pg_0079
5.
Process Improvement
5.3.
Choosing an experimental design
5.3.3.
How do you select an experimental design.
5.3.3.4.
Fractional factorial designs
Full factorial
experiments
can require
many runs
The ASQC (1983) Glossary & Tables for Statistical Quality Control
defines fractional factorial design in the following way: "A factorial
experiment in which only an adequately chosen fraction of the
treatment combinations required for the complete factorial experiment
is selected to be run."
A carefully
chosen
fraction of
the runs may
be all that is
necessary
Even if the number of factors, k, in a design is small, the 2
k
runs
specified for a full factorial can quickly become very large. For
example, 2
6
= 64 runs is for a two-level, full factorial design with six
factors. To this design we need to add a good number of centerpoint
runs and we can thus quickly run up a very large resource requirement
for runs with only a modest number of factors.
Later
sections will
show how to
choose the
"right"
fraction for
2-level
designs -
these are
both
balanced and
orthogonal
The solution to this problem is to use only a fraction of the runs
specified by the full factorial design. Which runs to make and which to
leave out is the subject of interest here. In general, we pick a fraction
such as ½, ., etc. of the runs called for by the full factorial. We use
various strategies that ensure an appropriate choice of runs. The
following sections will show you how to choose an appropriate fraction
of a full factorial design to suit your purpose at hand. Properly chosen
fractional factorial designs for 2-level experiments have the desirable
properties of being both
balanced
and
orthogonal
.
2-Level
fractional
factorial
designs
emphasized
Note: We will be emphasizing fractions of two-level designs only. This
is because two-level fractional designs are, in engineering at least, by
far the most popular fractional designs. Fractional factorials where
some factors have three levels will be covered briefly in
Section
5.3.3.10
.
5.3.3.4. Fractional factorial designs
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