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5. Process Improvement
5.5. Advanced topics
5.5.4. What is a mixture design?

5.5.4.1.

Mixture screening designs

Screening experiments can be used to identify the important mixture factors  In some areas of mixture experiments, for example, certain chemical industries, there is often present a large number, q, of potentially important components that can be considered candidates in an experiment. The objectives of these types of experiments is to screen these components to identify the ones that are most important. In this type of situation, the experimenter should consider a screening experiment to reduce the number of possible components. 
The construction of screening designs and their corresponding models often begins with the first order or first degree mixture model 
A first order mixture model
where the beta coefficients are non negative and sum to one.
Choices of types of screening designs depend on constraints If the experimental region is a simplex, it is generally a good idea to make the ranges of the components as similar as possible. Then the relative effects of the components can be assessed by ranking the ratios of the parameter estimates i, where i = 1,...,q, relative to their standard errors. Designs, called simplex screening designs are recommended for those cases where it is possible to experiment over the total simplex region. Constrained mixture designs are suggested when the proportions of some or all of the components are restricted by upper and lower bounds. If these designs are not feasible in this situation, then D-optimal designs for a linear model are always an option. 
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