Abstract
Quaternary-code (QC) designs, an attractive class of nonregular fractional factorial designs, have received much attention due to their theoretical elegance and practical applicability. Some recent works of QC designs revealed their good properties over their regular counterparts under commonly used criteria. We develop an optimization tool that can maximize the generalized resolution of a QC design of a given size. The problem can be recast as an integer linear programming (ILP) problem through a linear simplification that combines the \(k\)- and \(a\)-equations, even though the generalized resolution does not linearly depend on the aliasing indexes. The ILP surprisingly improves a class of \((1/16)\)th-fraction QC designs with higher generalized resolutions. It also applies to obtain some \((1/64)\)th-fraction QC designs with maximum generalized resolutions, and these QC designs generally have higher generalized resolutions than the regular designs of the same size.
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Acknowledgments
This work was supported by (a) Career Development Award of Academia Sinica (Taiwan) grant number 103-CDA-M04 for Phoa, (b) National Science Council (Taiwan) Grant number 102-2628-M-001-002-MY3 for Phoa and Lin, and (c) National Science Council (Taiwan) postdoctoral researcher Grant number 102-2811-M-001-148-001 for Wang.
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Phoa, F.K.H., Wang, TC. & Lin, SC. A search of maximum generalized resolution quaternary-code designs via integer linear programming. Stat Comput 26, 277–283 (2016). https://doi.org/10.1007/s11222-014-9496-7
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DOI: https://doi.org/10.1007/s11222-014-9496-7