## 4 Practical Application  
A comprehensive manufacturing process quality and manufacturing time performance evaluation model has been constructed in Section 3. Manufacturers can set a quality level according to their own capacity and the requirements of their clients. This section uses the manufacturing process of a bearing connector in our case study. The case company collected sample information through random sampling. The number of sampling groups was set to \(m=20\) and the sample size was set to \(n=11\). Additionally, the Kolmogorov-Smirnov test was used to determine whether the samples were in the normal distribution. The results suggested that the values were all larger than 0.07 and \(p\) values were all bigger than 0.05. This indicated that the samples had a normal distribution. The data are presented in Table 5. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Region** & **Manufacturing Process Quality** & **Situation** \\ \hline \(Z_{A}\) & Satisfactory & Both accuracy and precision have met the standard \\ \hline \(Z_{B}\) & Unsatisfactory & Insufficient accuracy and manufacturing process is skewed to the left \\ \hline \(Z_{C}\) & Unsatisfactory & Insufficient accuracy and manufacturing process is skewed to the right \\ \hline \(Z_{D}\) & Unsatisfactory & Insufficient precision with excessive process variation \\ \hline \(J_{MT}\) Outer & Satisfactory & Manufacturing time performance has met the standard \\ \hline \(J_{MT}\) Inner & Unsatisfactory & Failure to meet the standard and requires improvement \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of manufacturing process quality and manufacturing time performance. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Indicator** & **Characteristic** & **External Diameter (A)** & **Internal Diameter (B)** & **Threads (C)** \\ \hline \multirow{2}{*}{Manufacturing process quality index} & Ks = 0.084 & Ks = 0.084 & Ks = 0.093 \\ \cline{2-4}  & \(p>0.05\) & \(p>0.05\) & \(p>0.05\) \\ \hline \multirow{2}{*}{Manufacturing time performance index} & Ks = 0.073 & Ks = 0.091 & Ks = 0.097 \\ \cline{2-4}  & \(p>0.05\) & \(p>0.05\) & \(p>0.05\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Kolmogorov–Smirnov test. Figure 7: Manufacturing process performance evaluation chart with 5-sigma. Three crucial nominal-the-best process quality characteristics were estimated and analyzed. Sampling was conducted separately for manufacturing process quality and manufacturing time performance, and the means and standard deviations of the sampling were found. The results of the sampling are presented in Table 6.  
The variables \(\delta\) and \(\gamma\) in Table 7 can be used to construct a joint confidence region, with coordinates that represent the maximum and minimum values of precision and accuracy, respectively. The coordinate points of the three aforementioned pivotal process quality characteristics were subsequently drawn into an evaluation diagram of pivotal process quality characteristics of the bearing connectors. Analyzing the diagram of pivotal process quality characteristics can help determine whether a bearing connector has met the manufacturer's requirements. Figure 8 illustrates that quality characteristic A (external diameter) was located in the satisfactory region \(Z_{A}\), quality characteristic B (internal diameter ) was located in the satisfactory region \(Z_{A}\), and quality characteristic C (threads) was located in the unsatisfactory region \(Z_{C}\). This indicates that the accuracy of the manufacturing process was insufficient and skewed to the right.