An unreplicated composite mixture design and statistical model are proposed to simultaneously optimize mixture systems having interaction effects. A split-plot design is made up of standard mixture designs at both the main-plot and sub-plot levels. The model is obtained by multiplying Scheffe mixture models for each mixture system. Equations for the coefficients of a special cubic-special cubic balanced model are presented as well as their standard errors for both random and split-plot design structures. The design is applied to the simultaneous optimization of both mobile phase chromatographic mixtures and extraction mixtures for the Baccharis mill flora (Less.) DC plant. The whole-plot extraction mixtures contained varying proportions of ethanol, ethyl acetate and dichloromethane in a simplex centroid design. The sub-plot reversed phase chromatographic mixtures also followed a simplex centroid design in varying proportions of methanol, acetonitrile and a methanol-acetonitrile-water 15:15:70% v/v mixture. Assuming random execution of experiments normal probability graphs for the coefficients of a saturated model were plotted to make an initial determination of significant model coefficients. These parameters were then refined using a reduced model containing a split-plot error structure. Two models were developed to estimate the number of peaks observed using the chromatographic detector at both 2 10 and 254 nm wavelengths. The significant model coefficients are interpreted physically in terms of interacting linear, curvature and special cubic effects. (c) 2007 Elsevier B.V. All rights reserved.8928289