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

Journal Article · · Quality Engineering
 [1]; ORCiD logo [1];  [1];  [2];  [1];  [1]
  1. BATTELLE (PACIFIC NW LAB)
  2. SAS Institute Inc.
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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 nonlinear MCCs; 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-response 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.

Research Organization:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Organization:
USDOE
DOE Contract Number:
AC05-76RL01830
OSTI ID:
1567268
Report Number(s):
PNNL-SA-136270
Journal Information:
Quality Engineering, Vol. 31, Issue 3
Country of Publication:
United States
Language:
English

References (7)

Uniform Designs for Highly Constrained Mixture Experiments journal January 2009
On uniform design of experiments with restricted mixtures and generation of uniform distribution on some domains journal January 2000
Space-filling designs for computer experiments: A review journal January 2016
Maximum projection designs for computer experiments journal March 2015
Fast Flexible Space-Filling Designs for Nonrectangular Regions journal March 2014
Designing a mixture experiment when the components are subject to a nonlinear multiple-component constraint journal December 2015
Hierarchical Grouping to Optimize an Objective Function journal March 1963

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Related Subjects

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