Optimal design for step-stress accelerated degradation tests

Today, many products are designed to function for a long period of time before they fail. For such highly-reliable products, collecting accelerated degradation test (ADT) data can provide useful reliability information. However, it usually requires a moderate sample size to implement an ADT. Hence, ADT is not applicable for assessing the lifetime distribution of a newly developed or very expensive product which only has a few available test units on hand. Recently, a step-stress ADT (SSADT) has been suggested in the literature to overcome the above difficulty. However, in designing an efficient SSADT experiment, the issue about how to choose the optimal settings of variables was not discussed, such as sample size, measurement frequency, and termination time. In this study, we first use a stochastic diffusion process to model a typical SSADT problem. Next, under the constraint that the total experimental cost does not exceed a predetermined budget, the optimal settings of these variables are obtained by minimizing the asymptotic variance of the estimated 100p^th percentile of the product´s lifetime distribution. Finally, an example is used to illustrate the proposed method.