doe module 2 minitab

8/8/2019 DOE Module 2 Minitab

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Design Of Experiments

Review and Minitab

Presented by I. Miletic, 2009



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 ‘ ’


common sense is always needed



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


• lots of automated analysis is available

• can customize as well



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


Ask for the fully capable professional version priced for

academic use



MINITAB is ca able of erformin man

statistical calculations

commands:

- - pull-down menu system

-develop macros for automating complex or




Starting Minitab Start>All Programs menu in Windows

Find the Minitab executable mtb12.exe

(mtb13.exe, mtb14.exe, etc) and double click it




worksheet - edit data

session window - entercommands and see results




Menus are contextual Start Command Line

Click on Session Window

Customize environment

or


oo s p ons



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\


macros are open form - edit with any text editor



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


MTB > exec 'C:\temp\teaching\mac\winter2009\CHE_4C03\CHE_Module_1_First_Macro.txt'



The macro

the worksheetand produces

session window

Graphs are

dotplot and thehistogram

graphs byclicking theobjects in them


and double

clicking for atoolbar



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

−= =


Dotplot, Box and Whisker Plot, Scatter Plot,etc



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


Data 9.00 18.00 11.25 16.50



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


n



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


Defect Type



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


10 20 30 40 50 60 70 80 90 100

Data1



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




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




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


15 90

16 9016 100



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 =




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


σ



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.


• mtb> pdf c1 c2;





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


C1 Graph> Scatter Plot



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) =


. - . = .



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


, ,



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

., , .


doe module 2 minitab

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