ENBIS-12 in Ljubljana

9 – 13 September 2012 Abstract submission: 15 January – 10 May 2012

How to Design Experiments when Categoric Mixture Components Go to Zero

11 September 2012, 17:10 – 17:30


Submitted by
Pat Whitcomb
Pat Whitcomb (Stat-Ease, Inc.)
Mixture experiments are used when one wants to vary ingredients and the response depends on their relative proportion to the other ingredients. In some mixture experiments the formulator wants one (or more) of the ingredients to be present at alternate and mutually exclusive categoric levels. For example, an ingredient might be available from one of three vendors, or, perhaps, only one of two different materials can be used in a given formulation. The usual approach is to simply cross the mixture model with the categoric model. This works well so long as the proportion of the categoric ingredient does not go to zero. If any categoric components do go to zero, the crossed model contradicts itself by predicting different response values for the different levels of the categoric factor, even though it is completely absent from the blend! This presentation proposes a new form of mixture model that corrects this problem when the ingredient is zero and becomes equivalent to the crossed model when the categoric factor exceeds its zero level.
A preservative blend (used to maximize shelf life of a food product) with a categoric factor whose proportion goes to zero is used to illustrate the method.
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