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

ABSTRACT

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.

KEYWORDS:

• Step-stress accelerated degradation test
• Wiener process
• correlation
• optimal test plan

Acknowledgements

The authors thank the associate editor and the referees for their constructive suggestions that greatly improved the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes on contributors

Lei He is a Ph.D candidate in the Department of Mathematics at Shanghai Normal University.

Rong-Xian Yue is a professor in Shanghai Normal University.

Daojiang He is a professor in Anhui Normal University.

Additional information

Funding

Rong-Xian Yue's research was supported by the National Natural Science Foundation of China [grant number 11471216]. Daojiang He's research was supported by the National Natural Science Foundation of China [grant number 11201005].