This paper proposes a maintenance model considering the Inherent availability of certain requirement and two types of failures, repairable or irrepairable. In this model, the system is replaced in time when it doesn't meet the inherent availability requirement despite of all repairable failures; Otherwise it is replaced by the first irrepairable failure. Assuming that the j-th failure is repairable with probability ^αi, minimal repairs are performed for repairable failures between replacements. We drive the expected cost rate through the application of NHPP(Non-Homogeneous Poisson Process) in order to determine the optimal number n*. The model includes some previous studies as special cases.