigue and certain electronic components. This article extends the existing maximum likelihood theory for test planning to the nonconstant σ model and presents test plans for a large range of practical testing situations. The test plans are optimum in that they minimize the asymptotic variance of the maximum likelihood estimator of a specified quantile at the design stress. The development and discussion in the article, as well as the theory given in the Appendix, applies to accelerated-life-test models in which the log time-to-failure can be modeled as a location-scale distribution. The test setup assumes simultaneous testing of units with time censoring. We give particular numerical results for the Weibull failure-time distribution.