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

Abstract

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 c i ( y). The mathematical model is defined and general analytical results are obtained.