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A practical, important system performance index for analyzing real world systems is NP-hard multi-state two-terminal reliability. Contributions of this paper are 1) it presents a direct, correct decomposition method for solving NP-hard multi-state two-terminal reliability, and 2) it does not require a priori the multi-state minimal paths/cuts of the system. Because all the exact methods solve the multi-state two-terminal reliability problem in terms of two/three NP-hard problems, excluding the impractical complete enumeration method, and Doulliez & Jamoulle's popular but incorrect decomposition method, development of such an exact, direct, and practical algorithm is thus worthwhile. Computational experiments verify that the proposed method is practical, fast, and efficient in comparison with the complete enumeration method.
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Jane et al. (2008) studied this question.
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