5-2 计量型统计过程控制

LCL The limit of lower 99.73% of values of the population. This is not the lower specification limit. (Lower control limit)
控制下限，是整体数据中99.73%的下限，不是规格下限。
Historical Background: when Shewhart developed these charts in the 1920’s, there was no easy way to calculate the standard deviation. Thus, the range approach became ingrained in SPC appliaction. 历史背景：当施华德在1920年开发这些控制图时，没有简 单的方法来计算出标准差。那么，极差方法就成为SPC应 用中根深蒂固的方法。
2. Compute the Moving Range for each subgroup starting with subgroup2. MR equals the Range for the subgroup and the previous subgroup’s value. 从第二附属组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。
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Creating I – MR Chart 创建I-MR图
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Creating I – MR Chart 创建I-MR图
6. Plot the center line and control limits in the 2 charts. Complete the x chart and MR chart.画出两个图的中心线和控制限，画出X图和MR图
UCL The limit of upper 99.73% of values of the population. This is not the
upper
specification limit. ( Upper control limit)
控制上限，是整体数据中99.73%的上限，不是规格上限。
X The average value of all sample 所有X的平均值
R The range of a subgroup (maximum value-minimum value 每组样本中数据的极差 (最大减最少)
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来自百度文库
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Definition: 定义
R The average value of all ranges 所有R的平均数
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Definition: 定义
n The number of sample in a subgroup 每组样本数量
X The value of individual samples 个别数据
X The average value of all samples in a subgroup 每组样本的数据平均值
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Variables Control Charts: The Xbar Chart 计量型控制图:Xbar图
The center line of the chart is represented by the long-term average of the averages, or X-Double bar Xbar图的中心线由平均值的长期平均水平或X-double bar描绘出来
j建立下列控制图:
Variables计量型: 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(均值与标准差图)
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subgroup2: MR=8.5-8.0=0.5
Subgroup3: MR=8.5-7.4=1.1 Subgroup4: MR=10.5-7.4=3.1 ………..以此类推
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Creating I – MR Chart 创建I-MR图
Sample 1
X
8.00
MR
2 8.50 0.50
Individual Value
14 12 10
8 6 4 2 0
1
5 4.5
4 3.5
3 2.5
2 1.5
1 0.5
0 2
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Individual Control Chart
UCLx Xbar
LCLxbar X
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4
5
Subgroup Number
Range Control Chart
2.Np Chart: About the number of befectives np图：关于不良品
3.U Chart: About the number of defects per unit U图：关于缺陷率
4.C Chart: About the total number of defects C图：关于缺陷数图，子群数应固定
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Creating the Xbar & R Control Charts 创建Xbar & R控制图
If all points show only random variation 如果所有的点只是显示出随 机变化：
¾ Use the calculated control limits for monitoring the next 75 or so subgroups使用计算出的控制界限来监控紧接着的大约75个子集
The control limits bound the +/-3sigma, or 99.7% confidence interval on the mean
控制界限限定了范围在+/-3sigma，或在平均值上的99.7%内的置信 区间。
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Variables Control Charts: The Range® Chart 计量型控制图:极差（R）图
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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 XBar-R图：均值和极差图
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Creating I – MR Chart 创建I-MR图
Sample 1
X
8.00
MR
2 8.50 0.50
3
4
7.40 10.50
1.10 3.10
5
6
7
9.30 11.10 10.40
1.20
1.80 0.70
1. Record the individual measurements for each subgroup为每个子群记录 个体的测量值
Variable Statistical Process Control 计量型统计过程控制
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Learning Objectives 学习目的
Upon completion of this module, the participants will be able to:完成对本模快的学习后,学员将能够: Construct the following control charts:
Xbar=(8.0+8.5+7.4+10.5+9.3+11.1+10.4)/7=9.31
4. Compute Rbar, the average of all of the MR’s. Rbar will give the center line on the MR chart. 计算Rbar, 所有MR’s的平均值，Rbar 将会给出MR图的中心线。
3
4
7.40 10.50
1.10 3.10
5
6
7
9.30 11.10 10.40
1.20
1.80 0.70
3. Compute Xbar, the average of all of the individual values. Xbar will give the center line on the X chart. 计算均值，所有个体值的平均 值，Xbar将会给出X图的中心线。
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Formula for I-MR chart Calculation I-MR 图控制界限计算公式
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Constants for I-MR Charts I-MR 图控—控制图常数
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Range Vs. Standard Deviation 极差VS标准偏差
3. XBar-S Chart: Xbar and Standard Deviation Chart XBar-s 图：均值和标准差图
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Control Chart Types 控制图类型
Attribute Control Charts: 计数型控制图
1.P Chart: About the proportion of defectives P图：关于不良品比率
¾ If the process is still in control, re-calculate the control limits using all of data (then keep them there)如果过程仍在控制之下，使用所 有数据重新计算控制界限（然后将其保留在那里）
If patterns indicate special causes of variation如果图形样式显示出 变异特殊原因：
The Range, or R chart monitors the variability within subgroup over time 极差，或R图监控在子群体内部随时间的变动 The center line of the chart is represented by the long-term average of the ranges, or R-bar 图的中心线由极差的长期平均水平或R-bar所代表 The control limits bound the +/-3(sigma of the range) confidence interval on the range 控制界限限定了范围在平均值上+/-3(sigma of the range)内的置信 区间
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UCLr Rbar
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LCLr MR
4 Subgroup Numbe r
5
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7
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M oi vngRange
Xbar-R Chart Xbar-R图
The Xbar, R chart plots averages and ranges Xbar, R图画出均值和极差 Xbar, R charts enable process owners to evaluate changes in central tendency and stability using sub-grouping Xbar, R图使过程所有者使用子群体能够估计中心趋势和稳定性变化 Variables Control Charts involve continuous variables, wherein the statistics of interest are central tendency and variability (dispersion) 计量型控制图涉及连续性变量，其中所关注的统计量是中心趋势和变异 (散布） The Xbar chart measures the central tendency of the variable over time. It uses the mean, or Xbar, from samples of size n. Xbar图随时测量变量的中心趋势。它使用来自大小为n的样本的平均值， 或X-bar.