Dr. Qianmei Feng is a Professor and the Brij and Sunita Agrawal Faculty Fellow in the Department of Industrial Engineering at the University of Houston, Houston, Texas. She received a Ph.D. degree in Industrial Engineering from the University of Washington, Seattle, Washington, in 2005. Her research interests include the areas 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. She has published over 40 articles in refereed journals, such as IISE Transactions, IEEE Transactions on Reliability, Reliability Engineering and System Safety, Computers and Industrial Engineering, Journal of Operational Research Society, and Risk Analysis. Her research has been supported by the National Science Foundation, Department of Homeland Security, Texas Department of Transportation, and the Texas Higher Education Coordinating Board. She is a member of INFORMS, IIE, ASQ, and Alpha Pi Mu.
For engineering systems subjected to more than one complex degradation process with random shocks, the analysis of multiple degradation processes is a challenging problem in studying the reliability of the system. These degradation processes are typically dependent due to complicated internal and external conditions of the system. To integrally handle the jump uncertainties in degradation and the dependence among degradation processes, we construct multi-dimensional Lévy processes to describe multiple dependent degradation processes in engineering systems. The evolution of each degradation process can be modeled by a one-dimensional Lévy subordinator with a marginal Lévy measure, and the dependence among all dimensions can be described by Lévy copulas and the associated multi-dimensional Lévy measure. This Lévy measure is obtained from all its one-dimensional marginal Lévy measures and the Lévy copula. We use the Fokker-Planck equations to derive the Laplace transform of reliability function and lifetime moments. Numerical examples are used to demonstrate our models in lifetime analysis. The results demonstrate that our multi-dimensional Lévy subordinator model performs well and provides a general stochastic model to analyze degradation in reliability and lifetime analysis for a system that degrades over time.