Uncertainty Estimates for Volume Calibration Measurements that Exhibit Significant Run-to-run Variability

Volume calibration functions are typically estimated from pairs of height and volume measurements obtained from a series of calibration runs. A major problem is the appropriate statistical treatment of calibration data that exhibit significant run-to-run variability. Procedures for estimating the variance of volume estimates in this case have recently been proposed. While these procedures appear to work well in practice, they are not supported by a coherent underlying theory or model, and they require a certain amount of \"user judgement\" to implement. In this paper, we present a model that provides a unified theory from which to derive estimates. The model includes parameters that explicitly account for the run-to-run perturbations in the slope and intercept of the underlying calibration function. Variance estimates of these parameters are obtained using a \"components of variance\" approach. These estimates are used in turn to estimate volume measurement uncertainty. The resulting estimates of volume measurement uncertainty are applicable regardless of whether run-to-run variability is significant. Thus, with the \"components of variance\" approach proposed in this paper, it is unnecessary to consider cases when computing estimates of uncertainty.