Resilience analysis of multi-state systems with time-dependent behaviors

Abstract

Most of existing resilience models assume that system performances are continuous. In this paper, we consider resilience modeling and analysis for multi-state systems, whose performances are characterized by discrete, rather than continuous variables. A non-homogeneous Semi-Markov reward process model is developed for resilience analysis of multi-state systems. In the developed model, system performance changes, caused by either disruptive events or system recoveries, are modeled as state transitions, and rewards are used to model financial losses incurred during and after the disruptions. Four resilience metrics are defined to quantify different aspects of resilience. As the developed model is non-homogeneous, it can capture time-dependent system behaviors and their impact on system resilience. An efficient resilience analysis algorithm is also designed based on linear interpolation and implemented using vectorization. The computational benefits of the developed algorithm are demonstrated through two numerical experiments. We apply the developed method on two practical case studies, an oil tank farm and a re-configurable computing system. The results show that the developed methods can quantify resilience of multi-state systems accurately and efficiently.