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This paper proposes and efficient algorithm for computing the failure frequencies of telecommunications networks. The proposed method is based on a special modification that transforms the formula for computing the reliability into a formula that also gives the failure frequency. A number of algorithms have been produced, and the factoring algorithm has been shown to be the most efficient. This algorithm has not yet been transformed, because its graph operations contraction and deletion of a link produce complicated expressions in the failure-frequency case. A new matrix-style decomposition formula is derived in this paper, and allows us to transform the factoring algorithm into an algorithm that gives failure frequency as well as reliability. Some numerical examples show that this new algorithm simultaneously computes both measures with high efficiency.