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You may rely on the reliability polynomial for much more than you might think. (English) Zbl 1078.90014

Let \(R_{{\mathcal S}}(p)\) be the reliability polynomial of a collection \({\mathcal S}\) of subsets of a finite set \(X\), where \(X\) is the edge set of a graph. A polynomial, called inclusion-exclusion polynomial, which is equivalent to \(R_{{\mathcal S}}(p)\) is introduced. A theorem is proved how to apply the inclusion-exclusion polynomial for obtaining the probabilities of certain events. The use of the theorem is illustrated by an example.

MSC:

90B15 Stochastic network models in operations research
68R10 Graph theory (including graph drawing) in computer science
90B25 Reliability, availability, maintenance, inspection in operations research
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References:

[1] Colbourn C. J., The International Series of Monographs on Computer Science 4 (1987)
[2] Colbourn C. J., Congressus Numerantium 93 pp 187– (1993)
[3] Edmonds J., J. Comb. Theo. 8 pp 298– (1970)
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