The stability of the repairable system with three units and vacation was investigated by two different methods in this
note. The repairable system is described by a set of  ordinary differential equation  coupled with partial differential equations
with initial values and integral boundaries. To apply the theory of positive  operator semigroups to discuss the repairable system,
the system equations  were transformed into an abstract Cauchy problem oo some Banach lattice.  The system equations has a unique
non-negative dynamic solution and positive steady-state solution and dynamic solution strongly converges to  steady-state solution
were shown on the basis of the detailed spectral analysis of the system operator. Furthermore, the Ces\`{a}ro mean ergodicity of the semigroup $T(t)$ generated by the system operator was also shown through the irreducibility of the semigroup.