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On allocation of redundant components for systems with dependent components

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  • Belzunce, Félix
  • Martínez-Puertas, Helena
  • Ruiz, José M.

Abstract

In this paper we consider the problem of optimal allocation of a redundant component for series, parallel and k-out-of-n systems of more than two components, when all the components are dependent. We show that for this problem is naturally to consider multivariate extensions of the joint bivariates stochastic orders. However, these extensions have not been defined or explicitly studied in the literature, except the joint likelihood ratio order, which was introduced by Shanthikumar and Yao (1991). Therefore we provide first multivariate extensions of the joint stochastic, hazard rate, reversed hazard rate order and next we provide sufficient conditions based on these multivariate extensions to select which component performs the redundancy.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:230:y:2013:i:3:p:573-580
    DOI: 10.1016/j.ejor.2013.05.004
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    References listed on IDEAS

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    1. da Costa Bueno, Vanderlei & Martins do Carmo, Iran, 2007. "Active redundancy allocation for a k-out-of-n:F system of dependent components," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1041-1051, January.
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    6. Zhao, Peng & Chan, Ping Shing & Ng, Hon Keung Tony, 2012. "Optimal allocation of redundancies in series systems," European Journal of Operational Research, Elsevier, vol. 220(3), pages 673-683.
    7. Valdés, José E. & Arango, Gerardo & Zequeira, Romulo I. & Brito, Gerandy, 2010. "Some stochastic comparisons in series systems with active redundancy," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 945-949, June.
    8. Ha, Chunghun & Kuo, Way, 2006. "Reliability redundancy allocation: An improved realization for nonconvex nonlinear programming problems," European Journal of Operational Research, Elsevier, vol. 171(1), pages 24-38, May.
    9. da Costa Bueno, Vanderlei, 2005. "Minimal standby redundancy allocation in a k-out-of-n:F system of dependent components," European Journal of Operational Research, Elsevier, vol. 165(3), pages 786-793, September.
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    Cited by:

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    4. Hamideh Jeddi & Mahdi Doostparast, 2022. "Allocation of redundancies in systems: a general dependency-base framework," Annals of Operations Research, Springer, vol. 312(1), pages 259-273, May.
    5. 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.
    6. Rychlik, Tomasz, 2017. "Evaluations of quantiles of system lifetime distributions," European Journal of Operational Research, Elsevier, vol. 256(3), pages 935-944.
    7. Rui Fang & Xiaohu Li, 2017. "On matched active redundancy allocation for coherent systems with statistically dependent component lifetimes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(7), pages 580-598, October.
    8. 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.
    9. Wei Wei, 2019. "Single machine scheduling with stochastically dependent times," Journal of Scheduling, Springer, vol. 22(6), pages 677-689, December.
    10. Li, Chen & Li, Xiaohu, 2020. "Preservation of weak SAI’s under increasing transformations with applications," Statistics & Probability Letters, Elsevier, vol. 164(C).
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    12. 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).
    13. Rui Fang & Xiaohu Li, 2016. "On allocating one active redundancy to coherent systems with dependent and heterogeneous components' lifetimes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(4), pages 335-345, June.
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    15. Qi Feng & J. George Shanthikumar, 2018. "Arrangement Increasing Resource Allocation," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 935-955, September.

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