Abstract
In some practical situations, most systems would degrade with time and suffer failure finally by both causes of additive and independent damages. From such a viewpoint, this paper considers replacement models for combining 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 at periodic times and increases approximately with time linearly. Using the techniques of cumulative processes in reliability theory, expected cost rates are obtained and optimal policies which minimize them are derived analytically. Finally, optimal policies are computed and compared numerically, and useful discussions for such results are done.
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