ABSTRACT

An example of regular fractional factorial designs was discussed in Section 8.4. Some basic properties of regular fractional factorial designs are presented in this chapter. When only a fraction of the treatment combinations are observed, the factorial effects are mixed up (aliased). Under a regular fractional factorial design, aliasing of the factorial effects can be determined in a simple manner. Such designs are easy to construct, have nice structures, and are relatively straightforward to analyze, but the number of levels must be a prime number or power of a prime number. We show that all regular fractional factorial designs are orthogonal arrays. An algorithm for constructing a regular fractional factorial design under which certain required effects are estimable is presented. We also discuss connections of regular fractional factorial designs with finite projective geometries and linear codes. Results from finite projective geometry and coding theory provide useful tools for studying the structures and construction of regular fractional factorial designs.