An application of projection design in product development

Abstract The area of mixture design and analysis is of vital importance in food science and industry, since all foods are mixtures of a number of different ingredients. Mixture methods respect constraints among the ingredients in both the set-up of the design and the analysis of the results. This methodology is, therefore, more complex than, e.g., factorial and fractional factorial designs. Projection design methodology as proposed by Hau and Box [I.Hau, G. Box, Constrained experimental designs: Part I. Construction of projection designs, I, Center for Quality and Productivity Improvement, University of Wisconsin, Madison, WI, USA, 1990; I. Hau, G. Box, Constrained experimental designs: Part II. Analysis of projection designs, II, Center for Quality and Productivity Improvement, University of Wisconsin, Madison, WI, USA, 1990; I. Hau, G. Box, Constrained experimental designs: Part III. Properties of projection designs, III, Center for Quality and Productivity Improvement, University of Wisconsin, Madison, WI, USA, 1990] is developed to keep some of the simplicity of the factorial approach while working with the more complex area of mixture designs and constrained situations in general. The method is based on setting up a fractional factorial design and then projecting this onto a space determined by the set of constraints. In some cases, the analysis can also be done by “factorial-like” techniques. In the present paper, the projection design method is investigated and compared with the more conventional mixture model method [J.A. Cornell, Experiments with Mixtures. Designs, Models and the Analysis of Mixture Data, 2nd edn., 1990, Wiley-Interscience]. The discussion is based on a case study where process and mixture variables are combined. Both design and modelling aspects are discussed. The overall conclusion is that both approaches are useful. However, the mixture model approach seems somewhat more flexible with respect to design region and also somewhat easier to analyse and interpret. The projection design approach seems to be a useful and simple way of providing fractional versions of combined designs. This may be difficult by using other techniques.