Some results on blocked regular 2-level fractional factorial designs with clear effects

Blocking is commonly used in design of experiments to reduce systematic variation and increase precision of effect estimation. In this article, the clear effect concept is discussed for the blocked fractional factorial designs. First, some theoretical results on the existence of clear main effects and two-factor interactions (2fi's) in regular 2^{m - p} : 2^l designs with resolution III, IV^- and IV are obtained, where a 2^{m - p} : 2^l design means a 2^{m - p} design in 2^l blocks. Then, the blocked designs containing clear 2fi's are mainly considered and the upper and lower bounds on the maximum number of clear 2fi's in 2^{m - p} : 2^l designs with resolution III and IV^- are derived. The lower bounds are achieved by constructing specific designs. Some tables are also given for comparing the bounds with true values, which show that many designs constructed by our methods have the maximum number of clear 2fi's.