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Box-Behnken design

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RSM
RSM Array

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Factorial Arrays
Full Factorial Array
Orthogonal Array
Plackett–Burman Array
Box-Behnken design
Central Composite design

Center point


In the Box-Behnken design the Levels of the factors are at the midpoints of the edges (
Red dots
) and in the center the Center point (
Blue dot
). This array is often used in a RSM to construct a response surface. For each factor are 3 levels required.

Box-Behnken compared with Central Composite

As you can see there are less data point needed compared with a Central Composite design. Compared to the Central Composite design it is missing the corner points, it will never occur that all the factors are high or low at the same time (No extreme combinations).
With a Box-Behnken design every factor is having 3 levels compared to Central Composite 5 with 2 of them outside the setting.
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

Box-Behnken compared Full Factorial Array 3 Levels

Box-Behnken design Full Factorial Array 3 Levels
Compare
-No Corner points+Corner points
+Less tests-more tests
+Rotatable-Not Rotatable
-Always 3 Levels+Flexible in the amount of levels
+Multiple Center points+/-One Center points But they can easy be add

The arrays

Name Factors Rows center points
BB3 3 16 3
BB4 4 26 3
BB5 5 45 5
BB6 6 54 6

BB3

Tests↓ Factors
ABC
1-1-10
21-10
3-110
4110
5000
60-1-1
70-11
801-1
9011
10000
11-10-1
12-101
1310-1
14101
15000
Graphical image of the BB3 array

BB4

Tests Factors
ABCD
1-1-100
2-1100
31-100
41100
500-1-1
600-11
7001-1
80011
90000
10-100-1
11-1001
12100-1
131001
140-1-10
150-110
1601-10
170110
180000
19-10-10
20-1010
2110-10
221010
230-10-1
240-101
25010-1
260101
270000

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