The optimal replacement problem of a multistate deteriorate system with preventive maintenance

In this paper, a multistate deteriorate system with preventive repair is studied. Assume that the system has K different failure states. The work will be interrupted and the preventive repair will be executed as soon as the system reliability reaches an undetermined constant R. Our objective is to find the optimal policy such that the long-run expected cost per unit time is minimal. By using a bivariate replacement policy (R, N), the explicit expression of the long-run expected cost per unit time is derived. The corresponding optimal policy is provided numerically.