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Copula-based representations for the reliability of the residual lifetimes of coherent systems with dependent components

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  • Navarro, Jorge
  • Durante, Fabrizio

Abstract

In the context of coherent systems, we obtain representations for the reliability function of the residual lifetime at time t under different assumptions. Specifically, four cases are considered based on system information at time t: the system is working (case 1); all the components of the system are working (case 2); some components have failed at given times t1,…,tr

Suggested Citation

  • Navarro, Jorge & Durante, Fabrizio, 2017. "Copula-based representations for the reliability of the residual lifetimes of coherent systems with dependent components," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 87-102.
    • Handle: RePEc:eee:jmvana:v:158:y:2017:i:c:p:87-102
    DOI: 10.1016/j.jmva.2017.04.003
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    References listed on IDEAS

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    1. Navarro, Jorge & Rychlik, Tomasz, 2010. "Comparisons and bounds for expected lifetimes of reliability systems," European Journal of Operational Research, Elsevier, vol. 207(1), pages 309-317, November.
    2. Jorge Navarro & M. Carmen Gomis, 2016. "Comparisons in the mean residual life order of coherent systems with identically distributed components," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(1), pages 33-47, January.
    3. Jorge Navarro, 2016. "Stochastic comparisons of generalized mixtures and coherent systems," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 150-169, March.
    4. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
    5. E. Salehi & M. Asadi & S. Eryılmaz, 2012. "On the mean residual lifetime of consecutive k-out-of-n systems," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 93-115, March.
    6. Norros, Ilkka, 1985. "Systems weakend by failures," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 181-196, September.
    7. Jorge Navarro & Pedro Hernandez, 2008. "Mean residual life functions of finite mixtures, order statistics and coherent systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 277-298, April.
    8. Navarro, Jorge & Pellerey, Franco & Di Crescenzo, Antonio, 2015. "Orderings of coherent systems with randomized dependent components," European Journal of Operational Research, Elsevier, vol. 240(1), pages 127-139.
    9. Jorge Navarro & Fabio Spizzichino, 2010. "Comparisons of series and parallel systems with components sharing the same copula," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(6), pages 775-791, November.
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    Citations

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    Cited by:

    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. Krzysztof Jasiński, 2021. "Some conditional reliability properties of k-out-of-n system composed of different types of components with discrete independent lifetimes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1241-1251, November.
    3. Jorge Navarro & Maria Longobardi & Franco Pellerey, 2017. "Comparison results for inactivity times of k-out-of-n and general coherent systems with dependent components," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(4), pages 822-846, December.
    4. Li, Chen & Li, Xiaohu, 2023. "On k-out-of-n systems with homogeneous components and one independent cold standby redundancy," Statistics & Probability Letters, Elsevier, vol. 203(C).
    5. 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).
    6. repec:bpj:demode:v:6:y:2018:i:1:p:156-177:n:10 is not listed on IDEAS
    7. 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).
    8. Shilan Li & Jianxin Shi & Paul Albert & Hong-Bin Fang, 2022. "Dependence Structure Analysis and Its Application in Human Microbiome," Mathematics, MDPI, vol. 11(1), pages 1-14, December.
    9. Elham Khaleghpanah Noughabi & Majid Chahkandi & Majid Rezaei, 2022. "On the Mean and Variance Residual Life Comparisons of Coherent Systems with Identically Distributed Components," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2801-2822, December.
    10. Wang, Fan & Li, Heng & Dong, Chao, 2021. "Understanding near-miss count data on construction sites using greedy D-vine copula marginal regression," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    11. Dui, Hongyan & Zhang, Chi & Tian, Tianzi & Wu, Shaomin, 2022. "Different costs-informed component preventive maintenance with system lifetime changes," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    12. Emilio De Santis & Yaakov Malinovsky & Fabio Spizzichino, 2021. "Stochastic Precedence and Minima Among Dependent Variables," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 187-205, March.
    13. Jorge Navarro & Camilla Calì & Maria Longobardi & Fabrizio Durante, 2022. "Distortion representations of multivariate distributions," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 925-954, October.
    14. Serkan Eryilmaz & Frank P.A. Coolen & Tahani Coolen‐Maturi, 2018. "Mean residual life of coherent systems consisting of multiple types of dependent components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(1), pages 86-97, February.

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