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On the hazard rate and reversed hazard rate orderings in two-component series systems with active redundancies

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  • Brito, Gerandy
  • Zequeira, Romulo I.
  • Valdés, José E.

Abstract

The lifetimes of two-component series systems with two active redundancies are compared using the hazard rate and the reversed hazard rate orders. We study the problem of where to allocate the spares in a system to obtain the best configuration. We compare redundancy at component level vs. system level using the likelihood ratio order. For this problem we find conditions under which there is no hazard rate ordering between the lifetimes of the systems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:2:p:201-206
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    References listed on IDEAS

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    1. Philip J. Boland, 1997. "A reliability comparison of basic systems using hazard rate functions," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 13(3‐4), pages 377-384, September.
    2. 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.
    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.
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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. 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.
    3. Hamed Ahmadzade & Rong Gao, 2018. "Reversed hazard function of uncertain lifetime," Fuzzy Optimization and Decision Making, Springer, vol. 17(4), pages 387-400, December.
    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. 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.
    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. Zhao, Peng & Zhang, Yiying & Li, Long, 2015. "Redundancy allocation at component level versus system level," European Journal of Operational Research, Elsevier, vol. 241(2), pages 402-411.
    8. 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.
    9. 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.

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