A generalization of the block replacement policy (BRP) is proposed and analysed. The new policy differs from the ordinary BRP in that at failure epochs the replacement of the failed unit is not mandatory and instead a minimal repair can be made. The choice between these two possible actions is based on the repair cost which is assumed to be random. Planned replacements are carried out at timeskT(k=1,2,3#x2026;.), like in the ordinary BRP, and the aim of the paper is to find the optimal block intervalTwhich minimizes the long run expected cost per unit time of the policy.
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