Uncertainty Evaluation and Validation of a Comparison Methodology to Perform In-house Calibration of Platinum Resistance Thermometers using a Monte Carlo Method

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Abstract

The uncertainty required by laboratories and industry for temperature measurements based on the practical use of platinum resistance thermometers (PRTs) can commonly be achieved by calibration using temperature reference conditions and comparison methodologies (TCM) instead of the more accurate primary fixed-point (ITS-90) method. TCM is suitable for establishing internal traceability chains, such as connecting reference standards to transfer and working standards. The data resulting from the calibration method can be treated in a similar way to that prescribed for the ITS-90 interpolation procedure, to determine the calibration coefficients. When applying this approach, two major tasks are performed: (i) the evaluation of the uncertainty associated with the estimate of temperature (a requirement shared by the ITS-90 method), based on knowledge of the uncertainties associated with the temperature fixed points and the measured electrical resistances, and (ii) the validation of this practical comparison considering that the reference data are obtained using the ITS-90 method. The conventional approach, using the GUM uncertainty framework, requires approximations with unavoidable loss of accuracy and might not provide adequate uncertainty evaluation for the methods mentioned, because the conditions for its valid use, such as the near-linearity of the mathematical model relating temperature to electrical resistance, and the near-normality of the measurand (temperature), might not apply. Moreover, there can be some difficulty in applying the GUM uncertainty framework relating to the formation of sensitivity coefficients through partial derivatives for a model that, as here, is somewhat complicated and not readily expressible in an explicit form. Alternatively, uncertainty evaluation can be carried out by a Monte Carlo method (MCM), a numerical implementation of the propagation of distributions that is free from such conditions and straightforward to apply. In this paper, (a) the use of MCM to evaluate uncertainties relating to the ITS-90 interpolation procedure, and (b) a validation procedure to perform in-house calibration of PRTs by comparison are discussed. An example illustrating (a) and (b) is presented.

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