Stability of a general repairable human-machine system

Availability is an important index of repairable human-machine system. Both dynamic availability and steady availability of the system is investigated in this paper. To study the relationship between dynamic and steady availability, an integral-differential mathematical model is constructed. With this model, the paper shows that dynamic availability and steady availability of the system is existent and unique. 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. That is, such repairable human-machine system is asymptotic stability.