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

A condition-based maintenance modeling approach is proposed for a multi-state system under competing failures and imperfect repairs. The system experiences three states (normal, defective and failed) over its lifecycle. Two competing failure processes, i.e., natural degradation and external shocks, cause these state changes. If the system becomes defective, an imperfect repair is adopted to restore it to a normal state. Imperfect repairs addressing defects are mathematically characterized. Based on this, two system renewal scenarios and their occurrence probabilities are simulated and derived. The cost of downtime caused by hidden failures is then deduced. A maintenance model of the expected cost rate is constructed, and the optimal inspection period that minimizes the expected cost rate is determined. Finally, a numerical example verifies the correctness and effectiveness of the maintenance model.