Variance of measurements from a calibration function derived from data which exhibit run-to-run differences

The volume of liquid in a nuclear process tank is determined from a calibration equation which expresses volume as a function of liquid level. Successive calibration runs are made to obtain data from which to estimate either the calibration function or its inverse. For tanks equipped with high-precision measurement systems to determine liquid level, it frequently happens that run-to-run differences due to uncontrolled or uncontrollable ambient conditions are large relative to within-run measurement errors. In the strict sense, a calibration function cannot be developed from data which exhibit significant run-to-run differences. In practice, run-to-run differences are ignored when they are small relative to the accuracy required for measurements of the tank's contents. The use of standard statistical techniques in this situation can result in variance estimates which severely underestimate the actual uncertainty in volume measurements. This paper gives a method whereby reasonable estimates of the calibration uncertainty in volume determinations can be obtained in the presence of statistically significant run-to-run variability. 4 references, 3 figures, 2 tables