Very often experimenters do not have adequate time, resources or budget to carry out
FFEs. If the experimenters can reasonably assume that certain higher-order interactions
(third order and higher) are not important, then information on the main effects
and two-order interactions can be obtained by running only a fraction of the FFE.
A type of orthogonal array design which allows experimenters to study main effects
and desired interaction effects in a minimum number of trials or experimental runs
is called a fractional factorial design. These fractional factorial designs are the most
widely and commonly used types of design in industry. These designs are generally
represented in the form 2(k−p), where k is the number of factors and 1/2p represents
the fraction of the full factorial 2k (Box et al., 1978). For example, 2(5−2) is a 1/4th
fraction of a 25 FFE. This means that one may be able to study 5 factors at 2-levels in
just 8 experimental trials instead of 32 trials.