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Minitab-Basic Minitab-基础

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While the training is in Progress, we seek your kind assistance to have all Mobile Phones & Pagers Switched to Silent Mode

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What can Minitab do for us?
Boxplot of productivity
450 400
productivity

350

300

250

200 line Shift 1 2 D 3 4 1 2 N 3 4

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Purpose目的

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1. Become experts in the Minitab software. 熟悉Minitab软件;
2. Apply the tools to make your work more efficiently. 应用工具使您的工作更加高效; 3. Cascade the use of the tools into your organisation. 把工具的使用带回您的部门.

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Table of Contents目录 ?
1.Minitab 视窗介绍

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? 2.Data processing数据处理

? ? ? ? ? ?

3.Hypothesis test假设检验
4.DOE实验设计 5.Regression analysis回归分析 6.MSA测量系统分析 7.SPC 管制图 8.Graph图表

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35 53 63 72 89

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?Minitab Windows 视窗介绍
?1.Shortcut and License 快捷方式与许可代码

Minitab 15 shortcut

29000@sacnt.167.americas.ad.flextronics.com

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?Minitab Windows 视窗介绍
?2 .Session and Data window 报告和数据窗口

报告生成窗口:
分析输出.

Session Window:
Analysis output

Data Window:

数据窗口:
? 工作表,而非简单的数据表 ? 工作表上第一行即为每列数据的名称 ? 同一行的数据被认为是同一个变量.

? A Worksheet, not a Spreadsheet ? Column names are above first row ? Everything in a column is considered to be the same variable

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?Minitab Windows 视窗介绍
?3.Common Toolbar introduction 常用工具栏介绍
Open File Save File Print Window

Previous Command Next Command Find Find Next

Manage Graphs Close Graphs Cancel

Cut Copy

Help

Paste
Undo

Last Dialog Box
Session Window Data Window

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?Data processing数据处理
?1.Generate random data 生成随机数 Path: Calc/random data/ normal
?Generate 50 random data 生成50个随机数; ?Mean:100; 均值:100; ?Standard deviation:10; 标准方差:10

?2. Random sample 随机取样 path: Calc/random data/ sample from columns
?Generate 7 random sample; 产生7个随机数据 ?From:C1 来自:C1 ?Store:C2 储存:C2
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?Data processing数据处理
?3.Calculator 计算器 path: Calc/Calculator
? Store result in C3; 结果存放在C3; ? Expression: c1*2+8 关系式: c1*2+8
We can input expression in the window, also we can Select functions in the window .

我们可以在此窗口中输入关系式也可以选用函数

?4. Column statistic 列统计 Path: Calc/Column statistic
? Calculate the standard deviation of C3 ?计算C3列数据的标准方差.
Raw statistic is the same as column statistic. 行统计的使用方法与列统计一样.

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?Data processing数据处理
?5.Standardize标准化 path: Calc/Standardize
?Input C1; ?Store result in C4 ?Standardize data from -1 to +1
Of course, other 4 method may also fit some of you. 当然了,另外4种方法部分同事也可能使用到.

?6. Simple set of numbers 简单数据设置 path: Calc/Make patterned data/Simple set of numbers
?First value:1; ?Last vaule:9 ?Step:2
You can change “Number of times to list each value” and “Number of times list the sequence” to find the difference. 大家可以改变”每个值出现的次数”和”每个序列出现的次数”来发现二者有什 么样不同.

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?Data processing数据处理
?7. Probability distribution 概率分布 path: Calc/ Probability distribution/normal
?Calculate the probability from sigma level 通过西格玛水平计算概率; ?Calculate the sigma level from probability. 通过概率计算西格玛水平.

Exercise练习:

1. If a product have 3 sigma process capability, what is the defect rate if the data is normally distribution? 如果一个产品具有3个西格玛的制程能力,假定数据正态分布,请问产品的不良率是多少?

2. If a process have 99.5% yield rate, what’s the sigma level can we say? 如果制程良率99.5%,我们可以说西格玛水平等于多少?

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?Data processing数据处理
?8. Stack data 堆叠数据 Path: Data/ Stack/Columns

?Generate 3 column data firstly; 首先生成3列数据; ? Stack the 3 columns to one column 然后把3列数堆叠成1列.

You can input column in the optional item or not, then find the difference in the data window. 大家可以在可选项中输入列号或不输入,然后观 察数据窗中的差异.

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?Data processing数据处理
?9. Unstack data数据反堆叠 Path: Data/ Unstack Columns
?Unstack the c4 columns to three columns. 大家练习把C4列中的数据分成三列.

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?Data processing数据处理
?10. Code 编码 Path: Data/ code/Number to text
Code 1 2 3 1 2 3 2 2 3 3 Text Monday Tuesday Wednesday Monday Tuesday Wednesday Tuesday Tuesday Wednesday Wednesday

?How to如何做到: Change the code to text? 代码转换为文本? Change the test to code? 文本转换为代码? Change code to code? 代码转换? Change text to text? 文本转换? 15

?Data processing数据处理
?11. Change data type 转换数据类型 Path: Data/ Change data type/ Test to number
?In our actual analysis, we may often encounter data type transfer problem. 在实际分析中,我们会经常遇到数据类型 转换的问题.

?How to 如何: Change number to text? 数据格式转换文本格式? Change text to number? 文本格式转换数据格式? and so on?等等.

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?Hypothesis test假设检验
?1. Graphical summary 概要图 Path: Stat/ Basic statistic/ Graphical summary
C1 18.8075 22.7352 13.4433 28.8196 11.5394 37.7595 31.9753 34.6343 51.3913 25.3746 23.8889 31.8536 17.8271 39.6089 38.0237

What can we conclude from the Data of C1 column? 我们可以从右边C1列数据得出什么 结论?

Can you guess what will happen if we Change the confidence level from 95 to 99? 大家猜测一下,这里我们把95改成99会发 生什么情况?

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?Hypothesis test假设检验
Summary for C4
C5 = C1
A nderson-Darling Normality Test A -Squared P -V alue M ean StDev V ariance Skew ness Kurtosis N M inimum 1st Q uartile M edian 3rd Q uartile M aximum 22.461 20.275 9 5 % Confidence Inter vals
Mean Median 20 24 28 32 36

0.16 0.932 28.512 10.926 119.386 0.286513 -0.188247 15 11.539 18.808 28.820 37.760 51.391 34.563 36.592 17.232

Normally test: P-value>0.05 |Skewness|<1 |Kurtosis|<1

-10

0

10

20

30

40

50

95% C onfidence Interv al for M ean 95% C onfidence Interv al for M edian 95% C onfidence Interv al for StDev 7.999

Display data显示数据: Mean平均值; StDev标准方差; Min最小值; Max最大值; Median中位数; 1st Quartile 1/4分位数 3rd Quartile ?分位数 Confidence interval 置信区间

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?Hypothesis test假设检验
? 2 1-Sample Z test Path: Stat/ Basic statistic / 1-Sample Z

?Test Condition 测试条件:
Generate 30 random data firstly, mean:10, stdev:1 先生成30个随机数,均值为10,标准方差为1; Ho: Mean is not bigger than 8; Ha: Sample mean is bigger than 8; 原假设:样本均值小于等于8, 对立假设:样本均值大于8 19

?Hypothesis test假设检验
(with Ho and 95% Z-confidence interval for the Mean, and StDev = 1) 6 5 4
Frequency

Histogram of C1

(with Ho and 95% Z-confidence interval for the Mean, and StDev = 1)

Boxplot of C1

3 2 1
Ho _ X
_ X Ho

0 -1

Ho is out of interval
10 C1 11 12

8

9

8

9

10 C1

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One-Sample Z: C1 Test of mu = 8 vs > 8 The assumed standard deviation = 1 95% Lower Variable N Mean StDev SE Mean C1 30 9.861 1.050 0.183

session window

Bound 9.560

Z P 10.19 0.000

P<0.05, 接收 Ha.

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?Hypothesis test假设检验
? 3 2-Sample t test Path: Stat/ Basic statistic / 2-Sample t
Supplier A 8.4919 10.3924 9.8686 11.3955 9.2016 10.6866 11.0432 8.9287 9.3441 8.9690 9.0571 10.6907 8.5656 8.2236 9.9109 Supplier B 15.6517 14.6298 11.7025 12.7961 13.9791 15.9526 20.0062 13.8126 14.9988 14.7197 15.0284 12.1650 15.0482 16.1603 17.8253

?Assumed Condition假定条件:
Supplier A: mean:10, stdev:1; Supplier B: Mean:15, sedev:2 Ho: A<=B, Ha: A>B 21

?Hypothesis test假设检验
Boxplot of Supplier A, Supplier B
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Data

Individual Value Plot of Supplier A, Supplier B
20 18 16
Data

14 12 10 8 Supplier A Supplier B

14 12 10 8 Supplier A Supplier B

Two-sample T for Supplier A vs Supplier B N Mean StDev SE Mean Supplier A 15 9.65 1.00 0.26 Supplier B 15 14.97 2.11 0.54 Difference = mu (Supplier A) - mu (Supplier B) Estimate for difference: -5.314 95% lower bound for difference: -6.352 T-Test of difference = 0 (vs >): T-Value = -8.82 P-Value = 1.000

session window

P>0.05, accept Ho.

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?Hypothesis test假设检验
? 4 2-Proportion test Path: Stat/ Basic statistic / 2-Proportion

Line A B

Def Total ect s 5 100 7 174

?Assumed Condition假设条件:
Line A and Line B are normal production line. 产线A,B为正常生产线; Ho: A=B, Ha: A=/B 原假设:A=B, 对立假设:A=/B 23

?Hypothesis test假设检验
Test and CI for Two Proportions Sample X N Sample p 1 5 100 0.050000 2 7 174 0.040230

session window

Difference = p (1) - p (2) Estimate for difference: 0.00977011 95% CI for difference: (-0.0419709, 0.0615111) Test for difference = 0 (vs not = 0): Z = 0.37 P-Value = 0.711

P>0.05, accept Ho.

The same with 1-Proportion test, Path: Stat / Basic statistic/ 1-proportion test, You can exercise this after class.

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?Hypothesis test假设检验
?5. 2variance Test (F test) Path: Stat/ Basic statistic / 2-vairiance
Supplier A 8.4919 10.3924 9.8686 11.3955 9.2016 10.6866 11.0432 8.9287 9.3441 8.9690 9.0571 10.6907 8.5656 8.2236 9.9109 Supplier B 15.6517 14.6298 11.7025 12.7961 13.9791 15.9526 20.0062 13.8126 14.9988 14.7197 15.0284 12.1650 15.0482 16.1603 17.8253

?Assumed Condition假设条件:
The data is normally distributed.数据正态分布; Ho: A=B, Ha: A=/B; 原假设:A=B,对立假设:A=/B; 25

?Hypothesis test假设检验
Test for Equal Variances for Supplier A, Supplier B
F-Test Supplier A Test Statistic P-Value Levene's Test Test Statistic P-Value 5.16 0.031 0.31 0.037

Test for Equal Variances: Supplier A, Supplier B 95% Bonferroni confidence intervals for standard deviations

Supplier B

1.0

1.5 2.0 2.5 3.0 3.5 95% Bonferroni Confidence Intervals for StDevs

4.0

N Lower StDev Upper Supplier A 15 0.92205 1.31376 2.22675 Supplier B 15 1.64886 2.34934 3.98201

Supplier A

F-Test (Normal Distribution) Test statistic = 0.31, p-value = 0.037

P<0.05, accept Ha.

Supplier B

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10

12

14 Data

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18

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Levene's Test (Any Continuous Distribution) Test statistic = 5.16, p-value = 0.031

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?Hypothesis test假设检验
?6. One way ANOVA (Unstack) Path: Stat/ANOVA/One way ANOVA

A 13.0993 12.3709 11.7953 13.9837 13.3198 13.8469 12.5932 13.2986 11.7422 13.2272 12.6204 12.4630 13.3141 13.3177 12.7934

B 12.6862 12.4406 12.0768 13.6509 15.4770 16.5808 13.3025 14.1800 16.0066 18.5578 15.4146 14.7696 13.3503 16.9512 14.0623

C 13.0515 8.7819 3.5389 6.3000 12.1711 9.6874 5.6038 8.6894 7.9968 13.9839 15.3965 9.7636 5.3049 10.6236 10.5685

假设条件: Ho: No obvious difference with the three factors. 各因子之间没有明显差异; Ha: There is a factor at least different with others 至少有一个因子与其它因子存在明显差异.

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?Hypothesis test假设检验
Boxplot of A, B, C
20.0 17.5 15.0 12.5 10.0 7.5 5.0

One-way ANOVA: A, B, C Source DF SS MS F P Factor 2 210.90 105.45 20.79 0.000 Error 42 213.00 5.07 Total 44 423.90 S = 2.252 R-Sq = 49.75% R-Sq(adj) = 47.36%

Data

A

B

C

Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev ---------+---------+---------+---------+ A 15 12.919 0.661 (-----*----) B 15 14.634 1.849 (-----*-----) C 15 9.431 3.371 (-----*-----) ---------+---------+---------+---------+ 10.0 12.0 14.0 16.0

Conclusion结论: 1. P value=0<0.05, indicate at least have one factor is different with others; P value=0<0.05, 说明至少有一个因子与其它因子有明显差异; 2.From the box plot and confidence interval, we can see there is no obvious difference between A and B, but C have obvious difference with A and B; 从箱形图或置信区间可以看出,A,B之间没有明显差异, C与A,B有明显差异; Extend 拓展: One Way ANOVA(数据堆叠),如何操作?

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?Hypothesis test假设检验
?7. Two way ANOVA Path: Stat/ANOVA/Two way ANOVA produ Shi cti f vit tline y D 1 450 D 2 300 D 3 250 D 4 400 N 1 400 N 2 250 N 3 210 N 4 380 D 1 430 Assume2 D condition 假设条件: 330 Ho: No obvious difference with the three factors. 各因子之间没有明显差异; D 3 230 Ha: There is a factor at least different with others 至少有一个因子与其它因子存在明显差异. D 4 389 N 1 410 N 2 270

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?Hypothesis test假设检验
Boxplot of productivity
450

Two-way ANOVA: productivity versus Shift, line Source DF SS MS F P Shift 1 5625 5625.0 31.45 0.001 line 3 98461 32820.3 183.48 0.000 Interaction 3 475 158.3 0.89 0.489 Error 8 1431 178.9 Total 15 105992

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productivity

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300

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S = 13.37 R-Sq = 98.65% R-Sq(adj) = 97.47%
200 line Shift 1 2 D 3 4 1 2 N 3 4

Conclusion结论: 1. Shift P value=0.001<0.05, Indicate have obvious variance between shifts, and from the plot, we can see D shift’s productivity is higher than N . Shift P value=0.001<0.05, 说明班次之间有明显差异, 从图中可以看出, D班比N班产能要高. 2. Line P value=0<0.05,indicate have obvious variance between lines, from the plot, we see line1 is highest, line 3 is lowest. Line P value=0<0.05, 说明产线之间有明显差世,从图中可以看出, 1线产能最高, 3线最低. 3. There is no obvious interaction between Shift and line. Shift 与line 之间没有明显交互作用.

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?Hypothesis test假设检验
8. Main effect plot 主效果图 Path: Stat/ANOVA/Main effect plot produ Shi cti f vit tline y D 1 450 D 2 300 D 3 250 D 4 400 N 1 400 N 2 250 N 3 210 N 4 380 D 1 430 Conclusion结论: D 1. From the shift main effect, we can see D shift’s productivity is higher than N shift. 2 330 D 从Shift 230 3 的主效果图可以看出, D班次比N班次产能高; D 2. From the line main effect, we can see the sequence of productivity is:1,4,2,3; 4 389 N 从Line 410 1 的主效果图可以看出,产能按从大到小的顺序为:1,4,2,3 N 2 270 N 3 200

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?Hypothesis test假设检验
9. interaction plot 交互作用图 Path: Stat/ANOVA/Interaction plot A B C Y 10 1 1 1 0 1 1 2 90 1 2 1 40 1 2 2 29 2 1 1 60 2 1 2 78 2 2 1 50 2 2 2 40

Conclusion结论: From the interaction plot, we can see there are obvious interaction within A,B,C. 从交互作用图可能看出, A,B,C之间都存在明显的交互作用.

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?Hypothesis test假设检验
? 10 Common hypothesis test table常用假设检验对照表
均值检验 1-Sample t test 2-Sample t test 样本n =1 =2 方差检验 1-vairance 2-variance 样本n =1 >=2 比率检验 1-P 2-P 样本n =1 =2

检验种 类

Paired t test
ANOVA

=2
>=2

Chi-square

>=2

样本为正态分布时使用; 使用情 了解一个或几个总体的方差是 了解一个或几个总体的比率时 了解一个或几个总体的平均值是否 况 否一致时使用 否一致时使用 一致时使用 数据形 态

连续数据

连续数据

离散数据

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?DOE 实验设计
?1. Full Factorial DOE 全因子实验设计 优点: 实验简单, 所有因子之间交互作用都会考虑到; 缺点: 实验次数较多, 成本高; 适用: K≤5;
1.1 实验次数设计 假设:3因子2水平,均值差异为5, Stdev为1;
路径:Stat/Power and sample size/2level factorial design

因子个数 除去中心点的实验次数

Power and Sample Size 2-Level Factorial Design Alpha = 0.05 Assumed standard deviation = 1 Factors: 3 Base Design: 3, 8 Blocks: none Center Total Target Actual Points Effect Reps Runs Power Power 0 5 2 16 0.9 1.00000

重复次数 现在与目标的差值 统计能力

目前标准偏差

?报告显示, 要达到90%以上的统计能力 ,需要重复一次实验,运行16次实验.
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?DOE 实验设计
1.2 实验参数表设计
路径:Stat/DOE/Factorial/Create factorial design

?All DOE must ensure the random of experiment
sequence. Because this can avoid noise. ?所有DOE必须确保实验顺序的随机性; 因为保持实验顺序的 随机性,可以有效避免噪音因子的干扰.

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?DOE 实验设计
1.3 实验及分析
路径:Stat/DOE/Factorial/Analyze factorial design
RunO StdOr Cente r d r d Blocks e P e r t r 5 4 1 2 1 1 1 1

A

B

C

y

-1 1

-1 1

1 -1

70 55

1
9 8 12 15 14 13 11 16 6 10 7 2

3
4 5 6 7 8 9 10 11 12 13 14 15

1
1 1 1 1 1 1 1 1 1 1 1 1

1
1 1 1 1 1 1 1 1 1 1 1 1

-1
-1 1 1 -1 1 -1 -1 1 1 1 -1 1

-1
-1 1 1 1 -1 -1 1 1 -1 -1 1 -1

-1
-1 1 -1 1 1 1 -1 1 1 -1 1 -1

120
130 30 46 38 40 80 67 34 33 99 59 95

3 16 1 1 -1 ?Run experiment base on 1 run order; the -1 86

按Run order顺序进行实验; 36

?DOE 实验设计
1.3 实验及分析
路径:Stat/DOE/Factorial/Analyze factorial design

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?DOE 实验设计
1.4 实验结果分析
路径:Stat/DOE/Factorial/Analyze factorial design
Pareto 柏拉图 Estimated Effects and Coefficients for y (coded units) Term Effect Coef Constant 67.63 A -27.25 -13.63 B -31.50 -15.75 C -39.25 -19.63 A*B 6.00 3.00 A*C -0.25 -0.12 B*C 16.00 8.00 A*B*C 5.00 2.50 SE Coef T 2.132 31.71 2.132 -6.39 2.132 -7.39 2.132 -9.20 2.132 1.41 2.132 -0.06 2.132 3.75 2.132 1.17 P 0.000 0.000 0.000 0.000 0.197 0.955 0.006 0.275

Four in one(四图合一)

S = 8.52936 PRESS = 2328 R-Sq = 96.11% R-Sq(pred) = 84.43% R-Sq(adj) = 92.70%

?结论:
1. From the pareto and result, we can see C,B,A,B*C are significant. 从柏拉图和分析结果可以看出,C,B,A,B*C对输出影响显著; 2. There is no abnormity in the four in one chart, so regression is available.四合一图中,没有异常, 回归方程可用.

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?DOE 实验设计
1.5 减少模型
路径:Stat/DOE/Factorial/Create factorial design

In term option, we only select significant factors, then redo the analysis. 在Term中只选择显著因子,然后重新进行分析.

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?DOE 实验设计
1.5 减少模型
路径:Stat/DOE/Factorial/Create factorial design
Factorial Fit: y versus A, B, C Estimated Effects and Coefficients for y (coded units) Term Effect Coef Constant 67.63 A -27.25 -13.63 B -31.50 -15.75 C -39.25 -19.63 B*C 16.00 8.00 SE Coef T P 2.167 31.21 0.000 2.167 -6.29 0.000 2.167 -7.27 0.000 2.167 -9.06 0.000 2.167 3.69 0.004

S = 8.66681 PRESS = 1748.10 R-Sq = 94.47% R-Sq(pred) = 88.31% R-Sq(adj) = 92.46%

?Conclusion结论:
1.From the pareto and result, we can see all factors are significant.从柏拉图和分析结果可以看出,现在所有因子都显著; 2.In the four in one, find no abnormity, so regression available. 四合一图中,没有异常, 回归方程可用.

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?DOE 实验设计
1.6 主效果和交互作用分析
路径:Stat/DOE/Factorial/ factorial plots

?From main effect plot, we can see A,B,C are significant.
从主效果图上可以看出, A,B,C主效应显著; ?From the interaction plot, we can see there is some interaction between B and C; 从交互作用图上可以看出,B,C 之间有一定交互作用. ?So for most optimized parameter, we will use optimizer to do further optimization. 因此为了找出最优参数组合,下一步用优化器进行统一优化. 41

?DOE 实验设计
1.7 优化器
路径:Stat/DOE/Factorial/ Response Optimizer

?There are Maximum, Minimum, Target three options in the Goal’s menu, here we set Y as a
target model, target:100, LSL:80, USL:120 ?在Goal下拉菜单中有望大,望小,望目标三个选项, 这里我们设置Y为望目标类型, 目标值100, 下限80,上限120. 42

?DOE 实验设计
1.7 优化器
路径:Stat/DOE/Factorial/ Response Optimizer
The red color remark parts are the most optimized parameter, base on the experiments have been done, we can obtain 100.24; 红色圈注部分,为最优参数设置, 基于之前的实验,理论上可把Y优化 到100.04.

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?DOE 实验设计
?2. Fractional Factorial DOE 部分因子实验设计 优点: 实验次数相对较少,成本低; 缺点: 因子之间的交互作用,以及高阶复合因子的交互作用可能被忽略. 适用: K≥5;
操作步骤及方法与全因子DOE是一样的,不同之处在于引入了混淆度的概念:
举例来说: 如果混淆度设为3, 则意味着: A+BC B+AC C+AB I+ABC

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?DOE 实验设计
?3. Response surface DOE 部分因子实验设计 优点: 可以精确模拟出响应曲线,从而找出最优点 缺点: 实验次数较多,费用较高 适用: K<5;
3.1 设计实验表
路径:Stat/DOE/Response surface/Create response surface

?In the options window, we select
randomize run, others use default setup; ?选项中,选中随机运行,其它使用默认设置.

45

?DOE 实验设计
3.2 实验及分析
路径:Stat/DOE/Response surface/Analyze response surface design

Std Run O O r r PtT Blo d d y c e e p k r r e s A 1 8 1 1 -1 2 6 1 1 1 3 16 1 1 -1 4 12 1 1 1 5 9 1 1 -1 6 3 1 1 1 7 1 1 1 -1 8 19 1 1

Y 20 30 44 78 34 78 80 11 1 1 1 8 1 . 6

B -1 -1 1 1 -1 -1 1

C -1 -1 -1 -1 1 1 1

?按Run order顺序进行实验; ?进行Terms和Graph设置,完成后进行分析.

46

?DOE 实验设计
3.2 实验及分析
路径:Stat/DOE/Response surface/Analyze response surface design
Term Coef SE Coef T P Constant 56.568 2.867 19.729 0.000 A 15.383 1.902 8.087 0.000 B 18.589 1.902 9.771 0.000 C 13.799 1.902 7.254 0.000 A*A -1.006 1.852 -0.543 0.599 B*B 1.292 1.852 0.698 0.501 C*C 2.176 1.852 1.175 0.267 A*B 2.250 2.486 0.905 0.387 A*C 4.750 2.486 1.911 0.085 B*C 1.750 2.486 0.704 0.497
Residual Plots for Y
Normal Probability Plot
99 90
Residual Percent

Versus Fits
10 5 0 -5 -10

50 10 1 -10 -5 0 Residual 5 10

30

60 90 Fitted Value

120

Histogram
4.8
Frequency Residual

Versus Order
10 5 0 -5 -10

3.6 2.4 1.2 0.0 -10 -5 0 Residual 5 10

S = 7.03017 PRESS = 3355.34 R-Sq = 95.67% R-Sq(pred) = 70.57% R-Sq(adj) = 91.76%

2

4

6 8 10 12 14 16 Observation Order

18

20

?4合一图没有发现异常, 回归方程可以信任; ?观察P值, 发现A,B,C,A*C显著; ?R-sq(adj)=91.76%

47

?DOE 实验设计
3.3 减小模型 重复上步操作,在Terms中去掉不显著因子,操作如下:

48

?DOE 实验设计
Term Coef SE Coef T Constant 58.250 1.494 38.981 A 15.383 1.808 8.507 B 18.589 1.808 10.279 C 13.799 1.808 7.631 A*C 4.750 2.363 2.010 P 0.000 0.000 0.000 0.000 0.063
Residual Plots for Y
Normal Probability Plot
99 10 90 50 10 1 -10 0 Residual 10
Residual Percent

Versus Fits

5 0 -5 -10 20 40 60 80 Fitted Value 100

Histogram

Versus Order
10
Residual

Frequency

S = 6.68272 PRESS = 1427.89 R-Sq = 94.12% R-Sq(pred) = 87.48% R-Sq(adj) = 92.56%

4 3 2 1 0 -7.5 -5.0 -2.5 0.0 2.5 Residual 5.0 7.5 10.0

5 0 -5 -10 2 4 6 8 10 12 14 16 Observation Order 18 20

?4合一图没有发现异常, 回归方程可以信任; ?观察P值, 发现A,B,C,A*C均显著; ?R-sq(adj)=92.56%,比之前模型回归效果更好. ?回归方程:Y=58.25+15.383*A+18.589*B+13.799*C+4.74*A*C

49

?DOE 实验设计
3.4 Contour/Surface plot 等高/曲面图 路径:Stat/DOE/response surface/Contour surface plots

通过等高线,可以快速给我们指明方向, 我们 可以沿着与等高线垂直方向上升或下降,从而快速 达到目标;

通过曲面图,我们可以看出两两因子之间的交互作用.

50

?DOE 实验设计
3.5 优化参数 路径: Stat/DOE/Response surface/Response optimizer
这里设置Y为望目型, 目标值50, 下限40,上限60 通过优化器模拟,最终可以达成目标,最优参数设置 如图中红色圈注部分.

51

? Regression analysis 回归分析
1. 多元回归 路径: Stat/Regression/
Y X1 78. 57 74. 31 10 4 . 311 87. 611 95. 97 10 9 . 211 10 X2 X3 X4 26 6 60 29 15 52

56 8 20 31 8 47 52 6 33

55 9 22
52

? Regression analysis 回归分析
The regression equation is Y = 62.4 + 1.55 X1 + 0.510 X2 + 0.102 X3 - 0.144 X4
Percent

Residual Plots for Y
Normal Probability Plot of the Residuals
99 90 50 10 1 -5.0 -2.5 0.0 Residual 2.5 5.0 4

Residuals Versus the Fitted Values

Residual

2 0 -2 -4 80 90 100 Fitted Value 110 120

Frequency

Residual
-3 -2 -1 0 1 Residual 2 3 4

Predictor Coef SE Coef T P Constant 62.41 70.07 0.89 0.399 X1 1.5511 0.7448 2.08 0.071 X2 0.5102 0.7238 0.70 0.501 X3 0.1019 0.7547 0.14 0.896 X4 -0.1441 0.7091 -0.20 0.844

Histogram of the Residuals
3 2 1 0 4 2 0 -2 -4

Residuals Versus the Order of the Data

S = 2.44601 R-Sq = 98.2% R-Sq(adj) = 97.4%

1

2

3

4

5 6 7 8 9 10 11 12 13 Observation Order

报告中, R-Sq(adj)=97.4%, 四合一图没有发同异常, 但是否是最好的回归模型呢? Minitab可以帮我们来确认. 在此之前,我们先学习几个判定原则: ?R-Sq(adj)越大越好; ?Cp越小越好,Cp<K+1 ?S越小越好.

53

? Regression analysis 回归分析
路径: Stat/Regression/ Best Subsets
Best Subsets Regression: Y versus X1, X2, X3, X4

Response is Y
Mallows XXXX Vars R-Sq R-Sq(adj) C-p S 1234 1 67.5 64.5 138.7 8.9639 X 1 66.6 63.6 142.5 9.0771 X 2 97.9 97.4 2.7 2.4063 X X 2 97.2 96.7 5.5 2.7343 X X 3 98.2 97.6 3.0 2.3087 X X X 3 98.2 97.6 3.0 2.3121 X X X 4 98.2 97.4 5.0 2.4460 X X X X

根据刚刚学到的三个判定原则, 大家判断如何得到最好的回归方程?
Predictor Coef SE Coef T P Constant 71.65 14.14 5.07 0.001 X1 1.4519 0.1170 12.41 0.000 X2 0.4161 0.1856 2.24 0.052 X4 -0.2365 0.1733 -1.37 0.205 S = 2.30874 R-Sq = 98.2% R-Sq(adj) = 97.6%

去掉x3, 重新回归, 得到最优的回归方程:

54

? Regression analysis 回归分析
1. 一元回归 1.1 一元线性回归

一元回归即只含有一个自变量, 这里我们: 1.选择一元线性回归; 2.图表中选择四图合一;

55

? Regression analysis 回归分析
Regression Analysis: Y versus X The regression equation is Y = - 51168 + 2333 X

S = 6504.54 R-Sq = 92.8% R-Sq(adj) = 92.5%
Analysis of Variance Source DF SS MS F P Regression 1 1.52125E+10 1.52125E+10 359.56 0.000 Error 28 1.18465E+09 4.23090E+07 Total 29 1.63971E+10

模型判定原则: S越小越好; R-sq(adj)越大越好; P值<0.05,说明回归方程显著.

1

2

编号

1

2

3

4 正常

图视结 明显弯 非正态 非正态 果 曲
3 4

结论: 数据殘差存在明显弯曲, 需增加二次或三次 项进行回归.

56

? Regression analysis 回归分析
1.2一元二次回归

这里我们: 1.选择一元二次回归; 2.图表中选择四图合一;

57

? Regression analysis 回归分析
The regression equation is Y = 18875 - 1765 X + 55.81 X**2 S = 677.372 R-Sq = 99.9% R-Sq(adj) = 99.9%

Analysis of Variance Source DF SS MS F P Regression 2 1.63847E+10 8192365991 17854.78 0.000 Error 27 1.23885E+07 458833 Total 29 1.63971E+10
Sequential Analysis of Variance Source DF SS F P Linear 1 1.52125E+10 359.56 0.000 Quadratic 1 1.17226E+09 2554.88 0.000

结论: 1. S=677, R-sq(adj)=99.9%, Pvalue=0 说明回归方程拟合比较好; 2. 四合一图中,殘差变异不对称,有一定的 弯曲; 3. 可以加入立方项进行回归;
58

? Regression analysis 回归分析
1.3一元三次回归

这里我们: 1.选择一元三次回归; 2.图表中选择四图合一;

59

? Regression analysis 回归分析
The regression equation is Y = - 100.0 + 50.00 X + 2.000 X**2 + 0.5000 X**3 S = 0 R-Sq = 100.0% R-Sq(adj) = 100.0% Analysis of Variance Source DF SS MS F P Regression 3 1.63971E+10 5465706826 * * Error 26 0.00000E+00 0 Total 29 1.63971E+10 Sequential Analysis of Variance Source DF SS F P Linear 1 1.52125E+10 359.56 0.000 Quadratic 1 1.17226E+09 2554.88 0.000 Cubic 1 1.23885E+07 * *

结论: 1. S=0, R-sq(adj)=100%, Pvalue=0 说明回归方程与数据完全拟合. 2. 四合一图中,没有发现异常,回归方 程可信任.

60

? MSA测量系统分析
MSA 即为Measurement system analysis, 通常从以下几个方面对测量系统进行评判: 1. 分辨力;即为最小测量单位,要求:Unit≤Min(6σ/10,USL-LSL/10) 2. 稳定性, 要求线性和偏倚的Pvalue均<0.05; 3. 重复性和再现性,即大家常说的GRR: a.计量型测量系统的全格标志
%GageR&R或%P/T<10% 测量系统能力

小于10%
介于10%~30% 大于30%

良好
勉强可接受 不合格

b.计量型测量系统的全格标志
Percent (All appraisers VS standard) 大于90% 介于80%~90% 小于80% 测量系统能力 良好 勉强可接受 不合格

61

? MSA测量系统分析
1. 分辨力
分辨力是指测量系统识别并显示被测量最小变化的能力, 往往通过最小刻度来反映, 分辨力最起码要求为: Unit≤Min(6σ/10, USL-LSL/10)

直尺 测径规 测微计

6mm 5.9mm 5.88mm
62

? MSA测量系统分析
2. 稳定性
2.1 偏倚和线性
偏倚是指多次测量的理论上的平均值u与参考值Vr之间的差异; 线性是指在测量系统预期的量程范围内,各点处的偏倚与参考值呈现线性关系.

63

? MSA测量系统分析
2.2 结果分析

回归方程: Bais=0.020222x(参考值)-0.09264, 数据在20附近时, 偏倚最大为3%, 线性和偏倚P值均小于0.05, 说明测量系统在整个范围内存在线性偏倚. 实际使用中,我们可以根据回归方程对实测值进行修正.
64

? MSA测量系统分析
3. 重复性和再现性GRR
3.1 连续型测量系统分析(Crossed)
要求: 样品数量: 5~10个; 评判人员:2~3人; 每人重复:2~3次

路径:Stat/Quality tool/Gage study/ Gage R&R study/(crossed)

65

? MSA测量系统分析
Gage R&R %Contribution Source VarComp (of VarComp) Total Gage R&R 0.0171 0.03 Repeatability 0.0125 0.02 Reproducibility 0.0045 0.01 作业者 0.0000 0.00 作业者 *部件 0.0045 0.01 Part-To-Part 55.4780 99.97 Total Variation 55.4951 100.00 Study?Var %Study?Var %Tolerance Source StdDev (SD) (6?*?SD) (%SV) (SV/Toler) Total Gage R&R 0.13066 0.7840 1.75 9.80 Repeatability 0.11197 0.6718 1.50 8.40 Reproducibility 0.06735 0.4041 0.90 5.05 作业者 0.00000 0.0000 0.00 0.00 作业者 *部件 0.06735 0.4041 0.90 5.05 Part-To-Part 7.44835 44.6901 99.98 558.63 Total Variation 7.44950 44.6970 100.00 558.71 Number of Distinct Categories = 80

结论: ?%SV=1.75%, SV/Toler=9.8%,均小于10%, ?NDC=80>4 测量系统良好.

66

? MSA测量系统分析
3.2 连续型测量系统分析(Nested)
路径:Stat/Quality tool/Gage study/Gage R&R study/(Nested)
说明: 比如说有些破坏性实验,一次性实验结束后,别人要想再做实验必须另选样品; 比如我们要做一个MSA, 样品分别在马来西亚, 美国,珠海, 相距太远,不可能一个样品相互之间传输; 此时嵌套式的MSA可以为我们解决这些问题.

67

? MSA测量系统分析
Gage R&R %Contribution Source VarComp (of VarComp) Total Gage R&R 1.8333 14.50 Repeatability 1.8333 14.50 Reproducibility 0.0000 0.00 Part-To-Part 10.8083 85.50 Total Variation 12.6417 100.00

Study?Var %Study?Var %Tolerance Source StdDev (SD) (6?*?SD) (%SV) (SV/Toler) Total Gage R&R 1.35401 8.1240 38.08 50.78 Repeatability 1.35401 8.1240 38.08 50.78 Reproducibility 0.00000 0.0000 0.00 0.00 Part-To-Part 3.28760 19.7256 92.46 123.29 Total Variation 3.55551 21.3331 100.00 133.33

Number of Distinct Categories = 3

结论: ?%SV=38.08%, SV/Toler=50.78%,均大于30%, ?NDC=3<5 测量系统不合格.

68

? MSA测量系统分析
4. 计数型测量系统分析
路径:Stat/Quality tool/Attribute agreement analysis

69

? MSA测量系统分析
Within Appraisers Assessment Agreement Appraiser #?Inspected #?Matched Percent 95 % CI 钱 6 3 50.00 (11.81, 88.19) 孙 6 4 66.67 (22.28, 95.67) 赵 6 6 100.00 (60.70, 100.00) # Matched: Appraiser agrees with him/herself across trials. Each Appraiser vs Standard Assessment Agreement Appraiser #?Inspected #?Matched Percent 95 % CI 钱 6 2 33.33 ( 4.33, 77.72) 孙 6 4 66.67 (22.28, 95.67) 赵 6 6 100.00 (60.70, 100.00) # Matched: Appraiser's assessment across trials agrees with the known standard. Between Appraisers Assessment Agreement #?Inspected #?Matched Percent 95 % CI 6 1 16.67 (0.42, 64.12) # Matched: All appraisers' assessments agree with each other. All Appraisers vs Standard Assessment Agreement #?Inspected #?Matched Percent 95 % CI 6 1 16.67 (0.42, 64.12) # Matched: All appraisers' assessments agree with the known standard.
Assessment Agreement
Date of study: Reported by: Name of product: Misc:

Within Appraisers
100
95.0% ?C I Percent

Appraiser vs Standard
100
95.0% ?C I Percent

80

80

Percent

40

Percent

60

60

40

20

20

0 Appraiser

0 Appraiser

结论: ?红色圈注的Percent 小于80%,测量系统不合格. ?三个操作员中,钱某的一致性差,准确性也差,需 分析原因. 孙某的一致性差, 赵某做的最好.

70

? SPC管制图
选取正确的控制图类型
属性数据 变量数据
数据类型

缺陷

以缺陷还是 不良计数

不良品
单值

单值还是 子组形式

测量 分组

每次取样样本量 固定不变

Yes

c
正态分布

Yes

I, MR No

子组大于8

No

Yes

u
子组大小固定

Yes

X-bar, R

np

X-bar, s

No

p

71

? SPC管制图
1. I-MR chart Path:Stat/Control chart/Variable chart for individual/I-MR

如果我们要对比一个制程改善前后的状况,可以在此输入 分界点,输出图中会自动增加分界线.

我们可以在Scale中设置参考线.具体操作 如图所示:

72

? SPC管制图

73

? SPC管制图
SPC 8项判稳原则,在软件中已经设好(如左图所示), 大家可以勾选用还是不用:

最终生成的I-MR chart 如右图 所示: 图中和报告中没有显示出异常点, 制程稳定.

74

? SPC管制图
2. X-bar R chart Path:Stat/Control chart/Variable chart for subgroup/X-bar R 2.1 设置

选择相应的数据列

这里我们设置5个数 据为一个子组.

Scale 和 Option 选项操 作与前面一样.

75

? SPC管制图
2.2 控制图输出

150个数据分成 30组,每组5个数, 左图为30组数平 均值的平均值.

150个数据分成 30组,每组5个数, 左图为每小组的 极差图.

76

? SPC管制图
2.3 报告输出
根据8项判稳原则,如果所有点都没有异常, Session 窗口中不会有结果输出,显示如下: Xbar-R Chart of C2

如果有异常点,报告会列出违反了 哪了条原则,具体是哪个点,如下显 示:
Test Results for R Chart of X-bar R TEST 1. One point more than 3.00 standard deviations from center line. Test Failed at points: 22, 23 TEST 2. 9 points in a row on same side of center line. Test Failed at points: 9, 19, 20, 21

77

? SPC管制图
3. X-bar S chart Path:Stat/Control chart/Variable chart for subgroup/X-bar S 3.1 设置

选择相应的数据列

这里我们设置10个 数据为一个子组.

Scale 和 Option 选项操 作与前面一样.

具体设置与X-bar R 图的制做方法一样.
78

? SPC管制图
3.2 输出图形

150个数据分成 15组,每组10个数, 左图为15组数平 均值的平均值.

150个数据分成 15组,每组10个数, 左图为15个子组, 每组数据标准偏 差的推移图

79

? SPC管制图
4. P chart Path:Stat/Control chart/Attributes chart/ P-chart 4.1 设置

?Subgroup size is variable, not a constant. 子组大小是可变的,不是一个常数.

80

? SPC管制图
4.2 图形输出

p ?

k ?1 m

? Nk ? nk
p(1 ? p) nk

m

k ?1

UCL

? p ?3

LCL

? p ?3

p(1 ? p) nk

Measures the proportion of defective units in a subgroup; The subgroup size can be variable 测量每个子组中不良品的比例;子组大小可以变化.
81

? SPC管制图
5. NP chart Path:Stat/Control chart/Attributes chart/ NP-chart 5.1 设置

选择不良品数量

这里我们假设子组大小为 5000.

?Subgroup size a constant. 子组大小是一个常数. 82

? SPC管制图
5.2 图形输出
m

np ?

k ?1

? Nk m

UCL ? n p ? 3 n p (1 ? p )

LCL ? n p ? 3 n p (1 ? p )

Measures the number of defective items in a subgroup, Requires a constant subgroup size. 测量子组的不良品数目,要求子组样本量相同.

83

? SPC管制图
6. U chart Path:Stat/Control chart/Attributes chart/ U-chart 6.1 设置

选择缺陷数量

选择子组所在的列.

?Subgroup size is variable, not a constant. 子组大小是可变的,不是一个常数. 84

? SPC管制图
6.2 图形输出

u?

k ?1 m

? ck ? nk
u nk

m

k ?1

UCLk ? u ? 3

LCLk ? u ? 3

u nk

Measures the number of defects/unit of product (dpu) ,The subgroup size can be variable 测量每个产品的缺陷数量,子组数量可以变化.
85

? SPC管制图
7. C chart Path:Stat/Control chart/Attributes chart/ C-chart 7.1 设置

选择缺陷数量

?Subgroup size is variable, not a constant. 子组大小是一个常数. 86

? SPC管制图
7.2图形输出
m

c ?

k ?1

? ck m

UCL ? c ? 3 c

LCL ? c ? 3 c

Measures the total number of defects in a subgroup; requires a constant subgroup size 测量每个子组的缺陷数,要求子组数为常数.
87

? Graph 图表
1. Normally test 正态测试图 Path: Stat /Basic Statistic/ Normally test
1. 2. 3. 选择数据列; Percentitle line: None; Tests: Anderson-Darling

1.

Pvalue=0.946>0.05, 数据正态分布

88

? Graph 图表
2. Process capability analysis chart 制程能力分析图 Path: Stat /Quality tool / Capability analysis / Normal
1. 2. 3. 选择数据列; 设置上下控制限 如果数据为非正态,可以进行转换

1. 2. 3.

短期能力指数: Cp, Cpk 长期能力指数:Pp, Ppk; 不良率,DPPM….

89

? Graph 图表
3. Pareto chart 柏拉图 Path: Stat /Quality tool / Capability analysis / Normal

1. 2.

如果数据没有经过分类, 选中第1个方框; 如果数据已分类,选中第2个方框内容;

1. 2. 3.

柏拉图可以帮我们识别关键因子. 通常用80/20原则找出关键的少数. 大家可以根据需要改变相应的设置

90

? Graph 图表
4. Histogram 柱状图 Path: Graph / Histogram

简易柱状图

群组柱状图

1. 2. 3.

柱状图可以看出数据的分布状况. 图中显示平均值,标准差等信息. 大家可以根据需要改变相应的设置

91

? Graph 图表
5. Box plot 箱形图 Path: Graph / Box Plot

简易箱形图 只有1个Y

群组箱形图 多个Y值

92

? Graph 图表

最大值=Min( Q3+1.5Range, Max value)

Q3, 3分位数 Media, 中位数 Q1, 1分位数

最小值=Max( Q1-1.5Range, Min value)

异常点

箱形图可以显示出数据的集中分布状况, 箱形图越窄, 说明数据越集中; 异常点是我们必须要先去解决的问题, 必须清楚了解原因所在.

93

? Graph 图表
6. Pie plot 饼图 Path: Graph / Pie Plot

1. 2.

如果数据未分类整理,选中第一项; 如果数据已分类整理,选中第二项;

1. 2.

饼图可以显示各类别的分布状况. Minitab中可以同时生成多少图形;

94

? Graph 图表
7. Scatter Plot 散布图 Path: Graph / Scatter

1.

散布图可以帮我们识别两组数据之间的 相关性, 判断两个因子之间是否有影响;

95

? Graph 图表
Scatter Plot correlation 散布图相关性

Strong positive correlation 强正相关

Strong negative correlation 强负相关

Slightly correlation 弱相关

No correlation 不相关

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? Q&A

Answer Questions?

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