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


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 a large number, q, of potentially important components that can be considered candidates in an experiment. The objective of these types of experiments is to screen the 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.  
A first order mixture model 
The construction of screening designs and their corresponding models
often begins with the firstorder or firstdegree mixture model
\[ E(Y) = \beta_{1}x_{1} + \beta_{2}x_{2} + \cdots \beta_{q}x_{q} \] for which the beta coefficients are nonnegative 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.e., the estimates of the \( \beta_{i} \), relative to their standard errors. Simplex screening designs are recommended when 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 Doptimal designs for a linear model are always an option. 