Constrained mixture designs

Table V. Design II 3 Component Constrained Mixture Design...

Note that, again, three different types of variables were combined chain length, component ratio, and absolute component level. Thus, a "standard" constrained mixture design was not appropriate. In this case a full factorial, central composite design was used, with a total of 20 data points. The star points were... 

Figure 7. Constrained mixture design, showing relationship between real and pseudocomponents.

Figure 12.28 Conversion of a 3 full factorial design to a give a constrained mixture design. See text for details.

Constrained mixture designs are often difficult to set up, but there are four fundamental situations, exemplified in Figure 2.35, each of which requires a different strategy. 

Four situations encountered in constrained mixture designs... 

Table 2.39 Constrained mixture design with three lower bounds.

Table 2.40 Constrained mixture designs with upper bounds established in advance. ...

Table 2.42 illustrates two constrained mixture designs, one with six and die other... 

Table 2.42 Constrained mixture design where both upper and lower limits are known in advance.

Problem 2.11 Use of a Constrained Mixture Design to Investigate the Conductivity of a Molten Salt System... 

As shown, mixture components are subject to the constraint that they must equal to the sum of one. In this case, standard mixture designs for fitting standard models such as simplex-lattice and simplex-centroid designs are employed. When mixtures are subject to additional constraints, constrained mixture designs (extreme-vertices) are then appropriate. Like the factorial experiments discussed above, mixture experimental errors are independent and identically distributed with zero mean and common variance. In addition, the true response surface is considered continuous over the region being studied. Overall, the measured response is assumed to depend only on the relative proportions of the components in the mixture and not on the amount. 

Pelissari FM, Yamashita F, Garcia MA, Martino MN, Zaritzky NE, Grossmann MVE (2012) Constrained mixture design applied to the development of cassava starch-blown films. J Food Eng 108 262—267... 

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