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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

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  • 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. 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.
    3. Norros, Ilkka, 1985. "Systems weakend by failures," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 181-196, September.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
    9. 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.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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).
    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. 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.
    6. 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.
    7. 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.
    8. 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).
    9. 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).
    10. 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).
    11. 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.
    12. 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.
    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).
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