Modeling zoned shock effects on stochastic degradation in dependent failure processes

Abstract

This article studies a system that experiences two dependent competing failure processes, in which shocks are categorized into different shock zones. These two failure processes, a stochastic degradation process and a random shock process, are dependent because arriving shocks can cause instantaneous damage on the degradation process. In existing studies, every shock causes an abrupt damage on degradation. However, this may not be the case when shock loads are small and within the tolerance of system resistance. In the proposed model, only shock loads that are larger than a certain level are considered to cause abrupt damage on degradation, which makes this new model realistic and challenging. Shocks are divided into three zones based on their magnitudes: safety zone, damage zone, and fatal zone. The abrupt damage is modeled using an explicit function of shock load exceedances (differences between load magnitudes and a given threshold). Due to the complexity in modeling these two dependent stochastic failure processes, no closed form of the reliability function can be derived. Monte Carlo importance sampling is used to estimate the system reliability. Finally, two application examples with sensitivity analyses are presented to demonstrate the models.

Keywords:

• Gamma process
• peaks-over-threshold (PoT) method
• shock load exceedances
• truncated generalized Pareto distribution
• Monte Carlo importance sampling

Funding

This research article was based on work supported by the Texas Norman Hackerman Advanced Research Program under grant no. 003652-0122-2009 and by USA National Science Foundation under grants 0970140 and 0969423. The statements made herein are solely the responsibility of the authors.

Additional information

Notes on contributors

Lei Jiang

Lei Jiang received a Ph.D. degree in Industrial Engineering from the University of Houston, Houston, Texas, in 2014 and a B.S. degree in Mechanical Engineering from Huazhong University of Science and Technology, China, in 2010. Her research focuses on mathematical modeling of multiple dependent degradation processes and condition-based maintenance optimization for complex systems.

Qianmei Feng

Qianmei Feng is an Associate Professor and the Brij and Sunita Agrawal Faculty Fellow in the Department of Industrial Engineering at the University of Houston. She received a Ph.D. degree in Industrial Engineering from the University of Washington, Seattle, Washington in 2005. She has dedicated her research to the area of system modeling, analysis, and optimization in quality and reliability engineering, with applications in evolving technologies (e.g., MEMS, biomedical implant devices), homeland security, and healthcare. Her research has been supported by the NSF, Department of Homeland Security, Texas Department of Transportation, and Texas Higher Education Coordinating Board. She served as the president for the Division of Quality Control & Reliability Engineering in the Institute of Industrial Engineers 2009–2010. She is also a member of INFORMS, ASQ, and Alpha Pi Mu.

David W. Coit

David W. Coit is a Professor in the Department of Industrial & Systems Engineering at Rutgers University. He received a B.S. degree in Mechanical Engineering from Cornell University, an MBA from Rensselaer Polytechnic Institute, and M.S. and Ph.D. degrees in Industrial Engineering from the University of Pittsburgh. He also has over 10 years of experience working for IIT Research Institute (IITRI), Rome, New York (now called Alion Science and Technology), where he was a reliability analyst, project manager, and an engineering group manager. In 1999, he was awarded a CAREER grant from NSF to study reliability optimization. His current research involves reliability prediction and optimization, risk analysis, and multi-criteria optimization considering uncertainty. His research has been funded by the NSF, U.S. Navy, U.S. Army, power utilities, and industry. He is a member of IIE and INFORMS.