Resilience modeling for discrete-time multi-state systems based on aggregated Markov chains

Large-scale critical infrastructures are frequently susceptible to natural disasters, resulting in substantial damage and structural destruction. This research endeavors to examine the performance of critical infrastructure amidst natural disasters by introducing a resilience model for multi-state systems under the threat of disasters based on Markov chains. A thorough analysis of resilience performance is undertaken across five dimensions, covering resistance, absorption, recovery, adaptation, and overall resilience. Taking into account attributes inherent during design and those acquired during service, two indices, inherent and acquired, are proposed for each dimension. Analytical expressions for these indices are obtained through the theory of aggregated stochastic processes, complemented by proposed simulation algorithms to validate the derived formulas. A case study involving waterworks infrastructure is suggested to validate the proposed models. The findings demonstrate that our framework can extensively outline changes in resilience indices affected by various factors, which provides valuable insights and guidance for both designers and users of critical infrastructures.