Transcript EEE436 - Universiti Sains Malaysia

EEM332
Design of Experiments
En. Mohd Nazri Mahmud
MPhil (Cambridge, UK)
BEng (Essex, UK)
[email protected]
Room 2.14
Ext. 6059
EEM332 Lecture Slides
1
Agenda
ANOVA with Excel and Minitab exercises
EEM332 Lecture Slides
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Example 3-1page62
Graphical examination of the data using scatter plots
In Excel choose XY scatter plot
In Minitab , choose >Graph>Plot>Specify X and Y variable
Etch Rate
720
y
620
520
160
170
180
190
200
210
220
RF Power
The scatter diagram indicates increasing etch rate with power
EEM332 Lecture Slides
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Example 3-1page62
Graphical examination of the data using boxplots
In Minitab , choose >Graph>Boxplots
Etch Rate
720
y
620
520
160
180
200
220
RF Power
The boxplot indicates increasing etch rate with power
EEM332 Lecture Slides
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Example 3-1page62
Graphical examination of the data using Regression Model (page 86)
useful to see the response at intermediate factor levels
Linear Model
In Excel >Insert>Chart>XYScatter and add trendline and show equations
Chart Title
750
y = 2.527x + 137.62
R2 = 0.8843
700
650
Etch Rate
Linear (Etch Rate)
600
550
500
150
160
170
180
190
200
210
220
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Example 3-1page62
Graphical examination of the data using Regression Model useful to see the
Response and intermediate factors
Quadratic Model – choose Polynomial order 2
Chart Title
750
700
y = 0.0284x 2 - 8.2555x + 1147.8
R2 = 0.92
650
Etch Rate
Poly. (Etch Rate)
600
550
500
150
170
190
210
230
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Example 3-1page62
Graphical examination of the data using Regression Model
In Minitab , choose >Stat>Regression
Regression Analysis: Etch Rate versus RF Power
The regression equation is
Etch Rate = 138 + 2.53 RF Power
Predictor
Constant
RF Power
S = 21.54
Coef SE Coef
137.62
41.21
2.5270
0.2154
R-Sq = 88.4%
T
P
3.34 0.004
11.73 0.000
R-Sq(adj) = 87.8%
The boxplot indicates increasing etch rate with power
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Example 3-1page62
ANOVA
In Minitab , choose >Stat>ANOVA>One-way
Can also tick Boxplot and Boxplot to select
One-way ANOVA: Etch Rate versus RF Power
Analysis of Variance for Etch Rat
Source
DF
SS
RF Power 3 66871
Error
16
5339
Total
19 72210
MS
22290
334
F
P
66.80 0.000
> Between treatment mean square >> within-treatment(error) mean square
F-value 66.8 > F 0.05,3,16 (3.24)
P-value is very small
EEM332 Lecture Slides
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Analysis of variance –
Exercises using Minitab
Question 1
The tensile strength of portland cement is being studied.
Four different mixing techniques can be used economically.
A completely randomised experiment was conducted and the following data collected.
Mixing
Technique
Tensile Strength
1
3129
3000
2865
2890
2
3200
3300
2975
3150
3
2800
2900
2985
3050
4
2600
2700
2600
2765
Perform ANOVA using Minitab to test the hypotheses that mixing techniques affect
the tensile strength
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Analysis of variance - Exercise
Q2
A manufacturer of television sets is interested in the effect of tube conductivity
of four different types of coating for color picture tubes. The following conductivity data
are obtained.
Coating
Type
Conductivity
1
143
141
150
146
2
152
149
137
143
3
134
136
132
127
4
129
127
132
129
Perform ANOVA using Minitab to test the hypotheses that coating types affect
the conductivity.
EEM332 Lecture Slides
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Analysis of variance - Exercises
Q3
Four different designs for a digital circuits are being studied in order to compare
the amount of noise present. The following data have been obtained.
Circuit
designs
Noise observed
1
19
20
19
30
8
2
80
61
73
56
80
3
47
26
25
35
50
4
95
46
83
78
97
Perform ANOVA using Minitab to test the hypotheses whether the noise are the same
for all the four designs or not.
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