A production model with imperfect preventive maintenance

We study a production system subjected to a continuous deteriorating which can go "out-of-control" while producing items. Once out of control, the process produces a fixed proportion of defective items until the "out-of-control" state is restored by a scheduled maintenance. To operate the system economically, lot sizing and periodic maintenance of the process are needed. In this study, we assume that the life distribution of the system changes after each maintenance in such a way that its failure rate function increases with the number of maintenances carried out. Also, the restoration cost is assumed to be non-decreasing with the number of maintenance. The formula for the long-run expected average cost per unit time is obtained. The objective is to minimize the expected average cost so as to determine an optimal production and maintenance policy. A solution procedure is provided for the optimal policy. Several previous results are shown to be an extension of this study. To gain some insights, numerical examples are performed with various parameters combination is given.