PNNL

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 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.