Designs with Multiple Groups of Factors

Identities about the wordlength patterns of regular s designs and their complementary designs are established through a first-order differential equation satisfied by a structure function. The identities are then generalized to s designs with multiple groups of factors. An advantage of using the structure function and partial differential equation is that it can easily adapt to some structural constraints of designs. The application of this approach to regular blocked fractional factorial designs generates identities relating the split wordlength patterns of regular (s, s) blocked designs and their complementary blocked designs. Practical rules are proposed for selecting optimal blocking schemes in terms of their complementary designs.