Three Kinds of Replacement Models Combined with Additive and Independent Damages

Abstract In some practical situations, most systems would fail roughly with time by both causes of additive and independent damages. From such viewpoints, this paper considers three combined replacement policies with two kinds of damages: The unit is replaced at a planned time or when the total additive damage exceeds a failure level, whichever occurs first, and undergoes minimal repair when independent damage occurs. First, a standard cumulative damage model where the unit suffers some damage due to shocks and the total damage is additive is considered. Second, the total damage is measured only at periodic times. Third, the total damage approximately increases linearly with time t. Using the theory of cumulative processes, expected cost rates are obtained, and optimal policies which minimize them are derived analytically.