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Abstract
In this paper, a shock model for the maintenance problem of a repairable system is studied. Assume that shocks will arrive according to a Poisson process. If the inter arrival time of two successive shocks is less than a threshold, then the system will fail. For an improving system, we assume that the successive threshold values are geometrically decreasing after repair, and the consecutive repair times after failure form a decreasing partial sum process. A replacement policy N is adopted by which we shall replace the system by an identical new one at the time following the N-thfailure. Then for an improving system, an optimal policy N^* for minimizing the long run average cost per unit time is determined explicitly.
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