Planning Accelerated Destructive Degradation Test with Block Effects

Abstract

An accelerated destructive degradation test (ADDT) offers an effective way to timely assess the reliability information of highly reliable products whose key performance characteristic can be measured only once. The grouping of samples in a reliability experiment introduces block effects to the data obtained, but the designing of an optimum plan with consideration of these effects is not sufficiently addressed in an ADDT. Motivated by one real application of the seal strength test, this study proposes models that deal with block effects and tackles the subsequent optimal design problems. Specifically, the block effects are identified as randomness from the environment, which manifest as the batch effects. We aim to minimize the large sample approximate variance of the estimated pth lifetime quantile at use condition by optimally choosing the stress levels, number of test run replications under each stress level and the number of samples measured at each predetermined test time within a test run. Theoretical results and numerical solutions are derived where feasible. A thoroughly investigated illustrative example reveals the necessity to consider the block effects in the optimal design, as the optimum plans as well as the objective values with and without block effects differ significantly.