Minimal Path Sets with Known Size in a Consecutive-2-out-of-n:F System

K.G. Ramamurthy [4] showed that the number of minimal path sets of a linear consecutive-2-out-of-n:F system is the rounded value of the expression ρn (1 + ρ)2 / (2ρ + 3) where ρ is the unique real root of the cubic equation x3 − x −1 = 0. This paper gives two others formulae for the same. The first...

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Bibliographic Details
Published in:Opsearch 2001-08, Vol.38 (4), p.352-371
Main Authors: Seth, Arvind, Sadegh, Mohammad Khanjari
Format: Article
Language:English
Subjects:
Binomial coefficients
Formulas (mathematics)
Operations research
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Summary:K.G. Ramamurthy [4] showed that the number of minimal path sets of a linear consecutive-2-out-of-n:F system is the rounded value of the expression ρn (1 + ρ)2 / (2ρ + 3) where ρ is the unique real root of the cubic equation x3 − x −1 = 0. This paper gives two others formulae for the same. The first formula is in terms of the binomial coefficients. While the second formula is in terms of the number of minimal path sets with known size of a linear consecutive-2-out-of-n:F system. It is shown that the number of minimal path sets of a circular consecutive-2-out-of-n:F system is the rounded value of ρn, for n≥ 10.
ISSN:0030-3887
0975-0320
DOI:10.1007/BF03398643