## 6 Conclusions  
According to the machine learning experiments, \(D_{\Delta,\beta}(k)\) and the FFNN generate the best computational cost and good performance in shape and quality classification. The results are obtained because \(D_{\Delta,\beta}(k)\) has only deviation features, and the tolerance zone \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Part** & \multicolumn{3}{c}{**Operator A-**} & \multicolumn{3}{c}{**Operator B-**} & \multicolumn{3}{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 & 0.71 & 0.70 & 0.71 & 0.01 & 0.71 & 0.71 & 0.00 & 0.71 & 0.71 & 0.71 & 0.00 \\
2 & 0.69 & 0.69 & 0.71 & 0.02 & 0.71 & 0.69 & 0.71 & 0.02 & 0.69 & 0.69 & 0.71 & 0.02 \\
3 & 0.59 & 0.56 & 0.55 & 0.04 & 0.58 & 0.61 & 0.59 & 0.03 & 0.55 & 0.56 & 0.52 & 0.04 \\
4 & 0.66 & 0.70 & 0.71 & 0.05 & 0.69 & 0.67 & 0.71 & 0.04 & 0.65 & 0.69 & 0.70 & 0.05 \\
5 & 0.56 & 0.54 & 0.56 & 0.02 & 0.55 & 0.00 & 0.56 & 0.56 & 0.71 & 0.70 & 0.70 & 0.01 \\
6 & 0.59 & 0.69 & 0.69 & 0.10 & 0.71 & 0.58 & 0.59 & 0.13 & 0.52 & 0.56 & 0.51 & 0.05 \\
7 & 0.61 & 0.66 & 0.63 & 0.05 & 0.60 & 0.59 & 0.59 & 0.01 & 0.62 & 0.69 & 0.63 & 0.07 \\
8 & 0.68 & 0.66 & 0.62 & 0.06 & 0.69 & 0.67 & 0.63 & 0.06 & 0.65 & 0.63 & 0.59 & 0.06 \\
9 & 0.58 & 0.69 & 0.59 & 0.11 & 0.56 & 0.58 & 0.61 & 0.05 & 0.69 & 0.63 & 0.61 & 0.08 \\
10 & 0.63 & 0.66 & 0.63 & 0.03 & 0.65 & 0.62 & 0.68 & 0.06 & 0.69 & 0.69 & 0.67 & 0.02 \\ \hline \(R\) & \multicolumn{3}{c}{0.040} & \multicolumn{3}{c}{0.096} & \multicolumn{3}{c}{0.04} \\ \(\hat{X}\) & 0.6417 & \multicolumn{3}{c}{0.6183} & \multicolumn{3}{c}{0.646} & \multicolumn{3}{c}{0.646} \\ Repeatability & 0.475 & \multicolumn{3}{c}{Reproducibility} & \multicolumn{3}{c}{11\%} & \multicolumn{3}{c}{R\&R} & \multicolumn{3}{c}{10.9\%} \\ \hline \hline \end{tabular}
\end{table} 
Table 13: NIIM R& Study. \begin{table}
\begin{tabular}{l c} \hline
**Error** & **CMM** & **NIIM** \\ \hline Average Relative Error (ARE) & 0.0257 & 0.0301 \\ Root Mean Square Error (RMSE) & 0.0781 & 0.0812 \\ Coefficient of Correlation (\(R^{2}\)) & 0.9318 & 0.9265 \\ Accuracy & 97.43\% & 96.99\% \\ \hline \end{tabular}
\end{table} 
Table 14: Comparison between CMM and NIIM. is represented with 100 frequency elements (it can be seen in Section 2.3.3. The obtained performance of \(D_{\Delta,\beta}(k)\) is due to the form deviation feature vector being a signature of the CNC milling process that generates the profile of the calibration piece. Moreover, according to the discussion section, the \(D_{\Delta,\beta}(k)\) feature vector generates high energy when the piece has a shape deformation and can be used to identify if the profile machine process accomplishes the geometric standard tolerances. CNNs with \(r_{\alpha,\beta}(n)\), \(M_{\alpha,\beta}(k)\), or \(l_{\alpha,\beta}(x,y)^{G}\) and \(P_{x,\beta}(x,y)\) generate good performance in shape classification but regular results in quality classification. The results are obtained because the inputs concentrate the energy in shape information and have little energy in form deviation information. Then, the CNNs generate features unrelated to deviation and quality contour shape profiles. SVM and SLTM methods generate regular results in shape and quality classification due to overlap between classes and the misinterpretation of contour frequencies. The networks VGG-16, ResNet, and Inception generate regular results because they analyze many abstract features that are irrelevant to shape and quality analysis. In conclusion, while contact measurement methods such as CMM may offer slightly better accuracy in specific metrics, NIIM delivers a remarkable 96.99% accuracy, low computational demands, 100% inspection capability, quality classification, and superior overall effectiveness. Furthermore, the NIIM methodology provides valuable insights that manufacturing engineers can leverage to refine machining parameters.