Global Sensitivity Analysis for Mixture Experiments

Abstract

A mixture experiment is characterized by having two or more inputs that are specified as a percentage contribution to a total amount of material. In such situations, the input variables are correlated because they must sum to one. Consequently, additional care must be taken when fitting statistical models or visualizing the effect of one or more inputs on the response. In this article, we consider the use of a Gaussian process to model the output from a computer simulator taking a mixture input. We introduce a procedure to perform global sensitivity analysis of the code output providing main effects and revealing interactions. The resulting methodology is illustrated using a function with analytically tractable results for comparison, a chemical compositional simulator, and a physical experiment. Supplementary materials providing assistance with implementing this methodology are available online.

KEY WORDS:

• Computer experiment
• Gaussian process
• Mixture experiment
• Simplex designs
• Visualization

ACKNOWLEDGMENTS

The research of Loeppky was supported by a grant from the Natural Sciences and Engineering Research Council of Canada. We thank the editor, associate editor, and two reviewers for helpful comments that substantially improved earlier versions of this article. Los Alamos National Laboratory, an affirmative action/equal opportunity employer, is operated by Los Alamos National Security, LLC, for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396.