Stochastic modeling of degradation branching processes

Abstract

Degradation branching is a common phenomenon in many real-life applications. The degradation of a location not only increases with time, but also propagates to other locations in the same system. While the degradation of an individual location has been studied extensively, research on degradation branching is sparse. In this paper, we develop a general stochastic degradation branching model that characterizes both the degradation growth and degradation propagation. The probabilistic properties of the general degradation branching processes are analyzed. Reliability metrics such as the mean time to failure, mean residual life, failure probability and others are also investigated. In particular, closed-form expressions for the expectation and variance of the degradation and selected reliability metrics are obtained when the time to branch follows an exponential distribution. The model is validated using actual crack growth data.

Keywords:

• Degradation branching processes
• reliability estimation
• failure time distribution
• expected degradation
• expected number of branches

Acknowledgments

The authors would like to thank the reviewers, the Associate Editor and the Editor for the detailed comments and valuable suggestions which lead to significant improvements of the paper. Special thanks to Dr. Ryan Sills from the Department of Materials Science and Engineering at Rutgers University for his inputs, comments and discussions throughout the revision of the paper.

Additional information

Notes on contributors

Changxi Wang

Changxi Wang received his BE and ME degrees in materials science and engineering from Harbin Institute of Technology, Harbin, China, in 2013 and 2015, respectively. He received his MS degree in industrial and systems engineering from Rutgers University, Piscataway, NJ, in 2020. He is currently a PhD candidate in the Department of Industrial and Systems Engineering, Rutgers University. He is the winner of the Data Challenge Award in 2019 IISE Annual Conference and a finalist in the QCRE Best Student Paper Competition in 2019 IISE Annual Conference and 2017 INFORMS New Jersey Chapter Student Contest Award. He is the receipient of Colgate Doctoral Fellowship Award. His research interests include reliability engineering, machine learning and stochastic modeling of degradation processes.

Elsayed A. Elsayed

Elsayed A. Elsayed is a Distinguished Professor in the Department of Industrial and Systems Engineering at Rutgers University, NJ. His research interests are in the areas of quality and reliability engineering and production planning and control. He is the author of Reliability Engineering (John Wiley & Sons, 2012). He is also the author and co-author of work published in IIE Transactions, IEEE Transactions and the International Journal of Production Research. His research has been funded by the DoD, FAA, NSF, and industry. He has been a consultant for the DoD, AT&T Bell Laboratories, IngersollRand, Johnson & Johnson, Personal Products, AT&T Communications, Ethicon, and other companies. He was the Editor-in-Chief of IIE Transactions and the Editor of IIE Transactions on Quality and Reliability Engineering. He is also an Editor for the International Journal of Reliability, Quality and Safety Engineering.