Competing risks-based resilience approach for multi-state systems under multiple shocks

Effective measurement of system resilience provides a comprehensive understanding of the system's characteristics. However, little research has been devoted to the resilience of a technical system that is affected by both the degradation process of the system and the external shocks. In addition, existing studies have mainly evaluated the resilience of systems without considering competing risks, and rarely investigated the transient resilience evaluation subjected to the interaction of shocks and maintenance. In this paper, a new resilience model is proposed for the systems under competing risks. The paper first introduces a competing risk model to depict the failure modes of the single-component system, and then uses semi-Markov processes to describe the state transition process when the system suffers the attacks of multiple shocks. Then, according to the multi-state division of the system, the resistibility index, absorbability index and recoverability index are proposed and the overall resilience is then introduced. Considering that the system needs to meet the reliability requirement, constrained by limit budget for maintenance, a reliability and cost-based resilience model is proposed. Finally, the case of a radar system subjected to shocks of one type and multiple types of shocks is given to illustrate the concept developed in this paper.