Mathematical modeling applied to the uncertainty analysis of a tank prover calibration: Understanding the influence of calibration conditions on the GUM validation using the Monte Carlo method.

This paper presents the calibration of the volume of a tank prover using the gravimetric method. A mathematical model of this calibration has been developed and it is non-linear. An evaluation of measurement uncertainty of the tank prover calibration has been carried out using the "Guide to the Expression of Uncertainty in Measurement" (GUM) and the Monte Carlo method. The measurement results have been compared. The influence of calibration conditions on the validation of GUM method by means of the Monte Carlo method (MCM) has been investigated computationally, as well as the behavior of the expanded uncertainty (GUM method) as a function of these calibration conditions. Seven case studies have been analyzed in this research work. In reference case, the tank prover calibration is carried out in the normal laboratory condition. In other case studies, the tank prover calibration is modeled in various hypothetical situations, such as change in tank prover scale quality, variation of calibration water density during calibration, large temperature gradient of water inside the tank prover and combination of the above conditions. In general, GUM method has not been validated by MCM due to one or more of the following conditions: a) the dominant source of uncertainty is a rectangular distribution; b) the uncertainty budget contains large uncertainty and the measurand model is non-linear; c) the measurand probability distribution is not normal. • The tank prover volume has been calibrated using the gravimetric method. • A mathematical model of the measurand has been conceived and it is non-linear. • The analysis of uncertainty of the tank prover calibration has been developed using GUM approach and Monte Carlo method (MCM). • The influence of calibration conditions on the validation of GUM method by MCM has been investigated in case studies. [ABSTRACT FROM AUTHOR]