pg_0148
5.
Process Improvement
5.3.
Choosing an experimental design
5.3.3.
How do you select an experimental design.
5.3.3.10.
Three-level, mixed-level and
fractional factorial designs
Mixed level
designs have
some factors
with, say, 2
levels, and
some with 3
levels or 4
levels
The 2
k
and 3
k
experiments are special cases of factorial designs. In a
factorial design, one obtains data at every combination of the levels.
The importance of factorial designs, especially 2-level factorial designs,
was stated by Montgomery (1991): It is our belief that the two-level
factorial and fractional factorial designs should be the cornerstone of
industrial experimentation for product and process development and
improvement. He went on to say: There are, however, some situations in
which it is necessary to include a factor (or a few factors) that have
more than two levels.
This section will look at how to add three-level factors starting with
two-level designs, obtaining what is called a mixed-level design. We
will also look at how to add a four-level factor to a two-level design.
The section will conclude with a listing of some useful orthogonal
three-level and mixed-level designs (a few of the so-called Taguchi "L"
orthogonal array designs), and a brief discussion of their benefits and
disadvantages.
Generating a Mixed Three-Level and Two-Level Design
Montgomery
scheme for
generating a
mixed
design
Montgomery (1991) suggests how to derive a variable at three levels
from a 2
3
design, using a rather ingenious scheme. The objective is to
generate a design for one variable, A, at 2 levels and another, X, at three
levels. This will be formed by combining the -1 and 1 patterns for the B
and C factors to form the levels of the three-level factor X:
TABLE 3.38 Generating a Mixed Design
Two-Level
Three-Level
B
C
X
-1
-1
x
1
+1
-1
x
2
-1
+1
x
2
+1
+1
x
3
Similar to the 3
k
case, we observe that X has 2 degrees of freedom,
which can be broken out into a linear and a quadratic component. To
illustrate how the 2
3
design leads to the design with one factor at two
levels and one factor at three levels, consider the following table, with
particular attention focused on the column labels.
5.3.3.10. Three-level, mixed-level and fractional factorial designs
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