Step-stress accelerated degradation test planning based on Wiener process with correlation

To assess the lifetime distribution of highly reliable or expensive product, one of the most commonly used strategies is to construct step-stress accelerated degradation test (SSADT) which can curtail the test duration and reduce the test cost. In reality, it is not unusual for a unit with a higher degradation rate which exhibits a more volatile degradation path. Recently, Ye, Chen, and Shen [(2015). A new class of Wiener process models for degradation analysis. Reliability Engineering and System Safety, 139, 58–67] proposed a Wiener process to capture the positive correlation between the drift rate and the volatility. In this paper, an optimal SSADT plan is developed under the assumption that the underlying degradation path follows the Wiener process with correlation. Firstly, the stochastic diffusion process is introduced to model a typical SSADT problem. Then the design variables, including the sample size, the measurement frequency and the numbers of measurements under each stress level, are optimised by minimising the asymptotic variance of the estimated p-percentile of the product's lifetime distribution subject to the total experimental cost not exceeding a pre-specified budget. Finally, a numerical example is presented to illustrate the proposed method.