Maintenance Modeling for a Multi-State System Under Competing Failures and Imperfect Repairs

A condition-based maintenance modeling approach for a multi-state system under competing failures and imperfect repairs is proposed. The multi-state system will experience three states (normal, defective and failed) through its lifecycle caused by two competing failure processes, i.e., natural degradation and external shocks. If the system becomes defective, an imperfect repair is adopted to restore the system to a normal state. Firstly, imperfect repairs aimed at addressing defects are mathematically characterized, based on which two kinds of system renewal scenarios and corresponding occurrence probabilities are simulated and derived, respectively. Subsequently, the cost of downtime caused by hidden failures are deduced. Then, a maintenance model of the expected cost rate is constructed and the optimal inspection period that minimizes the expected cost rate is determined. Finally, the correctness and effectiveness of the constructed maintenance model are verified by a numerical example.