OPTIMAL BLOCKING SCHEMES FOR 2(N) AND 2(N-P) DESIGNS

Systematic sources of variations in factorial experiments can be effec tively reduced without biasing the estimates of the treatment effects by grouping the runs into blocks. For full factorial designs, optimal blocking schemes are obtained by applying the minimum aberration crite rion to the block defining contrast subgroup. A related concept of ord er of estimability is proposed. For fractional factorial designs, beca use of the intrinsic difference between treatment factors and block va riables, the minimum aberration approach has to be modified. A concept of admissible blocking schemes is proposed for selecting block design s based on multiple criteria. The resulting 2(n) and 2(n-p) designs ar e shown to have better overall properties for practical experiments th an those in the literature.