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designs are fractional factorial or Plackett-Burman designs (Montgomery,
1997; Lewis et al., 1999). When the number of factors,
f
, is small, then
full factorial design can also be used for screening purposes (Dejaegher
and Heyden, 2011). Screening designs allow simultaneous investigation
of both qualitative (discrete) and quantitative (continuous) factors, which
makes them extremely useful for preliminary formulation development.
When
f
factors are varied on two levels, all possible combinations of
these variations make up the two-level full factorial design. The number
of experiments,
N
, in this design is
L
f
=
2
f
. Note that designs are usually
denoted as
e
f
, meaning that in a 2
3
design, 3 factors (f) are varied on
2 levels (e) (as represented in Table 3.1). Note that factor levels are in
coded values, which enables them to be compared. The lower factor level
is denoted as −1, and 1 stands for the upper factor level.
When the experiments are organized and conducted according to an
experimental design, the results are used to calculate factor effects, which
demonstrate to what extent certain factors infl uence the output (i.e.
studied dependent variable).
Factor effects are used to build the regression model:
[3.1]
where
y
is the response (dependent variable), β
0
the intercept, and β
i
the
regression coeffi cients (regression coeffi cients stand for factor effects).
Full factorial designs allow identifi cation of factor interactions.
Independent variables, that is, factors can interact meaning that the
Table 3.1
2
3
full factorial design
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
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