## 6 Results of Uncertainty Simulations for Multiple Cases of Use of Radiation Thermometry

Table 8: Model parameter values, standard uncertainties (\(k=1\)) of the direct model parameters and standard uncertainty contributions (\(k=1\)) of the simulated temperature measurement in case 1. Distributions of measurement parameters in partial contribution simulation are displayed in Figure 13. The histogram relating to the influence of relative humidity exhibits the highest influence of non-linearity in the system of radiation thermometry. A histogram of partial contributions is presented in Figure 14.  
Figure 13: Input parameter distribution (left) and output result distribution (right) of Monte Carlo simulation of partial uncertainty contributions when measuring the laboratory black body calibrator at 1000 \({}^{\circ}\)C using Heitronics KT19.01 II. Results of the Monte Carlo simulation in the form of standard uncertainty are plotted in Figure 15.  
The histogram in Figure 16 displays the spread of combined measurement uncertainty simulation results at 1000 \({}^{\circ}\)C.  
While the Monte Carlo simulation samples the model's sensitivity to input uncertainties using a high number of samples, the analytical method conducts the sampling using  
Figure 16: Histogram of common measurement uncertainty simulation results when measuring the laboratory black body calibrator at 1000 \({}^{\circ}\)C using Heitronics KT19.01 II. Figure 14: Histogram of partial uncertainty contributions (\(k=1\)) when measuring the laboratory black body calibrator at 1000 \({}^{\circ}\)C using Heitronics KT19.01 II. Figure 15: Monte Carlo simulated standard measurement uncertainty (\(k=1\)) of the laboratory black body temperature measurement using the Heitronics KT19.01 II. only two simulations, one for the first positive standard deviation and one for the first negative standard deviation. While both methods can propagate uncertainty contributions through the model of radiation thermometry, the Monte Carlo method accounts for the output probability distribution, whereas the analytical calculation assumes a linear transformation. Table 9 presents the analytical simulation results of two methods (calculating the highest and the mean influence of a parameter's one standard deviation in both directions and using an analytical formula to sum the total measurement uncertainty) and the Monte Carlo simulation results. The Monte Carlo result is used as a reference to compare analytical methods. Mismatch between the columns is a consequence of the non-linearity of the system of measurement. Case 2: Measuring with a Low Temperature Reference Radiation Thermometer in Calibration of a Flat Plate Calibrator  
Case 2 is the calibration uncertainty of a typical flat plate calibrator. While flat plate calibrators are simple and economically accessible, their design omits a black body cavity. Contrary to the cavity calibrators, flat plate calibrators only exhibit the spectral emissivity of a radiator material, without geometric enhancements. Radiator emissivity is therefore spectrally variable and prone to instability with both time and temperature, exhibiting greater emissivity uncertainty than cavity calibrators. Typical nominal emissivity of a flat plate calibrator is 0.95 \(\pm\) 0.02 (bounds). As the flat plate calibrators operate up to 500 \({}^{\circ}\)C, they are appropriate for calibrations of low temperature radiation thermometers, typically operating in the 8 \(\upmu\)m-14 \(\upmu\)m range. At LMK, evaluations of flat plate calibrators below 500 \({}^{\circ}\)C are performed by using the Heitronics TRT II reference pyrometer. As no atmospheric correction is used by the TRT II, atmospheric condition uncertainty corresponds to the change in conditions between instrument calibration and use. Similar input uncertainties as in case 1 are therefore considered and applied in this case. Partial uncertainty contributions in Table 10 are obtained by simulating deviations of an individual input parameter. The combined standard measurement uncertainty at 500 \({}^{\circ}\)C is calculated separately and accounts for 1.94 \({}^{\circ}\)C.