A New Approach for Efficient Computation of Marginal Reliability Importance

This paper proposes a new approach to computing marginal reliability importance (MRI) for every component of a system when the system is represented by a combinatorial model and the sum of disjoint products (SDP) method is used to compute its reliability. MRI is very useful in the reliability design of systems, because it clarifies the priority that components should be improved to ensure a reliable system under budget constraints. The computational complexity of the standard method of computing MRI for every component is proportional to the computational complexity of computing the reliability of the system multiplied by the number of components. While a study reported to have reduced this to only the computational complexity of computing the reliability of the system, its method can only be applied to a very narrow range of models called ‘reducible
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networks’, which are directed graphs reducible to a single link by special reduction rules. This paper proposes a new method to reduce the computational complexity for the whole class of combinatorial models, which is a much wider range than reducible
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networks, when the SDP method is used to compute the system reliability.