Row-Wise Complementary Designs

Abstract

The technique of (column-wise) complementary designs, proposed independently by Chen and Hedayat (1996) and Tang and Wu (1996), is powerful for characterizing designs with a large number of factors. In this paper, we extend the idea and propose row-wise complementary designs which are particularly useful in handling designs with large run sizes. A pair of designs are mutually row-wise complementary of order r if they are row partition of a full factorial design with r replicates. Based on a polynomial representation approach for factorial designs called indicator function, we establish a series of relationships between a design and its row-wise complementary design, which includes isomorphism, orthogonality, generalized word length pattern, minimum aberration, moment aberration, and uniformity. In addition, we apply the technique of row-wise complementary design to identify minimum aberration two-level designs with larger run sizes. The method can be generalized and applied to higher-level, mixed-level, or blocked factorial designs. This is a joint work with Dr. Shao-Wei Cheng