Optimal burn-in policies for multiple dependent degradation processes

Abstract

Many complex engineering devices experience multiple dependent degradation processes. For each degradation process, there may exist substantial unit-to-unit heterogeneity. In this article, we describe the dependence structure among multiple dependent degradation processes using copulas and model unit-level heterogeneity as random effects. A two-stage estimation method is developed for statistical inference of multiple dependent degradation processes with random effects. To reduce the heterogeneity, we propose two degradation-based burn-in models, one with a single screening point and the other with multiple screening points. At each screening point, a unit is scrapped if one or more degradation levels pass their respective burn-in thresholds. Efficient algorithms are devised to find optimal burn-in decisions. We illustrate the proposed models using experimental data from light-emitting diode lamps. Impacts of parameter uncertainties on optimal burn-in decisions are investigated. Our results show that ignoring multiple dependent degradation processes can cause inferior system performance, such as increased total costs. Moreover, a higher level of dependence among multiple degradation processes often leads to longer burn-in time and higher burn-in thresholds for the two burn-in models. For the multiple-screening-point model, a higher level of dependence can also result in fewer screening points. Our results also show that burn-in with multiple screening points can lead to potential cost savings.

Keywords:

• Degradation-based burn-in
• multiple screening points
• multiple dependent degradation processes
• copulas
• two-stage estimation method

Additional information

Funding

This work was supported in part by the U.S. National Science Foundation under Award 1855408.

Notes on contributors

Yue Shi

Yue Shi is a PhD student in Department of Industrial, Manufacturing & Systems Engineering at Texas Tech University. She received her BS degree in Ecommerce from Guangdong University of Foreign Studies, China and MS degree in management science and engineering from Sun Yat-sen University, China. Her research interests include decision-making under uncertainty, maintenance optimization, and multivariate degradation modeling. She is a student member of INFORMS.

Yisha Xiang

Dr. Yisha Xiang is an assistant professor in the Department of Industrial, Manufacturing & Systems Engineering at Texas Tech University. Her current research and teaching interests involves reliability modeling and optimization, maintenance optimization, and decision-making under uncertainty. Her research has been funded by the National Science Foundation (NSF), including a CAREER grant, and industry. She has published articles in refereed journals, such as INFORMS Journal on Computing, IISE Transactions, European Journal of Operational Research, and IEEE Transactions on Reliability. She was the recipient of the Ralph A. Evans/P.K. McElroy Award for the best paper at the 2013 Reliability and Maintainability Symposium, and Stan Oftshun Best Paper Award from Society of Reliability Engineers in 2013 and 2017. She received her BS in industrial engineering from Nanjing University of Aero. & Astro., China, and MS and PhD in industrial engineering from University of Arkansas. She is an associate editor for IEEE Transactions Automation Science and Engineering, and she is a member of IISE and INFORMS.

Ying Liao

Ying Liao is a PhD student in Department of Industrial, Manufacturing & Systems Engineering at Texas Tech University. She received her BS and MS in statistics from Sun Yat-sen University, China. Her research interest includes reliability modeling, statistical machine learning, and Bayesian analysis. She is a student member of INFORMS.

Zhicheng Zhu

Zhicheng Zhu is a PhD candidate in Department of Industrial, Manufacturing & Systems Engineering at Texas Tech University. He received his BS and MS in electrical engineering from Sun Yat-sen University, China. His main research interests are maintenance optimization, decision-making under uncertainty, and reliability modeling. He is a student member of INFORMS.

Yili Hong

Yili Hong received his PhD in statistics from Iowa State University in 2009. He is professor of statistics at Virginia Tech. His research interests include machine learning and engineering applications, reliability analysis, and spatial statistics. He has more than 90 publications in publications such as Journal of the American Statistical Association, Annals of Applied Statistics, Technometrics, and IEEE Transactions on Reliability. He is currently an associate editor for Technometrics and Journal of Quality Technology. He is an elected member of International Statistical Institute. He won the 2011 DuPont Young Professor Award, and the 2016 Frank Wilcoxon Prize in statistics.