## 3 Round Robin Test (RRT) and Reliability Analysis
### PAUT Reliability Analysis Results  
For applying the PAUT technique to the inspection of tube welds in the boilers of thermal power plant facilities, it is necessary to evaluate the applicable target range. Therefore, in this study, a reliability evaluation was performed for different materials of the specimens to determine the application range of PAUT. In addition, a reliability evaluation was performed by dividing the flaws into volumetric flaws (porosity, slag inclusions), which are difficult to detect using the PAUT technique, and planar flaws (crack, lack of fusion), which more significantly affect the integrity of the facilities. A POD evaluation was performed using the MH1823 POD analysis software, which is widely used for the reliability assessment of NDT [16]. For POD analysis, the logistic model of Equation (2) was used, and a regression analysis was performed using the maximum likelihood estimation method. Figure 2 presents the results of the POD analysis for the entirety of the tube weld specimens. The analysis results for the PAUT data obtained by six teams for 30 specimens are shown. In the graph, the black line indicates the POD according to the flaw length, and the red dotted line indicates the 90% confidence interval. The POD analysis results indicated that \(a_{50}\) was 3.23 mm and \(a_{80}\) was 6.93 mm for flaw detection. Here, \(a_{50}\) represents the minimum flaw length at which the flaws can be detected with 50% probability. In addition, the value of \(a_{80/90}\) representing the 90% confidence interval exhibited a large error of 8.14 mm, which was attributed to the differences in the performance of the participating teams. A POD analysis was performed for each team, and the results are presented in Table 5. For \(a_{80}\), the teams with the best and worst performance obtained values of 5.59 and 10.77 mm, respectively, exhibiting a considerable difference. In the RRT, the same inspection system \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Wave Type** & \begin{tabular}{c} **Array** \\ **Type** \\ \end{tabular} & \begin{tabular}{c} **Frequency** \\ **[MHz]** \\ \end{tabular} & \begin{tabular}{c} **No. of** \\ **Element** \\ \end{tabular} & \begin{tabular}{c} **Pitch** \\ **[mm]** \\ \end{tabular} & \
\begin{tabular}{c} **Elevation** \\ **[mm]** \\ \end{tabular} &
\begin{tabular}{c} **Wedge** \\ **Angle [\({}^{\circ}\)]** \\ \end{tabular} \\ \hline Shear & 1D & 7.5 & 16 & 0.5 & 10 & 60 \\ Longitudinal & DLA & 5 & 32 & 0.75 & 5 & 70 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Specification of PA Probe and Wedge. Figure 1: Picture of performing RRT for PAUT data acquisition. and procedure were applied, and the tests were performed under the same temporal-spatial conditions. The large difference is ascribed to the differences in the performance of the inspectors among the participating teams. The POD results calculated according to the flaw types are shown in Figure 3. Figure 3a presents the POD analysis results for volumetric flaws (e.g., porosity and slag inclusions), and Figure 3b presents the analysis results for planar flaws (e.g., cracks and lack of fusion). In general, the ultrasonic inspection method has poor detection performance for volumetric flaws such as porosity and slag, owing to the low sensitivity of the reflected signals. However, the method has good detection performance for planar flaws such as cracks and lack of fusion because of the high sensitivity of the reflected signals. The RRT results of the present study followed this trend. The reliability analysis results indicated that 80% POD was obtained at a flaw length of 6.55 mm for volumetric flaws and 5.15 mm for planar flaws. The large deviation of the 90% confidence interval in Figure 3a is due to the significant difference in the detection performance among the participating teams for volumetric flaws, which are difficult to detect via the PAUT technique. Figure 4 shows the results of the reliability evaluation for different materials of the test specimens.