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Some results about the NBUC class of life distributions

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  • Li, Xiaohu
  • Li, Zehui
  • Jing, Bing-Yi

Abstract

NBUC class life distributions are dealt with in this paper. Firstly, a lower bound of the reliability function based upon mean and variance (both assumed finite) is presented. It is shown that the bound effectively improves "known bounds" for NBU life distributions. Secondly, a sufficient condition characterized by the excess lifetime at t>0 in a renewal process is obtained. In effect, the decreasing in convex ordering of excess lifetime may result in NBUC interarrivals. Finally, we prove that the NBUC class is preserved under the formation of the parallel system.

Suggested Citation

  • Li, Xiaohu & Li, Zehui & Jing, Bing-Yi, 2000. "Some results about the NBUC class of life distributions," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 229-237, February.
    • Handle: RePEc:eee:stapro:v:46:y:2000:i:3:p:229-237
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    References listed on IDEAS

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    1. Robert L. Launer, 1984. "Inequalities for NBUE and NWUE Life Distributions," Operations Research, INFORMS, vol. 32(3), pages 660-667, June.
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    Cited by:

    1. Li, Yulin, 2004. "Closure of NBU(2) class under the formation of parallel systems," Statistics & Probability Letters, Elsevier, vol. 67(1), pages 57-63, March.
    2. Chen Li & Xiaohu Li, 2020. "Weak aging properties for coherent systems with statistically dependent component lifetimes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 559-572, October.
    3. Félix Belzunce & Eva-María Ortega & José Ruiz, 2005. "A note on replacement policy comparisons from NBUC lifetime of the unit," Statistical Papers, Springer, vol. 46(4), pages 509-522, October.
    4. Xiaohu Li & Guoxin Qiu, 2007. "Some preservation results of NBUC aging property with applications," Statistical Papers, Springer, vol. 48(4), pages 581-594, October.
    5. Xiaohu Li & Richard Yam, 2005. "Reversed preservation properties of some negative aging conceptions and stochastic orders," Statistical Papers, Springer, vol. 46(1), pages 65-78, January.
    6. Anis Mohammed Z., 2010. "On Testing Exponentiality Against DMRL Alternatives," Stochastics and Quality Control, De Gruyter, vol. 25(2), pages 281-299, January.
    7. 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.

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