Property-Composition-Temperature Modeling of Waste Glass Melt Data Subject to a Randomization Restriction
Properties such as viscosity and electrical conductivity of glass melts are functions of melt temperature as well as glass composition. When measuring such a property for several compositions, the property is typically measured at several temperatures for one composition, then at several temperature...
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Published in | Journal of the American Ceramic Society Vol. 91; no. 10; pp. 3222 - 3228 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
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Malden, USA
Blackwell Publishing Inc
01.10.2008
Blackwell Wiley Subscription Services, Inc |
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Abstract | Properties such as viscosity and electrical conductivity of glass melts are functions of melt temperature as well as glass composition. When measuring such a property for several compositions, the property is typically measured at several temperatures for one composition, then at several temperatures for the next composition, and so on. This data collection process involves a restriction on randomization, which is referred to as a split‐plot experiment. The split‐plot data structure must be accounted for in developing property–composition–temperature models and the corresponding uncertainty equations for model predictions. Instead of ordinary least squares (OLS) regression methods, generalized least squares (GLS) regression methods using restricted maximum likelihood (REML) estimation must be used. This article summarizes the methodology for developing property–composition–temperature models and corresponding prediction uncertainty equations using the GLS/REML regression approach. Viscosity data collected on 197 simulated nuclear waste glasses are used to sequentially develop a viscosity‐composition‐temperature model. The final model has 29 terms in 15 components, reduced from the initial model of 44 terms in 22 components. For the initial model, the correct results using GLS/REML regression are compared with the incorrect results obtained using OLS regression. |
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AbstractList | Properties such as viscosity and electrical conductivity of glass melts are functions of melt temperature as well as glass composition. When measuring such a property for several compositions, the property is typically measured at several temperatures for one composition, then at several temperatures for the next composition, and so on. This data collection process involves a restriction on randomization, which is referred to as a split-plot experiment. The split-plot data structure must be accounted for in developing property-composition-temperature models and the corresponding uncertainty equations for model predictions. Instead of ordinary least squares (OLS) regression methods, generalized least squares (GLS) regression methods using restricted maximum likelihood (REML) estimation must be used. This article summarizes the methodology for developing property-composition-temperature models and corresponding prediction uncertainty equations using the GLS-REML regression approach. Viscosity data collected on 197 simulated nuclear waste glasses are used to sequentially develop a viscosity-composition-temperature model. The final model has 29 terms in 15 components, reduced from the initial model of 44 terms in 22 components. For the initial model, the correct results using GLS-REML regression are compared with the incorrect results obtained using OLS regression. The methodology for developing property-composition-temperature models and corresponding prediction uncertainty equations using the generalised least squares (GLS)/restricted maximum likelihood (REML) regression approach is summarised. Viscosity data collected on 197 simulated nuclear waste glasses were used to sequentially develop a viscosity-composition-temperature model. The final model had 29 terms in 15 components, reduced from the initial model of 44 terms in 22 components. For the initial model, the correct results using GLS/REML regression were compared with the incorrect results obtained using ordinary least squares regression. 16 refs. Properties such as viscosity and electrical conductivity of glass melts are functions of melt temperature as well as glass composition. When measuring such a property for several glasses, the property is typically measured at several temperatures for one glass, then at several temperatures for the next glass, and so on. This data-collection process involves a restriction on randomization, which is referred to as split-plot experiment. The split-plot data structure must be accounted for in developing property-composition-temperature models and the corresponding uncertainty equations for model predictions. Instead of ordinary least squares (OLS) regression methods, generalized least squares (GLS) regression methods using restricted maximum likelihood (REML) estimation must be used. This article describes the methodology for developing property-composition-temperature models and corresponding prediction uncertainty equations using the GLS/REML regression approach. Viscosity data collected on 197 simulated nuclear waste glasses are used to illustrate the GLS/REML methods for developing a viscosity-composition-temperature model and corresponding equations for model prediction uncertainties. The correct results using GLS/REML regression are compared to the incorrect results obtained using OLS regression. Properties such as viscosity and electrical conductivity of glass melts are functions of melt temperature as well as glass composition. When measuring such a property for several compositions, the property is typically measured at several temperatures for one composition, then at several temperatures for the next composition, and so on. This data collection process involves a restriction on randomization, which is referred to as a split-plot experiment. The split-plot data structure must be accounted for in developing property-composition-temperature models and the corresponding uncertainty equations for model predictions. Instead of ordinary least squares (OLS) regression methods, generalized least squares (GLS) regression methods using restricted maximum likelihood (REML) estimation must be used. This article summarizes the methodology for developing property-composition-temperature models and corresponding prediction uncertainty equations using the GLS/REML regression approach. Viscosity data collected on 197 simulated nuclear waste glasses are used to sequentially develop a viscosity-composition-temperature model. The final model has 29 terms in 15 components, reduced from the initial model of 44 terms in 22 components. For the initial model, the correct results using GLS/REML regression are compared with the incorrect results obtained using OLS regression. [PUBLICATION ABSTRACT] |
Author | Heredia-Langner, Alejandro Cooley, Scott K. Piepel, Greg F. |
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Cites_doi | 10.1080/16843703.2007.11673155 10.1080/00224065.2002.11980160 10.1002/9781118204221 10.1137/1.9780898718393 10.1198/004017002753398344 10.1080/00224065.2006.11918603 10.1080/00224065.2004.11980249 10.1198/00401700152404291 10.1198/004017002188618725 |
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Keywords | Randomization Property composition relationship Waste treatment Glass waste Glass Temperature effect Theoretical study Composition effect Manufacturing Glass melt Fabrication property relation Modeling |
Language | English |
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Notes | istex:B2BB2DA04E993E571441A75AECC7B9C43E851933 ArticleID:JACE02590 ark:/67375/WNG-5C192GVR-B I. Tanaka—contributing editor This work was conducted in the Waste Treatment Plant Support Program at the Pacific Northwest National Laboratory. The work was performed under Contract DE‐AC05‐76RL01830 with the U. S. Department of Energy and MOA #24590‐QL‐HC9‐WA49‐00001 with Bechtel National, Inc., the lead contractor on the Waste Treatment and Immobilization Plant at the Hanford Site near Richland, WA. ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 ObjectType-Article-2 ObjectType-Feature-1 content type line 23 PNNL-SA-58808 USDOE AC05-76RL01830 |
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References | G. F. Piepel, S. K. Cooley, A. Heredia-Langner, S. M. Landmesser, W. K. Kot, H. Gan, and I. L. Pegg, IHLW PCT, Spinel T1%, Electrical Conductivity, and Viscosity Model Development, VSL-07R1240-4, Rev. 0, Vitreous State Laboratory. The Catholic University of America, Washington, DC. JMP, JMP Release 7. SAS Institute, Inc, Cary, NC, 2007. D. R. Bingham and R. R. Sitter, "Fractional Factorial Split-Plot Designs for Robust Parameter Experiments," Technometrics, 45 [1] 80-9 (2003). G. F. Piepel, J. M. Szychowski, and J. L. Loeppky, "Augmenting Scheffé Linear Mixture Models with Squared and/or Crossproduct Terms," J. Qual. Tech., 34 [3] 297-314 (2002). P. Goos and M. Vanderbroek, "Outperforming Completely Randomized Designs," J. Qual. Tech., 36 [1] 12-26 (2004). D. C. Montgomery, E. A. Peck, and G. G. Vining, Introduction to Linear Regression Analysis, 3rd edition, John Wiley and Sons, New York, 2001. J. A. Cornell, Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data, 3rd edition, John Wiley, New York, 2002. S. M. Kowalski, J. A. Cornell, and G. G. Vining, "Split-Plot Designs and Estimation Methods for Mixture Experiments With Process Variables," Technometrics, 44 [1] 72-9 (2002). H. Gan and I. L. Pegg, Development of Property-Composition Models for RPP-WTP HLW Glasses, VSL-01R3600-1, Rev. 0, Vitreous State Laboratory. The Catholic University of America, Washington, DC, 2001. R. Ihaka and R. Gentleman, "R: A Language for Data Analysis and Graphics," J. Comp. Graph. Stat., 5 [3] 299-314 (1996). R Development Core Team, R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2006 URL http://www.R-project.org. P. Goos, I. Langhans, and M. Vandebroek, "Practical Inference from Industrial Split-Plot Designs," J. Qual. Tech., 38 [2] 162-79 (2006). L. A. Trinca and S. G. Gilmour, "Multistratum Response Surface Designs," Technometrics, 43 [1] 25-33 (2001). SAS, SAS Release 9.1.3. SAS Institute, Inc, Cary, NC, (2005). W. F. Smith, Experimental Design for Formulation. Society for Industrial and Applied Mathematics\American Statistical Association, Philadelphia, PA\Alexanderia, VA, 2005. G. F. Piepel, "A Component Slope Linear Model for Mixture Experiments," Qual. Tech. Quant. Mgmt., 4 [3] 331-43 (2007). 2001 2004; 36 2006; 38 2002; 34 2002; 44 2007 2006 2005 2007; 4 2002 1996; 5 2003; 45 2001; 43 Piepel G. F. (e_1_2_9_12_2) Trinca L. A. (e_1_2_9_5_2) 2001; 43 SAS (e_1_2_9_8_2) 2005 Goos P. (e_1_2_9_3_2) 2004; 36 Kowalski S. M. (e_1_2_9_6_2) 2002; 44 Montgomery D. C. (e_1_2_9_4_2) 2001 Ihaka R. (e_1_2_9_10_2) 1996; 5 R Development Core Team (e_1_2_9_11_2) 2006 JMP (e_1_2_9_9_2) 2007 Piepel G. F. (e_1_2_9_17_2) 2007; 4 e_1_2_9_14_2 Gan H. (e_1_2_9_13_2) 2001 Piepel G. F. (e_1_2_9_16_2) 2002; 34 e_1_2_9_15_2 Goos P. (e_1_2_9_7_2) 2006; 38 Bingham D. R. (e_1_2_9_2_2) 2003; 45 |
References_xml | – reference: S. M. Kowalski, J. A. Cornell, and G. G. Vining, "Split-Plot Designs and Estimation Methods for Mixture Experiments With Process Variables," Technometrics, 44 [1] 72-9 (2002). – reference: SAS, SAS Release 9.1.3. SAS Institute, Inc, Cary, NC, (2005). – reference: P. Goos, I. Langhans, and M. Vandebroek, "Practical Inference from Industrial Split-Plot Designs," J. Qual. Tech., 38 [2] 162-79 (2006). – reference: H. Gan and I. L. Pegg, Development of Property-Composition Models for RPP-WTP HLW Glasses, VSL-01R3600-1, Rev. 0, Vitreous State Laboratory. The Catholic University of America, Washington, DC, 2001. – reference: JMP, JMP Release 7. SAS Institute, Inc, Cary, NC, 2007. – reference: G. F. Piepel, J. M. Szychowski, and J. L. Loeppky, "Augmenting Scheffé Linear Mixture Models with Squared and/or Crossproduct Terms," J. Qual. Tech., 34 [3] 297-314 (2002). – reference: J. A. Cornell, Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data, 3rd edition, John Wiley, New York, 2002. – reference: G. F. Piepel, "A Component Slope Linear Model for Mixture Experiments," Qual. Tech. Quant. Mgmt., 4 [3] 331-43 (2007). – reference: W. F. Smith, Experimental Design for Formulation. Society for Industrial and Applied Mathematics\American Statistical Association, Philadelphia, PA\Alexanderia, VA, 2005. – reference: D. R. Bingham and R. R. Sitter, "Fractional Factorial Split-Plot Designs for Robust Parameter Experiments," Technometrics, 45 [1] 80-9 (2003). – reference: R Development Core Team, R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2006 URL http://www.R-project.org. – reference: P. Goos and M. Vanderbroek, "Outperforming Completely Randomized Designs," J. Qual. Tech., 36 [1] 12-26 (2004). – reference: L. A. Trinca and S. G. Gilmour, "Multistratum Response Surface Designs," Technometrics, 43 [1] 25-33 (2001). – reference: G. F. Piepel, S. K. Cooley, A. Heredia-Langner, S. M. Landmesser, W. K. Kot, H. Gan, and I. L. Pegg, IHLW PCT, Spinel T1%, Electrical Conductivity, and Viscosity Model Development, VSL-07R1240-4, Rev. 0, Vitreous State Laboratory. The Catholic University of America, Washington, DC. – reference: D. C. Montgomery, E. A. Peck, and G. G. Vining, Introduction to Linear Regression Analysis, 3rd edition, John Wiley and Sons, New York, 2001. – reference: R. Ihaka and R. Gentleman, "R: A Language for Data Analysis and Graphics," J. Comp. Graph. Stat., 5 [3] 299-314 (1996). – volume: 38 start-page: 162 issue: [2] year: 2006 end-page: 79 article-title: Practical Inference from Industrial Split‐Plot Designs publication-title: J. Qual. 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Mgmt. – volume: 44 start-page: 72 issue: [1] year: 2002 end-page: 9 article-title: Split‐Plot Designs and Estimation Methods for Mixture Experiments With Process Variables publication-title: Technometrics – volume: 34 start-page: 297 issue: [3] year: 2002 end-page: 314 article-title: Augmenting Scheffé Linear Mixture Models with Squared and/or Crossproduct Terms publication-title: J. Qual. Tech. – volume: 36 start-page: 12 issue: [1] year: 2004 end-page: 26 article-title: Outperforming Completely Randomized Designs publication-title: J. Qual. Tech. – volume: 4 start-page: 331 issue: 3 year: 2007 ident: e_1_2_9_17_2 article-title: A Component Slope Linear Model for Mixture Experiments publication-title: Qual. Tech. Quant. Mgmt. doi: 10.1080/16843703.2007.11673155 – volume: 34 start-page: 297 issue: 3 year: 2002 ident: e_1_2_9_16_2 article-title: Augmenting Scheffé Linear Mixture Models with Squared and/or Crossproduct Terms publication-title: J. Qual. Tech. doi: 10.1080/00224065.2002.11980160 – volume-title: R: A Language and Environment for Statistical Computing year: 2006 ident: e_1_2_9_11_2 – ident: e_1_2_9_14_2 doi: 10.1002/9781118204221 – ident: e_1_2_9_15_2 doi: 10.1137/1.9780898718393 – volume-title: SAS Release 9.1.3 year: 2005 ident: e_1_2_9_8_2 – volume-title: IHLW PCT, Spinel T1%, Electrical Conductivity, and Viscosity Model Development, VSL‐07R1240‐4, Rev. 0, Vitreous State Laboratory ident: e_1_2_9_12_2 – volume: 44 start-page: 72 issue: 1 year: 2002 ident: e_1_2_9_6_2 article-title: Split‐Plot Designs and Estimation Methods for Mixture Experiments With Process Variables publication-title: Technometrics doi: 10.1198/004017002753398344 – volume-title: Development of Property‐Composition Models for RPP‐WTP HLW Glasses, VSL‐01R3600‐1, Rev. 0, Vitreous State Laboratory year: 2001 ident: e_1_2_9_13_2 – volume: 38 start-page: 162 issue: 2 year: 2006 ident: e_1_2_9_7_2 article-title: Practical Inference from Industrial Split‐Plot Designs publication-title: J. Qual. Tech. doi: 10.1080/00224065.2006.11918603 – volume: 36 start-page: 12 issue: 1 year: 2004 ident: e_1_2_9_3_2 article-title: Outperforming Completely Randomized Designs publication-title: J. Qual. Tech. doi: 10.1080/00224065.2004.11980249 – volume: 43 start-page: 25 issue: 1 year: 2001 ident: e_1_2_9_5_2 article-title: Multistratum Response Surface Designs publication-title: Technometrics doi: 10.1198/00401700152404291 – volume: 5 start-page: 299 issue: 3 year: 1996 ident: e_1_2_9_10_2 article-title: R publication-title: A Language for Data Analysis and Graphics – volume-title: JMP Release 7 year: 2007 ident: e_1_2_9_9_2 – volume: 45 start-page: 80 issue: 1 year: 2003 ident: e_1_2_9_2_2 article-title: Fractional Factorial Split‐Plot Designs for Robust Parameter Experiments publication-title: Technometrics doi: 10.1198/004017002188618725 – volume-title: Introduction to Linear Regression Analysis year: 2001 ident: e_1_2_9_4_2 |
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Snippet | Properties such as viscosity and electrical conductivity of glass melts are functions of melt temperature as well as glass composition. When measuring such a... The methodology for developing property-composition-temperature models and corresponding prediction uncertainty equations using the generalised least squares... |
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SubjectTerms | Applied sciences Building materials. Ceramics. Glasses Chemical industry and chemicals Conductivity ELECTRIC CONDUCTIVITY Exact sciences and technology FORECASTING GLASS Glasses Least squares method MANAGEMENT OF RADIOACTIVE WASTES, AND NON-RADIOACTIVE WASTES FROM NUCLEAR FACILITIES Manufacture Mathematical analysis Mathematical models Melting Melts Physical properties RADIOACTIVE WASTES Randomization Regression SIMULATION Temperature effects VISCOSITY WASTES |
Title | Property-Composition-Temperature Modeling of Waste Glass Melt Data Subject to a Randomization Restriction |
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