Nonregular fractions of the 2k [John (1971)].

Consider a 24 design. We must estimate the four main effects and the six two-factor interactions, but the full 24 factorial cannot be run. The largest possible block size contains 12 runs.

These 12 runs can be obtained from the four one-quarter replicates defined by I = ±AB = ±ACD = ±BCD by omitting the principal fraction. Showhowthe remaining three 24−2 fractions can be combined to estimate the required effects, assuming three-factor and higher interactions are negligible. This design could be thought of as a three-quarter fraction.