Abstract: We discussed the stability problem of a repairable system with two different failure modes by using operator semigroup theory. By  transforming the system model into an abstract Cauchy problem, we analyzed the distribution of spectral points of system operators, and  proved that  spectral points of system operators were all located  in the left half plane of the complex plane, and there were no spectral points  on the imaginary axis expect for 0 point. Furthermore, we gave the 
 asymptotic stability of the system solution. Finally, we analyzed the steadystate indices of the system from the perspective of eigenvector.

Key words: stability, repairable system, spectral analysis, reliability index