Fractional simplex designs for interaction screening in complex mixtures

In mixture experiments, one may be interested in estimating not only main e ffects but also some interactions. Main effects and significant interaction s in a mixture may be estimated through appropriate mixture experiments, su ch as simplex-centroid designs. However, for mixtures with a large number o f factors, the run size for these designs becomes impractically large. A su bset of a full simplex-centroid design may be used, but the problem remains regarding which factor-level settings should be selected. In this paper, w e propose a solution that considers design points with either one or p indi vidual nonzero factor-level settings. These fractional simplex designs prov ide a means of screening for interactions and of investigating the behavior of many-component mixtures as a whole while greatly reducing the run size compared with full simplex-centroid designs. The means of construction of t he design arrays is described, and designs for less than or equal to 31 fac tors are presented. Some of the proposed methodology is illustrated using g enerated data.