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Trends in Chemical Engineering   Volumes    Volume 19 
A primer on constructing I-optimal designs for mixtures using R – Part I: 3-component mixtures
Stuart H. Munson-McGee, Aravind Mannarswamy, Paul K. Andersen
Pages: 19 - 34
Number of pages: 16
Trends in Chemical Engineering
Volume 19 

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I-optimal designs are a class of experimental designs in which experimental points are selected to minimize the average prediction variance over the experimental region. Although the theory of I-optimal design is well developed, relatively little progress has been made on devising simple, rapid, and robust techniques for creating such designs. This is especially true for mixture experiments. In this work, we present such a method to calculate locally I-optimal designs for both unconstrained and constrained 3-component mixtures. The method takes advantage of the speed of evaluating the trace of the weighted inverse moment matrix to calculate the average prediction variance within a multivariate minimization. The optimization variables are the locations of the experimental design points (x1, x2, x3 = 1 – x1 x2) written in terms of their relative position within the experimental space. The method is illustrated for both unconstrained and constrained examples.
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