We study asymptotic property of the solution of the model describing a repairable

standby human & machine system by using C0- semigroup theory.First we prove that all points on the imaginary axis except for zero belong to the resolvent set of the operator corresponding to the model

second prove that 0 is an eigenvalue of the operator and its adjoint operator with geometric multiplicity and algebraic multiplicity one

last by using theabove results we obtain that the time-dependent solution of the model strongly converges to the steady-state solution of the model.