title: A stochastic hybrid systems based framework for modeling dependent failure processes.
abstract: In this paper, we develop a framework to model and analyze systems that are subject to dependent, competing degradation processes and random shocks. The degradation processes are described by stochastic differential equations, whereas transitions between the system discrete states are triggered by random shocks. The modeling is, then, based on Stochastic Hybrid Systems (SHS), whose state space is comprised of a continuous state determined by stochastic differential equations and a discrete state driven by stochastic transitions and reset maps. A set of differential equations are derived to characterize the conditional moments of the state variables. System reliability and its lower bounds are estimated from these conditional moments, using the First Order Second Moment (FOSM) method and Markov inequality, respectively. The developed framework is applied to model three dependent failure processes from literature and a comparison is made to Monte Carlo simulations. The results demonstrate that the developed framework is able to yield an accurate estimation of reliability with less computational costs compared to traditional Monte Carlo-based methods.
authors.affiliation: School of Reliability and Systems Engineering, Beihang University, Beijing, China.
authors.forename: Mengfei
authors.initials: M
authors.lastname: Fan
authors.affiliation: Chair System Science and the Energy Challenge, Fondation Electricité de France (EDF), CentraleSupélec, Université Paris Saclay, Chatenay-Malabry, France.
authors.forename: Zhiguo
authors.initials: Z
authors.lastname: Zeng
authors.affiliation: Chair System Science and the Energy Challenge, Fondation Electricité de France (EDF), CentraleSupélec, Université Paris Saclay, Chatenay-Malabry, France.|Energy Department, Politecnico di Milano, Milan, Italy.
authors.forename: Enrico
authors.initials: E
authors.lastname: Zio
authors.affiliation: School of Reliability and Systems Engineering, Beihang University, Beijing, China.
authors.forename: Rui
authors.initials: R
authors.lastname: Kang
authors.affiliation: School of Reliability and Systems Engineering, Beihang University, Beijing, China.
authors.forename: Ying
authors.initials: Y
authors.lastname: Chen
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D008962:Models, Theoretical; D009010:Monte Carlo Method; D015203:Reproducibility of Results; D013269:Stochastic Processes