Performance efficiency and cost analysis of multi-state systems with successive damage and maintenance in multiple shock events

Real-world systems are often exposed to shocks likes earthquakes and hurricanes during service life, and these shocks may occur multiple times. However, existing studies lack research on damage and maintenance interacting processes under multiple shocks. In this paper, a new performance efficiency and budget surplus rate model for multi-state systems is developed under the interaction of damage and maintenance. System performance efficiency measures the ability of the system to recover its performance from multiple shocks. The budget surplus rate model is introduced for measuring the system's ability to respond to losses from multiple shocks. Multiple cumulative shocks not only cause the system to transfer from a high-performance state to a low-performance state, but also accelerate the performance degradation of the system bringing successive damage, which is reflected by the reduced transition time between states. Markov processes are used to characterize the state transition process between the system suffering damage and maintenance under multiple shock events. A case study of a nuclear power plant is used to demonstrate the proposed methods. Sensitivity analysis of performance efficiency and budget surplus rate is also performed to reflect the shock resistance and maintenance capability of the nuclear power plant system.