A generalized block replacement policy with minimal repair and general random repair costs for a multi-unit system

A generalization of the block replacement policy (BRP) is proposed and analysed for a multi-unit system which has the specific multivariate distribution. Under such a policy an operating system is preventively replaced at times kT (k=1,2,3,...), as in the ordinary BRP, and the replacement of the failed system at failure is not mandatory; instead, a minimal repair to the component of the system can be made. The choice of these two possible actions is based on some random mechanism which is age-dependent. The cost of the ith minimal repair of the component at age y depends on the random part C(y) and the deterministic part ci(y). The aim of the paper is to find the optimal block interval T which minimizes the long-run expected cost per unit time of the policy.