pg_0144
5.
Process Improvement
5.3.
Choosing an experimental design
5.3.3.
How do you select an experimental design.
5.3.3.9.
Three-level full factorial designs
Three-level
designs are
useful for
investigating
quadratic
effects
The three-level design is written as a 3
k
factorial design. It means that k factors
are considered, each at 3 levels. These are (usually) referred to as low,
intermediate and high levels. These levels are numerically expressed as 0, 1,
and 2. One could have considered the digits -1, 0, and +1, but this may be
confusing with respect to the 2-level designs since 0 is reserved for center
points. Therefore, we will use the 0, 1, 2 scheme. The reason that the three-level
designs were proposed is to model possible curvature in the response function
and to handle the case of nominal factors at 3 levels. A third level for a
continuous factor facilitates investigation of a quadratic relationship between
the response and each of the factors.
Three-level
design may
require
prohibitive
number of
runs
Unfortunately, the three-level design is prohibitive in terms of the number of
runs, and thus in terms of cost and effort. For example a two-level design with
center points is much less expensive while it still is a very good (and simple)
way to establish the presence or absence of curvature.
The 3
2
design
The simplest
3-level design
- with only 2
factors
This is the simplest three-level design. It has two factors, each at three levels.
The 9 treatment combinations for this type of design can be shown pictorially as
follows:
FIGURE 3.23 A 3
2
Design Schematic
5.3.3.9. Three-level full factorial designs
http://www.itl.nist.gov/div898/handbook/pri/section3/pri339.htm (1 of 4) [5/7/2002 4:02:04 PM]
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