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 2IVm−p:2l designs are obtained, where 2IVm−p:2l denotes a regular resolution IV blocked design with mm treatment factors, ll block factors, and 2m−p2m−p runs. An algorithm is proposed for constructing 2IVm−p:2l designs with the maximum number of clear 2fi’s. Based on this algorithm, the 16-, 32-, and 64-run 2IVm−p:2l designs containing the maximum number of clear 2fi’s are constructed and tabulated.