On optimal replacement policy

summary:A system with a single activated unit which can be in $k+1$ states is considered. Inspections of the system are carried out at discrete time instants. The process of deterioration of the unit is supposed to be Markovian. The unit by its operation brings an income which is monotonically dependent on its state. A replacement of the unit is associated with certain costs. The paper gives an effective algorithm for finding the replacement strategy maximizing the average income of the system per unit time. It requests to investigate not more than $\text{log}_2$ $k$ time-stationary replacement strategies