Planning of step-stress accelerated degradation test with stress optimization

For highly-reliable products, Accelerated Degradation Testing (ADT) data can provide useful reliability information. Moreover, Step-Stress Accelerated Degradation Testing (SSADT) usually requires a less sample size, shorter time and less cost than Constant-Stress Accelerated Degradation Testing (CSADT). However, in designing an efficient SSADT, the issue about how to choose accelerated stress level was seldom discussed. In this study, first we use drift Brownian motion to model a typical SSADT performance degradation process. Then, under the situation that total experiment cost is not given while the sample size, total test time and the interval of performance inspection are specified, our objective is to minimize the asymptotic variance of the estimation of the reliability of the p^th quantile of product's lifetime under use condition. Form the derivation of our objective, we find a way to improve the speed of optimal algorithm for SSADT. The optimal plan can give the stress levels and test time at each stress level. Finally a simulation example is used to illustrate the proposed method.