随机寿命数据威布尔分布的二维γ1 - γ2图
Two Dimensional γ1 - γ2 Plots of Weibull Distribution for Random Life Data Sets

作者: 王桂金 :钢铁研究总院,北京;

关键词: 威布尔分布斜度过剩峭度Weibull Distribution Skewness Excess Kurtosis

摘要:
本文首先根据形状参数计算威布尔分布的斜度和过剩峭度的理论值,再画出相应的二维γ1 - γ2图。然后对一组100个随机数产生的寿命及两组实测轴承寿命数据计算截尾数10到全样本的实际斜度和过剩峭度。结果表明,实验数据随斜度的增加逐步逼近威布尔理论分布。

Abstract: First, the two dimensional γ1 - γ2 Plot of Weibull distribution is drawn by calculating skewness and excess kurtosis defined by the shape parameter, then one set of 100 random life data and two sets of bearing life data are used to evaluate skewness and excess kurtosis when they are right censored from 10 up to full sample size. It is found that random life dataset and lab-test datasets both are able to gradually approach to the expected two dimensional γ1 - γ2 plot of Weibull distribution.

文章引用: 王桂金 (2015) 随机寿命数据威布尔分布的二维γ1 - γ2图。 统计学与应用, 4, 15-20. doi: 10.12677/SA.2015.41003

参考文献

[1] Pearson, K. (1895) Contributions to the mathematical theory of evolution II: Skew variation in homogeneous material. Philosophical Transactions of Royal Society, 186, 343-414.

[2] Pearson, E.S. and Hartley, H.O. (1966, 1972) Bio-metrica, tables for statisticians, vol. 1 and 2. Cambridge University Press, Cambridge.

[3] Rinne, H. (2009) The Weibull distribution, a handbook. CRC Press, New York.

[4] 王桂金 (2012) Weibull随机寿命的统计量. 轴承, 3, 38-42.

[5] 王桂金 (2012) Weibull随机寿命的信息熵. 轴承, 12, 28-31.

[6] Samuel, M.S. (1974) Standard ma-thematical tables. 21st Edition, CRC Press, Cleveland.

[7] 徐人平, 胡志勇, 何复超 (1992) 滚动轴承疲劳寿命的概率分布.云南工学院学报, 4, 67-71.

[8] 徐跃进 (2007) 滚动轴承的疲劳可靠性计算. 轴承, 8, 27-30.

分享
Top