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Appendix: Control Chart Constants : X-MR 附录：控制图表常数 X-MR
Subgroup Size n
2 3 4 5 6 7 8 9 10
E2 2.660 1.772 1.457 1.290 1.184 1.109 1.054 1.010 0.975
D3 * * * * * 0.076 0.136 0.184 0.223
1.2
1.8
0.7
1. Record the individual measurements for each subgroup 为每个子 群记录个体的测量值
2. Compute the Moving Range for each subgroup starting with subgroup 2. MR equals the Range for the subgroup and the previous subgroup's value. 从subgroup 2 开始为每个子群计算变动范围 MR 等于子群和当前子群值的变动范围。
Variable Statistical Process Control
计量型统计过程控制
1
Learning Objectives 学习目的
Upon completion of this module, the participants will be able to: 完成对本模块的学习后，学员将能够：
? Construct the following Control Charts :
建立下列控制图：
? Variables: ? I-MR: Individuals and Moving Range
(个体与移动极差图)
? Xbar & R: Xbar and Range
(均值与极差图)
? Xbar & S: Xbar and Standard deviation
the MR chart
1 R = 6 ( .5 +.9 + 3.1 + 1.2 +1.8 + .7) = 1.37
计算R，所有MR ‘S的平均值，R将会给出MR图的中心线
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Formula For I-MR Chart Calculation I-MR Chart控制限计算公式：
MR Chart MR 图
? Plot I-MR Chart 画出:I-MR图
7
Creating I –图
14
Value Individual
13 12 11 10
9 8 7 6
5
Subgroup
1
5
Range
4 3
oving
2 1
M
0
I and MR Chart for C1
Subgroup 2 : MR = 8.5 - 8.0 = .5
Subgroup 3 : MR = 8.5 - 7.4 = 1.1
Subgroup 4 : MR = 10.5 - 7.4 = 3.1
9
Creating the I-MR Control Charts 创建 I-MR 控制图
Sample X MR
(8.0 + 8.5 + 7.4 + 10.5 + 9.3 + 11.1 + 10.4) = 9.31
7 计算X，所有个体值的平均值， X将会给出 X图的中心线
4. Compute R, the average of all of the MR's. R will give the center line on
12
D4 3.267 2.575 2.282 2.115 2.004 1.924 1.864 1.816 1.777
d2 1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078
Creating the I-MR Control Charts 创建 I-MR 控制图
1
2
3
4
8
8.5
7.4
10.5
0.5
0.9
3.1
5
6
7
9.3
11.1
10.4
1.2
1.8
0.7
3. Compute X, the average of all of the individual values. X will give the center line on the X chart.
1 X =
2
3
4
5
6
UCL=13.04 Mean=9.314 LCL=5.591 7 UCL=4.574
R=1.4 LCL=0
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Creating the I-MR Control Charts 创建 I-MR 控制图
Samp le
X
MR
1
2
3
4
5
6
7
8
8.5
7.4
10.5
9.3
11.1
10.4
0.5
1.1
3.1
XBar-R 图: 均值和极差图
3 XBar-S Chart: Xbar and Standard Deviation Chart
XBar-S 图：均值和标准差图
3
Creating I – MR Chart with Minitab 用Minitab 创建I-MR 图
? I – MR Chart: Individuals and moving Range Chart. Each subgroup is made up by a single sample. I-MR: 个体与移动极差图,也叫X-MR图,子群由单一的测量值组成
(均值与标准差图)
2
Control Chart Types 控制图类型
Variable Control Charts: 计量型控制图:
1 I-MR Chart: Individual and Moving Range Chart
I-MR 图: 个体和移动极差图
2 XBar-R Chart: Xbar and Range Chart
5. Calculate the Control Limits : 计算控制限：
UCL MR=D4R LCL MR=D3R
X Chart X图
UCL X=X+E2R LCL X=X－E2R
In I-MR Charts, E 2=2.66. Other constants refer
to the follow table. 在I- MR 图中,E2=2.66, 公式中其它常数见下表 或本节后附录.