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On preservation of some shifted and proportional orders by systems

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  • Belzunce, Félix
  • Ruiz, José M.
  • Ruiz, M. Carmen

Abstract

In this paper, we establish some comparison results of two coherent structures formed from a set of components or from two sets of components with respect to some shifted and proportional stochastic orders. Both cases, independent and identically distributed and not necessarily identically distributed components, are considered. As a consequence of our results, we get new comparisons of systems with different k-out-of-n structures and some results on closure of aging classes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:60:y:2002:i:2:p:141-154
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    References listed on IDEAS

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    1. Khaledi, Baha-Eldin & Kochar, Subhash, 2000. "On dispersive ordering between order statistics in one-sample and two-sample problems," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 257-261, February.
    2. Hu, Taizhong & Zhu, Zegang, 2001. "An analytic proof of the preservation of the up-shifted likelihood ratio order under convolutions," Stochastic Processes and their Applications, Elsevier, vol. 95(1), pages 55-61, September.
    3. Lillo, Rosa E. & Nanda, Asok K. & Shaked, Moshe, 2001. "Preservation of some likelihood ratio stochastic orders by order statistics," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 111-119, January.
    4. 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.
    5. Khaledi, Baha-Eldin & Kochar, Subhash, 1999. "Stochastic orderings between distributions and their sample spacings - II," Statistics & Probability Letters, Elsevier, vol. 44(2), pages 161-166, August.
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    Cited by:

    1. Félix Belzunce & Moshe Shaked, 2004. "Failure profiles of coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(4), pages 477-490, June.
    2. Jorge Navarro & Hon Keung Tony Ng & Narayanaswamy Balakrishnan, 2012. "Parametric inference for component distributions from lifetimes of systems with dependent components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(7), pages 487-496, October.
    3. Zhao, Peng & Li, Xiaohu & Balakrishnan, N., 2009. "Likelihood ratio order of the second order statistic from independent heterogeneous exponential random variables," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 952-962, May.

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