Optimum Step-stress Accelerated Degradation Test for Wiener Degradation Process under Constraints

Abstract

To quickly assess products’ reliability for subsequent managerial decisions, Accelerated Degradation Test (ADT) has been used to obtain reliability information in a timely manner. Step-Stress ADT (SSADT) is one of the most commonly used stress loadings for shortening test duration and reducing the required sample size. In order to make precise statistical inferences and improve the experimental efficiency, the optimum design of SSADT has been studied extensively recently. We have noticed that in many studies, although the objectives considered are quite different, empirical results have suggested that the optimum SSADT plan is actually a simple SSADT plan using only two stress levels. However, most of these results were obtained numerically on a case-by-case basis and lack theoretical justifications. In this paper, we provide proofs to show that, under the Wiener process model and some practical constraints, a multi-level SSADT plan will degenerate to a simple SSADT plan under many commonly used optimization criteria. A numerical example is presented to compare the efficiencies of the proposed optimum simple SSADT plans and a SSADT plan proposed by a previous study. In addition, a simulation study is conducted for investigating the efficiencies of the proposed SSADT plans when the sample size is small. Keywords: (I) Reliability, Accelerated Degradation Test, Step-Stress ADT, Wiener Process, Inverse Gaussian Distribution.