Optimal Imperfect Maintenance in a Multi-state System with Two Failure Types

In this research, we are concerned with the modeling of optimal maintenance actions in multi-state systems with two failure types. We consider an imperfect maintenance model, that is, the impact of a preventive maintenance action is not minimal (as bad as old) and not perfect (as good as new) but lies between these boundary cases. Further, we assume that the costs of maintenance depend on the degree of repair. If a failure occurs, the system is maintained according to the failure type. Minor failures (type I) are removed through minimal repair and after major failures the system have to be replaced. Cost optimal maintenance policies for some cost functions and different discrete lifetime distributions are considered.