IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v25y2023i1d10.1007_s11009-023-10023-4.html
   My bibliography  Save this article

Multi-State Joint Survival Signature for Multi-State Systems with Shared Multi-State Components

Author

Listed:
  • He Yi

    (Beijing University of Chemical Technology)

  • Narayanaswamy Balakrishnan

    (McMaster University)

  • Xiang Li

    (Beijing University of Chemical Technology)

Abstract

In this paper, the multi-state joint survival signature is proposed for two multi-state semi-coherent or mixed systems with shared independent and identically distributed (i.i.d.) multi-state components, and then its properties are studied along with the related multi-state joint signature. By using the idea of equivalent systems, generalized triangle rule for order statistics and the independence assumption of component lifetimes at different states, transformation formulas of multi-state joint survival signatures of different sizes are presented so that stochastic comparisons of multi-state semi-coherent or mixed system pairs that share different numbers of multi-state components can be carried out. For illustrating the theoretical results established here, some examples are presented. Finally, some concluding remarks are made.

Suggested Citation

  • He Yi & Narayanaswamy Balakrishnan & Xiang Li, 2023. "Multi-State Joint Survival Signature for Multi-State Systems with Shared Multi-State Components," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-18, March.
  • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-10023-4
    DOI: 10.1007/s11009-023-10023-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-023-10023-4
    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/s11009-023-10023-4?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. Coolen-Maturi, Tahani & Coolen, Frank P.A. & Balakrishnan, Narayanaswamy, 2021. "The joint survival signature of coherent systems with shared components," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    2. Marichal, Jean-Luc & Mathonet, Pierre & Navarro, Jorge & Paroissin, Christian, 2017. "Joint signature of two or more systems with applications to multistate systems made up of two-state components," European Journal of Operational Research, Elsevier, vol. 263(2), pages 559-570.
    3. Ilya Gertsbakh & Yoseph Shpungin, 2012. "Multidimensional Spectra of Multistate Systems with Binary Components," Springer Series in Reliability Engineering, in: Anatoly Lisnianski & Ilia Frenkel (ed.), Recent Advances in System Reliability, chapter 0, pages 49-61, Springer.
    4. Jorge Navarro & Francisco J. Samaniego & N. Balakrishnan & Debasis Bhattacharya, 2008. "On the application and extension of system signatures in engineering reliability," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 313-327, June.
    5. 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.
    6. Somayeh Ashrafi & Majid Asadi & Jorge Navarro, 2022. "Joint Reliability Function of Coherent Systems with Shared Heterogeneous Components," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1485-1502, September.
    7. Eryilmaz, Serkan & Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2018. "Marginal and joint reliability importance based on survival signature," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 118-128.
    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. Yi, He & Cui, Lirong & Balakrishnan, Narayanaswamy, 2021. "Computation of survival signatures for multi-state consecutive-k systems," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    2. 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).
    3. 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).
    4. He Yi & Narayanaswamy Balakrishnan & Lirong Cui, 2021. "Comparisons of Multi-State Systems with Binary Components of Different Sizes," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1309-1321, December.
    5. Qin, Jinlei & Coolen, Frank P.A., 2022. "Survival signature for reliability evaluation of a multi-state system with multi-state components," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    6. Somayeh Ashrafi & Majid Asadi & Jorge Navarro, 2022. "Joint Reliability Function of Coherent Systems with Shared Heterogeneous Components," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1485-1502, September.
    7. 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.
    8. Yi, He & Balakrishnan, Narayanaswamy & Li, Xiang, 2024. "Joint reliability of linear consecutive k-type systems with shared components in a zigzag structure," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    9. Jia, Xujie & Shen, Jingyuan & Xu, Fanqi & Ma, Ruihong & Song, Xueying, 2019. "Modular decomposition signature for systems with sequential failure effect," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 435-444.
    10. Burkschat, M. & Samaniego, F.J., 2018. "Dynamic IFR concepts for coherent systems," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 1-7.
    11. M. Kelkin Nama & M. Asadi, 2014. "Stochastic Properties of Components in a Used Coherent System," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 675-691, September.
    12. Markos V. Koutras & Ioannis S. Triantafyllou & Serkan Eryilmaz, 2016. "Stochastic Comparisons Between Lifetimes of Reliability Systems with Exchangeable Components," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1081-1095, December.
    13. A. Toomaj & M. Doostparast, 2016. "On the Kullback Leibler information for mixed systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(10), pages 2458-2465, July.
    14. Jorge Navarro & Rafael Rubio, 2011. "A note on necessary and sufficient conditions for ordering properties of coherent systems with exchangeable components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(5), pages 478-489, August.
    15. Huang, Xianzhen & Aslett, Louis J.M. & Coolen, Frank P.A., 2019. "Reliability analysis of general phased mission systems with a new survival signature," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 416-422.
    16. M. Kelkinnama & M. Asadi, 2019. "Stochastic and ageing properties of coherent systems with dependent identically distributed components," Statistical Papers, Springer, vol. 60(3), pages 805-821, June.
    17. Serkan Eryilmaz & Altan Tuncel, 2016. "Generalizing the survival signature to unrepairable homogeneous multiā€state systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(8), pages 593-599, December.
    18. 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).
    19. Foschi Rachele & Nappo Giovanna & Spizzichino Fabio L., 2021. "Diagonal sections of copulas, multivariate conditional hazard rates and distributions of order statistics for minimally stable lifetimes," Dependence Modeling, De Gruyter, vol. 9(1), pages 394-423, January.
    20. Narayanaswamy Balakrishnan & Hon Ng & Jorge Navarro, 2011. "Exact nonparametric inference for component lifetime distribution based on lifetime data from systems with known signatures," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(3), pages 741-752.

    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:25:y:2023:i:1:d:10.1007_s11009-023-10023-4. 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.