## 2 Case Introduction
### Explanation of Manufacturing Process Quality and Manufacturing Time Performance Evaluation Model  
A comprehensive manufacturing process quality and manufacturing time performance evaluation model has been constructed in the previous section. Subsequently, in terms of quality, this study uses \(5\sigma\) as the standard. First, a few different scenarios that can occur in the process performance evaluation chart are defined. This study defines four performance regions, namely \(Z_{A}\), \(Z_{B}\), \(Z_{C}\), and \(Z_{D}\), as follows using precision (\(\gamma\)), accuracy (\(\delta\)), and manufacturing time performance index \(J_{MT}\):  
\[Z_{A}=\left\{\delta,\;\gamma,\;J_{MT}\big{|}\;\delta-(k-1.5)\gamma\geq-1,\; \delta+(k-1.5)\gamma\leq 1,\;\gamma\geq 0,\;0\leq J_{MT}\leq 1\big{|}\right\}\]  
\[Z_{B}=\left\{\delta,\;\gamma,\;J_{MT}\big{|}\;\delta-(k-1.5)\gamma\leq-1,\; \gamma\geq 0,\;\delta<0,0\leq J_{MT}\leq 1\big{|}\right\}\]  
\[Z_{C}=\left\{\delta,\;\gamma,\;J_{MT}\big{|}\;\delta+(k-1.5)\gamma\geq-1,\; \gamma\geq 0,\;\delta>0,0\leq J_{MT}\leq 1\big{|}\right\}\]  
\[Z_{D}=\left\{\delta,\;\gamma,\;J_{MT}\big{|}\;\delta-(k-1.5)\gamma\leq-1,\; \delta+(k-1.5)\gamma\geq 1,\;\gamma\geq 0,\;0\leq J_{MT}\leq 1\big{|}\right\}\]  
As mentioned previously, precision and accuracy indices can adequately identify reasons for poor quality in the manufacturing process. When a process quality characteristic falls into region \(Z_{A}\), it indicates that the process quality characteristic is satisfactory and its precision and accuracy are above the required quality level. When a process quality characteristic falls into region \(Z_{B}\), it indicates that the process quality characteristic has insufficient accuracy and its manufacturing process is skewed to the left. When a quality characteristic falls into region \(Z_{C}\), it indicates that the process quality characteristic has insufficient accuracy and its manufacturing process was skewed to the right. When a process quality characteristic falls into region \(Z_{D}\), it indicates that the quality characteristic has insufficient precision and process variation is overly large. Subsequently, the quality region is depicted in Figure 6.  
In terms of manufacturing time performance, the manufacturing time performance defect rate \(J_{MT}\) is used as the \(Z\)-axis, as shown in Figure 7. When the height of the set \(S\) is within the model, it indicates that the manufacturing time performance has met the requirements of the company. When the height of aggregate \(S\) is outside of the model, it indicates that the manufacturing time performance has fallen short of the standard allowed by the company and improvement is needed. Through the use of the  
Figure 6: Quality region of manufacturing process performance evaluation chart.  
model, whether the manufacturing process of each product has met the standard can be seen clearly. Additionally, a table for the comparison of manufacturing process quality and manufacturing time performance is made for reference and is shown in Figure 3. The Table 4 allows quick identification of process quality characteristics whose manufacturing time performance has not met the standard, enabling companies to focus on the problems and improve them accordingly.