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Some aging properties of parallel and series systems with a random number of components

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  • Nil Kamal Hazra
  • Asok K. Nanda
  • Moshe Shaked

Abstract

In this article, we study aging properties of parallel and series systems with a random number of components. We show that the decreasing likelihood ratio property is closed under the formation of random minima. We also show, by counterexamples, that other aging properties are not closed under the formation of random minima or maxima. Some mistakes in the literature are corrected. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 238–243, 2014

Suggested Citation

  • Nil Kamal Hazra & Asok K. Nanda & Moshe Shaked, 2014. "Some aging properties of parallel and series systems with a random number of components," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(3), pages 238-243, April.
    • Handle: RePEc:wly:navres:v:61:y:2014:i:3:p:238-243
    DOI: 10.1002/nav.21580
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    References listed on IDEAS

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    1. Asok Nanda & Moshe Shaked, 2001. "The Hazard Rate and the Reversed Hazard Rate Orders, with Applications to Order Statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(4), pages 853-864, December.
    2. Xiaohu Li & Guoxin Qiu, 2007. "Some preservation results of NBUC aging property with applications," Statistical Papers, Springer, vol. 48(4), pages 581-594, October.
    3. Xiaohu Li & Ming J. Zuo, 2004. "Preservation of stochastic orders for random minima and maxima, with applications," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(3), pages 332-344, April.
    4. Bartoszewicz, Jaroslaw, 2001. "Stochastic comparisons of random minima and maxima from life distributions," Statistics & Probability Letters, Elsevier, vol. 55(1), pages 107-112, November.
    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.
    6. P.C. Consul, 1984. "On The Distributions Of Order Statistics For A Random Sample Size," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 38(4), pages 249-256, December.
    7. Abouammoh, A. & El-Neweihi, E., 1986. "Clusure of the NBUE and DMRL classes under formation of parallel systems," Statistics & Probability Letters, Elsevier, vol. 4(5), pages 223-225, August.
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    Cited by:

    1. Bobotas, Panayiotis & Koutras, Markos V., 2024. "On the preservation of ageing properties under random maxima," Statistics & Probability Letters, Elsevier, vol. 210(C).
    2. Bobotas, Panayiotis & Koutras, Markos V., 2019. "Distributions of the minimum and the maximum of a random number of random variables," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 57-64.

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