TY - DATA T1 - Constructing Two-Level Designs by Concatenation of Strength-3 Orthogonal Arrays PY - 2018/05/16 AU - Alan R. Vazquez AU - Peter Goos AU - Eric D. Schoen UR - https://tandf.figshare.com/articles/dataset/Constructing_Two-Level_Designs_by_Concatenation_of_Strength-3_Orthogonal_Arrays/6275204 DO - 10.6084/m9.figshare.6275204.v1 L4 - https://ndownloader.figshare.com/files/11471753 L4 - https://ndownloader.figshare.com/files/11471756 L4 - https://ndownloader.figshare.com/files/11471759 L4 - https://ndownloader.figshare.com/files/11471762 L4 - https://ndownloader.figshare.com/files/11471765 L4 - https://ndownloader.figshare.com/files/11471768 L4 - https://ndownloader.figshare.com/files/11471771 L4 - https://ndownloader.figshare.com/files/11471774 L4 - https://ndownloader.figshare.com/files/11471777 L4 - https://ndownloader.figshare.com/files/11471780 L4 - https://ndownloader.figshare.com/files/11471783 L4 - https://ndownloader.figshare.com/files/11471786 L4 - https://ndownloader.figshare.com/files/11471789 L4 - https://ndownloader.figshare.com/files/11471792 L4 - https://ndownloader.figshare.com/files/11471795 L4 - https://ndownloader.figshare.com/files/11471798 L4 - https://ndownloader.figshare.com/files/11471801 L4 - https://ndownloader.figshare.com/files/11471804 L4 - https://ndownloader.figshare.com/files/11471807 L4 - https://ndownloader.figshare.com/files/11471810 KW - Even-odd design KW - generalized aberration KW - local search KW - second-order saturated KW - two-factor interaction KW - variable neighborhood search N2 - Two-level orthogonal arrays of N runs, k factors and a strength of 3 provide suitable fractional factorial designs in situations where many of the main effects are expected to be active, as well as some two-factor interactions. If they consist of N/2 mirror image pairs, these designs are fold-over designs. They are called even and provide at most N/2 − 1 degrees of freedom to estimate interactions. For k < N/3 factors, there exist strength-3 designs that are not fold-over designs. They are called even-odd designs and they provide many more degrees of freedom to estimate interactions. For N ≤ 48, attractive even-odd designs can be extracted from complete catalogs of strength-3 orthogonal arrays. However, for larger run sizes, no complete catalogs exist. In order to construct even-odd designs with N > 48, we develop an algorithm for an optimal concatenation of strength-3 designs involving N/2 runs. Our approach involves column permutations of one of the concatenated designs, as well as sign switches of the elements of one or more columns of that design. We illustrate the potential of the algorithm by generating two-level even-odd designs with 64 and 128 runs involving up to 33 factors, because this allows a comparison with benchmark designs from the literature. With a few exceptions, our even-odd designs outperform or are competitive with the benchmark designs in terms of the aliasing of two-factor interactions and in terms of the available degrees of freedom to estimate two-factor interactions. ER -