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Preservation of some partial orderings under the formation of coherent systems

Author

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  • Nanda, Asok K.
  • Jain, Kanchan
  • Singh, Harshinder

Abstract

The reversed (backward) hazard rate ordering is an ordering for random variables which compares lifetimes with respect to their reversed hazard rate functions. In this paper, we have given some sufficient conditions under which the ordering between the components with respect to the reversed hazard rate is preserved under the formation of coherent systems. We have also shown that these sufficient conditions are satisfied by k-out-of-n systems. Both the cases when components are identically distributed and not necessarily identically distributed are discussed. Some results for likelihood ratio order are also obtained. The parallel (series) systems of not necessarily iid components have been characterized by means of a relationship between the reversed hazard rate (hazard rate) function of the system and the reversed hazard rate (hazard rate) functions of the components.

Suggested Citation

  • Nanda, Asok K. & Jain, Kanchan & Singh, Harshinder, 1998. "Preservation of some partial orderings under the formation of coherent systems," Statistics & Probability Letters, Elsevier, vol. 39(2), pages 123-131, August.
    • Handle: RePEc:eee:stapro:v:39:y:1998:i:2:p:123-131
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    Cited by:

    1. Bera, Smaranika & Bhattacharyya, Dhrubasish & Khan, Ruhul Ali & Mitra, Murari, 2023. "Test for harmonic mean residual life function: A goodness of fit approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 58-70.
    2. Bo H. Lindqvist & Francisco J. Samaniego, 2019. "Some new results on the preservation of the NBUE and NWUE aging classes under the formation of coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(5), pages 430-438, August.
    3. Belzunce, Félix & Ruiz, José M. & Ruiz, M. Carmen, 2002. "On preservation of some shifted and proportional orders by systems," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 141-154, November.
    4. Chen Li & Xiaohu Li, 2018. "Preservation of increasing convex/concave order under the formation of parallel/series system of dependent components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(4), pages 445-464, May.
    5. Manuel Franco & M. Ruiz & José Ruiz, 2003. "A note on closure of the ILR and DLR classes under formation of coherent systems," Statistical Papers, Springer, vol. 44(2), pages 279-288, April.

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