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researcher to select the number of levels for each factor, depending on its
nature and desired experimental domain. The Doehlert design describes a
spherical experimental domain and stresses uniformity in space fi lling. For
two variables, the design consists of one central point and six points
forming a regular hexagon, and therefore is situated on a circle (Ferreira
et al., 2004) (Table 3.8). Doehlert designs are effi cient in the mapping of
experimental domains: adjoining hexagons can fi ll a space completely and
effi ciently, since the hexagons fi ll space without overlapping (Massart
et al., 2003). In this design, one variable is varied on fi ve levels, whereas
the other is varied on three levels (Table 3.8). Generally, it is preferable to
choose the variable with the stronger effect as the factor with fi ve levels, in
order to obtain most information from the system (Ferreira et al., 2004).
A comparison between the BBD and other response surface designs
(central composite, Doehlert matrix, and three-level full factorial design)
has demonstrated that the BBD and Doehlert matrix are slightly more
effi cient than the CCD, but much more effi cient than the three-level full
factorial designs, where the effi ciency of one experimental design is
defi ned as the number of coeffi cients in the estimated model divided by
the number of experiments (Ferreira et al., 2007).
Asymmetrical designs are used for investigation in the asymmetrical
experimental domain. Typical examples are D-optimal designs. These
(asymmetrical) designs can also be adapted for investigation of the
symmetrical experimental domain, which is not the case for application of
symmetrical designs for the asymmetrical domain. D-optimal designs are
computer-generated designs tailor-made for each problem, allowing great
fl exibility in the specifi cations of each problem and are particularly useful
Table 3.8
Doehlert matrix for two variables
Factors
Experiment
A
B
1
0
0
2
1
0
3
0.5
0.866
4
−1
0
5
−0.5
−0.866
6
0.5
−0.866
7
−0.5
0.866
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