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.
Highlights
Data Availability Statement: All relevant data are within the paper
A MEMS device is subject to two dependent failure processes, i.e., soft failures caused by wear and debris from shock loads, and hard failures due to spring fracture caused by shock loads [20]
The soft failure is modeled by a continuous degradation process and the hard failure is modeled by a random shock process
Summary
For models that consider the dependencies between degradation and random shock processes, like these above, it is often too complicated, if not intractable, to evaluate system reliability analytically. Simulation methods, such as Monte Carlo methods [28], are used, often with limitations due to heavy computational burden. In this respect, Stochastic Hybrid Systems (SHS) [29] offer a new way to model the stochastic behavior of systems that involve both discrete and continuous states [30,31,32,33]. We choose SHS because the type of dependent degradation and shock processes allows for modeling by SHS and, in general, SHS has a better computational performance than SHA
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