Developing a space-filling mixture experiment design when the components are subject to linear and nonlinear constraints

Abstract

This article presents a case study of developing a space-filling design (SFD) for a constrained mixture experiment when the experimental region is specified by single-component constraints (SCCs), linear multiple-component constraints (LMCCs), and nonlinear multiple-component constraints (NMCCs). Traditional methods and software for designing constrained mixture experiments with SCCs and LMCCs (using either optimal design or SFD approaches) are not directly applicable because of the NMCCs. A SFD algorithm in the JMP^® software was modified to accommodate the NMCCs; the modification is described in this article. The case study involves high-level waste (HLW) glass that is subject to the formation of nepheline crystals as the glass cools. This can significantly reduce the durability of HLW glass (which is undesirable). The goal of the study was to develop a SFD for the HLW glass compositional region where nepheline may form, and generate data for modeling nepheline formation as a function of HLW glass composition. The HLW glass composition region was specified in terms of eight components with SCCs, two LMCCs, and two NMCCs. The NMCCs were based on a nonlinear logistic regression model for a binary nepheline response that was developed from previous data. This article discusses the HLW glass example, the constraints specifying the experimental composition region, and how an existing algorithm for generating SFDs was modified to accommodate the NMCCs. The methodology discussed in this article can be applied to any example in which the experimental region is specified by one or more nonlinear constraints in addition to linear constraints on mixture components and/or non-mixture variables.

Keywords:

• Mixture experiment
• space-filling experimental design
• nonlinear constraint
• high-level waste glass
• nepheline crystals

Acknowledgments

This work was conducted at Pacific Northwest National Laboratory (PNNL). PNNL is a multiprogram national laboratory operated for the U.S. Department of Energy by Battelle under Contract DE-AC05-76RL01830. The authors thank Aimee Holmes (PNNL) who statistically reviewed and provided comments on the manuscript prior to journal submission. The authors also acknowledge the reviews and comments of the editor and two reviewers. This manuscript has been cleared by PNNL for public release as PNNL-SA-136270.

Funding

The authors gratefully acknowledge the financial support of the U.S. Department of Energy’s Waste Treatment and Immobilization Plant Federal Project Office under the direction of Albert A. Kruger.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.