Resilience modeling for multi-state systems based on Markov processes

Modern systems are increasingly under the threaten of disruptive events like earthquakes, floods and storms. Under real life scenarios, multi-state models are often used to describe the behaviors of the system exposed to disruptive events. This article develops a comprehensive resilience modeling and quantifying framework for a multi-state system in which the evolution of the performance level over time is described by a time-homogeneous Markov process. In order to characterize the different dimensions of the system resilience, four types of resilience metrics are proposed to describe the resistant, absorption, recovery, and overall resilience, where each type is divided into an inherent resilience metric and an acquired resilience metric. The theory of aggregated stochastic processes is applied to derive explicit formulas for the four types of resilience metrics. Meanwhile, simulation-based algorithms are proposed to verify the correctness of analytical formulas. They are first exploited to the resilience analysis of a nuclear power plant under the threat of earthquakes, and then used in a numerical example to illustrate the applicability of the proposed method in dealing with the state space explosion problem. The results show that the developed resilience modeling and quantifying framework is able to comprehensively describe the resilience of multi-state systems threatened by disruptive events, and further, some practical suggestions are given to the designers and operators of the system based on the results.