Availability of a v-out-of-m+r:G System

State equations are derived for the steady-state probability of degraded or failed state in a continuously operating system consisting of m similar units with k spares, and r service facilities, in which failure is defined to be less than v units in active operation; v = 1, 2, ..., m. Spares are considered to be either hot or cold. Transition rates are constant. By solving the state equations, system availability and unavailability are obtained under the condition of r service facilities; r = 1, 2, ..., m + k.