Two models of a system with a single activated unit which can be in a finite number of states are considered. The unit is subject to Markovian deterioration, and it is possible to replace it before its failure. Inspections of the system are carried out at discrete time instants. The only difference between the two models is when the replacements take effect — immediately at the instant when the corresponding decision is made, or with the next inspection. The paper shows that this difference is much more essential than one might expect, and proves a relation between the optimal replacement strategies in the models concerned.
