Validation of the GUM using the Monte Carlo method when applied in the calculation of the measurement uncertainty of a compact prover calibration

This article presents the calibration of a compact prover using the weighing method. An evaluation of measurement uncertainty of the prover calibration has been developed using the GUM and Monte Carlo methodologies. A water draw kit was utilized to direct the liquid flow from the compact prover to a water container in order to weigh the transferred water mass on a balance. This amount of mass was used as reference for the calculation of the prover base volume. A modeling of the flow rate into the water draw kit as a function of time was conceived. This modeling was applied for calculating the error in the liquid volume of the water container due to the switching of two solenoid valves of the water draw kit. A mathematical model of the prover base volume has been developed. This model is non-linear and the two largest sources of uncertainty are related to the balance calibration certificate that together account for 31.84% of the uncertainty budget. This work showed that the GUM approach was validated by Monte Carlo method in the calculation of the measurement uncertainty of the calibration of a compact prover. The absolute differences of the respective endpoints of the coverage intervals of these two methods are less than 0.00023% of estimate of the prover base volume whose value is 151.427 dm³. This result was obtained for a coverage probability of 95% and ${10}^6$ Monte Carlo iterations. The density of the calibration water and its uncertainty have been calculated through an innovative approach.