Mixture Experiment Design Varying One, Two, and Three Components at a Time

• Activity Number: 104
• Type: Invited
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Greg F. Piepel* and Scott K. Cooley and John D. Vienna and Jarrod V. Crum
• Companies: Pacific Northwest National Laboratory and Pacific Northwest National Laboratory and Pacific Northwest National Laboratory and Pacific Northwest National Laboratory
• Keywords: Mixture experiment ; Experimental design ; Component effect direction ; Optimal design

Abstract

Experimental designs for mixture experiments are often developed by specifying constraints on the proportions of the q components, then using optimal design methods to generate the designs. Because common optimal design criteria are variance-based (e.g., D-, I-, G-optimality), design points tend to be on or near the vertices and edges of the constrained region. Vertices and edge points must respectively satisfy q?1 and q?2 constraints, and hence involve varying nearly all of the components simultaneously. However, in some problems this is undesirable, and rather it is desired to vary components at most two- or three-at-a-time (recognizing that variations in mixture components one-, two-, or three-at-a-time must be offset with changes to one or more of the remaining components). The presentation describes a method for designing a mixture experiment that includes a subset of variations of components two- and/or three-at-a-time (with offsetting changes in remaining components), and may include varying components along component effect directions. The method is illustrated for a problem to predict crystal growth in glass as a function of specific components in glass compositions.