Optimal blocking for general resolution-3 designs

This paper presents a general method for nding optimal blocking arrangements of pure-level and mixed-level orthogonal designs of resolution 3. The method requires enumeration of all non-isomorphic `parent designs' that include the treatment factors as well as the future blocking factor. For all these designs, word-length frequency vectors expressing the aliasing between main e ects and two-factor interactions as well as the aliasing among two-factor interactions are calculated. The same is done for all projections into `child designs' obtained by dropping any possible blocking factor. The word-length frequency vectors of the parent and child designs then allow the selection of blocking arrangements that are optimal with respect to ve criteria appropriate for blocking resolution-3 orthogonal designs. We provide optimal blocking arrangements for orthogonal pure-level and mixed-level designs of 12, 16, 18, 20 and 27 runs.