This presentation describes methods used for the first time to construct a space-filling design (SFD) to augment existing points over a constrained mixture experiment region specified by linear and nonlinear constraints. A mixture experiment (ME) involves (i) combining various proportions (summing to 1.0) of the components in a mixture making up an end product, and (ii) measuring the values of one or more responses for each mixture.
The experimental design problem addressed in this presentation was challenging for several reasons. First, there is no existing literature or software that directly addresses augmenting existing points using a SFD approach. The literature for augmenting experimental designs focuses on optimal design approaches. Second, until recently, approaches and software for constructing mixture experiment SFDs or optimal designs over constrained regions have been limited to constraints linear in the mixture components, and have not accommodated nonlinear constraints. Third, our experimental design problem was high-dimensional, for which many SFD criteria do not work well. Ultimately, we addressed these challenges using (i) SFD capabilities in JMP, and (ii) the JMP scripting language to access control parameters and calculations done outside of JMP.
The presentation uses a case study involving nuclear waste glass to discuss and illustrate the SFD methods used. Low-activity waste (LAW) at the Hanford site in Washington state will be immobilized in glass. The LAW glass composition region of interest for a new study phase was the same as for the previous phase, specified by lower and upper bounds on 15 components, as well as one nonlinear and several linear multiple-component constraints. The 42 LAW glasses from the previous phase included center points and points on outer and inner layers of the experimental region. The goal of the new phase was to augment the 42 glasses to better fill the experimental region, because of some complicated response-glass composition relationships. The methods discussed in the presentation were used to generate 40 different 20-glass SFDs to augment the 42 glasses. SFD metrics and design visualizations were used to assess how well each of the 40 designs covered the experimental region and to select the 20-glass SFD used.
The methods discussed in this presentation can be used for any experimental design problem involving mixture and/or nonmixture variables with an experimental region specified by linear and/or nonlinear constraints.
- : Bryan A. Stanfill, Greg F. Piepel, Charmayne E. Lonergan, and Scott K. Cooley
- : Pacific Northwest National Laboratory
- : Greg Piepel
- : experimental_design
- : intermediate
- : firstname.lastname@example.org
- : 509-375-6911
Constructing a Space-Filling Mixture Experiment Design to Augment Existing Points Over a Region Specified by Linear and Nonlinear Constraints