Minimax approach to accelerated life tests

Abstract

This article explores how the minimax approach to designing experiments applies to the Weibull and lognormal regression models used in accelerated life testing (ALT). When tackling these problems, the local optimal approach assumes the parameters in the information matrix known, while in the Bayes approach, prior distributions are imposed on them. By contrast, the minimax strategy searches for the design that minimizes the maximum of the optimality function criteria over the parameter region of interest. For an offshoot of the criterion based on minimizing the volume of the joint statistical-confidence region for the model parameters (D-optimality), the authors prove that the restricted minimax designs coincide with the local optimal designs at the 'lower left corner' of the parameter region. Extensive simulation shows that this phenomenon also holds for the criterion based on maximizing the precision of estimation of a prespecified quantile of the life distribution. Based on their findings, they recommend that the locally optimal designs be used, but for the most extreme set of feasible parameters instead of implementing them for the best guess for the parameters, as is usually done.