ABSTRACT
A regular fractional factorial design is determined by its defining effects. Different choices of defining effects may lead to designs with different statistical properties. In this chapter, we address the issue of selecting defining effects. When the experimenter has prior knowledge about the relative importance of certain effects, the algorithm proposed by Franklin and Bailey (1977) and Franklin (1985), as discussed in Section 9.7, can be used to select defining effects for constructing designs under which certain required effects are estimable. Here we concentrate on the situation where prior knowledge is diffuse concerning the possible greater importance of factorial effects. Minimum aberration is an established criterion for design selection under the hierarchical assumption that lower-order effects are more important than higher-order effects and effects of the same order are equally important. We discuss some basic properties of this criterion, including a statistical justification showing that it is a good surrogate for maximum estimation capacity under model uncertainty. We also discuss connections to coding theory and finite projective geometry, and present some results on the characterization and construction of minimum aberration designs. One application of coding theory is the equivalence of minimum aberration to a criterion called minimum moment aberration. This equivalence provides a useful tool for determining minimum aberration designs. We end the chapter by presenting a Bayesian approach to factorial designs.
