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Allocation of two redundancies in two‐component series systems

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  • Peng Zhao
  • Ping Shing Chan
  • Long Li
  • Hon Keung Tony Ng

Abstract

The allocation of redundancies in a system to optimize the reliability of system performance is an interesting problem in reliability engineering and system security. In this article, we focus on the optimal allocation of two exponentially distributed active (standby) redundancies in a two‐component series system using the tool of stochastic ordering. For the case of active redundancy, stochastic comparisons are carried out in terms of the likelihood ratio and reversed hazard rate orders. For the case of standby redundancy, a likelihood ratio ordering result is developed. The results established here generalize and strengthen corresponding results in the recent literature. In addition, several numerical examples are used to explicate the results. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:60:y:2013:i:7:p:588-598
    DOI: 10.1002/nav.21554
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    1. Harshinder Singh & Radhey S. Singh, 1997. "Note: Optimal allocation of resources to nodes of series systems with respect to failure‐rate ordering," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(1), pages 147-152, February.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Xiaohu Li & Zhengcheng Zhang & Yudan Wu, 2009. "Some new results involving general standby systems," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(5), pages 632-642, September.
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    Cited by:

    1. 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.

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