IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i12p2181-d457936.html
   My bibliography  Save this article

The Residual Lifetime of Surviving Components of Coherent System under Periodical Inspections

Author

Listed:
  • Zhouxia Guo

    (College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China)

  • Jiandong Zhang

    (College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China)

  • Rongfang Yan

    (College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China)

Abstract

In this manuscript, we gain a mixture representation for reliability function of the residual lifetime of unfailed components in a coherent system under periodical inspections, given that the number of failed components before time t 1 is r ( ≥ 0 ) , but the system is still operating at time t 1 , and the system eventually failed at time t 2 ( > t 1 ) . Some aging properties and stochastic orders of the residual lifetime on survival components are also established. Finally, some numerical examples and graphs are given in order to confirm the theoretical results.

Suggested Citation

  • Zhouxia Guo & Jiandong Zhang & Rongfang Yan, 2020. "The Residual Lifetime of Surviving Components of Coherent System under Periodical Inspections," Mathematics, MDPI, vol. 8(12), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2181-:d:457936
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/12/2181/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/12/2181/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Marichal, Jean-Luc & Mathonet, Pierre, 2011. "Extensions of system signatures to dependent lifetimes: Explicit expressions and interpretations," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 931-936, May.
    2. Subhash Kochar & Hari Mukerjee & Francisco J. Samaniego, 1999. "The “signature” of a coherent system and its application to comparisons among systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(5), pages 507-523, August.
    3. Salehi, Ebrahim & Tavangar, Mahdi, 2019. "Stochastic comparisons on conditional residual lifetime and inactivity time of coherent systems with exchangeable components," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 327-337.
    4. Sareh Goli, 2019. "On the conditional residual lifetime of coherent systems under double regularly checking," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(4), pages 352-363, June.
    5. Navarro, Jorge & Rychlik, Tomasz, 2007. "Reliability and expectation bounds for coherent systems with exchangeable components," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 102-113, January.
    6. A. Parvardeh & N. Balakrishnan & Azam Arshadipour, 2018. "A note on the conditional residual lifetime of a coherent system under double monitoring," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(10), pages 2373-2378, May.
    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. Sareh Goli, 2019. "On the conditional residual lifetime of coherent systems under double regularly checking," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(4), pages 352-363, June.
    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. 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.
    4. Krzysztof Jasiński, 2021. "The number of failed components in a coherent working system when the lifetimes are discretely distributed," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(7), pages 1081-1094, October.
    5. 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.
    6. Serkan Eryilmaz & Markos V. Koutras & Ioannis S. Triantafyllou, 2011. "Signature based analysis of m‐Consecutive‐k‐out‐of‐n: F systems with exchangeable components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(4), pages 344-354, June.
    7. 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.
    8. Marichal, Jean-Luc & Mathonet, Pierre & Waldhauser, Tamás, 2011. "On signature-based expressions of system reliability," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1410-1416, November.
    9. Roy Cerqueti, 2022. "A new concept of reliability system and applications in finance," Annals of Operations Research, Springer, vol. 312(1), pages 45-64, May.
    10. Salehi, Ebrahim & Tavangar, Mahdi, 2019. "Stochastic comparisons on conditional residual lifetime and inactivity time of coherent systems with exchangeable components," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 327-337.
    11. 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.
    12. 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.
    13. Jorge Navarro & Marco Burkschat, 2011. "Coherent systems based on sequential order statistics," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(2), pages 123-135, March.
    14. Krzysztof Jasiński, 2023. "On conditional residual lifetimes of coherent systems consisting of components with discrete lifetimes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(2), pages 205-218, February.
    15. He Yi & Narayanaswamy Balakrishnan & Lirong Cui, 2022. "On Dependent Multi-State Semi-Coherent Systems Based on Multi-State Joint Signature," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1717-1734, September.
    16. 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.
    17. Serkan Eryilmaz & Cihangir Kan & Fatih Akici, 2009. "Consecutive k‐within‐m‐out‐of‐n:F system with exchangeable components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(6), pages 503-510, September.
    18. Mahdi Tavangar, 2014. "Some comparisons of residual life of coherent systems with exchangeable components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(7), pages 549-556, October.
    19. Mansour Shrahili & Mohamed Kayid, 2023. "Stochastic Orderings of the Idle Time of Inactive Standby Systems," Mathematics, MDPI, vol. 11(20), pages 1-21, October.
    20. Shuang Li & James Lynch, 2010. "Some elementary ideas concerning the complexity of system structure," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(7), pages 626-633, October.

    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:8:y:2020:i:12:p:2181-:d:457936. 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.