Central Composite design

A Central Composite design is test array specially designed for response surface methodology. 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 () and in the center the center points () and extra points circumscribed from the sides (). 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
	A	B
1	-1	-1
2	1	-1
3	-1	1
4	1	1
5	0	0
6	0	0
7	-1.414	0
8	1.414	0
9	0	-1.414
10	0	1.414
11	0	0
12	0	0
13	0	0

Graphical image of the CCD2 array

CCD3

Tests	Factors
	A	B	C
1	-1	-1	-1
2	1	-1	-1
3	-1	1	-1
4	1	1	-1
5	-1	-1	1
6	1	-1	1
7	-1	1	1
8	1	1	1
9	0	0	0
10	0	0	0
11	0	0	0
12	-1.682	0	0
13	1.682	0	0
14	0	-1.682	0
15	0	1.682	0
16	0	0	-1.682
17	0	0	1.682
18	0	0	0
19	0	0	0
20	0	0	0

Graphical image of the CCD3 array

CCD4

Tests	Factors
	A	B	C	D
1	-1	-1	-1	-1
2	1	-1	-1	-1
3	-1	1	-1	-1
4	1	1	-1	-1
5	-1	-1	1	-1
6	1	-1	1	-1
7	-1	1	1	-1
8	1	1	1	-1
9	-1	-1	-1	1
10	1	-1	-1	1
11	-1	1	-1	1
12	1	1	-1	1
13	-1	-1	1	1
14	1	-1	1	1
15	-1	1	1	1
16	1	1	1	1
17	0	0	0	0
18	0	0	0	0
19	0	0	0	0
20	-2	0	0	0
21	2	0	0	0
22	0	-2	0	0
23	0	2	0	0
24	0	0	-2	0
25	0	0	2	0
26	0	0	0	-2
27	0	0	0	2
28	0	0	0	0
29	0	0	0	0
30	0	0	0	0

Links

• http://www.itl.nist.gov/div898/handbook/pri/section3/pri3361.htm
• https://en.wikipedia.org/wiki/Central_composite_design