minitab manual.ppt

v

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

Return to overview page

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


5

The Basics

Minitab WindowsToolbarsPerforming CalculationsCopying to other applications


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


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


shortcut keys


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


shortcut keys


shortcut keys


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


shortcut keys


shortcut keys


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



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:


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


13

Working with Data

Changing Data TypeStacking Data/Data BlocksCreating Patterned DataRe-coding DataTransforming Data


14

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


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

(*)


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



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



18

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



19


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



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...


21


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


Creating Patterned Data

22

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 ????


23

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


Enter new textEnter new text


Re-coding Data

24


Original dataOriginal data

Re-coded dataRe-coded data


Re-coding Data

25

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


Transforming Data

26

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...


Transforming Data

27

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




Transforming Data

28


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


Transforming Data

29

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


30

Statistical Problem Description

Stat => Quality Tools => Capability Analysis (Normal)...



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


31


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



32

Stat => Basic Statistics => Display descriptive statistics

Select column

Select column

Select Graphs

Select Graphs



33

The worksheet output Histogram of data

Histogram of data

Quartiles, median and min, max values

Quartiles, median and min, max values



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



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




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 ?


Gage R&R

36

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


Gage R&R

37

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


Gage R&R

38

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 a title for your diagram if

wanted


wanted



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


Normality test

40

Run Chart

Select:Stat => Quality Tools => Run Chart...

Select column containing data

Select column containing data

Enter subgroup sizeEnter subgroup size



41


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


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



If wanted it is possible to generate boxplot or dotplot of

data

If wanted it is possible to generate boxplot or dotplot of

data


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


ANOVA test

46

One sample t-test

Select:Stat => Basic Statistics => 1-Sample t...

Select alternative hypothesis from drop down box




Enter mean you want to test against

Enter mean you want to test against



Select Graph option if desired


47


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


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


Enter column containing data for the second sample to be

tested

Enter column containing data for the second sample to be

tested



Select Graph option if desired. Dot- and boxplots available

Select Graph option if desired. Dot- and boxplots available


49


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


Two sample t-test

50

Homogeneity of Variance

Select:Stat => ANOVA => Homogeneity of Variance...




wanted


wanted


Enter column containing subscripts that identify from which group data

come from

Enter column containing subscripts that identify from which group data

come from


51


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


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



53


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


Chi Square test

54

DoE

Create Factorial DoE DesignAnalyze Factorial DoE DesignMain Effect PlotsInteraction Plots


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


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


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


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



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


Analyze Factorial Design

59

Main Effect Plots

Select:Stat => ANOVA => Main Effects Plots...

Enter factorsEnter factors

Enter response column




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


Main Effect Plots

61

Select:Stat => ANOVA => Interactions Plots...

Enter factors

Enter factors






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



Read across to identify Y axes

Read across to identify Y axes


Interaction Plots

63

Regression

RegressionFitted line plotsResiduals analysis


64

Select:Stat => Regression => Regression... Y variable in

equation

Y variable in equation

Store fits, residuals, coefficients etc.


Possible xPossible x

Graph options for residuals

Graph options for residuals Click OK to get

results



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


Regression

66

Select:Stat => Regression => Fitted Line Plot... Identify Y and X

columns

Identify Y and X columns



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


Optional display of confidence bands and prediction bands

Optional display of confidence bands and prediction bands


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


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


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 ?


Residuals analysis

70

Product Report

Select:Six Sigma => Product Report...

The worksheet setup Enter column containing data



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


72

Process Report

Select:Six Sigma => Process Report...

The worksheet setup


73

Process Report


Click OK to get resultsType in Lower and Upper specs and Target


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


75

Select:Stat => Graph => Probability Plot...

Data in different colums (more then 2 allowed..)

Data in different colums (more then 2 allowed..)




Probability plot

76

This tool allows you to visualize various distributions in one graph.

For validation you can also perform an unstacked Anova.


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

minitab manual.ppt

Documents

process capabilitystep

process report72

product capabilitystep

product report70

measurement systemstep

interactive windows

datachanging data type13

factorial doe design57