Reliability analysis of a repairable paralleling redundant system is studied in the paper. By the method of functional analysis, specially, the semi-group theories on Banach space, we proved the existence of the rigorous dominant eigenvalue of the system. The essential spectral radius of the system operator is also discussed before and after perturbation. The results show that the dynamic solution of the system is exponential stability and tends to the steady solution of the system. At last, we analyze the reliability of the system.
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