Comparison of several design augmentation strategies

Industrial experiments often involve many variables, of which only a few are expected to be important. Typically a sequential design approach is used in which a screening phase is followed by a more detailed design on a subset of the variables. Screening designs are usually highly-fractionated factorials or Plackett-Burman designs; the subsequent stages usually involve folding over the Plackett-Burman design, augmenting the fractional factorials, or a completely new less-fractionated factorial using a subset of the original variables. In all of these designs, the alias structure can cause difficulties in detecting the correct model. This paper examines the foldover properties of the Plackett-Burman versus those of three-quarter fractional factorials, comparing and contrasting the efficacy of these two alternative approaches relative to convergence to an a priori known correct model. The results suggest that an initial fractional factorial (that can be subsequently extended to a three-quarter fraction) supports better model identification than the Plackett-Burmann design (with subsequent full foldover).