Working with Mixture screening Designs
Mixture screening designs are used when there are so many components the number of runs required to estimate higher-order, blending effects, terms exceeds the budget. One must make the assumption that the linear effects will be enough to decide which components truly matter to the process.
The goal of a mixture screening experiment is to use as few runs as possible to decide which components will be studied in more detail during the latter phases of the experimentation process.
Mixture screening designs require at least 2 vertices per component to estimate the linear effects. Usually replicated center points are added to the base designs to provide a more powerful test and allow the detection of substantial blending effects. Although a mixture screening design can detect blending, there is usually not enough information to determine which components are contributing to the blending effect. The choice of which subset of the components take part in the blending requires the informed opinions of subject matter experts.
The analysis concentrates on estimating the linear gradients and effects of the individual components. These estimate are shown on the ANOVA any time a linear model is fit during the analysis of a mixture design. The Trace plot is a great visual representation of the relative effects coming from the components.
Components that have about the same gradient across all the critical responses can be treated like a family and combined into a single component for future work. This decision must be supported by subject matter expert opinion. If there is no science to justify combining components, then they shouldn’t be combined.
An example of combinable components is blending flours to make cupcakes. Three flours are used cake, bread, and all-purpose – these flours have about the same effect on taste and texture for this example. Because they are all flour, in makes sense that flour blends could be used in place of single flour. A very important part of combining factors is the similarities must carry across all critical responses.
When there are minimize and/or maximize goals for the responses, components that drive the response the wrong way can be set to the minimum possible for future work. If components have little to no beneficial effect on the response (gradient close to 0) these can also be fixed to nominal values for future work. Fixing the setting of a component removes it as a variable from future work.
Combining components into families, removing or minimizing detrimental components and fixing the levels of non-involved components accomplishes the goal of simplifying future work.