﻿ 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

Statistical and Application
Vol.04 No.01(2015), Article ID:14893,5 pages
10.12677/SA.2015.41003

Two Dimensional γ1 - γ2 Plots of Weibull Distribution for Random Life Data Sets

Guijin Wang

Central Iron & Steel Research Institute, Beijing

Email: meiwg6234@gmail.com

Received: Feb. 9th, 2015; accepted: Feb. 22nd, 2015; published: Feb. 28th, 2015

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.

Keywords:Weibull Distribution, Skewness, Excess Kurtosis

Email: meiwg6234@gmail.com

1. 引言

2. 计算过程

2.1. 威布尔分布的γ1 - γ2曲线

(1)

(2)

2.2. 模拟和实测寿命数据威布尔分布的γ1 - γ2曲线

2.2.1. 含100随机数的数组

(3)

(1) 100个无序准随机失效寿命的γ1 - γ2曲线

Figure 1. The γ1 - γ2 plot of Weibull distribution

Figure 2. The γ1 - γ2 plot of 100 random life data, right censored from 10 to 100

(2) 100个有序准随机失效寿命的g1 - g2曲线

2.2.2. 一组60个7208轴承失效数据的γ1 - γ2曲线

(1) 60个7208轴承无序准随机失效寿命的γ1 - γ2曲线

Figure 3. The γ1 - γ2 plot of 100 ascent random life data, right censored from 10 to 100

Figure 4. The γ1 - γ2 plot of 60 random life data in 7208 bearing, right censored from 10 to 60

Figure 5. The γ1 - γ2 plot of 60 ascent life data in 7208 bearing, right censored from 10 to 60

(2) 60个7208轴承有序准随机失效寿命的γ1 - γ2曲线

2.2.3. 一组37个H208轴承失效数据的γ1 - γ2曲线

(1) 37个H208轴承无序准随机失效寿命的γ1 - γ2曲线

(2) 37个H208轴承有序准随机失效寿命的γ1 - γ2曲线

3. 结果讨论

a) 当疲劳寿命数据组足够大，而且呈准随机分布，在它们的γ1 - γ2图中通常可以在高γ1低κ处找到数据的过剩峭度γ2接近MLE的威布尔分布的γ2o。κo和κ两条曲线的交点和文献[7] [8] 的结果相当接近。这表明，γ1 - γ2图可以作为一种有效的工具和文献[3] [4] 一起用来判断威布尔分布形状参数κ估计的合理性。

Figure 6. The γ1 - γ2 plot of 37 random life data in H208 bearing, right censored from 10 to 37

Figure 7. The γ1 - γ2 plot of 37 ascent life data in H208 bearing, right censored from 10 to 37

b) 一组已知准随机疲劳寿命数据可以分别按有序和无序排列进行MLE截尾计算。如果不同截尾无序数组给出平稳收敛的形状参数κ，则有序数组的κ也有逼近图1中κo曲线的趋势，然而后者的变化区间较大。

c) 随着全样本尺寸从100下降到37，无序与有序数组的形状参数κ逼近期望值κo过程的波动幅度逐步增大。所以，在条件许可时使用较大样本会有更好的统计行为。

d) 当全样本尺寸足够大，经过严格控制试样材料成分，热处理，机械加工，以及寿命试验操作之后如果失效数据还不能得到满意的γ1 - γ2图，也许应考虑其他分布的可能性。

Two Dimensional γ1 - γ2 Plots of Weibull Distribution for Random Life Data Sets. 统计学与应用,01,15-20. doi: 10.12677/SA.2015.41003

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