An optimal replacement policy for a degenerative system with two-types of failure states

In this paper, a deteriorating simple repairable system with two-types of failure states, is studied. Assume that the system after repair cannot be as good as new, and the deterioration is stochastic. Under these assumptions, a new general monotone process model for the degenerative system is introduced which is a generalization of the αα-series process model. We use a replacement policy NN based on the failure number of the system, then our aim is to determine an optimal replacement policy N∗N∗ such that the average cost rate is minimized. We derive the optimal replacement policy analytically or numerically. Finally, we provide a numerical example, and carry through some discussions and sensitivity analysis of the model in this paper.