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Table 3.9
Doehlert matrix for three variables
Factors
Experiment
A
B
C
1
0
0
0
2
1
0
0
3
0.5
0.866
0
4
0.5
0.289
0.817
5
−1
0
0
6
−0.5
−0.866
0
7
−0.5
−0.289
−0.817
8
0.5
−0.866
0
9
0.5
−0.289
−0.817
10
−0.5
0.866
0
11
0
0.577
−0.817
12
−0.5
0.289
0.817
13
0
−0.577
0.817
when it is necessary to constrain a region and no classical design exists.
D-optimal design is an effi cient tool in experimental design, making it
possible to detect the best subset of experiments from a set of candidate
points. Starting from an initial set, several subsets with different type and
number of experiments are selected. When analyzing the quality criteria
(i.e. determinant of the information matrix, infl ation factors) of each
subset of different size, it is possible to fi nd a good compromise between
the quality of information obtained and the number of experiments to be
performed (Frank and Todeschini, 1994). D-optimal designs are used for
irregular experimental regions, multi-level qualitative factors in screening,
optimization designs with qualitative factors, when the desired number of
runs is smaller then required by a classical design, model updating,
inclusions of already performed experiments, combined designs with
process, and mixture factors in the same experimental plan (Eriksson et al.,
2008). In D-optimal designs, N experiments forming the D-optimal design
are selected from the candidate points, forming a grid over the asymmetrical
domain. These experiments are the
best
subset of experiments selected
from a candidate set (Eriksson et al., 2008). The term 'best' refers to the
selection of experimental runs according to a given criterion. The criterion
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