The Dependence of the Average Income of a System on Its Initial State

A system with one unit which can be in a finite number of states is considered. The system is inspected at discrete time instants. It is possible to replace the unit by a new one at these instants. The system is controlled by the rule: Replace a unit if and only if its state is worse than or equal to a given state. The paper deals with the effect of the initial state of the system upon the average total income achieved during a finite number of inspections.