Fractional factorial analysis approach

In the case of constraints on proportions of components the approach is known, simplex-centroid designs are constructed with coded or pseudocomponents [23]. Coded factors in this case are linear functions of real component proportions, and data analysis is not much more complicated in that case. If upper and lower constraints (bounds) are placed on some of the X resulting in a factor space whose shape is different from the simplex, then the formulas for estimating the model coefficients are not easily expressible. In the simplex-centroid x 23 full factorial design or simplex-lattice x 2n design [5], the number of points increases rapidly with increasing numbers of mixture components and/or process factors. In such situations, instead of full factorial we use fractional factorial experiments. The number of experimental trials required for studying the combined effects of the mixture com-... 

Marine lipids with their diversity of unsaturated and branched chain acid moieties are a difficult class of materials to analyze. Ruminants (sheep, goats, cows, etc.) have a bacterial "factory" in the rumen which is able to produce branched-chain partially-hydrogenated lipids from ingested plant lipids. These lipids are incorporated into the milk and meat of the animals and eventually into animals which feed upon the ruminants. As a rule animal lipids are highly complex in comparison to plant materials. Although the branched chain materials are usually present in low concentration when compared to the common fatty acid moieties, complete description of these fats requires more sophisticated GC and thus long open tubular columns in tandem with mass spectrometry and computer analysis of the data has become an important approach. Even with a 100-m column, subcutaneous lipids of barley-fed lambs were so complex that prior fractionation with urea adducts was necessary (17). 

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