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Redundancy in systems with heterogeneous dependent components

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  • Navarro, Jorge
  • Fernández-Martínez, Pedro

Abstract

We study different redundancy mechanisms in coherent systems with possibly dependent heterogeneous components. The dependence is modelled through copulas. We use distortion functions to obtain general results for different redundancy procedures. This model includes the popular active redundancy and minimal repair procedures. The purpose is to determine where these redundant components should be located in the system, according to its structure. We study series and parallel systems in detail. In the first case (series systems), it is well known that active and minimal repair redundancies should be assigned to the weakest component. However, we show that, surprisingly, this is not always the case for all the redundancy mechanisms. Moreover, we give a condition on the redundancy mechanism to get this expected property. Similar results are obtained for parallel systems. In these systems one can think that the best option is to assign the redundancy to the strongest component. However, we prove that this is not always the case. We include results for other system structures as well and we show that these properties also depend on the copula (dependence structure).

Suggested Citation

  • Navarro, Jorge & Fernández-Martínez, Pedro, 2021. "Redundancy in systems with heterogeneous dependent components," European Journal of Operational Research, Elsevier, vol. 290(2), pages 766-778.
    • Handle: RePEc:eee:ejores:v:290:y:2021:i:2:p:766-778
    DOI: 10.1016/j.ejor.2020.08.011
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    References listed on IDEAS

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    1. Antonio Arriaza & Jorge Navarro & Alfonso Suárez‐Llorens, 2018. "Stochastic comparisons of replacement policies in coherent systems under minimal repair," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(6-7), pages 550-565, September.
    2. Lin, Feng & Peng, Liang & Xie, Jiehua & Yang, Jingping, 2018. "Stochastic distortion and its transformed copula," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 148-166.
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    5. Jorge Navarro, 2018. "Stochastic comparisons of coherent systems," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(4), pages 465-482, May.
    6. Belzunce, Félix & Martínez-Puertas, Helena & Ruiz, José M., 2013. "On allocation of redundant components for systems with dependent components," European Journal of Operational Research, Elsevier, vol. 230(3), pages 573-580.
    7. Huynh, K.T., 2020. "Modeling past-dependent partial repairs for condition-based maintenance of continuously deteriorating systems," European Journal of Operational Research, Elsevier, vol. 280(1), pages 152-163.
    8. Navarro, Jorge & Arriaza, Antonio & Suárez-Llorens, Alfonso, 2019. "Minimal repair of failed components in coherent systems," European Journal of Operational Research, Elsevier, vol. 279(3), pages 951-964.
    9. Félix Belzunce & Carolina Martínez‐Riquelme & José M. Ruiz, 2019. "Allocation of a relevation in redundancy problems," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(3), pages 492-503, May.
    10. Jorge Navarro & Nuria Torrado & Yolanda del Águila, 2018. "Comparisons Between Largest Order Statistics from Multiple-outlier Models with Dependence," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 411-433, March.
    11. Aven, Terje & Castro, I.T., 2008. "A minimal repair replacement model with two types of failure and a safety constraint," European Journal of Operational Research, Elsevier, vol. 188(2), pages 506-515, July.
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    1. Jiandong Zhang & Yiying Zhang, 2023. "Stochastic comparisons of relevation allocation policies in coherent systems," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(3), pages 865-907, September.
    2. Longxiang Fang & Yu Ruan & N. Balakrishnan, 2025. "Redundancy in Two-series-parallel and Two-parallel-series Systems with Independent Components Randomly Chosen from Two Batches," Methodology and Computing in Applied Probability, Springer, vol. 27(4), pages 1-21, December.
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    5. Meifang Cheng & Longxiang Fang & Qi Zheng, 2025. "Two redundancy mechanisms in series and parallel systems with heterogeneous dependent components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(6), pages 1051-1068, August.
    6. Meifang Cheng & Longxiang Fang & Qi Zheng, 2025. "Two redundancy mechanisms in series and parallel systems with heterogeneous dependent components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 88(7), pages 1009-1026, October.
    7. 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).

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