Abstract
The present paper studies a cold standby repairable system consisting of two identical components namely component 1, component 2 and onerepairman is studied. Assume that each component after repair is not 'as good as new' and also the successive working times form a decreasing a-series process, the successive repair time's form an increasing geometric process and both the processes are exposing to exponential failure law. Under these assumptions we study an optimal replacement policy N in which we replace the system when the number of failures of component 1 reaches N. It can be determined that an optimal repair replacement policy N* such that the long run average cost per unit time is minimized. It can also be derived an explicit expression of the long-run average cost and the corresponding optimal replacement policy N* can be determined analytically. Numerical results are provided to support the theoretical results
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