Abstract
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.
Similar content being viewed by others
References
Bollinger R C and Salvia, A.A. “Consecutive-k-Out-Of-n:F Networks”. IEEE Transaction on Reliability. 31 (1982) 53–56.
Chiang D T and Niu S C “Reliability of Consecutive-k-Out-Of-n:F System”. IEEE Transaction on Reliability. 30 (1981) 87–89.
Kontoleon J M “Reliability Determination of a r-Successive-Out-Of-n:F System”. IEEE Transaction on Reliability. 29 (1980) 437.
Ramamurthy K G “Number of Minimal Path Sets of A Consecutive-2-Out-Of-n:F System”. Unpublished manuscript (1996).
Spickerman W R “Binet’s Formula for the Fibonacci Sequence”. Fibonacci Quarterly, 20 (1982) 118–120.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Seth, A., Sadegh, M.K. Minimal Path Sets with Known Size in a Consecutive-2-out-of-n:F System. OPSEARCH 38, 352–371 (2001). https://doi.org/10.1007/BF03398643
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03398643