I-Optimal Designs for Mixture Experiments with Linear Inequality Constraints

• Activity Number: 128
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Laura Lancaster*+ and Christopher Gotwalt
• Companies: SAS Institute Inc. and SAS Institute Inc.
• Keywords: Design of Experiments ; I-Optimality ; Mixture Experiments ; Nonlinear Programming

Abstract

Predictive capability is an important objective of many mixture experiments. Although I-Optimal designs would be useful in a mixture context because they minimize the average prediction variance over the design region, they have not been investigated. This is because creating I-Optimal designs for mixture experiments with linear inequality constraints on the factors can be challenging in two regards. First, the objective function involves a moments matrix whose calculation requires several integrals over a linearly constrained region. The other challenge involves finding the optimal design in the presence of linear inequality constraints, as nonlinear programming methods are needed for the optimization. We will show how a Monte Carlo method for generating random uniform points over an arbitrary linearly constrained region can be used to calculate the moments matrix and how the Wolfe reduced gradient method can be used for optimizing the design. In addition, we demonstrate the improved predictive capacity of I-Optimal mixture designs by comparing them with other methods for generating mixture designs.