Optimal replacement and maintenance of systems subject to semi-Markov damage

A system is subject to damage, the damage process is assumed to be an increasing semi-Markov process. The system fails once the damage exceeds the capacity of the system. The system can be replaced before or at failure, and it is maintained continuously. The maintenance and non-failure costs are state dependent. The authors determine the optimal replacement policies, within the class of control limit policies, according to the total discounted and long-run average cost per unit time criterion.