## 2 Materials and Methods
### Pairwise Comparison of Expert Evaluation Criteria  
On the basis of personal recollection and interviews with experts, data were obtained to select the following criteria:  
* Degree of education\(f_{1}\);
* Practical experience with RE systems\(f_{2}\);
* Theoretical knowledge in the field of quality inspection\(f_{3}\);
* Economic knowledge\(f_{4}\). Practical experience is necessary so that the expert can evaluate the technical specifications of a particular product from its manual. In addition, they should know something about quality inspection because not all of the machines compared are able to measure to the required degree of accuracy [27; 28]. A study of the firm's finances should ensure that there are sufficient funds to purchase a device with all the necessary gadgets. Finally, a reasonable level of education expresses the ability to carry out an analysis from the available documents and information (Table 4) [29; 30]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Criterion** & \(f_{1}\) & \(f_{2}\) & \(f_{3}\) & \(f_{4}\) \\ \hline \(f_{1}\) & 1 & 1/9 & 1/8 & 1/5 \\ \(f_{2}\) & 9 & 1 & 3 & 5 \\ \(f_{3}\) & 8 & 1/3 & 1 & 3 \\ \(f_{4}\) & 5 & 1/5 & 1/3 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Pairwise criteria comparison for evaluation of experts. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Parameter** & **XC65 Dx** & **LC60 Dx** & **LC15 Dx** \\ \hline Price (EUR) & 97,130 & 65,110 & 64,850 \\ Weight (kg) & 0.44 & 0.39 & 0.37 \\ Dimensions (mm) & \(155\times 86\times 142\) & N/A & \(100\times 104\times 58\) \\ Measuring speed (pts/s) & 75,000 & 75,000 & 70,000 \\ Accuracy (mm) & 0.012 & 0.009 & 0.006 \\ Spacing distance (mm) & 75 & 95 & 60 \\ Depth/width FOV (mm) & \(3\times 65/3\times 65\) & 60/- & 15/- \\ Operating humidity range (\%) & 10–90\% & 10–90\% & 10–90\% \\ Working temperature (\({}^{\circ}\)C) & 10–40 \({}^{\circ}\)C & 10–40 \({}^{\circ}\)C & 10–40 \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Technical specification of Nikon products. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter** & **Metronor DUO** & **ATOS III Triple Scan** \\ \hline Price (EUR) & 41,700 & 98,540 \\ Weight (kg) & 0.52 & 7.5 \\ Dimensions (mm) & \(500\times 200\times 30\) & \(155\times 86\times 142\) \\ Measuring speed (pts/s) & 35 & 75,000 \\ Accuracy (mm) & 0.025 & 0.01 \\ Spacing distance (mm) & 1500–15,000 & 490–2000 \\ Depth FOV (Field of View) (mm) & & 230 \\ Width FOV (Field of View) (mm) & & \(250\times 250\) \\ Working temperature (\({}^{\circ}\)C) & 10–45 \({}^{\circ}\)C & 5–40 \({}^{\circ}\)C \\ Operating humidity range (\%) & \textless{}90\% & 10–90\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Technical specification of products Metronor DUO and ATOS III Triple Scan. From the table above it is necessary to determine the characteristic polynomial by development of the following determinant:  
\[\det(A_{i}-\lambda\cdot J)=0 \tag{1}\]  
where \(A_{i}\) is the pairwise comparison matrix and \(J\) is the identity matrix. [PERSON]'s development of the determinant was used in the following calculation:  
\[det|A|=\sum_{i=1}^{n}(-1)^{i+j}.a_{ij}.M_{ij}^{A} \tag{2}\]  
where \(M_{ij}^{A}\) is the minor of a particular matrix \(\left|S_{ij}^{A}\right|\). From the calculated characteristic polynomial, we have identified the roots that are used to count the eigenvalue of the matrix [31], which are as follows:  
\[ \begin{array}{c}\lambda_{1}=0.0186+0.28505\mathrm{i}\\ \lambda_{2}=0.0186-0.28505\mathrm{i}\\ \lambda_{3}=4.1746\\ \lambda_{4}=0.1373\end{array} \]  
The eigenvalue of the matrix is then calculated according to the following formula:  
\[max|\lambda_{i}|=\lambda_{max}=4.1746 \tag{3}\]  
Consistency index \(\lambda_{max}\) represents the condition for the acceptance of a reciprocal pairwise comparison matrix.