Optimal block replacement policies with multiple choice at failure

A generalization of the block replacement policy is proposed and analysed. Under such a policy, an operating system is preventively replaced at times kT (k=1,2,3,...), independently of its failure history. At failure an operating system is either replaced by a new or a used one or minimally repaired or remains inactive until the next planned replacement. The cost of the ith minimal repair of the new subsystem at age y depends on the random part C(y) and the deterministic part ci(y). The mathematical model is defined and general analytical results are obtained.