Construction of minimum aberration blocked two-level regular factorial designs

Abstract

ABSTRACTIn this article, we consider the construction of minimum aberration 2n − k: 2p designs with respect to some existing combined wordlength patterns, where a 2n − k: 2p design is a blocked two-level design with n treatment factors, 2p blocks, and N = 2q runs with q = n − k. Two methods are proposed for two situations: n ⩽ 2q − p − 1 and n > N/2. These methods enable us to obtain some new minimum aberration 2n − k: 2p designs from existing minimum aberration unblocked and blocked designs. Examples are included to illustrate the theory.