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Space tracking, telemetry and command (TT&C) system is essentially a dynamic structure system with multiple mission phases. When there are a large number of equipments in a system, the transition matrix of the Markov model of the system is a large sparse matrix whose solution is hard to gain directly. This paper suggests a Runge Kutta method based on the sparse matrix storage scheme to numerically solve and analyze the reliability model. Examples with numerical results show the effectiveness of the solution method. The efficiency of the proposed method is also proved through an analysis on its storage space and solving time.