Planning of step-stress accelerated degradation test based on the inverse Gaussian process

Abstract

The step-stress accelerated degradation test (SSADT) is a useful tool for assessing the lifetime distribution of highly reliable or expensive product. Some efficient SSADT plans have been proposed when the underlying degradation follows the Wiener process or Gamma process. However, how to design an efficient SSADT plan for the inverse Gaussian (IG) process is still a problem to be solved. The aim of this paper is to provide an optimal SSADT plan for the IG degradation process. A cumulative exposure model for the SSADT is adopted, in which the product degradation path depends only on the current stress level and the degradation accumulated, and has nothing to do with the way of accumulation. Under the constraint of the total experimental budget, some design variables are optimized by minimizing the asymptotic variance of the estimated p-quantile of the lifetime distribution of the product. Finally, we use the proposed method to deal with the optimal SSADT design for a type of electrical connector based on a set of stress relaxation data. The sensitivity and stability of the SSADT plan are studied, and we find that the optimal test plan is quite robust for a moderate departure from the values of the parameters.