Experimental design application and interpretation in pharmaceutical technology - Computer-Aided Applications in Pharmaceutical Technology - page 38

CCD for three factors

Table 3.5

Factors

Experiment

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 − α 0 0

10 + α 0 0

11 0 − α 0

12 0 + α 0

13 0 0 − α

14 0 0 + α

15 (+ replicates) 0 0 0

A BBD is described for a minimum of three factors and contains N =
(2 f ( f − 1)) + c 0 experiments, of which c 0 is the number of center points
(Box and Behnken, 1960). The BBD is the most common alternative to
the CCD (Vining and Kowalski, 2010). BBDs are second-order designs
based on three-level incomplete factorial designs (Ferreira et al., 2007). It
can be seen, from Table 3.6, that the fi rst 4 experiments (i.e. the fi rst
experimental block) is a full 2 2 design for factors A and B, whereas factor
C is constantly at the level 0 . The second experimental block is a full 2 2
design for factors A and C (factor B is at level 0), whereas the third
experimental block is a full 2 2 design for factors B and C (factor A is
at level 0). Therefore, BBD can be presented in a simplifi ed manner
(Table 3.7). When there are 5 or more factors, Box and Behnken
recommended using all possible 2 3 designs, holding the other factors
constant (Vining and Kowalski, 2010). One of the main advantages of
BBD is that it does not contain combinations for which all factors are
simultaneously at their highest or lowest levels, meaning that experiments

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