A Markov Model for Production and Maintenance Decision

In this paper, we consider a production machine which may fail and it is necessary to repair the machine after each failure and there are two statuses for each repair; in one case, we should replace the machine because of catastrophic failure and in the other case, only small repairs are needed. Times between failures and repair and replace times are random and demands are satisfied by inventory during repairing and replacing the machine; shortage level is limited. We model described system as a Markov chain and develop an algorithm to compute the expected number of transitions among states.