On blocked resolution IV designs containing clear two-factor interactions

Blocking is an effective method for reducing systematic variations and increasing the precision of effect estimation when the experimental units are not homogeneous. Clear two-factor interactions (2fi’s) can be estimated under the weak assumption that interactions involving three or more factors can be ignored. Some theoretical results on the existence of clear 2fi’s in 2 IV : 2 l designs are obtained, where 2 IV : 2 l denotes a regular resolution IV blocked design withm treatment factors, l block factors, and 2m−p runs. An algorithm is proposed for constructing 2 IV : 2 l designs with the maximum number of clear 2fi’s. Based on this algorithm, the 16-, 32-, and 64-run 2 IV : 2 l designs containing the maximum number of clear 2fi’s are constructed and tabulated. © 2013 Elsevier Inc. All rights reserved.