Factorial designs are the
most common type of experimental
design. In a factorial design
several factors are controlled at two or
more levels, and the effect on the response
is investigated.
There are two main types:
Full Factorial Designs and
Fractional
Factorial Designs. In Fractional
Factorial designs the amount of testing
is reduced, but the downside is that some
interactions and factors are aliased. One
of the limitations of Fractional Factorial
designs is that the number of runs is 2^{n},
if there are more than a few factors this
leads to large gaps in the available options
(4, 8, 16, 32, 64, 128, etc.). PlackettBurman
designs overcome this, but
at the expense of confounding. Other approaches
to the Design of Experiments include Response
Surface Methods and Taguchi
Designs.
