Results for Two-Level Designs with General Minimum Lower-Order Confounding

The general minimum lower-order confounding (GMC) criterion for two-level design not only reveals the confounding information of factor effects but also provides a good way to select the optimal design, which was proposed by Zhang et al. (2008). The criterion is based on the aliased effect-number pattern (AENP). Therefore, it is very important to study properties of AENP for two-level GMC design. According to the ordering of elements in the AENP, the confounding information between lower-order factor effects is more important than that of higher-order effects. For two-level GMC design, this paper mainly shows the interior principles to calculate the leading elements (1) (#) C (2) and (2) (#) C (2) in the AENP. Further, their mathematical formulations are obtained for every GMC 2(n−m) design with N = 2(n−m) according to two cases: (i) 5N/16 + 1 ≤ n < N/2 and (ii) N/2 ≤ n ≤ N − 1.