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Minitab 12 for Windows - A Six Sigma application
LEAN Six Sigma
2
Content
The basics– Minitab Windows 6– Toolbars 7 - 9– Performing Calculations
10 - 11– Copying to other applications 12
Working with data– Changing Data Type 13 - 15– Stacking Data/Data Blocks 16 - 19– Creating Patterned Data
20 - 21– Re-coding Data 22 - 24– Transforming Data 25 - 28
Data analysis 29– Capability analysis 30 - 31– Descriptive statistics 32 - 33– Product report 70 - 71– Process report 72 - 74
Gage R&R– Gage R&R 34 - 37
Hypothesis tests– Normality test 38 - 39– Probability Plot 75 - 76– Run Chart 40 - 43– ANOVA test 44 - 45– One sample t-test 46 - 47– Two sample t-test 48 - 49– Homogeneity of Variance (F-test) 50 - 51– Chi Square test 52 - 53
Design of experiments 54– Create Factorial DoE Design 55 - 56– Analyze Factorial DoE Design 57 - 58– Main Effect Plots 59 - 60– Interaction Plots 61 - 62
Regression 63– Regression 64 - 65– Fitted line plots 66 - 67– Residuals analysis 68 - 69
Slide Slide
3
DMAIC overview
Define
Measure
Analyze
Improve
Control
A. Identify Project CTQ’s Y -> yB. Develop Team CharterC. Define Process
1. Select CTQ Characteristics y2. Define Performance Standards y3. Validate Measurement System y
4. Establish Product Capability y5. Define Performance Objectives y6. Identify Variation Sources Many x’s
7. Screen Potential Causes Vital x8. Discover Variable Relationship Vital x9. Establish Operating Tolerances Vital x
10. Validate Measurement System Vital x11. Determine Process Capability Vital x12. Implement Process Controls Vital x
Translate Successes y -> Y
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4
Tool overview
Step ObjectiveFM EA
Process map
Anova, t/F test
Regression, correlation
GR&RCapability Analysis
Zst, ZltNormality
plotConfidence
intervalsDOE Run chart
Step 1 Select internal CTQ
Step 2 Define performance standards
Step 3 Validate measurement system
Step 4 Establish product capability
Step 5 Define performance objectives
Step 6 Identify variation sources
Step 7 Screen potential causes
Step 8 Discover variable relationships
Step 9 Establish operating tolerances
Step 10 Validate measurement system
Step 11 Determine process capability
Step 12 Implement process controls
Some Tools supported by Minitab
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5
The Basics
Minitab WindowsToolbarsPerforming CalculationsCopying to other applications
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6
Minitab Windows
Session Window- Analytical output
Session Window- Analytical output
Data Window- A worksheet, NOT a spreadsheet- Column are above first row- Everything in a column is considered to be the same variable
Data Window- A worksheet, NOT a spreadsheet- Column are above first row- Everything in a column is considered to be the same variable
Menu BarMenu Bar
Info Window- Synopsis of worksheet
Info Window- Synopsis of worksheet
History Window- Stores commands
History Window- Stores commands
- Four interactive windows- Only one open at a time- Windows saved separately
- Four interactive windows- Only one open at a time- Windows saved separately
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7
The Data window toolbar
Open File
Save File
Print Window
Insert Cells
Insert Rows
Insert Columns
Move ColumnsMove Cells
Manage Worksheets
Manage Graphs
Close GraphsCancel
Cut
Copy
PasteUndo
Next Brushed Row
Last Dialog Box
Session WindowData Window
Previous Brushed Row
Help
These commands can also be found in drop down menu's, or accessed with
shortcut keys
These commands can also be found in drop down menu's, or accessed with
shortcut keys
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8
The Session window toolbar
Open File
Save File
Print Window
Previous Command
Next Command
Find
Find Next
Manage Worksheets
Manage Graphs
Close GraphsCancel
Cut
Copy
PasteUndo
Last Dialog Box
Session Window
Data WindowHelp
These commands can also be found in drop down menu's, or accessed with
shortcut keys
These commands can also be found in drop down menu's, or accessed with
shortcut keys
Return to overview page
9
The Graph window toolbar
Open File
Save File
Print Window
View Mode
Edit Mode
Brush Mode
Manage Worksheets
Manage Graphs
Close GraphsCancel
Cut
Copy
PasteUndo
Last Dialog Box
Session Window
Data WindowHelp
These commands can also be found in drop down menu's, or accessed with
shortcut keys
These commands can also be found in drop down menu's, or accessed with
shortcut keys
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10
Mathematical Calculations
Select:Calc => Calculator... Enter column
where results of calculation must
be stored
Enter column where results of calculation must
be stored
Enter formula. You can click on
functions from list and/or keys.
Enter formula. You can click on
functions from list and/or keys.
Click OK to get results
Click OK to get results
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11
Mathematical Calculations
Note: The output column DOES NOT update if a
value in a input column is changed. The column will only update if commands
are executed again.
Note: The output column DOES NOT update if a
value in a input column is changed. The column will only update if commands
are executed again.
Original dataNew column with Sorted data
The Worksheet Output:
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12
Copying to other applications
From session window
– Highlight text to copy– Select Edit => Copy (or Ctrl + c)– Open application copying into– Select Edit => Paste (or Ctrl + v)– Use new Courier font to preserve column spacing
From graph window
– Must be in View Mode– Left click on mouse– Select Copy Graph– Open application copying into– Select Edit => Paste (or Ctrl + v) or Edit => Past Special... select Picture
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13
Working with Data
Changing Data TypeStacking Data/Data BlocksCreating Patterned DataRe-coding DataTransforming Data
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Changing Data Type
If a column is coded as text and needs to be recorded as numeric…
Manip => Change Data Type => Text to Numeric...Initial Column (“T” in column header).Note that text is left justified.
Initial Column (“T” in column header).Note that text is left justified. Column to
be changed
Column tobe changed
Column for converted data. May be same as original, if desired
Column for converted data. May be same as original, if desired
Click OK to get resultsClick OK to get results
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15
The worksheet outputColumn type is now numeric. Note
that numeric columns are right justified
Column type is now numeric. Note that numeric columns are right
justified
Non numeric values are replaced with asterisk
(*)
Non numeric values are replaced with asterisk
(*)
Return to overview page
Changing Data Type
16
Stacking Data/Data Blocks
Manip => Stack/Unstack => Stack Columns...Enter columns to stack.
Fists column entered will be at the top of the
stacked column followed by second column etc.
Enter columns to stack. Fists column entered will
be at the top of the stacked column followed by second column etc.
Enter column for stacked
output
Enter column for stacked
output
Subscripts can be used to identify separate input
columns
Subscripts can be used to identify separate input
columns
Click OK to get resultsClick OK to get results
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17
Data from the three original columns is now stacked into one
column
Data from the three original columns is now stacked into one
column
The worksheet output
Subscripts can be used to identify original
column/group
Subscripts can be used to identify original
column/group
Return to overview page
Stacking Data/Data Blocks
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Manip => Stack/Unstack => Stack Blocks of columns...
Columns contained in first data block. These will be across columns at top of stacked block
Columns contained in first data block. These will be across columns at top of stacked block
Columns contained in second block. Up to five blocks can be stacked with this dialog box
Columns contained in second block. Up to five blocks can be stacked with this dialog box
Subscripts can be used to identify separate blocks
Subscripts can be used to identify separate blocks
Click OK to get resultsClick OK to get resultsColumn to store
new stacked blocks
Column to store new stacked
blocks
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Stacking Data/Data Blocks
19
The worksheet output
Original dataOriginal data
Optional subscript column. Can use to track blocks. In this example, the first
block contained data for standard equipment, the second contained data
for new equipment
Optional subscript column. Can use to track blocks. In this example, the first
block contained data for standard equipment, the second contained data
for new equipment
First data blockFirst data block
Second data blockSecond data block
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Stacking Data/Data Blocks
20
Creating Patterned Data
Calc => Make Patterned Data => Simple Set of Numbers...
Last number in patternLast number in pattern
Increment number by ?
Increment number by ?
Use to repeat numbers I.e.
1,1,2,2...
Use to repeat numbers I.e.
1,1,2,2...Click OK to get resultsClick OK to get resultsUse to repeat entire list I.e. 1,2,3,1,2,3...
Use to repeat entire list I.e. 1,2,3,1,2,3...
First number in patternFirst number in pattern
Select column that will contain the patterned data
Select column that will contain the patterned data
Note: Data/Time sequence data can be generated with:Calc => Make Patterned Data => Data/Time Values...
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The worksheet output
Example shown in dialog box
Example shown in dialog box
An example for repeated values
An example for repeated values
An example for a date sequence
An example for a date sequence
Any pattern sequence can be generated
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Creating Patterned Data
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Re-coding Data
In column c11 the machines are called 1, 2 and 3. We would like them to have more recognizable names: 1 = Saw, 2 = Drill and 3 = Mill. How do I do that in an easy and smart way ????
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Manip => Code => Numeric to Text…Other possible transformations: Text to Numeric, Numeric to Numeric, Text to Text
Enter original valueEnter original value
Enter column where to store re-coded
data
Enter column where to store re-coded
data
Select column contai-ning data to re-code
Select column contai-ning data to re-code
Click OK to get resultsClick OK to get results
Enter new textEnter new text
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Re-coding Data
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The worksheet output
Original dataOriginal data
Re-coded dataRe-coded data
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Re-coding Data
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Most of the statistical tools require a normal distribution. Only few processes are really normally distributed… If you have a hard limit in your spec (e.g. 100% as maximum, or 0% as minimum) and your process looks normal (one process…) there is a possibility to transform the data to normal with the box-cox transformation. You need to double check this with the normality plot…..
Stat => Control Charts => Box-Cox Transformation…
Note: This transformation is for positive data only
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Transforming Data
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If your data is not normally distributed and belong to one process !!You have a hard limit that limits your data from passing a certain level.
You can transform your data via Box-cox transformation to see whether they are normal or not...
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Transforming Data
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Select:Stat => Control Charts => Box-Cox Transformation…
Column for transformed data
Column for transformed data
Enter subgroup size if applicable. If not use 1
Enter subgroup size if applicable. If not use 1
Data to be transformed
Data to be transformed
Click OK to get results
Click OK to get results
Return to overview page
Transforming Data
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The worksheet output
Original data
Original data
Transformed data
Transformed data
The Graphical output
Objective is to minimize standard deviation. 95 % confidence interval for lambda (power)
Objective is to minimize standard deviation. 95 % confidence interval for lambda (power)
Transform power used to generate C2
Transform power used to generate C2
Transformation Power (p)Cube 3Square 2No Change 1Square Root 0,5Logarithm 0Reciprocal Root -0,5Reciprocal -1
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Transforming Data
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Commonly used tools in Minitab
Capability analysisDescriptive statisticsNormality testRun chartANOVA testOne sample t-testTwo sample t-testHomogeneity of variance (F-test)Chi Square testDesign of ExperimentRegression analysis
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30
Statistical Problem Description
Stat => Quality Tools => Capability Analysis (Normal)...
Click OK to get results
Click OK to get results
Enter specification limits. At least one required. Check “Hard Limit” if applicable I.e. cycle time can´t go below zero
Enter specification limits. At least one required. Check “Hard Limit” if applicable I.e. cycle time can´t go below zero
Enter column containing data. Enter Subgroup size
Enter column containing data. Enter Subgroup size
For subgroup size of 1, select Average moving range. For subgroups >1 select Pooled standard deviation
For subgroup size of 1, select Average moving range. For subgroups >1 select Pooled standard deviation
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31
The worksheet output
Histogram of data
Histogram of data
Minitab will always draw normal line, even if the data isn´t normal. Can select under edit mode and delete. See Graph Editing
Minitab will always draw normal line, even if the data isn´t normal. Can select under edit mode and delete. See Graph Editing Mean and
standard deviation etc.
Mean and standard deviation etc.
DPMO level DPMO level
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Statistical Problem Description
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Stat => Basic Statistics => Display descriptive statistics
Select column
Select column
Select Graphs
Select Graphs
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Statistical Problem Description
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The worksheet output Histogram of data
Histogram of data
Quartiles, median and min, max values
Quartiles, median and min, max values
Mean and standard deviation etc.
Mean and standard deviation etc.
Confidence intervals
Confidence intervals
109 115 121 127 133 139
95% Confidence Interval for Mu
123 124 125 126
95% Confidence Interval for Median
Variable: C1
A-Squared:P-Value:
MeanStDevVarianceSkewnessKurtosisN
Minimum1st QuartileMedian3rd QuartileMaximum
123.463
5.648
122.922
0.4640.250
124.739 6.433
41.38520.2312004.30E-02
100
106.991120.757123.543128.803140.803
126.015
7.473
125.951
Anderson-Darling Normality Test
95% Confidence Interval for Mu
95% Confidence Interval for Sigma
95% Confidence Interval for Median
Descriptive Statistics
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Statistical Problem Description
34
Gage R&R
Select:Stat => Quality Tools => Gage R&R Study...
Enter tolerance range
Enter tolerance range
Enter column containing data for: Parts, operators and measured results
Enter column containing data for: Parts, operators and measured results
Click OK to get results
Click OK to get results
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35
The graphical output
How much variation is coming from parts ?
How much variation is coming from parts ?
How do the average readings for each
operator compare ?
How do the average readings for each
operator compare ?
How do the distribution of
readings for each operator compare
?
How do the distribution of
readings for each operator compare
?
How much variation do we see in readings for the same
part ?
How much variation do we see in readings for the same
part ?Is repeatability or
reproducibility the issue ?
Is repeatability or reproducibility
the issue ?
What percentage of the total variation is coming
from the gage ?
What percentage of the total variation is coming
from the gage ?
How much difference does each
operator see between 1st
and 2nd readings ?
How much difference does each
operator see between 1st
and 2nd readings ?
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Gage R&R
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First table
– ANOVA table• Shows weather part, operator or part* operator are major contributors to variation
in the data. Look for p-values < 0,05Second table
– Variance components– Standard deviation– A constant multiple of standard deviations, usually 5.15*sigma
• 99% of the area under a curve is within an interval of 5.15 standard deviations wide
• This number is also called the study variation and used to estimate how wide an interval one would need to capture 99 % of the measurements from a process
Third table
– % contribution to total variation made by each variance component• Each component is divided by the total variation then multiplied by 100
– % study variation• Standard deviation of each component is divided by the total standard deviation.
Total WILL NOT sum 100
– % tolerance• Enter tolerance range (upper limit - lower limit) under options, if desired
The session output
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Gage R&R
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Gage R&R Study - ANOVA Method
Two-Way ANOVA Table With InteractionSource DF SS MS F P Part 4 0,518000 0,129500 7,00000 0,01003Operator 2 0,028667 0,014333 0,77477 0,49253Operator*Part 8 0,148000 0,018500 2,92105 0,03508Repeatability 15 0,095000 0,006333 Total 29 0,789667
Gage R&RSource VarComp StdDev 5,15*SigmaTotal Gage R&R 0,012417 0,111430 0,573865 Repeatability 0,006333 0,079582 0,409849 Reproducibility 0,006083 0,077996 0,401678 Operator 0,000000 0,000000 0,000000 Operator*Part 0,006083 0,077996 0,401678 Part-To-Part 0,018500 0,136015 0,700476 Total Variation 0,030917 0,175831 0,905531
Source %Contribution %Study Var %ToleranceTotal Gage R&R 40,16 63,37 57,39 Repeatability 20,49 45,26 40,98 Reproducibility 19,68 44,36 40,17 Operator 0,00 0,00 0,00 Operator*Part 19,68 44,36 40,17 Part-To-Part 59,84 77,36 70,05 Total Variation 100,00 100,00 90,55
Number of Distinct Categories = 2
What are the major contributors ? Look for p-values < 0,05
What are the major contributors ? Look for p-values < 0,05
Estimate of interval needed to capture 99 %
of measurements
Estimate of interval needed to capture 99 %
of measurements
% gage R&R. Ideal is < 10 % of tolerance. < 30 % is acceptable
% gage R&R. Ideal is < 10 % of tolerance. < 30 % is acceptable
Distinct categories the measuring system can
distinguish. If less than 2, measurement can´t
distinguish. Two is go/ no go. Need 4 for a good system
Distinct categories the measuring system can
distinguish. If less than 2, measurement can´t
distinguish. Two is go/ no go. Need 4 for a good system
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Gage R&R
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Normality test
Select:Stat => Basic Statistics => Normality Test...
Various statistical normality tests. Anderson-Darling is typically fine as
default
Various statistical normality tests. Anderson-Darling is typically fine as
default
Enter column containing data
Enter column containing data
Enter a title for your diagram if
wanted
Enter a title for your diagram if
wanted
Click OK to get resultsClick OK to get results
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39
The worksheet outputIf data not normal
distributed (not following the red line) more
processes/reasons to the variation
If data not normal distributed (not following
the red line) more processes/reasons to the
variation
The higher the p-value, the more likely the data is
normally distributed. If p-
value is above 0,05 it is often concluded
that the data is normal distributed
The higher the p-value, the more likely the data is
normally distributed. If p-
value is above 0,05 it is often concluded
that the data is normal distributed
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Normality test
40
Run Chart
Select:Stat => Quality Tools => Run Chart...
Select column containing data
Select column containing data
Enter subgroup sizeEnter subgroup size
Click OK to get resultsClick OK to get results
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41
The worksheet output
Are any of the p-values below 0,05 ? If yes
there is either Clustering, Trends,
Mixtures or Oscillation.
Are any of the p-values below 0,05 ? If yes
there is either Clustering, Trends,
Mixtures or Oscillation.
H0: Data is random, special causes not presentHa: Data is not random, special causes present
Return to overview page
Run Chart
42Return to overview page
Run Chart
43Return to overview page
Run Chart
44
ANOVA test
Select:Stat => ANOVA => One Way...
Enter column containing
data
Enter column containing
data
Enter column containing grouping/sorting
information
Enter column containing grouping/sorting
information
Click OK to get results
Click OK to get results
If wanted it is possible to generate boxplot or dotplot of
data
If wanted it is possible to generate boxplot or dotplot of
data
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45
The session outputIf 1 = 2 = 3 = 4 = 5
then p-value > than 0,05. If one minimum
one of the ´s is different from the
others the p-value is < 0,05
If 1 = 2 = 3 = 4 = 5 then p-value > than
0,05. If one minimum one of the ´s is
different from the others the p-value is <
0,05
Mean and standard deviation for each of the groups of data
Mean and standard deviation for each of the groups of data
One-way Analysis of Variance
Analysis of Variance for C2 Source DF SS MS F PC1 4 5,69 1,42 1,39 0,254Error 45 46,18 1,03Total 49 51,87 Individual 95% CIs For Mean Based on Pooled StDevLevel N Mean StDev ---------+---------+---------+-------1 10 -0,375 0,496 (----------*----------) 2 10 0,413 1,291 (----------*----------) 3 10 -0,457 1,047 (---------*----------) 4 10 0,176 0,948 (----------*----------) 5 10 0,140 1,106 (---------*----------) ---------+---------+---------+-------Pooled StDev = 1,013 -0,60 0,00 0,60
How much overlap are there in the
confidence intervals ? The more overlap the less chance for
statistically difference
How much overlap are there in the
confidence intervals ? The more overlap the less chance for
statistically difference
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ANOVA test
46
One sample t-test
Select:Stat => Basic Statistics => 1-Sample t...
Select alternative hypothesis from drop down box
Select alternative hypothesis from drop down box
Enter column containing data
Enter column containing data
Enter mean you want to test against
Enter mean you want to test against
Click OK to get results
Click OK to get results
Select Graph option if desired
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47
The worksheet output
If p-value < 0,05 reject H0 hypothesis and accept Ha hypothesis. P < 0,05 reject H0 .Sample mean not equal to 1
If p-value < 0,05 reject H0 hypothesis and accept Ha hypothesis. P < 0,05 reject H0 .Sample mean not equal to 1
The session output
T-Test of the Mean
Test of mu = 1,000 vs mu not = 1,000
Variable N Mean StDev SE Mean T PC2 50 -0,021 1,029 0,146 -7,01 0,0000
Sample mean (X) is outside the 95 % confidence interval, reject H0
Sample mean (X) is outside the 95 % confidence interval, reject H0
Return to overview page
One sample t-test
48
Two sample t-test
Select:Stat => Basic Statistics => Normality Test... Enter column
containing data for the first sample to be
tested
Enter column containing data for the
first sample to be tested
Click OK to get resultsClick OK to get results
Enter column containing data for the second sample to be
tested
Enter column containing data for the second sample to be
tested
Select alternative hypothesis from drop down box
Select alternative hypothesis from drop down box
Select Graph option if desired. Dot- and boxplots available
Select Graph option if desired. Dot- and boxplots available
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49
The worksheet output
If p-value < 0,05 reject H0 hypothesis and accept Ha hypothesis. P < 0,05 reject
H0 .Mean for sample 1 not equal to mean for sample 2
If p-value < 0,05 reject H0 hypothesis and accept Ha hypothesis. P < 0,05 reject
H0 .Mean for sample 1 not equal to mean for sample 2
No overlap between means for the two
distributions and their 95 % confidence intervals
=> reject H0
No overlap between means for the two
distributions and their 95 % confidence intervals
=> reject H0
Two Sample T-Test and Confidence Interval
Two sample T for C2 vs C3
N Mean StDev SE MeanC2 50 -0,02 1,03 0,15C3 50 1,065 0,827 0,12
95% CI for mu C2 - mu C3: ( -1,46; -0,72)T-Test mu C2 = mu C3 (vs not =): T = -5,82 P = 0,0000 DF = 93
The session output
Return to overview page
Two sample t-test
50
Homogeneity of Variance
Select:Stat => ANOVA => Homogeneity of Variance...
Enter column containing data
Enter column containing data
Enter a title for your diagram if
wanted
Enter a title for your diagram if
wanted
Click OK to get resultsClick OK to get results
Enter column containing subscripts that identify from which group data
come from
Enter column containing subscripts that identify from which group data
come from
Return to overview page
51
The worksheet output
Use Bartlett´s test when the data comes from a
normal distribution. Use Levene´s test whan the
data comes from a continuous but not necessarily normal
distribution. P-values < 0,05 indicate the groups have different variances
Use Bartlett´s test when the data comes from a
normal distribution. Use Levene´s test whan the
data comes from a continuous but not necessarily normal
distribution. P-values < 0,05 indicate the groups have different variances
The 95 % confidence intervals. The middle dot is the standard deviation of
that group
The 95 % confidence intervals. The middle dot is the standard deviation of
that group
Return to overview page
Homogeneity of Variance
52
Chi Square test
Select:Stat => Tables => Chi-Square Test…Use this option when data is a table containing total counts
Enter columns containing data
Enter columns containing data
The worksheet setupThe worksheet setup
Click OK to get resultsClick OK to get results
Return to overview page
53
The worksheet output
Chi-Square calculated
Chi-Square calculated
If p-value < 0,05 there is a difference between the data
If p-value < 0,05 there is a difference between the data
Chi-Square Test
Expected counts are printed below observed counts
pass fail Total 1 50 37 87 60,92 26,08
2 55 20 75 52,52 22,48
3 37 10 47 32,91 14,09
4 100 30 130 91,03 38,97
5 78 40 118 82,63 35,37
Total 320 137 457
Chi-Sq = 1,957 + 4,571 + 0,117 + 0,274 + 0,508 + 1,187 + 0,884 + 2,065 + 0,259 + 0,605 = 12,429DF = 4, P-Value = 0,014
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Chi Square test
54
DoE
Create Factorial DoE DesignAnalyze Factorial DoE DesignMain Effect PlotsInteraction Plots
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55
Create Factorial Design
Select:Stat => DOE => Create Factorial Design...
Select number of factorsSelect number of factors
Select design from option list. Select number of
counterpoints, replicates, and
blocks
Select design from option list. Select number of
counterpoints, replicates, and
blocks
Enter names and levels for the factors if
desired
Enter names and levels for the factors if
desired
Select applicable options. Randomize
is default
Select applicable options. Randomize
is default
Return to overview page
56
The session output
If fractional design selected the confounding pattern would be listed
here
If fractional design selected the confounding pattern would be listed
here
Run order would be the same at Standard order, if the randomize
option wasn´t selected
Run order would be the same at Standard order, if the randomize
option wasn´t selected
Factorial Design
Full Factorial Design
Factors: 3 Base Design: 3; 8 Runs: 8 Replicates: 1 Blocks: none Center pts (total): 0
All terms are free from aliasing
The worksheet output
Actual factor names and values on
datasheet, if entered as option. If not,
matrix contain -1 and +1
Actual factor names and values on
datasheet, if entered as option. If not,
matrix contain -1 and +1
Return to overview page
Create Factorial Design
57
Select:Stat => DOE => Analyze Factorial Design... Select column
with responses of the DOE
Select column with responses
of the DOE
Select terms to be included in model. Can
select up to desired order through drop
down box or individually with < or > buttons. The >> or << buttons move all
terms.
Select terms to be included in model. Can
select up to desired order through drop
down box or individually with < or > buttons. The >> or << buttons move all
terms.
Select to store fits, residuals, etc.
Select to store fits, residuals, etc.
Select covariatesSelect covariates
Select to get effects and/or residual plots
Select to get effects and/or residual plots
Click OK to get resultsClick OK to get results
Return to overview page
Analyze Factorial Design
58
The session output Average effect of moving the factor from low to high
setting
Average effect of moving the factor from low to high
setting
Determine % contribution to variance by dividing SSsource by SStotal.
Likewise, determine % error (unaccounted for variation) by
SSerror/SStotal
Determine % contribution to variance by dividing SSsource by SStotal.
Likewise, determine % error (unaccounted for variation) by
SSerror/SStotal
The coefficient for regression equation.
Equal to effect/2
The coefficient for regression equation.
Equal to effect/2
Fractional Factorial Fit
Estimated Effects and Coefficients for Results (coded units)
Term Effect Coef StDev Coef T PConstant 91,6667 0,6319 145,06 0,000Speed 22,6667 11,3333 0,6319 17,94 0,000Temp 1,8333 0,9167 0,6319 1,45 0,166Angle 1,3333 0,6667 0,6319 1,06 0,307Speed*Temp 1,8333 0,9167 0,6319 1,45 0,166Speed*Angle 2,0000 1,0000 0,6319 1,58 0,133Temp*Angle 0,1667 0,0833 0,6319 0,13 0,897Speed*Temp*Angle 0,8333 0,4167 0,6319 0,66 0,519
Analysis of Variance for Results (coded units)
Source DF Seq SS Adj SS Adj MS F PMain Effects 3 3113,50 3113,50 1037,83 108,30 0,0002-Way Interactions 3 44,33 44,33 14,78 1,54 0,2423-Way Interactions 1 4,17 4,17 4,17 0,43 0,519Residual Error 16 153,33 153,33 9,58 Pure Error 16 153,33 153,33 9,58Total 23 3315,33
If p-value < 0,05 this a statistically
significant factor
If p-value < 0,05 this a statistically
significant factor
Adj SS/DF (Degrees of Freedom)
Adj SS/DF (Degrees of Freedom)
Adj MSsource/ Adj MSerror
Adj MSsource/ Adj MSerror
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Analyze Factorial Design
59
Main Effect Plots
Select:Stat => ANOVA => Main Effects Plots...
Enter factorsEnter factors
Enter response column
Enter response column
Click OK to get resultsClick OK to get results
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60
The output
Check range of experimental results, was it
large enough to be practical
significance ?
Check range of experimental results, was it
large enough to be practical
significance ?
The steeper he slope, the larger the effect
The steeper he slope, the larger the effectThe low (-1) and
high (+1) setting
The low (-1) and high (+1) setting
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Main Effect Plots
61
Select:Stat => ANOVA => Interactions Plots...
Enter factors
Enter factors
Enter response column
Enter response column
Click OK to get results
Click OK to get results
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Interaction Plots
62
The output
Solid line is low level for Y axis factor. Dashed
line is high level for Y axis factor
Solid line is low level for Y axis factor. Dashed
line is high level for Y axis factor
The stronger the interaction is, the more non-parallel are the lines
The stronger the interaction is, the more non-parallel are the lines
The low (-1) and high (+1) setting
The low (-1) and high (+1) setting
Read across to identify Y axes
Read across to identify Y axes
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Interaction Plots
63
Regression
RegressionFitted line plotsResiduals analysis
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64
Select:Stat => Regression => Regression... Y variable in
equation
Y variable in equation
Store fits, residuals, coefficients etc.
Store fits, residuals, coefficients etc.
Possible xPossible x
Graph options for residuals
Graph options for residuals Click OK to get
results
Click OK to get results
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Regression
65
The session output T-test for constant coefficient (Y-intercept) versus constant of zero. If p-value < 0,05 constant is
significant
T-test for constant coefficient (Y-intercept) versus constant of zero. If p-value < 0,05 constant is
significant
How good is the model ? If p-value is < 0,05 the model is significant
How good is the model ? If p-value is < 0,05 the model is significant
T-test for factor coefficient versus
zero. If p-value is < 0,05 coefficient is
significant
T-test for factor coefficient versus
zero. If p-value is < 0,05 coefficient is
significant
R-sq is % of variation in Y that is explained
by equation. If several x´s in
equation, use R-sq adj, as it adjusts for degrees of freedom
R-sq is % of variation in Y that is explained
by equation. If several x´s in
equation, use R-sq adj, as it adjusts for degrees of freedom
Regression Analysis
The regression equation isOutput = - 15,0 + 0,489 Temp
Predictor Coef StDev T PConstant -15,000 1,484 -10,11 0,000Temp 0,48929 0,01800 27,18 0,000
S = 0,9524 R-Sq = 99,3% R-Sq(adj) = 99,2%
Analysis of Variance
Source DF SS MS F PRegression 1 670,32 670,32 738,94 0,000
Residual Error 5 4,54 0,91Total 6 674,86
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Regression
66
Select:Stat => Regression => Fitted Line Plot... Identify Y and X
columns
Identify Y and X columns
Store fits, residuals, coefficients etc.
Store fits, residuals, coefficients etc.
Choose type of regression to fit
Choose type of regression to fit
Select if transformation of data is required
Select if transformation of data is required
Click OK to get resultsClick OK to get results
Optional display of confidence bands and prediction bands
Optional display of confidence bands and prediction bands
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Fitted Line Plot
67
The session output T-test for constant coefficient (Y-intercept) versus constant of zero. If p < 0,05 constant
is significant
T-test for constant coefficient (Y-intercept) versus constant of zero. If p < 0,05 constant
is significant
How good is the model ? If p is < 0,05 the model is significant
How good is the model ? If p is < 0,05 the model is significant
T-test for factor coefficient versus zero. If p is < 0,05 coefficient is
significant
T-test for factor coefficient versus zero. If p is < 0,05 coefficient is
significant
R-sq is % of variation in Y that is explained by equation. If several x´s, use R-sq adj
R-sq is % of variation in Y that is explained by equation. If several x´s, use R-sq adj
Regression
The regression equation isy = - 15,0 + 0,489 x
Predictor Coef StDev T PConstant -15,000 1,484 -10,11 0,000x 0,48929 0,01800 27,18 0,000
S = 0,9524 R-Sq = 99,3% R-Sq(adj) = 99,2%
Analysis of Variance
Source DF SS MS F PRegression 1 670,32 670,32 738,94 0,000Residual Error 5 4,54 0,91Total 6 674,86
The graphical output
• Black line is line of best fit• Dotted line (red) is 95 % confidence
interval• Dashed line (blue) is prediction interval
• Black line is line of best fit• Dotted line (red) is 95 % confidence
interval• Dashed line (blue) is prediction interval
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Fitted Line Plot
68
Residuals analysis
Select:Stat => Regression => Regression...
Select Standardized will convert
residuals to z-like values
Select Standardized will convert
residuals to z-like values
Select desired plotsSelect desired plots
Note: Can also be generated with Stat => Regression => Residuals Plots, but must have stored fits and residuals and can´s select standardized option
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69
The output How normal is the residuals
How normal is the residuals
Histogram - Bell curve ? (ignore if data set < 30)
Histogram - Bell curve ? (ignore if data set < 30)
Individual residuals trends ?
Outliers ? 95 % should be within +/- 2
standard residuals
Individual residuals trends ?
Outliers ? 95 % should be within +/- 2
standard residuals
Random about zero
without trends ?
Random about zero
without trends ?
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Residuals analysis
70
Product Report
Select:Six Sigma => Product Report...
The worksheet setup Enter column containing data
Click OK to get results
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71
Product Report
Total
3
2
1
Characteristic
2.382
3.034
2.421
1.931
ZBench
1.500
1.500
1.500
1.500
ZShift
188889
62500
178571
333333
PPM
0.188889
0.062500
0.178571
0.333333
DPO
0.062
0.179
0.333
DPU
450
160
140
150
TotOpps
1
1
1
Opps
160
140
150
Units
85
10
25
50
Defs
Report 7: Product Performance
The session output
Note: When dealing with Attribute data, it is assumed to be Long-Term,
and so the 1.5s shift is assumed to be in effect.
DPMO and Z-Bench
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72
Process Report
Select:Six Sigma => Process Report...
The worksheet setup
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73
Process Report
Enter column containing data
Click OK to get resultsType in Lower and Upper specs and Target
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74
Process Report
1.5
1.0
0.5
0.0
S=0.8616
3.0SL=1.479
-3.0SL=0.2444
54321
50.5
49.5
48.5
Xbar and S Chart
Subgroup
X=49.63
3.0SL=50.47
-3.0SL=48.78
5446
52.657447.3426
Potential (ST) CapabilityProcess Tolerance
Specifications
III
III
5446
52.363246.8868
Actual (LT) CapabilityProcess Tolerance
Specifications
III
III
Mean
StDev
Z.USL
Z.LSL
Z.Bench
Z.Shift
P.USL
P.LSL
P.Total
Yield
PPM
Cp
Cpk
Pp
Ppk
LTST
Capability Indices
Data Source:Time Span:Data Trace:
1.32
1.46
33.4959
99.9967
0.000033
0.000033
0.000001
0.4058
3.9867
3.9919
4.8178
0.9081
49.6250
1.36
1.51
5.60286
99.999
0.000006
0.000003
0.000003
0.4058
4.3925
4.5408
4.5408
0.8809
50.0000
Report 2: Process Capability for Dist 50
Actual (LT)
Potential (ST)
545352515049484746
Process Performance
USLLSL
Actual (LT)
Potential (ST)
1,000,000
100,000
10,000
1000
100
10
1
54321
Potential (ST)Actual (LT)
Sigma
PPM
(Z.Bench)
Process Benchmarks
5.60286
3.99
33.4959
4.39
Process Demographics
50
46
54
Opportunity:
Nominal:
Lower Spec:
Upper Spec:
Units:
Characteristic:
Process:
Department:
Project:
Reported by:
Date:
Report 1: Executive Summary
The session output
Mean, Standard Deviation, Z-bench
Z-shift, DPMO calculation ST and LT
Return to overview page
75
Select:Stat => Graph => Probability Plot...
Data in different colums (more then 2 allowed..)
Data in different colums (more then 2 allowed..)
Click OK to get results
Click OK to get results
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Probability plot
76
This tool allows you to visualize various distributions in one graph.
For validation you can also perform an unstacked Anova.
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Probability plot
Analysis of VarianceSource DF SS MS F PFactor 1 5589.4 5589.4 406.56 0.000Error 198 2722.1 13.7Total 199 8311.5 Individual 95% CIs For Mean Based on Pooled StDevLevel N Mean StDev ---+---------+---------+---------+---C1 100 24.393 4.782 (-*-) C2 100 34.966 2.151 (-*-) ---+---------+---------+---------+---Pooled StDev = 3.708 24.5 28.0 31.5 35.0