Volume Calibration of Process Vessels Using Repeated Measures Analysis

Process vessels used for nuclear material accounting purposes are typically calibrated by sequentially adding precisely measured volumes of liquid to the vessel and observing the fill height after each addition. The process is repeated several times, resulting in multiple calibration runs. Because the vessels are not emptied between successive additions, the observations collected within a given calibration run are correlated with one another. Historically, cumulative error models have been utilized which eliminate the correlation through the use of a transformation. Other more sophisticated models have ignored the correlation in order to allow for random run-to-run variations in the calibration parameters and to utilize a single model procedure that allows for segmented calibration functions. Both approaches have serious drawbacks and may result in poor estimates of volume measurement error variance. As an alternative, this paper demonstrates how modern statistical techniques often applied in the analysis of repeated measures data can be utilized to model the covariance structure of the calibration data, to estimate a measurement equation, and to estimate the variance associated with a volume measurement. Although the repeated measures approach appears more computationally exhaustive than the traditional approaches, widely used statistical software packages, such as SAS®, can be utilized to make implementation of the repeated measures approach straightforward.