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Estimation in coherent reliability systems through copulas

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  • Eryilmaz, Serkan

Abstract

The problem of estimating the parameter of a common distribution of components' lifetimes from system's lifetime data is of interest and importance in reliability engineering. The present paper deals with this problem when the common component distribution is exponential with mean μ and the lifetimes of components have an exchangeable joint distribution which is constructed by the help of Archimedean copula. In particular we obtain moment estimator of μ for Clayton and Ali-Mikhail-Haq copulas. We illustrate the findings of the paper for a special class of coherent systems called consecutive k-within-m-out-of-n:F system. A simulation study is performed to investigate the properties of the moment estimator. The method presented in this paper can be applied to all coherent systems.

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  • Eryilmaz, Serkan, 2011. "Estimation in coherent reliability systems through copulas," Reliability Engineering and System Safety, Elsevier, vol. 96(5), pages 564-568.
    • Handle: RePEc:eee:reensy:v:96:y:2011:i:5:p:564-568
    DOI: 10.1016/j.ress.2010.12.024
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    References listed on IDEAS

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    1. Tan, Zhibin, 2007. "Estimation of exponential component reliability from uncertain life data in series and parallel systems," Reliability Engineering and System Safety, Elsevier, vol. 92(2), pages 223-230.
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    3. Eryilmaz, Serkan & Kan, Cihangir & Akici, Fatih, 2009. "Consecutive k-within-m-out-of-n:F system with exchangeable components," MPRA Paper 26838, University Library of Munich, Germany.
    4. Guikema, Seth D., 2007. "Formulating informative, data-based priors for failure probability estimation in reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 92(4), pages 490-502.
    5. Sigeo Aki & Katuomi Hirano, 1996. "Lifetime distribution and estimation problems of consecutive-k-out-of-n:F systems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(1), pages 185-199, March.
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    Citations

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    Cited by:

    1. Ioannis S. Triantafyllou, 2024. "Archimedean Copulas-Based Estimation under One-Parameter Distributions in Coherent Systems," Mathematics, MDPI, vol. 12(2), pages 1-14, January.
    2. Serkan Eryilmaz & Altan Tuncel, 2016. "Generalizing the survival signature to unrepairable homogeneous multi‐state systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(8), pages 593-599, December.
    3. Jenab, K. & Sarfaraz, A. & Dhillon, B.S. & Seyed Hosseini, S.M., 2012. "Dynamic MLD analysis with flow graphs," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 80-85.
    4. M. Chahkandi & Jafar Ahmadi & S. Baratpour, 2014. "Non-parametric prediction intervals for the lifetime of coherent systems," Statistical Papers, Springer, vol. 55(4), pages 1019-1034, November.
    5. M. Kelkin Nama & M. Asadi & Z. Zhang, 2013. "On the residual lifelengths of the remaining components in a coherent system," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(7), pages 979-996, October.
    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. Kim, Taeyong & Song, Junho, 2018. "Generalized Reliability Importance Measure (GRIM) using Gaussian mixture," Reliability Engineering and System Safety, Elsevier, vol. 173(C), pages 105-115.
    8. 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.
    9. Feng, Liuyang & Zhang, Limao, 2021. "Assessment of tunnel face stability subjected to an adjacent tunnel," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    10. M. G. Kulkarni & M. B. Rajarshi, 2020. "Estimation of parameters of component lifetime distribution in a coherent system," Statistical Papers, Springer, vol. 61(1), pages 403-421, February.
    11. Asadi, Majid & Ebrahimi, Nader & Soofi, Ehsan S. & Zohrevand, Younes, 2016. "Jensen–Shannon information of the coherent system lifetime," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 244-255.
    12. 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).
    13. Ioannis S. Triantafyllou, 2023. "An Archimedean Copulas-Based Approach for m -Consecutive- k -Out-of- n : F Systems with Exchangeable Components," Stats, MDPI, vol. 6(4), pages 1-12, October.
    14. Xiang-Yu Li & Yu Liu & Chu-Jie Chen & Tao Jiang, 2016. "A copula-based reliability modeling for nonrepairable multi-state k-out-of-n systems with dependent components," Journal of Risk and Reliability, , vol. 230(2), pages 133-146, April.
    15. 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).
    16. Zhao, Xian & Dong, Bingbing & Wang, Xiaoyue, 2023. "Reliability analysis of a two-dimensional voting system equipped with protective devices considering triggering failures," Reliability Engineering and System Safety, Elsevier, vol. 232(C).

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