Scheffe simplex lattice design

The most frequently used mixture- composition-property designs of experiments belong to simplex-lattice designs suggested by Scheffe [5], The basis of this kind of designing experiments is a uniform scatter of experimental points on the so-called simplex lattice. Points, or design points form a [q,n] lattice in a (q-1) simplex, where q is the number of components in a composition and n is the degree of a polynomial. For each component there exist (n+1) similar levels Xp0,l/n,2/n.1 and all 

Results of such calculations are given in Table 3.13. To obtain a linear regression model, one has to do three design points in simplex vertices. To check lack of fit of the model, one has to do an additional design point in the simplex center. The design of the experiment is given in Table 3.14. 

As one may conclude from the above table, subscripts of the mixture property-response symbols indicate the relative proportion of each of the components in the mixture. For example, the mixture 1 (Table 3.14) contains the component Xi alone, 

The number of trials of simplex lattice designs, which depend on the number of components and the degree of regression model, is given Table 3.18. 

Regression model Response Number of components in mixture 

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In order that Scheffes simplex lattice designs may be applied to this case, a renormalization is performed and compositions at vertices Aj(j=l, 2,..., q) are taken to be independent pseudocomponents so that for all the range of the local simplex the condition be met ... 

Scheffe simplex lattice designs have many qualities ... 

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