Optimizing two‐variable gamma accelerated degradation tests with a semi‐analytical approach

Abstract In this paper, we provide a semi‐analytical approach to determine the optimal designs for two‐variable gamma accelerated degradation tests under three criteria: ‐optimality, ‐optimality, and ‐optimality. We first use general equivalence theorem to prove that the optimal approximate designs only allocate test units at the four vertices of a rectangular design region, and the corresponding optimal proportion of total number of measurements at each stress level is derived. Next, we apply the concept of prescribed accuracy level and total experimental cost to further determine optimal integer designs. More specifically, a numerical approach is used to resolve the number of test units and number of measurements at each stress level. Finally, an example is presented to illustrate the proposed procedure and compare the efficiency of optimal designs under three optimal criteria.