This paper discusses an algorithmic approach to constructing trend-free and orthogonally-blocked response surface designs. The constructed designs have the main effects, 2-factor interactions and second-order effects being orthogonal or near-orthogonal to the nuisance factors such as the time-trend or the blocking factors. The paper also provides a catalogue of (near-) trend-free Box–Behnkens designs and orthogonally blocked Box–Behnkens designs arranged in rows and columns.
Part of the book: Response Surface Methodology in Engineering Science
Box-Behnken designs (BBDs) are three-level second-order spherical designs with all points lying on a sphere, introduced by Box and Behnken, for fitting the second-order response surface models. They are available for 3–12 and 16 factors. Together with the central composite designs for the second-order model, BBDs are very popular response surface designs, especially for 3–7 factors. This chapter introduces an algorithm to produce cyclic generators for BBDs and similar designs, which we call cyclic BBDs (CBBDs). The new CBBDs offer more flexibility in choosing the designs for a specified number of factors. Comparisons between some BBDs and the new CBBDs indicate the superiority of the new CBBDs with respect to multiple design quality measures and graphical tools assessing prediction variance properties. A catalog of 24 new CBBDs, which includes orthogonally blocked CBBDs for 11, 13, and 14 factors, will be given.
Part of the book: Response Surface Methodology
Most screening experiments in chemometrics and science are quantitative, i.e. continuous factors. These factors should be 3-level and the designs for these experiments should also be 3-level. However, popular designs for screening experiments are still Plackett-Burman designs (PBDs) and 2-level fractional factorial designs (FFDs) such as resolution III and resolution IV FFDs. This chapter introduces the conference matrices as an alternative to PBDs and resolution III FFDs and definitive screening designs, a conference matrix-based class of designs, as an alternative to resolution IV FFDs. A table of conference matrices of up to order 32 and examples are also provided for illustration.
Part of the book: Novel Aspects of Gas Chromatography and Chemometrics