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Property–Composition–Temperature Modeling of Waste Glass Melt Data Subject to a Randomization Restriction
Author(s) -
Piepel Greg F.,
HerediaLangner Alejandro,
Cooley Scott K.
Publication year - 2008
Publication title -
journal of the american ceramic society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.9
H-Index - 196
eISSN - 1551-2916
pISSN - 0002-7820
DOI - 10.1111/j.1551-2916.2008.02590.x
Subject(s) - restricted maximum likelihood , regression analysis , ordinary least squares , viscosity , composition (language) , mathematics , property (philosophy) , regression , linear regression , statistics , partial least squares regression , thermodynamics , estimation theory , physics , linguistics , philosophy , epistemology
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.