## 6 Results of Uncertainty Simulations for Multiple Cases of Use of Radiation Thermometry
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{3}{*}{**Parameter**} & \multirow{3}{*}{\begin{tabular}{c} **Input** \\ **Deviation** \\ \end{tabular} } & \begin{tabular}{c} **Monte Carlo** \\ **Result** \\ \end{tabular} & \begin{tabular}{c} **Analytical Result** \\ **(Input Deviation \(\pm\sigma\))** \\ \end{tabular} & \begin{tabular}{c} **Mismatch Between** \\ **Analytical and** \\ **Monte Carlo Result** \\ \end{tabular} \\ \cline{3-7}  & & \begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} & \begin{tabular}{c} **Highest** \\ **(\({}^{\circ}\)C)** \\ \end{tabular} & \begin{tabular}{c} **Mean** \\ **(\({}^{\circ}\)C)** \\ \end{tabular} & \begin{tabular}{c} **Highest** \\ **(\({}^{\circ}\)C)** \\ \end{tabular} & \
\begin{tabular}{c} **Mean** \\ **(\({}^{\circ}\)\)** \\ \end{tabular} \\ \hline \hline Relative humidity & 10\% RH & 1.50 & 1.58 & 1.48 & 5.3\% & \(-1.3\%\) \\ Air temperature & 2 \({}^{\circ}\)C & 0.68 & 0.69 & 0.67 & 1.5\% & \(-1.5\%\) \\ Transfer path distance & 0.05 m & 0.42 & 0.43 & 0.42 & 2.4\% & 0.0\% \\ Emissivity &
\begin{tabular}{c} 0.00116 \\ (0.002/\(\sqrt{3}\)) \\ \end{tabular} & 0.29 & 0.29 & 0.29 & 0.0\% & 0.0\% \\ Atmospheric pressure & 10 hPa & 0.063 & 0.063 & 0.062 & 0.0\% & \(-1.6\%\) \\ Reflected temperature & 2 \({}^{\circ}\)C & \(2.8\times 10^{-8}\) & \(3.7\times 10^{-8}\) & \(2.5\times 10^{-8}\) & 32.1\% & \(-10.7\%\) \\ \hline Measurement & & & & & & \\ uncertainty & & 1.73 & 1.80 & 1.71 & & \\ (analytical sum) & & & & & & \\ \hline Measurement & & & & & & \\ uncertainty & & 1.72 & & & & \\ (Monte Carlo total) & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Standard uncertainty result comparison between the Monte Carlo and analytical simulation methods. Calculating individual uncertainty contribution as the standard deviation of the individually simulated measurement simulations, partial uncertainty contributions (in standard, \(k=1\) form) are listed and sorted by magnitude in Figure 17.  
Combined measurement uncertainty is simulated with all input parameters simultaneously deviating according to the uncertainty distribution. A plot of combined measurement uncertainty simulation results is displayed in Figure 18.  
Currently, the only established alternative method for the calculation of the influence of emissivity on measured temperature is an Excel spreadsheet by the Measurement and Standards Laboratory of New Zealand (MSL), accessible as an appendix to the Technical \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value with Standard Uncertainty** & **Probability Distribution** & **Standard Uncertainty** \\ \hline Emissivity & 0.95 \(\pm\) 0.0116 & & 500 \({}^{\circ}\)C \\  & (\(\pm\) 0.02/\(\sqrt{3}\)) & Uniform & 1.94 \({}^{\circ}\)C \\ Reflected temperature & (23 \(\pm\) 2) \({}^{\circ}\)C & Uniform & 0.00030 \({}^{\circ}\)C \\ Transfer path distance & (0.38 \(\pm\) 0.02) m & Normal & 0.00023 \({}^{\circ}\)C \\ Relative humidity & (40 \(\pm\) 10)\% RH & Uniform & 0.00023 \({}^{\circ}\)C \\ Atmospheric pressure & (1013.25 \(\pm\) 10) hPa & Uniform & 7.9 \(\times\) 10\({}^{-5}\)\({}^{\circ}\)C \\ Air temperature & (23 \(\pm\) 2) \({}^{\circ}\)C & Uniform & 7.8 \(\times\) 10\({}^{-5}\)\({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Model parameter values, standard uncertainties (\(k=1\), except for “boundary interval” with 100% coverage factor) of the direct model parameters and standard uncertainty contributions (\(k=1\)) of the simulated temperature measurement in case 2. Figure 17: Histogram of partial standard uncertainty contributions (\(k=1\)) when measuring a flat plate calibrator at 500 \({}^{\circ}\)C using Heitronics TRT II. Figure 18: Simulated standard uncertainty (\(k=1\)) of measurement of a flat plate calibrator over two temperature ranges of Heitronics TRT II. Guide 22 (TG22) [25].