Experimental design application and interpretation in pharmaceutical technology - Computer-Aided Applications in Pharmaceutical Technology - page 37

studied response. Therefore, it is possible to display the infl uence of the
two factors on the studied response in a graphically comprehensible
manner. For more than two factors, only fractions of the entire response
surface are visualized (Dejaegher and Heyden, 2011).
Response surface designs can be symmetrical or asymmetrical
(Montgomery, 1997). Symmetrical designs cover the symmetrical
experimental domain (Dejaegher and Heyden, 2011). Some of the most
often used symmetrical designs are three-level full factorial, central
composite, Box-Behnken design (BBD), etc. Three-level full factorial
design for three factors is represented in Figure 3.1.
In order to determine the experimental error, the central point is often
replicated several (3-5) times.
Central composite design (CCD) is composed of a two-level full
factorial design (2 f experiments), a star design (2 f experiments), and a
center point, therefore requiring N = 2 f + 2 f + 1 experiments to examine
the f factors (Montgomery, 1997) (Table 3.5). The points of the full
factorial design are situated at factor levels −1 and +1, those of the star
design at the factor levels 0, −α and +α, and the center point at factor
level 0. Depending on the value of α, two types of designs exist, a
face-centered CCD (FCCD) with |α | = 1, and a circumscribed CCD
(CCCD) with |α| > 1. Therefore, in the case of FCCD and CCCD, factors
are varied on three or fi ve levels, respectively.

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Three-level full factorial design for 3 factors, 3 3 design
with 27 experiments

Figure 3.1