Word-degree Pattern For Designs With Quantitative Factors

It is essential to determine the criterion for comparing different designs before a proper design is chosen. When experiments with qualitative factors or two-level quan-titative factors are considered, minimum aberration criterion is often recommended. However, for an experiment with high-level quantitative factors, it is not enough to choose a design only by minimum aberration criterion. In order to compare different designs with quantitative factors, we define the concept of word-degree pattern, and also propose the minimum degree aberration criterion.For regular designs, we consider the defining relationship subgroup and the distri-bution characteristics of its dual code and give the definition of word-degree pattern and the minimum degree aberration. We calculate the word-degree patterns for combi-natorially isomorphic designs L9(33) and L27(313), and illustrate the real application of word-degree pattern in comparing designs with the same parameters. For non-regular designs, we apply the MacWilliams identity in coding theory to generalize the con-cept and formula of word-degree pattern. We also use two L28(37) designs to explain the feasibility of employing word-degree pattern as a criterion to compare non-regular designs.