Abstract: From the fact that a series-parallel systemmade up of components has a complicated state space and transfer-probability matrix, the element classification and structural characteristic of the transfer- probability matrix of a series-parallel system with only a set of repair equipment were investigated. To describe the change ofthe transfer-probabilitymatrix, the conceptofgrowingmatrixwas introduced, and the change regularity of the transfer-probabilitymatrix, resulted fromthe variation of components in the system, was gained.