Extended block replacement policy with used item and general random minimal repair cost

Extended block replacement policy with used item is proposed and analyzed. Under such a policy, an operating system is preventively replaced by new ones at times kT (k=1, 2, 3,...) independently of the age and the state of the system. If systems fail in [(k–1)T, kT–δ), they are either replaced by new ones or minimally repaired, and if in [kT–δ, kT] they are either replaced by used ones or minimally repaired. The choice of these two possible actions is based on some random mechanism which is age-dependent. The cost of the i-th minimal repair of the system 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.