Fractional simplex designs for interaction screening in complex mixtures

In mixture experiments, one may be interested in estimating not only main effects but also some interactions. Main effects and significant interactions in a mixture may be estimated through appropriate mixture experiments, such as simplex-centroid designs. However, for mixtures with a large number of factors, the run size for these designs becomes impractically large. A subset of a full simplex-centroid design may be used, but the problem remains regarding which factor-level settings should be selected. In this paper, we propose a solution that considers design points with either one or p individual nonzero factor-level settings. These fractional simplex designs provide 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 the design arrays is described, and designs for < or = 31 factors are presented. Some of the proposed methodology is illustrated using generated data.