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Determining the exact reliability of a complex system can involve extremely large amounts of computation. This paper develops a number of upper and lower bounds for the reliability of multistate systems, that is, systems for which each component may exist in one of a finite number of states. These bounds are based on the notions of minimal paths and minimal cuts and are far more easily computed than the exact system reliability. To further reduce the computations required and to obtain sharper bounds, a modular-decomposition-based bound is developed for multistate systems.
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David A. Butler (1982) studied this question.
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