Generalized Subset Designs in Analytical Chemistry.

Design of experiments (DOE) is an established methodology in research, development, manufacturing, and production for screening, optimization, and robustness testing. Two-level fractional factorial designs remain the preferred approach due to high information content while keeping the number of experiments low. These types of designs, however, have never been extended to a generalized multilevel reduced design type that would be capable to include both qualitative and quantitative factors. In this Article we describe a novel generalized fractional factorial design. In addition, it also provides complementary and balanced subdesigns analogous to a fold-over in two-level reduced factorial designs. We demonstrate how this design type can be applied with good results in three different applications in analytical chemistry including (a) multivariate calibration using microwave resonance spectroscopy for the determination of water in tablets, (b) stability study in drug product development, and (c) representative sample selection in clinical studies. This demonstrates the potential of generalized fractional factorial designs to be applied in many other areas of analytical chemistry where representative, balanced, and complementary subsets are required, especially when a combination of quantitative and qualitative factors at multiple levels exists.