8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 1/28
Design Of Experiments
Review and Minitab
Presented by I. Miletic, 2009
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 2/28
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 3/28
analyzing numerical information.
information in order to reach valid conclusions
e.g. should I turn up the temperature to dry the
paint on manufactured parts faster in my factory?Why?
are u : data ≠ ‘information’, and ‘valid’ may not mean ‘ ’
Presented by I. Miletic, 2009
common sense is always needed
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 4/28
Software use Real industrial examples typically involve lots of data and
• Use manual calculations in this course to demonstrate theory andconcepts
o ware- ase ana ys s oo s are nee e o a n a aacquisition and calculations
• MINITAB, SAS, SPSS, MATLAB, SIMCA-P, SPLUS, EXCEL, R, VB/C,Netica, etc
• different capabilities, methods of data handling, control, scope, etc
Focus on MINITAB for the first art of the course• popular software tool that is used by companies across many sectors
(e.g. often as part of SixSigma tools)
• good for desktop analysis of data sets
Presented by I. Miletic, 2009
• lots of automated analysis is available
• can customize as well
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 5/28
Minitab can be obtained from
.
6 month rental, perpetual license, etc
the Mac Bookstore
the McMaster site license access for on campus use
For this course an Academic License ≠ StudentRelease
Student Release does not support DOE
Any of the ‘later’ Windows-based versions are ok forthis course: e.g. 12 and higher
Presented by I. Miletic, 2009
Ask for the fully capable professional version priced for
academic use
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 6/28
MINITAB is ca able of erformin man
statistical calculations
commands:
- - pull-down menu system
-develop macros for automating complex or
Presented by I. Miletic, 2009
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 7/28
Starting Minitab Start>All Programs menu in Windows
Find the Minitab executable mtb12.exe
(mtb13.exe, mtb14.exe, etc) and double click it
Presented by I. Miletic, 2009
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 8/28
worksheet - edit data
session window - entercommands and see results
Presented by I. Miletic, 2009
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 9/28
Menus are contextual Start Command Line
Click on Session Window
Customize environment
or
Presented by I. Miletic, 2009
oo s p ons
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 10/28
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 11/28
Minitab macros
scope: exec, global, local see Help menu
Easy way to create macros
copy commands from session window into amacro file and save it usin *.mtb
default path is \minitab install directory\Minitab12\Macros\
Presented by I. Miletic, 2009
macros are open form - edit with any text editor
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 12/28
An example macro written in Notepad...
# my first macro
#random 40 c1; # create a set of random data in column c1normal 300 20. # data are normal with mean 300 and standard deviation of 20
histogram c1 # plot a histogram of c1dotplot c1 # make a dotplot of c1boxplot c1 # make a boxplot of c1
. ex: SEP_Module_1_First_Macro.mtb
ex: SEP_Module_1_First_Macro.txt
Run the macro: mtb> exec ‘path\name.ext’ single quotes must be included
Presented by I. Miletic, 2009
MTB > exec 'C:\temp\teaching\mac\winter2009\CHE_4C03\CHE_Module_1_First_Macro.txt'
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 13/28
The macro
the worksheetand produces
session window
Graphs are
dotplot and thehistogram
graphs byclicking theobjects in them
Presented by I. Miletic, 2009
and double
clicking for atoolbar
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 14/28
obtained from data stored in Minitab columns mean median uartiles n
dx)x(xf )X(E
∫
∞
∞−
==µ
n
x
x 1i
i
==
Range = (max - min) and IQR = (Q3 - Q1)
s and s2n
2−
Five Number Dia ram
−=−== xx xxXEXV σ
1ns 1i2
−= =
Presented by I. Miletic, 2009
Dotplot, Box and Whisker Plot, Scatter Plot,etc
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 15/28
16 14 12 18 9 15
MTB > Describe 'Data'.
Stat>Basic Statistics>Display Descriptive Statistics
Descriptive Statistics
Variable N Mean Median TrMean StDevSE Mean
Data 6 14.00 14.50 14.00 3.161.29
Variable Minimum Maximum Q1 Q3
Presented by I. Miletic, 2009
Data 9.00 18.00 11.25 16.50
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 16/28
o construct a histogram, first divide the range of the data into
intervals (sometimes called classes or bins)
Usually the bins are of equal width
The number of bins must be chose wisely or else the plotswill not be informative
A rule of thumb is:
Count the number of data points that fall within each bin.his is the fre uenc .
nns ≈
Plot the frequency as a function of the bins center points. This is ahistogram.
frequency
Presented by I. Miletic, 2009
n
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 17/28
ex. : Create a bar plot of the following data
Minita 1 : rap > art Other versions see Graph Menu items
350
400
450
n c y
150
200
250
m o
f F r e q u
1 Scratches 450
2 Pits 150
Burrs Inclusions Other Pits Scratches
0
50100 S
u
4 Inclusions 505 Other 300
Presented by I. Miletic, 2009
Defect Type
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 18/28
ex: construct a histogram and a dot plot of the
52 88 56 79 72 91 85 88 68 63 76 73 86 95 12 69
Graph>Histogram and Graph>Dotplot
5
MTB > %Dotplot 'Data1'.Executing from file: C:\Program Files\MINITAB12\MACROS\Dotplot.MACMacro is running ... please wait
MTB > Histogram 'Data1';SUBC> MidPoint;
Dotplot for Data1
3
4
q u e n c y
SUBC> Bar;SUBC> ScFrame;SUBC> ScAnnotation.
MTB >
10 20 30 40 50 60 70 80 90
Data1
0
1
F r e
Presented by I. Miletic, 2009
10 20 30 40 50 60 70 80 90 100
Data1
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 19/28
Covariance is a measure of the linear association between random
variables.
Population covariance:
( )( ){ } YXYX
2
XY )XY(EYXE µ µ µ µ σ −=−−=
Sample covariance:
n
1ˆ 122
−
−−== =
n
y y x x
s i ii
XY XY σ
Presented by I. Miletic, 2009
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 20/28
Correlation: a scaled version of covariance. The scaling is done so
that the range of ρ is [-1, 1] .
Population correlation:
YX
2
XY
σ σ
σ ρ =
Sample correlation:
( )−−n
ii x x y y )(
( ) ( )
−
−
=∑∑
==
=n
i
i
n
i
i
i
y y x x
r
1
2
1
2
1
Presented by I. Miletic, 2009
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 21/28
Scatter plots can correlation coefficents can
90
100
a so e eve ope us ng e rap an amenu items
60
70
80
E x a m In Minitab 12:
Graph>Plot12 13 14 15 16
50
Quiz
Stat>Basic Stats>Correlation
12 5514 60
13 70
Correlations (Pearson)
Correlation of Quiz and Exam = 0.877, P-Value = 0.010
Presented by I. Miletic, 2009
15 90
16 9016 100
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 22/28
In engineering applications we often assume that measured
continuous random variables are normally distributed.
The mean defines the center of the normal probability function.
The standard deviation determines the spread (dispersion)
The normal probability density function is symmetric and bell-
sha ed.
The expression for the normal probability density function for therandom variable X is:
2x−−
( )22
x e2
,;xf σ
π σ
σ µ =
Presented by I. Miletic, 2009
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 23/28
he standard normal distribution refers to the normal distribution
with mean zero and variance one.
The standard normal distribution is important in that we can usetabulated values of the cumulative standard normal distribution forany normally distributed random variable by first standardizing it.
We standardize a random variable X that is N(µ, σ2) using:
σ
µ −=
XZ
)aX(P1)aX(P
)aX(P) bX(P) bXa(P
≤−=≥
≤−≤=≤≤
)aX(P1)aX(P)aX(P ≤−=≥=−≤
−
≤=≤µ a
zP)aX(P
Presented by I. Miletic, 2009
σ
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 24/28
Minitab can also be used to solve probabilitypro ems
ex. Plot the normal curve that has µ=400 and σ=20.
1 2 .the probabilty that x falls in this interval.
he relevant commands are• mtb> cdf x;
• subc> normal µ σ.
• subc> normal µ σ.
• mtb> pdf c1 c2;
Presented by I. Miletic, 2009
• subc> normal µ σ.
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 25/28
Session commands can be used...MTB > set c1 # define column for data
DATA> end # close set data clause
MTB > pdf c1 c2; # pdf at values in c1 stored in c2SUBC> normal 400 20. # type of pdf
MTB > plot c2*c1; # plot c2 by c1
370 410400
SUBC> reference 2 0; # horizontal (2) line at y=0
SUBC> reference 1 370 400 410; # vertical (1) lines at x=370
SUBC> connect. # connect dots on curve
0.01
0.02
C 2
0.00
0.625
Calc>Make Patterned Data>Simple Setof Numbers
Calc>Probabilit Distributions>Normal
Presented by I. Miletic, 2009
C1 Graph> Scatter Plot
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 26/28
MTB > cdf 370;SUBC> normal 400 20.
Cumulative Distribution Function
Normal with mean = 400.000 and standard deviation = 20.0000
x P( X <= x)370.0000 0.0668
MTB > cdf 410;
SUBC> normal 400 20.
Cumulative Distribution Function
Normal with mean = 400.000 and standard deviation = 20.0000
x P( X <= x). .
Then Φ(370<x<410 | µ=400, σ=20) =
Presented by I. Miletic, 2009
. - . = .
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 27/28
Other Minitab functions and menus aregeared toward hypothesis tests, ANOVA,Regression, MLR, DOE, GLM, etc.
We will look at each of these Minitab toolsin detail for this course:
R r i n n Inf r n R vi w
Hypothesis tests for multiple comparisons
Presented by I. Miletic, 2009
, ,
8/8/2019 DOE Module 2 Minitab
http://slidepdf.com/reader/full/doe-module-2-minitab 28/28
Box, G.E.P., Hunter, W.G. and Hunter, J.S., “Statistics for Experimenters”, Wiley, 1978.
Mathews, P. “Design of Experiments withMINITAB”, ASQ Quality Press, 2005.
ontgomery, . . an unger, . . pp eStatistics and Probability for Engineers”, First
., , .
Presented by I. Miletic, 2009
Top Related