Optimum Allocation Rule for Accelerated Degradation Tests with a Class of Exponential-Dispersion Degradation Models
Optimum allocation problem in accelerated degradation tests (ADTs) is an important task for reliability analysts. Several researchers have attempted to address this decision problem, but their results have been based only on specific degradation models. Therefore, they lack a unified approach toward general degradation models. This study proposes a class of exponential-dispersion (ED) degradation models to overcome this difficulty. Assuming that the underlying degradation path comes from the ED class, we analytically derive the optimum allocation rules (by minimizing the asymptotic variance of the estimated q quantile of product's lifetime) for 2-level and 3-level ADT allocation problems whether the testing stress levels are pre-fixed or not. For a 3-level allocation problem, we show that all test units should be allocated into two out of three stresses, depending on certain specific conditions. Two examples are used to illustrate the proposed procedure. Furthermore, the penalties of using non-optimum allocation rules are also addressed. This study demonstrates that a 3-level compromise plan with small proportion allocation in the middle stress, in general, is a good strategy for ADT allocation.