IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v26y2024i4d10.1007_s11009-024-10107-9.html
   My bibliography  Save this article

WNBUE Class and its Applications to Signature-Based Bounds for Reliability of Coherent Systems

Author

Listed:
  • Abdolsaeed Toomaj

    (Gonbad Kavous University)

  • Narayanaswamy Balakrishnan

    (McMaster University Hamilton)

Abstract

The inequalities are established here rational functions of the weighted moments and conditional weighted tail moments of the underlying failure distribution. In this paper, we first introduce a new notion of aging called “weighted new better (worse) than used in expectation” and then we present a procedure for developing reliability inequalities based on this new aging notion. Next, we apply it to obtain the reliability of a coherent system by using the Samaniego signature when the component lifetimes are independent and identically distributed. Specially, we use the new bounds for consecutive-type systems. These new bounds are easy to compute as they depend on the system signature and the parent distribution.

Suggested Citation

  • Abdolsaeed Toomaj & Narayanaswamy Balakrishnan, 2024. "WNBUE Class and its Applications to Signature-Based Bounds for Reliability of Coherent Systems," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-17, December.
    • Handle: RePEc:spr:metcap:v:26:y:2024:i:4:d:10.1007_s11009-024-10107-9
    DOI: 10.1007/s11009-024-10107-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-024-10107-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-024-10107-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Francisco J. Samaniego, 2007. "System Signatures and their Applications in Engineering Reliability," International Series in Operations Research and Management Science, Springer, number 978-0-387-71797-5, March.
    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. Erhard Cramer & Jorge Navarro, 2015. "Progressive Type‐II censoring and coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(6), pages 512-530, September.
    2. Gaofeng Da & Lvyu Xia & Taizhong Hu, 2014. "On Computing Signatures of k-out-of-n Systems Consisting of Modules," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 223-233, March.
    3. Feng, Geng & Patelli, Edoardo & Beer, Michael & Coolen, Frank P.A., 2016. "Imprecise system reliability and component importance based on survival signature," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 116-125.
    4. Zarezadeh, S. & Mohammadi, L. & Balakrishnan, N., 2018. "On the joint signature of several coherent systems with some shared components," European Journal of Operational Research, Elsevier, vol. 264(3), pages 1092-1100.
    5. Hindolo George-Williams & Geng Feng & Frank PA Coolen & Michael Beer & Edoardo Patelli, 2019. "Extending the survival signature paradigm to complex systems with non-repairable dependent failures," Journal of Risk and Reliability, , vol. 233(4), pages 505-519, August.
    6. Zhengcheng Zhang & N. Balakrishnan, 2016. "Representations of the inactivity time for coherent systems with heterogeneous components and some ordered properties," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(1), pages 113-126, January.
    7. Bo H. Lindqvist & Francisco J. Samaniego, 2019. "Some new results on the preservation of the NBUE and NWUE aging classes under the formation of coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(5), pages 430-438, August.
    8. Frank P. A. Coolen & Tahani Coolen-Maturi & Ali M. Y. Mahnashi, 2024. "Nonparametric Predictive Inference for Discrete Lifetime Data," Mathematics, MDPI, vol. 12(22), pages 1-14, November.
    9. Tomasz J. Kozubowski & Krzysztof Podgórski, 2018. "Kumaraswamy Distribution and Random Extrema," The Open Statistics and Probability Journal, Bentham Open, vol. 9(1), pages 18-25, July.
    10. Marichal, Jean-Luc & Mathonet, Pierre & Spizzichino, Fabio, 2015. "On modular decompositions of system signatures," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 19-32.
    11. Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2015. "Predictive inference for system reliability after common-cause component failures," Reliability Engineering and System Safety, Elsevier, vol. 135(C), pages 27-33.
    12. Nabakumar Jana & Samadrita Bera, 2024. "Estimation of multicomponent system reliability for inverse Weibull distribution using survival signature," Statistical Papers, Springer, vol. 65(8), pages 5077-5108, October.
    13. Marichal, Jean-Luc & Mathonet, Pierre, 2013. "On the extensions of Barlow–Proschan importance index and system signature to dependent lifetimes," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 48-56.
    14. M. Burkschat & J. Navarro, 2014. "Asymptotic behavior of the hazard rate in systems based on sequential order statistics," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(8), pages 965-994, November.
    15. Salomon, Julian & Winnewisser, Niklas & Wei, Pengfei & Broggi, Matteo & Beer, Michael, 2021. "Efficient reliability analysis of complex systems in consideration of imprecision," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    16. Patelli, Edoardo & Feng, Geng & Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2017. "Simulation methods for system reliability using the survival signature," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 327-337.
    17. Di Maio, Francesco & Pettorossi, Chiara & Zio, Enrico, 2023. "Entropy-driven Monte Carlo simulation method for approximating the survival signature of complex infrastructures," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    18. S Eryilmaz, 2010. "Review of recent advances in reliability of consecutive k-out-of-n and related systems," Journal of Risk and Reliability, , vol. 224(3), pages 225-237, September.
    19. Eryilmaz, Serkan, 2011. "The behavior of warm standby components with respect to a coherent system," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1319-1325, August.
    20. Doostparast, Mohammad & Kolahan, Farhad & Doostparast, Mahdi, 2014. "A reliability-based approach to optimize preventive maintenance scheduling for coherent systems," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 98-106.

    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:spr:metcap:v:26:y:2024:i:4:d:10.1007_s11009-024-10107-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.