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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (4): 590-598.doi: 10.3969/j.issn.1005-3085.2015.04.012

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有关逆Weibull分布序统计量的一些比较结果(英)

邱国新1,2,   姜海波1   

  1. 1- 陆军军官学院基础部，合肥 230031
    2- 中国科学技术大学统计金融系，合肥 230026
  • 收稿日期:2014-03-10 接受日期:2014-12-02 出版日期:2015-08-15 发布日期:2015-10-15
  • 基金资助:
    国家自然科学基金 (61170252)；陆军军官学院科学基金 (2012XYJJ005; 2012xyjj007).

Comparisons on Order Statistics from Heterogeneous Inverse Weibull Distributions

QIU Guo-xin1,2,   JIANG Hai-bo1   

  1. 1- Department of Science Course, Army Officer Academy of PLA, Hefei 230031
    2- Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026
  • Received:2014-03-10 Accepted:2014-12-02 Online:2015-08-15 Published:2015-10-15
  • Supported by:
    The National Natural Science Foundation of China (61170252); the Science Foundation of Army Officer Academy (2012XYJJ005; 2012XYJJ007).

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摘要： 考虑由独立元件组成的两个串(并)联系统，其元件寿命服从寿命参数不同，但形状参数相同的逆Weibull分布．证明了串联系统的生存函数(失效率函数)关于寿命参数向量在$p$-阶大序(占优序)意义下递减．若形状参数小于(大于)$1$，证明了并联系统的反向失效率关于寿命参数向量在占优序意义下递减(递增)．作为以上结论的简单应用，利用寿命参数的几何(代数)平均值，还建立了串(并)联系统可靠性函数的上界．

关键词: 逆Weibull分布, 失效率序, 反向失效率序, 色散序, 占优序, $p$-阶大序

Abstract:

In this paper, we consider two different systems consisting of independent components with inverse Weibull distributions whose characteristic life parameters are heterogeneous, but the shape parameters are common. It is shown that the survival function (hazard rate) of a series system is decreasing in the characteristic life parameter vector with respect to $p$-larger (majorization) ordering. It is also shown that the reversed hazard rate of a parallel system is decreasing (increasing) in characteristic life parameter vector with respect to majorization ordering if the common shape parameters are less (greater) than $1$. As a consequence, the simple upper bound on the survival function of the series (parallel) systems is built in terms of geometric (arithmetic) mean of the characteristic life parameters.

Key words: inverse Weibull distribution, hazard rate ordering, reversed hazard rate ordering, dispersive ordering, majorization ordering, $p$-larger ordering

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