ABSTRACT
In this chapter we study the structures of two-level regular fractional factorial designs, in particular those of resolution IV. The notion of maximal designs is introduced. Each regular fractional factorial design is the projection of a certain maximal design onto a subset of factors. Thus the characterization of maximal designs is useful for the construction of regular designs. While saturated regular designs are the only maximal designs of resolution III, typically there are many nonisomorphic maximal designs of resolution IV. The study of maximal designs of resolution IV brings forth the methods of partial foldover and doubling, in addition to the familiar method of foldover, for constructing resolution IV designs. The methods of partial foldover and doubling produce many resolution IV designs that cannot be constructed by the method of foldover. The structural theorems presented in this chapter are also useful for the determination of minimum aberration designs of resolution IV. In particular, we present a general complementary design theory for two-level designs that are constructed by the method of doubling.
