[1]李松臣,李育鹏,陈迎运,等.随机和非随机部件组成的串并联系统寿命比较[J].深圳大学学报理工版,2014,31(3):312-316.[doi:10.3724/SP.J.1249.2014.03312]
 Li Songchen,Li Yupeng,Chen Yingyun,et al.Comparisons of series and parallel systems with random and non-random dependent components[J].Journal of Shenzhen University Science and Engineering,2014,31(3):312-316.[doi:10.3724/SP.J.1249.2014.03312]
点击复制

随机和非随机部件组成的串并联系统寿命比较()
分享到:

《深圳大学学报理工版》[ISSN:1000-2618/CN:44-1401/N]

卷:
第31卷
期数:
2014年第3期
页码:
312-316
栏目:
数学与应用数学
出版日期:
2014-05-20

文章信息/Info

Title:
Comparisons of series and parallel systems with random and non-random dependent components
作者:
李松臣李育鹏陈迎运魏正红
深圳大学数学与计算科学学院, 深圳 518060
Author(s):
Li Songchen Li Yupeng Chen Yingyun and Wei Zhenghong
College of Mathematics and Computational Science, Shenzhen University, Shenzhen 518060, P.R.China
关键词:
应用统计数学可靠性理论次序统计量可交换Copula函数串并联一般随机序詹森不等式离散凸性
Keywords:
application of statistical mathematics reliability theory order statistics exchangeable copula series and parallel system usual stochastic order Jensen inequality discrete convexity
分类号:
O 211.9
DOI:
10.3724/SP.J.1249.2014.03312
文献标志码:
A
摘要:
针对随机数N个部件和非随机数n个部件组成的串并联系统,引入可交换Copula函数度量串并联系统中各部件寿命的相依性,研究串并联系统寿命的随机比较问题.利用离散函数的凸性及詹森不等式的概率论形式,证明当随机数N的期望满足条件E(N)≤n时,随机N部件组成串联系统的寿命以一般随机序优于非随机n部件组成串联系统的寿命;而当E(N)≤n时, 非随机n部件组成并联系统的寿命以一般随机序优于随机N部件组成并联系统的寿命.
Abstract:
Stochastic comparisons of series and parallel systems composed of random N and non-random n components were studied by implementing an exchangeable copula function. This copula function measures the dependence among the lifetime of each component in the series and parallel systems. By the use of the convexity of discrete functions and the Jensen inequality, when the random variable N satisfies E(N)≤n, we show that the lifetime of a series system composed of random N components is better than that of the system composed of non-random n components under the usual stochastic order; meanwhile, the lifetime of a parallel system composed of non-random n components is better than that of the system composed of random N components under the usual stochastic order.

参考文献/References:

[1] Raghunandanan K, Patil S A. On order statistics for random sample size[J]. Statistica Neerlandica, 1972, 26(4): 121-126.
[2] Gupta D, Gupta R C. On the distribution of order statistics for a random sample size[J]. Statistica Neerlandica, 1984, 38(1): 13-19.
[3] Rohatgi V K. Distribution of order statistics with random sample size[J]. Communications in Statistics-Theory and Methods, 1987, 16(12): 3739-3743.
[4] Consul P C. On the distributions of orders statistics for a random sample size[J]. Statistica Neerlandica,1984, 38(4): 249-256.
[5] Shaked M, Wong T. Stochastic orders based on ratios of Laplace transforms[J]. Journal of Applied Probability, 1997, 34(2): 404-419.
[6] Bartiszewucz J. Stochastic comparisons of random minima and maxima from life distributions[J]. Statistics & Probability Letters, 2001, 55(1): 107-112.
[7] Shaked M, Wong T. Stochastic comparisons of random minima and maxima[J]. Journal of Applied Probability, 1997, 34(2): 420-425.
[8] Li Songchen, Li Yupeng, ChenYingyun. Comparisons of series and parallel systems with random and non-random components[C]// International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering. Chengdu(China): 2013:388-390.
[9] Nelsen R B. An introduction to copulas Lecture Notes in Statistics[M]. New York(USA): Springer-Verlag Press, 2006:18-19.
[10] Jorge N, Fabio S. On the relationships between copulas of order statistics and marginal distributions[J]. Statistics and Probability Letters, 2010, 80(5/6): 473-479.
[11] Qi Feng, Guo Baini. Monotonicity of sequences involving convex function and sequence[J]. Mathematical Inequalities and Applications, 2006, 9(2): 247-254.

相似文献/References:

[1]柳向东,杨飞.基于期权价格的Lévy过程参数估计研究[J].深圳大学学报理工版,2014,31(3):325.[doi:10.3724/SP.J.1249.2014.03325]
 Liu Xiangdong and Yang Fei.The research of parameter estimation under the Lévy process based on option pricing[J].Journal of Shenzhen University Science and Engineering,2014,31(3):325.[doi:10.3724/SP.J.1249.2014.03325]
[2]柳向东,郭慧.基于市道轮换模型的SHIBOR市场利率[J].深圳大学学报理工版,2015,32(3):317.[doi:10.3724/SP.J.1249.2015.03317]
 Liu Xiangdong and Guo Hui.Research of market interest rates of the SHIBOR based on regime switching model[J].Journal of Shenzhen University Science and Engineering,2015,32(3):317.[doi:10.3724/SP.J.1249.2015.03317]
[3]柳向东,王星蕊.最小熵鞅测度下的半马氏市道轮换利率模型[J].深圳大学学报理工版,2016,33(2):154.[doi:10.3724/SP.J.1249.2016.02154]
 Liu Xiangdong and Wang Xingrui.Semi-Markov regime switching interest rate models under minimal entropy martingale measure[J].Journal of Shenzhen University Science and Engineering,2016,33(3):154.[doi:10.3724/SP.J.1249.2016.02154]
[4]柳向东,靳晓洁.市道轮换下的高频数据参数估计[J].深圳大学学报理工版,2018,35(4):432.[doi:10.3724/SP.J.1249.2018.04432]
 LIU Xiangdong and JIN Xiaojie.Parameter estimation via regime switching model for high frequency data[J].Journal of Shenzhen University Science and Engineering,2018,35(3):432.[doi:10.3724/SP.J.1249.2018.04432]

备注/Memo

备注/Memo:
Received:2013-06-29;Revised:2013-11-11;Accepted:2014-01-05
Foundation:National Natural Science Foundation of China (71101095)
Corresponding author:Professor Wei Zhenghong. E-mail: zhhwei@szu.edu.cn
Citation:Li Songchen, Li Yupeng, Chen Yingyun, et al. Comparisons of series and parallel systems with random and non-random dependent components[J]. Journal of Shenzhen University Science and Engineering, 2014, 31(3): 312-316.(in Chinese)
基金项目:国家自然科学基金资助项目(71101095)
作者简介:李松臣(1978—),男(汉族),湖北省洪湖市人,深圳大学讲师、博士. E-mail:lisongchen@szu.edu.cn
引文:李松臣, 李育鹏, 陈迎运,等. 随机和非随机部件组成的串并联系统寿命比较[J]. 深圳大学学报理工版,2014,31(3):312-316.
更新日期/Last Update: 2014-05-01