## 5 Discussion
#### Comparison Between CMM and NIIM  
A comparative analysis between NIIM and contact measurement was performed using a co-ordinate-measuring machine (CMM) to assess the reliability of the proposed method. The calibration pieces used for the study were aluminum and were mounted in the CMM surface plate referenced to datums A and B, as shown in Figure 39.  
The measuring of the profile of a line tolerance by CMM was performed based on the direction vector method [48], involving the assessment of 152 points from point C to D for each cross-section. The direction vectors were defined to direct the probe along the contour profile, enabling the capture of data points at predetermined positions. A 2 mm ball diameter probe was utilized to record multiple measurements and juxtapose them with a virtual boundary to measure the profile line. Figure 40 illustrates the average deviation of the profile of the line measures obtained by CMM. The upper label, 75.19549, corresponds to the overall profile of a line, while the lower label, 74.91963, pertains to the per-unit profile of a line. In both instances, the average 0.71579 deviation falls within the prescribed tolerance zone limits. Figure 38: Energy of zero frequency and frequencies regarding form deviations. Subsequently, a measurement study was conducted on the repeatability, reproducibility, and total Gage R&R for the 152 discrete points evaluating the average deviation, using 10 calibration pieces with three operators in three series. The results of these analyses are presented in Tables 12 and 13. Specifically, the 95 th percentile values for \(\sigma_{\text{R\&R}}\) were determined to be 7.9% for the NIIM and 10.9% for the CMM. The data in Table 12 show that the CMM R&R study presents a lower form deviation measurement than the NIIM R&R Study. However, the practical importance of this difference is relatively small and falls within acceptable industry standards. CMM and NIIM satisfy the criteria of an R&R study according to common benchmarks, which aim for a Gage R&R tolerance of under 30%. However, the advantage of the NIIM lies in its significantly faster inspection time and lower computational costs. These factors essentially determine the reliability of the NIIM system. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline
**Part** & \multicolumn{4}{c}{**Operator A**} & \multicolumn{4}{c}{**Operator B**} & \multicolumn{4}{c}{**Operator C**} \\
**No.** & **M-1** & **M-2** & **M-3** & **Range** & **M-1** & **M-2** & **M-3** & **Range** & **M-1** & **M-2** & **M-3** & **Range** \\ \hline
1 & 0.76 & 0.77 & 0.77 & 0.01 & 0.73 & 0.72 & 0.73 & 0.01 & 0.66 & 0.77 & 0.68 & 0.11 \\
2 & 0.75 & 0.74 & 0.75 & 0.01 & 0.74 & 0.64 & 0.65 & 0.10 & 0.67 & 0.73 & 0.66 & 0.07 \\
3 & 0.77 & 0.73 & 0.70 & 0.07 & 0.75 & 0.78 & 0.72 & 0.06 & 0.79 & 0.68 & 0.70 & 0.11 \\
4 & 0.69 & 0.68 & 0.68 & 0.01 & 0.77 & 0.65 & 0.74 & 0.12 & 0.75 & 0.68 & 0.65 & 0.10 \\
5 & 0.78 & 0.67 & 0.66 & 0.12 & 0.73 & 0.68 & 0.75 & 0.07 & 0.77 & 0.77 & 0.00 \\
6 & 0.77 & 0.72 & 0.71 & 0.06 & 0.72 & 0.74 & 0.76 & 0.04 & 0.78 & 0.78 & 0.73 & 0.05 \\
7 & 0.69 & 0.77 & 0.73 & 0.08 & 0.73 & 0.72 & 0.77 & 0.05 & 0.76 & 0.76 & 0.65 & 0.11 \\
8 & 0.72 & 0.79 & 0.75 & 0.07 & 0.68 & 0.65 & 0.74 & 0.09 & 0.70 & 0.77 & 0.77 & 0.07 \\
9 & 0.75 & 0.66 & 0.77 & 0.11 & 0.67 & 0.66 & 0.67 & 0.01 & 0.72 & 0.73 & 0.75 & 0.03 \\
10 & 0.77 & 0.69 & 0.76 & 0.08 & 0.70 & 0.67 & 0.69 & 0.03 & 0.69 & 0.75 & 0.75 & 0.06 \\ \hline \(\bar{R}\) & \multicolumn{4}{c}{0.062} & \multicolumn{4}{c}{0.058} & \multicolumn{4}{c}{0.071} \\ \(\bar{X}\) & \multicolumn{4}{c}{0.7317} & \multicolumn{4}{c}{0.7117} & \multicolumn{4}{c}{0.7273} & \multicolumn{4}{c}{0.7273} \\ Repeatability & 0.507 & \multicolumn{4}{c}{Reproducibility} & \multicolumn{4}{c}{8\%} & \multicolumn{4}{c}{R\&R} & \multicolumn{4}{c}{7.9\%} \\ \hline \end{tabular}
\end{table} 
Table 12: CMM R&R study. Figure 40: CMM contour profile measurement results. Figure 39: CMM contour profile measurement.