The Asymptotic Stability of a System with Warm Standby and Common Cause Failure

Availability is an important index of repairable system. Both dynamic availability and steady availability of the system is investigated in this paper. To study the relationship between dynamic and steady availability, the paper shows that dynamic availability and steady availability of the system is existent and unique in this model. Furthermore, by the method of functional analysis, the paper shows that the dynamic availability of the system converge the steady availability as time tends to infinity. As a result, the asymptotic stability of the system is obtained.