A new class of mechanism-equivalence-based Wiener process models for reliability analysis

Abstract

It is quite common to see that a unit of a product with a higher degradation rate also presents a more prominent dispersion. This phenomenon has motivated studies on developing new degradation models. In particular, a variety of Wiener process models have been developed by correlating the drift parameter and the diffusion parameter based on the statistical features of data. However, no insightful explanations are provided for such interesting correlations. In this article, degradation mechanism equivalence is first introduced based on the acceleration factor invariant principle, and the correlation between degradation rate and variation is explained using basic principles. Then, mechanism-equivalence-based Wiener process models, including a basic model and a random-effects model, are proposed to characterize such degradation behavior of a product. Analytical solutions for both point estimation and interval estimation of unknown model parameters are obtained using the maximum likelihood estimation method and an expectation–maximization algorithm. An extension of the proposed model that is able to handle accelerated degradation tests is developed. A simulation study and two real-world applications are provided to illustrate the effectiveness of the proposed models in product reliability estimation based on degradation data.

Keywords:

• Asymptotic variance
• degradation test
• mechanism equivalence
• Wiener process model
• random-effects

Acknowledgments

The authors are grateful to the editor, associate editor, and anonymous referees for many insightful suggestions that significantly improved the quality of this article.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [No. 52075020].

Notes on contributors

Han Wang

Han Wang received a PhD degree in systems engineering from Beihang University, Beijing, P.R. China, in 2020. He is currently a postdoctoral researcher with the School of Aeronautic Science and Engineering, Beihang University. His research interests include accelerated tests, stochastic degradation modelling, and remaining useful life prediction.

Haitao Liao

Haitao Liao received a PhD degree in industrial and systems engineering from Rutgers University, NJ, USA, in 2004. He is currently a professor, and John and Mary Lib White Endowed Systems Integration Chair with the Department of Industrial Engineering, University of Arkansas, Fayetteville, AR, USA. His current research interests include reliability and maintenance modelling, statistical models and data analysis, applied operations research, and probabilistic risk assessment. He is a Fellow of IISE.

Xiaobing Ma

Xiaobing Ma received a PhD degree in engineering mechanics from Beihang University, Beijing, P.R. China, in 2006. He is currently a professor with the School of Reliability and Systems Engineering, Beihang University. His current research interests include reliability data analysis, durability design, and system life modelling.

Rui Bao

Rui Bao received a PhD degree in solid mechanics from Beihang University, Beijing, P.R. China, in 2005. She is currently a professor with the School of Aeronautic Science and Engineering, Beihang University. Her research interests include aircraft structural fatigue, fracture mechanics, and durability design.

Yu Zhao

Yu Zhao received a PhD degree in systems engineering from Beihang University, Beijing, P.R. China, in 2005. He is currently a professor with the School of Reliability and Systems Engineering, Beihang University, where he is also the Associate Director of the Key Laboratory on Reliability and Environmental Engineering Technology. His current research interests include reliability engineering, quality management, and application of statistics techniques.