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Title: 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 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, themore » 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.« less

Authors:
 [1]; ORCiD logo [1];  [1];  [2];  [1];  [1]
  1. BATTELLE (PACIFIC NW LAB)
  2. SAS Institute Inc.
Publication Date:
Research Org.:
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1567268
Report Number(s):
PNNL-SA-136270
DOE Contract Number:  
AC05-76RL01830
Resource Type:
Journal Article
Journal Name:
Quality Engineering
Additional Journal Information:
Journal Volume: 31; Journal Issue: 3
Country of Publication:
United States
Language:
English
Subject:
Mixture experiment, space-filling experimental design, nonlinear constraint, high-level waste glass, nepheline crystals

Citation Formats

Piepel, Gregory F., Stanfill, Bryan A., Cooley, Scott K., Jones, Bradley, Kroll, Jared O., and Vienna, John D. Developing a space-filling mixture experiment design when the components are subject to linear and nonlinear constraints. United States: N. p., 2019. Web. doi:10.1080/08982112.2018.1517887.
Piepel, Gregory F., Stanfill, Bryan A., Cooley, Scott K., Jones, Bradley, Kroll, Jared O., & Vienna, John D. Developing a space-filling mixture experiment design when the components are subject to linear and nonlinear constraints. United States. doi:10.1080/08982112.2018.1517887.
Piepel, Gregory F., Stanfill, Bryan A., Cooley, Scott K., Jones, Bradley, Kroll, Jared O., and Vienna, John D. Fri . "Developing a space-filling mixture experiment design when the components are subject to linear and nonlinear constraints". United States. doi:10.1080/08982112.2018.1517887.
@article{osti_1567268,
title = {Developing a space-filling mixture experiment design when the components are subject to linear and nonlinear constraints},
author = {Piepel, Gregory F. and Stanfill, Bryan A. and Cooley, Scott K. and Jones, Bradley and Kroll, Jared O. and Vienna, John D.},
abstractNote = {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.},
doi = {10.1080/08982112.2018.1517887},
journal = {Quality Engineering},
number = 3,
volume = 31,
place = {United States},
year = {2019},
month = {6}
}

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Designing a mixture experiment when the components are subject to a nonlinear multiple-component constraint
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