Uncertainty Propagation for Platinum Resistance Thermometers Calibrated According to ITS-90

A new supplement to the GUM outlines uncertainty calculations using matrix algebra for models with more than one output quantity. This technique is applied to the problem of uncertainty propagation for platinum resistance thermometers (PRTs). PRTs are calibrated at specified sets of defining fixed points dependent on the desired temperature range. The problem of uncertainty propagation from the fixed-point calibration results plus the resistance of the PRT in use as input quantities to the coefficients of the deviation function as intermediate results and the temperature as a sole output quantity is discussed. A general solution in matrix form for any temperature range of the ITS-90 defined by PRTs is highlighted. The presented method allows for an easy consideration of the input quantity correlations, which differ with the circumstances of the accomplishment of the fixed-point calibrations and the resistance measurement of the thermometer in use. An example calculation for a specific temperature range based on a simplified model for the input quantity correlations demonstrates this benefit.