Bayesian analysis of a flow meter calibration problem

G J P Kok, A M H van der Veen, P M Harris, I M Smith and C Elster, Bayesian analysis of a flow meter calibration problem, Metrologia 52 (2015) 392-399.

Abstract:
A turbine flow meter indicates the volume of fluid flowing through the device per unit of time. Such a flow meter is commonly calibrated at a few known flow rates over its measurement range. A calibration curve relating the pulse factor of the meter to the flow rate is then fitted to calibration data using an ordinary least squares approach. This approach does not consider prior knowledge that may exist about the flow meter or the calibration procedure. A Bayesian analysis enables prior knowledge to be taken into account. A Bayesian inference results in a posterior distribution for the unknown parameters of the calibration curve that may be seen as the most comprehensive uncertainty information about these unknowns. This paper investigates for a flow meter calibration problem the effects of appreciating prior knowledge on values of the calibration curve and their associated uncertainties. It presents the results of a Bayesian analysis and compares them to those obtained by an ordinary least squares approach.

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