AbstractA 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 timeskT(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 theith minimal repair of the component at ageydepends on the random partC(y) and the deterministic partCi(y). The aim of the paper is to find the optimal block intervalTwhich minimizes the long-run expected cost per unit time of the policy.