IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v248y2024ics0951832024002217.html
   My bibliography  Save this article

On the residual lifetimes of dependent components upon system failure

Author

Listed:
  • Davies, Katherine
  • DembiÅ„ska, Anna

Abstract

In this paper, we consider coherent systems composed of identical yet possibly dependent components. The dependence structure among components is modelled via copulas. We investigate residual lifetimes of components that survived the failure of the system. The main result of the paper is a new general formula describing the joint distribution of these residual lifetimes. Using the new formula we look more closely at this distribution in the cases of Clayton, Gumbel–Hougaard and Frank copulas and standard exponential and Weibull margins. In particular, we present some comparative numerical results that enable us to examine the influence of the dependence among components on the residual lifetimes of the surviving ones. We observe that the results obtained under the assumption of dependence and independence may differ significantly, especially when the system breaks down just after it started working.

Suggested Citation

  • Davies, Katherine & DembiÅ„ska, Anna, 2024. "On the residual lifetimes of dependent components upon system failure," Reliability Engineering and System Safety, Elsevier, vol. 248(C).
    • Handle: RePEc:eee:reensy:v:248:y:2024:i:c:s0951832024002217
    DOI: 10.1016/j.ress.2024.110147
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832024002217
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2024.110147?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. 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.
    2. Eryilmaz, Serkan & Ozkut, Murat, 2020. "Optimization problems for a parallel system with multiple types of dependent components," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    3. Eryilmaz, Serkan, 2023. "Age based preventive replacement policy for discrete time coherent systems with independent and identical components," Reliability Engineering and System Safety, Elsevier, vol. 240(C).
    4. 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).
    5. Zhao, Xian & Qi, Xin & Wang, Xiaoyue, 2023. "Reliability assessment for coherent systems operating under a generalized mixed shock model with multiple change points of the environment," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    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. 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. Gao, Shan & Wang, Jinting & Zhang, Jie, 2023. "Reliability analysis of a redundant series system with common cause failures and delayed vacation," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    9. Torrado, Nuria & Arriaza, Antonio & Navarro, Jorge, 2021. "A study on multi-level redundancy allocation in coherent systems formed by modules," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    10. Zheng, Yide & Zhang, Yi, 2023. "Reliability analysis for system with dependent components based on survival signature and copula theory," Reliability Engineering and System Safety, Elsevier, vol. 238(C).
    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. 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.
    13. Zeng, Zhiguo & Barros, Anne & Coit, David, 2023. "Dependent failure behavior modeling for risk and reliability: A systematic and critical literature review," Reliability Engineering and System Safety, Elsevier, vol. 239(C).
    14. Liu, Yongchao & Wang, Guanjun & Liu, Peng, 2024. "A condition-based maintenance policy with non-periodic inspection for k-out-of-n: G systems," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    15. Tavangar, Mahdi & Bairamov, Ismihan, 2015. "On conditional residual lifetime and conditional inactivity time of k-out-of-n systems," Reliability Engineering and System Safety, Elsevier, vol. 144(C), pages 225-233.
    16. Qin, Shuidan & Wang, Bing Xing & Tsai, Tzong-Ru & Wang, Xiaofei, 2023. "The prediction of remaining useful lifetime for the Weibull k-out-of-n load-sharing system," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    17. Gupta, Nitin & Misra, Neeraj & Kumar, Somesh, 2015. "Stochastic comparisons of residual lifetimes and inactivity times of coherent systems with dependent identically distributed components," European Journal of Operational Research, Elsevier, vol. 240(2), pages 425-430.
    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. Torrado, Nuria, 2022. "Optimal component-type allocation and replacement time policies for parallel systems having multi-types dependent components," Reliability Engineering and System Safety, Elsevier, vol. 224(C).
    2. 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.
    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. Yu, Yaocheng & Shuai, Bin & Huang, Wencheng, 2024. "Resilience evaluation of train control on-board system considering common cause failure: Based on a beta-factor and continuous-time bayesian network model," Reliability Engineering and System Safety, Elsevier, vol. 246(C).
    5. 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).
    6. Murat Ozkut, 2022. "Comparison of the replacement policy in k-out-of-n systems having dependent components," Journal of Risk and Reliability, , vol. 236(1), pages 125-137, February.
    7. Rychlik, Tomasz, 2017. "Evaluations of quantiles of system lifetime distributions," European Journal of Operational Research, Elsevier, vol. 256(3), pages 935-944.
    8. 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.
    9. 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).
    10. Oszczypała, Mateusz & Konwerski, Jakub & Ziółkowski, Jarosław & Małachowski, Jerzy, 2024. "Reliability analysis and redundancy optimization of k-out-of-n systems with random variable k using continuous time Markov chain and Monte Carlo simulation," Reliability Engineering and System Safety, Elsevier, vol. 242(C).
    11. 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.
    12. 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).
    13. Liu, Yimeng & Sui, Shaobo & Lu, Dan & Peng, Rui & Bai, Mingyang & Li, Daqing, 2024. "Emergent lifetime distribution from complex network systems aging," Reliability Engineering and System Safety, Elsevier, vol. 247(C).
    14. Konul Bayramoglu Kavlak, 2017. "Reliability and mean residual life functions of coherent systems in an active redundancy," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(1), pages 19-28, February.
    15. 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.
    16. 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.
    17. 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.
    18. Zarezadeh, S. & Asadi, M. & Balakrishnan, N., 2014. "Dynamic network reliability modeling under nonhomogeneous Poisson processes," European Journal of Operational Research, Elsevier, vol. 232(3), pages 561-571.
    19. Jørgen Vitting Andersen & Roy Cerqueti & Giulia Rotundo, 2017. "Rational expectations and stochastic systems," Documents de travail du Centre d'Economie de la Sorbonne 17060, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2019.
    20. Che, Haiyang & Zeng, Shengkui & Zhao, Yingzhi & Guo, Jianbin, 2024. "Reliability assessment of multi-state weighted k-out-of-n man-machine systems considering dependent machine deterioration and human fatigue," Reliability Engineering and System Safety, Elsevier, vol. 246(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:eee:reensy:v:248:y:2024:i:c:s0951832024002217. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    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.