ABSTRACT
The run sizes of regular fractional factorial designs must be prime numbers or powers of prime numbers. Nonregular designs are more flexible in run sizes and are more abundant. For example, if the Hadamard conjecture is true, then Hadamard designs can be constructed for every run size that is a multiple of 4. The economy in run sizes makes these designs suitable for factor-screening experiments where the primary objective is to identify important factors for further exploration. In this chapter we briefly discuss some properties of nonregular designs and how some of the results presented in previous chapters can be extended to nonregular designs. The aliasing of factorial effects under a nonregular design is more complex than that under a regular design. This, however, leads to interesting projection properties with important implications. A design with good projections onto small subsets of factors can provide useful information in factor-screening experiments. For two-level designs, Deng and Tang (1999) proposed a generalized minimum aberration criterion as an extension of minimum aberration to nonregular designs. A simpler version, called minimum G2-aberration, was proposed in Tang and Deng (1999). When applied to regular designs, both versions are the same as minimum aberration. We concentrate on minimum G2-aberration and its generalizations, including Xu and Wu’s (2001) extension to mixed-level designs. When regular designs are available, there often exist better nonregular designs than minimum aberration regular designs under the generalized minimum aberration criterion. We also present some results on two-level supersaturated designs. Such designs, with more factors than the available degrees of freedom, are useful for factor screening. Other topics covered include parallel flats designs and saturated designs for hierarchical models.
