Optimal Designs and Inspection Time Decisions for Gamma Accelerated Degradation Tests

ABSTRACT This study analytically derives optimal designs for gamma accelerated degradation tests while incorporating inspection time as a design variable under both D‐ and V‐optimality criteria. Under D‐optimality, we prove that the optimal design allocates test units exclusively to the lowest and highest stress levels and adopts the longest inspection interval, resulting in only two test groups. In contrast, under V‐optimality, although test units are also allocated to the lowest and highest stress levels, the optimal inspection intervals may differ within the same stress level depending on the underlying model parameters, resulting in either two or three test groups. These results can also be applied to the optimal design for gamma‐accelerated destructive degradation tests. We further compared our proposed design with conventional V‐optimal designs that assume equal inspection intervals across all stress levels. The results demonstrate that conventional V‐optimal designs may result in a significant loss of efficiency. Two illustrative examples, an accelerated destructive degradation test and an accelerated degradation test, are provided to demonstrate the practical implementation of the proposed methods and their effectiveness in improving estimation accuracy. Finally, a sensitivity analysis demonstrates that the proposed optimal designs are more robust than the conventional V‐optimal design.