Optimal Blocking for General Resolution-3 Designs

• Autores: Eric D. Schoen, Bagus Sartono, Peter Roos
• Localización: Journal of quality technology: A quarterly journal of methods applications and related topics, ISSN 0022-4065, Vol. 45, Nº. 2, 2013, págs. 166-187
• Idioma: inglés
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• Resumen

  • This paper presents a general method for finding optimal blocking arrangements of pure-level and mixed-level orthogonal designs of resolution 3. The method requires enumeration of all nonisomorphic 'full designs' that include the treatment factors as well as the blocking factor. For all these designs, generalized word counts expressing the aliasing between main effects and two-factor interactions as well as as the aliasing among two-factor interactions are calculated. The same is done for all projections into treatment designs obtained by dropping any possible blocking factor. The generalized word counts of the full design and treatment designs then allow the selection of blocking arrangements that are optimal with respect to five 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.