IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i20p4252-d1257839.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/20/4252/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/20/4252/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ioannis S. Triantafyllou, 2020. "m -Consecutive- k -out-of- n : F Structures with a Single Change Point," Mathematics, MDPI, vol. 8(12), pages 1-14, December.
    2. Wang, Yan & Hu, Linmin & Yang, Li & Li, Jing, 2022. "Reliability modeling and analysis for linear consecutive-k-out-of-n: F retrial systems with two maintenance activities," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    3. Li, Mingjia & Hu, Linmin & Wu, Shaomin & Zhao, Bing & Wang, Yan, 2023. "Reliability assessment for consecutive-k-out-of-n: F retrial systems under Poisson shocks," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    4. Spiros D. Dafnis & Frosso S. Makri & Markos V. Koutras, 2021. "Generalizations of Runs and Patterns Distributions for Sequences of Binary Trials," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 165-185, March.
    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.
    6. Wei, Xiaohua & Bai, Sijun & Wu, Bei, 2023. "A novel shock-dependent preventive maintenance policy for degraded systems subject to dynamic environments and N-critical shocks," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    7. Hashemi, M. & Asadi, M. & Tavangar, M., 2022. "Optimal maintenance strategies for coherent systems: A warranty dependent approach," Reliability Engineering and System Safety, Elsevier, vol. 217(C).
    8. Zhu, Xiaojun & Balakrishnan, N., 2023. "Non-parametric inference based on reliability life-test of non-identical coherent systems with application to warranty time," Reliability Engineering and System Safety, Elsevier, vol. 232(C).
    9. Zhang, Nan & Cai, Kaiquan & Deng, Yingjun & Zhang, Jun, 2024. "Joint optimization of condition-based maintenance and condition-based production of a single equipment considering random yield and maintenance delay," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    10. Spiros D. Dafnis & Frosso S. Makri, 2022. "Weak runs in sequences of binary trials," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(5), pages 573-603, July.
    11. Safaei, Fatemeh & Ahmadi, Jafar & Taghipour, Sharareh, 2022. "A maintenance policy for a k-out-of-n system under enhancing the system’s operating time and safety constraints, and selling the second-hand components," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    12. Ioannis S. Triantafyllou & Miltiadis Chalikias, 2023. "Consecutive- k 1 and k 2 -out-of- n : F Structures with a Single Change Point," Stats, MDPI, vol. 6(1), pages 1-12, March.
    13. Fu, Yuqiang & Zhu, Xiaoyan, 2023. "A joint age-based system replacement and component reallocation maintenance policy: Optimization, analysis and resilience," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    14. Zhang, Ning & Qi, Faqun & Zhang, Chengjie & Zhou, Hongming, 2022. "Joint optimization of condition-based maintenance policy and buffer capacity for a two-unit series system," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    15. Yin, Juan & Cui, Lirong & Balakrishnan, Narayanaswamy, 2022. "Reliability of consecutive-(k,l)-out-of-n: F systems with shared components under non-homogeneous Markov dependence," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    16. Yan, R. & Dunnett, S.J. & Jackson, L.M., 2022. "Model-Based Research for Aiding Decision-Making During the Design and Operation of Multi-Load Automated Guided Vehicle Systems," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    17. Wang, Jingjing & Qiu, Qingan & Wang, Huanhuan & Lin, Cong, 2021. "Optimal condition-based preventive maintenance policy for balanced systems," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    18. Tavangar, Mahdi & Hashemi, Marzieh, 2022. "Reliability and maintenance analysis of coherent systems subject to aging and environmental shocks," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).
    19. Hamdan, K. & Tavangar, M. & Asadi, M., 2021. "Optimal preventive maintenance for repairable weighted k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    20. Yin, Juan & Cui, Lirong, 2021. "Reliability for consecutive-k-out-of-n: F systems with shared components between adjacent subsystems," Reliability Engineering and System Safety, Elsevier, vol. 210(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4252-:d:1257839. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.