A geometric process equivalent model for a multistate degenerative system

In this paper, a monotone process model for a one-component degenerative system with k+l states (k failure states and one working state) is studied. We show that this model is equivalent to a geometric process model for a two-state one component system such that both systems have the same long-run average cost per unit time and the same optimal policy. Furthermore, an explicit expression for the determination of an optimal policy is derived.