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Central Composite design

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Design of experiments (DOE)


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Factorial Arrays
Full Factorial Array
Orthogonal Array
Plackett–Burman Array
Box-Behnken design
Central Composite design Design of experiments (DOE)
RSM

In the Central Composite design arrays the Levels of the factors are on the edges, center and circumscribed at the center of side.
Red
Edge
Blue
Center point
Green
Circumscribed
A Central Composite Design is a array with all the corner points (
Red dots
) and in the center the center points (
Blue dot
) and extra points circumscribed from the sides (
Green dots
). This array is often used in a RSM to construct a response surface. For each factor are 5 levels required.

Central Composite compared with Box-Behnken

As you can see there are more data point needed compared with a Box-Behnken design. Compared with the Box-Behnken all the factors high or low at the same time will occur (extreme combinations).
With a Central Composite design every factor is having 5 levels compared to Box-Behnken 3.
Box-Behnken design Central Composite design
Compare
-No Corner points+Corner points
+3 Levels-5 Levels
+Less tests-more tests
+No Circumscribed points -The Circumscribed point especially
for the bigger arrays are far
from the normal setting

Central Composite compared Full Factorial Array 3 Levels

Central Composite design Full Factorial Array 3 Levels
Compare
+Less tests-more tests
+Rotatable-Not Rotatable
-Always 5 Levels+Flexible in the amount of levels
+Multiple Center points+/-One Center points But they can easy be add
-The Circumscribed point especially
for the bigger arrays are far
from the normal setting
+No Circumscribed points

The arrays

Name Factors Rows Center point Distance Circumscribed
CCD2 2 13 5 1.414
CCD3 3 20 6 1.682
CCD4 4 30 6 2.000
CCD5 5 52 10 2.378
CCD6 6 91 15 2.828

Modifications of the Central Composite Array

Standard CCC CCI CCF
Circumscribed Inscribed Face centered
Best fitting The extreme settings are extrapolated Poor Quadratic fitting
• 5 Levels
• 2 Levels outside the investigated limits
Rotatable
• 5 Levels
• All levels are within the investigated limits
Rotatable
• 3 Levels
• All levels are within the investigated limits
Not Rotatable

CCD2

Tests Factors
AB
1
-1-1
2
1-1
3
-11
4
11
5
00
6
00
7
-1.4140
8
1.4140
9
0-1.414
10
01.414
11
00
12
00
13
00
Graphical image of the CCD2 array

CCD3

Tests Factors
ABC
1
-1-1-1
2
1-1-1
3
-11-1
4
11-1
5
-1-11
6
1-11
7
-111
8
111
9
000
10
000
11
000
12
-1.68200
13
1.68200
14
0-1.6820
15
01.6820
16
00-1.682
17
001.682
18
000
19
000
20
000
Graphical image of the CCD3 array

CCD4

Tests Factors
ABCD
1-1-1-1-1
21-1-1-1
3-11-1-1
411-1-1
5-1-11-1
61-11-1
7-111-1
8111-1
9-1-1-11
101-1-11
11-11-11
1211-11
13-1-111
141-111
15-1111
161111
170000
180000
190000
20-2000
212000
220-200
230200
2400-20
250020
26000-2
270002
280000
290000
300000

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