Constrained mixture designs problem

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

In order to optimize the formulation, a different experimental design was used. Based on the results of the first design, the particular molecular weight of SiUMA was chosen which seemed to have the best chance of giving the desired balance of properties. Further, it had been established that Variable II (and not Variable III) was preferable for further work. With these variable types (i.e., not involving a component amount) eliminated, the problem was reduced to a "constrained mixture deslgn"(12,13) involving three components SiUMA-18, Variable I, and Variable II. 

Experimental designs to establish the effect of the composition of a mixture on its properties differ from other designs in that the initial parameters are not usually independent of one another. The properties of a mixture of three diluents, lactose, calcium phosphate and microcrystalline cellulose, for example, may be defined in terms of the percentage of each component. If we know the concentration of the first two components we can automatically find the concentration of the third. This non-independence of the variables means that designs of the type outlined above are unsuitable for many problems involving mixtures. However the classical designs may be used in two circumstances - for the choice of excipients, where the factors are purely qualitative, and also in problems where the proportions of all but one of the excipients are constrained to be relatively small. 

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