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Table 3.4
Plackett-Burman design for seven factors
Factors
Experiment
A
B
C
D
E
F
G
1
1
1
1
−1
1
−1
−1
2
−1
1
1
1
−1
1
−1
3
−1
−1
1
1
1
−1
1
4
1
−1
−1
1
1
1
−1
5
−1
1
−1
−1
1
1
1
6
1
−1
1
−1
−1
1
1
7
1
1
−1
1
−1
−1
1
8
−1
−1
−1
−1
−1
−1
−1
Fractional factorial design does not indicate potential factor interactions
and if it is highly fractioned, some factors effects are estimated together
(factors are confounded).
A special type of screening design, the Plackett-Burman design (1946),
allows estimation of factor effects for f = N - 1 factors, where N is the
number of experiments with a multiple of 4. These designs are especially
useful for preliminary investigations of huge numbers of potentially
infl uential factors, as represented in Table 3.4 for a 2 7-4 design.
Other special kinds of screening designs are asymmetrical,
supersaturated, or mixed-level designs. D-optimal design can also be
adapted for screening purposes (Dejaegher and Heyden, 2011).
When fractional factorial designs are applied, there is always a
possibility that a signifi cant factor effect is not detected, due to all possible
factor level combinations not being investigated.
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￿
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3.2.2 Response surface designs
Response surface designs are used to analyze effects of the most signifi cant
factors that are recognized by screening studies (or are known from the
previous experience), where the number of these factors is usually 2 or 3.
Factors are varied on at least three levels. The main goal of response
surface designs is usually optimization. Note that qualitative (discrete)
factors cannot be used in these designs. Response surface designs are
accompanied by visual representation of the factors' infl uence on the
 
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