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On the optimal allocation of an active redundancy in a two-component series system

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  • Valdés, José E.
  • Zequeira, Rómulo I.

Abstract

Let X1 and X2 be independent random variables representing the lifetimes of the components C1 and C2, and Y1 and Y2 be random variables, independent of X1 and X2, representing the lifetimes of the spares R1 and R2, respectively. Suppose that the components C1 and C2 form a series system. There are two options for using one of the spares R1 or R2 as an active redundancy: to allocate R1 in parallel with C1 or R2 in parallel with C2. In this paper we compare these options using failure rate ordering.

Suggested Citation

  • Valdés, José E. & Zequeira, Rómulo I., 2003. "On the optimal allocation of an active redundancy in a two-component series system," Statistics & Probability Letters, Elsevier, vol. 63(3), pages 325-332, July.
    • Handle: RePEc:eee:stapro:v:63:y:2003:i:3:p:325-332
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    Citations

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    Cited by:

    1. Yiying Zhang & Peng Zhao, 2019. "Optimal allocation of minimal repairs in parallel and series systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(6), pages 517-526, September.
    2. 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.
    3. 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.
    4. Peng Zhao & Ping Shing Chan & Long Li & Hon Keung Tony Ng, 2013. "Allocation of two redundancies in two‐component series systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(7), pages 588-598, October.
    5. 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.
    6. Lillo Rodríguez, Rosa Elvira & Laniado Rodas, Henry, 2013. "Allocation policies of redundancies in two-parallel-series and two-series-parallel systems," DES - Working Papers. Statistics and Econometrics. WS ws132622, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. 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.
    8. Misra, Amit Kumar & Misra, Neeraj, 2011. "A note on active redundancy allocations in k-out-of-n systems," Statistics & Probability Letters, Elsevier, vol. 81(10), pages 1518-1523, October.
    9. Li, Xiaohu & Hu, Xiaoxiao, 2008. "Some new stochastic comparisons for redundancy allocations in series and parallel systems," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3388-3394, December.
    10. 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.
    11. Wang, Jiantian & Laniado, Henry, 2015. "A note on allocation policy in two-parallel–series and two-series–parallel systems with respect to likelihood ratio order," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 17-21.
    12. 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.
    13. Zhao, Peng & Zhang, Yiying & Chen, Jianbin, 2017. "Optimal allocation policy of one redundancy in a n-component series system," European Journal of Operational Research, Elsevier, vol. 257(2), pages 656-668.
    14. Brito, Gerandy & Zequeira, Romulo I. & Valdés, José E., 2011. "On the hazard rate and reversed hazard rate orderings in two-component series systems with active redundancies," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 201-206, February.

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