A Numerical Stability Analysis in the Inclusion of an Inverse Term in the Design of Experiments for Mixtures

Abstract

A mixture experiment is one where the response depends only on the relative proportions of the ingredients present in the mixture. Different regression models are used to analyze mixture experiments, such as the Scheffé model, the Slack Variable model, and models with inverse terms. Models with inverse terms are worthy of consideration in certain applications. These models have been analyzed considering their fit quality, but not their numerical stability. This article analyzes the numerical stability of the model with inverse terms and the use of pseudo components. Likewise, a criterion is defined for the selection of the regression model with inverse terms, based on the quality of fit and numerical stability.

Keywords

• conditional number
• mixture experiments
• Scheffé model
• inverse terms in mixture models