Property-Composition-Temperature Modeling of Waste Glass Melt Data Subject to a Randomization Restriction

• Published in: Journal of the American Ceramic Society Vol. 91; no. 10; pp. 3222 - 3228
• Main Authors: Piepel, Greg F., Heredia-Langner, Alejandro, Cooley, Scott K.
• Format: Journal Article
• Language: English
• Published: Malden, USA Blackwell Publishing Inc 01.10.2008; Blackwell; Wiley Subscription Services, Inc
• Subjects: 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; Randomization; Property composition relationship; Waste treatment; Glass waste; Glass; Temperature effect; Theoretical study; Composition effect; Manufacturing; Glass melt; Fabrication property relation; Modeling
• ISSN: 0002-7820; 1551-2916
• DOI: 10.1111/j.1551-2916.2008.02590.x

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.