## 3 Application of Industrial Styling Decision-Making Methods
### Validation of the PFA-SEM Evaluation Model  
In the research process, the selected participants included industrial design and electromechanical automation-related university and college teachers, senior engineers from machine tool companies, and technical practitioners. Ultimately, 245 valid questionnaires were harvested, with 5 incomplete questionnaires excluded. The outcomes were subjected to reliability analysis with the assistance of SPSS software, and the [PERSON]'s alpha coefficient for the questionnaire was found to be 0.912, indicating high reliability. Model fitness detection produced the outcome of CMIN/DF (the ratio of chi-square minimum and degree of freedom) = 1.056, which fell within the range of 1-3. Additionally, the RMSEA (root mean square error of approximation) was 0.015, which was rated excellent, as it was below 0.05. Furthermore, the results of the additional tests, including the incremental fit index (IFI), the Tucker-Lewis index (TLI), and the comparative fit index (CFI), all exceeded the threshold of 0.9, indicating that the model had a good fit. Under the premise of a good fit of the scale confirmatory factor analysis (CFA) model, further examinations were made to assess the convergent validity (average variance extracted (AVE)) and composite reliability (CR) of various dimensions of the scale. The process involved calculating standardized factor loadings for each measurement item on its corresponding dimension within the established CFA model. AVE values should meet a minimum requirement of 0.5, whereas CR values should meet a minimum requirement of 0.7 to indicate good convergent validity and composite reliability. The outcomes are presented in Table 2, showing that all AVE values exceeded 0.5 and that the mean CR values were above 0.7, suggesting strong convergent validity and composite reliability for the model. The convergent validity and composite reliability results for the preliminary PFA-SEM theoretical model are displayed in Table 2.  
The model test results revealed that the \(\mathrm{CMIN}/\mathrm{DF}=1.043\), which fell within the range of 1-3, and that the RMSSEA = 0.013. Additionally, the results of the IFI, TLI, and CFI tests all exceeded the excellent level of 0.9. Therefore, given the analysis outcomes, it could be concluded that the machine tool styling SEM model exhibited a good fit. Table 3 presents the standardized coefficients of the model. The latent variables of the theoretical model were considered to exert a positive impact on PF satisfaction, reflecting that optimization in these four domains could contribute positively to overall product competitiveness. The \(p\)-values for each path were statistically significant, confirming the validity of H1-H4. The results of the PFA-SEM calculations can be seen in Figure 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Path Relationship** & **Estimate** & **AVE** & **CR** \\ \hline X11 \(\leftarrow\) Functional domain & 0.777 & & & \\ X12 \(\leftarrow\) Functional domain & 0.674 & & & \\ X13 \(\leftarrow\) Functional domain & 0.721 & & 0.508 & 0.805 \\ X14 \(\leftarrow\) Functional domain & 0.676 & & & \\ \hline X21 \(\leftarrow\) Technological domain & 0.806 & & & \\ X22 \(\leftarrow\) Technological domain & 0.751 & & & \\ X23 \(\leftarrow\) Technological domain & 0.704 & & & \\ X24 \(\leftarrow\) Technological domain & 0.819 & & & \\ \hline X31 \(\leftarrow\) Physical domain & 0.8 & & & \\ X32 \(\leftarrow\) Physical domain & 0.84 & & & \\ X33 \(\leftarrow\) Physical domain & 0.801 & & 0.656 & 0.884 \\ X34 \(\leftarrow\) Physical domain & 0.798 & & & \\ \hline X41 \(\leftarrow\) Design domain & 0.779 & & & \\ X42 \(\leftarrow\) Design domain & 0.681 & & & \\ X43 \(\leftarrow\) Design domain & 0.646 & & 0.515 & 0.808 \\ X44 \(\leftarrow\) Design domain & 0.757 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Examination of convergent validity and composite reliability of each element within the machine tool styling scale.