## 3 Results
### Semiconductor Manufacturing
 \tag{13}\]  
However, the \(p\)-values of the variables \(x_{1}x_{2}\) and \(x_{1}x_{3}\) are greater than 0.005. The adequate equation evaluated with the complete regression technique in this study is  
\[ \begin{split}\text{y}_{\text{SR}}=9.565-25.501x_{1}-0.168x_{2}-0. 275x_{3}+46.375{x_{1}}^{2}+0.00309{x_{2}}^{2}\\ (<\!0.001)\;(<\!0.001)\;(0.002)\;(<\!0.001)\;(0.002)\;(0.002)\\ +0.00815{x_{3}}^{2}+0.425{x_{1}}{x_{3}}\\ (0.014)\;(0.010)\\ R^{2}=0.973,\text{R}^{2}_{\text{adj}}=0.946,\text{s}=0.121,\text{ PRESS}=0.603\end{split}  \tag{14}\]  
The normality and constant variance tests are passed. Four influential data points are found (4 th, 6 th, 7 th, 12 th). Comparing the full and adequate equations, the adequacy equation has higher values of \(\text{R}^{2}_{\text{adj}}\) and s and a lower value of PRESS. This indicated that an adequate equation has better accuracy performance (\(\text{R}^{2}_{\text{adj}}\), s) and prediction (PRESS). [PERSON] et al. [25] investigated the optimization of dispatching rules for wafer manufacturing systems. The affecting variables were \(x_{1}\), the criterion of bottleneck, and \(x_{2}\) and \(x_{3}\), which were two coefficients of work-in-progress (WIP) status. The responses included \(y_{\text{CT}}\), the cycle time (CT); \(y_{WIP}\), work-in-progress (WIP); and \(y_{\text{TP}}\), throughput (TP). The authors proposed the full models [25], and contour and 3-D response surface plots were produced as curve surface plots. The results of the complete regression in our study are  
\[ \begin{split} y_{CT}=932.466\,-\,10.392x_{1}\,-\,31.055x_{2}+0.0685x _{1}{}^{2}+3.849x_{2}{}^{2}\\ \text{R}^{2}=0.813,\,\text{R}^{2}_{\text{adj}}=0.763,\,\text{s}=6.755, \,\text{PRESS}=2307.945\end{split}  \tag{15}\]  
Figure 1: Contour plots of the complete and adequate equations for the final polished surface roughness response of a silicon wafer. The contours present the effect of using the RSM equation on the relationship between the response variables and the influencing variables. **(a)** Full equation. **(b)** Adequate equation. The normality and constant variance tests were passed. Three influential data points were found. \[ \begin{split} y_{WIP}=10514.817-166.362x_{1}+1878.219x_{2}+2653.558x_{ 3}+1.765{x_{1}}^{2}-164.955{x_{3}}^{2}\\ -22.265x_{1}x_{2}\\ R^{2}=0.922,\,{R^{2}}_{\text{adj}}=0.886,\,\text{s}=162.678,\, \text{PRESS}=948,\!709.4\end{split}  \tag{16}\]  
The normality test was failed (\(p=0.008\)), and the constant variance test was passed. One data point was influential (13 th). \[ \begin{split} y_{TP}=-1920.381+40.347x_{1}+124.394x_{2}+248.409x_ {3}-0.184{x_{1}}^{2}-15.781{x_{2}}^{2}\\ -8.908{x_{3}}^{2}-1.204x_{1}x_{3}\\ R^{2}=0.768,\,{R^{2}}_{\text{adj}}=0.633,\,\text{s}=15.875,\, \text{PRESS}=13,\!369.7\end{split}  \tag{17}\]  
The normality test was failed (\(p=0.008\)), and the constant variance test was failed (\(p=0.003\)). Three influential data points were found (5 th, 15 th, 18 th). For the \(y_{CT}\) response, \({x_{3}}^{2}\) did not significantly affect the response. For the \(y_{WIP}\) response, \({x_{3}}^{2}\) was not included in this RSM equation. The authors presented plots of the surface curve using the full equation. However, this full equation was inappropriate. The \(y_{WIP}\) response was under non-normality conditions. Both tests of normality and constant variance failed for the \(y_{TP}\) response. An advanced regression technique needs to be performed to remedy these conditions. [PERSON] et al. (2016) optimized a tungsten chemical mechanical planarization (CMP) slurry for semiconductor manufacturing. The CCD experimental design was employed. The responses \(y_{W}\) and \(y_{Oxide}\) were the removal rates of the thickness of the W and oxide films. The full equations of the two responses were proposed ([PERSON] and [PERSON], 1996) and used to produce the contour and response surface plots. The adequate equations with datasets listed in the literature ([PERSON] and [PERSON], 1996) were evaluated by complete regression analysis:  
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