An approach to constructing good two-level orthogonal factorial designs with large run sizes
Due to the increasing demand for two-level fractional factorials in areas of science and technology, it is highly desirable to have a simple and convenient method available for constructing optimal factorials. Minimum G2-aberration is a popular criterion to use for selecting optimal designs. However, direct application of this criterion is challenging for large designs. In this project, we propose an approach to constructing a "good" factorial with a large run size using two small minimum G2-aberration designs. Theoretical results are derived that allow the word length pattern of the large design to be obtained from those of the two small designs. Regular 64-run factorials are used to evaluate this approach. The designs from our approach are very close to the corresponding minimum aberration designs, and they are even equivalent to the corresponding minimum aberration designs, when the number of factors is large. Keywords: Fractional factorial; Minimum aberration; Minimum G2-aberration; Word length pattern.