Abstract: In this paper the authors study reliability of a system with repair and multiple critical and non-critical errors. Under the functional frame work, they rewrite the system into an eqvolutionary equation in the state Banach space. Using the theory of semigroup of bounded linear operators, they investigate the well-poseness and the stability of the system. They prove that, under certain assumptions, the system is wellposed and associates a positive C₀ semigroup; There is a steady state of the system and solution of the system converges asymptotically to this steady state in the sense of norm. And hence the indices of the system determined by the steady state are reliable.

Key words: Repairable system, Wellposedness and stability, C₀ semigroup