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The Roots of the Reliability Polynomials of Circular Consecutive- k -out-of- n :F Systems

Author

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  • Marilena Jianu

    (Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania)

  • Leonard Dăuş

    (Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, 020396 Bucharest, Romania)

  • Vlad-Florin Drăgoi

    (Department of Mathematics and Computer Science, Faculty of Exact Sciences, “Aurel Vlaicu” University of Arad, 310330 Arad, Romania)

  • Valeriu Beiu

    (Department of Mathematics and Computer Science, Faculty of Exact Sciences, “Aurel Vlaicu” University of Arad, 310330 Arad, Romania)

Abstract

The zeros of the reliability polynomials of circular consecutive- k -out-of- n :F systems are studied. We prove that, for any fixed k ≥ 2 , the set of the roots of all the reliability polynomials (for all n ≥ k ) is unbounded in the complex plane. In the particular case k = 2 , we show that all the nonzero roots are real, distinct numbers and find the closure of the set of roots. For every n ≥ k , the expressions of the minimum root and the maximum root are given, both for circular as well as for linear systems.

Suggested Citation

  • Marilena Jianu & Leonard Dăuş & Vlad-Florin Drăgoi & Valeriu Beiu, 2023. "The Roots of the Reliability Polynomials of Circular Consecutive- k -out-of- n :F Systems," Mathematics, MDPI, vol. 11(20), pages 1-12, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4252-:d:1257839
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    References listed on IDEAS

    as
    1. Tereszkiewicz, Agnieszka & Wawreniuk, Izabela, 2015. "Generalized Jacobsthal polynomials and special points for them," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 806-814.
    2. Mohammadi, Fatemeh & Saenz-de-Cabezon, Eduardo & Wynn, Henry P., 2018. "Efficient multicut enumeration of k -out-of- n:F and consecutive k -out-of- n:F systems," LSE Research Online Documents on Economics 86460, London School of Economics and Political Science, LSE Library.
    3. Dafnis, Spiros D. & Makri, Frosso S. & Philippou, Andreas N., 2019. "The reliability of a generalized consecutive system," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 186-193.
    4. Eryilmaz, Serkan, 2020. "Age-based preventive maintenance for coherent systems with applications to consecutive-k-out-of-n and related systems," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    5. Ioannis S. Triantafyllou, 2020. "On the Consecutive k 1 and k 2 -out-of- n Reliability Systems," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
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