# Data-Driven Optimization of CNC Manufacturing Using Simulation and DOE Techniques
## 12 Design of Experiment  
The regression equation in uncoded units is as follows:  
\[\text{Output}=461.0\,-8.200\,\,\text{X1}-224.0\,\,\text{X2}+6.000\,\,\text{X3}+5.600 \,\,\text{X1*X2}-0.4000\,\,\text{X1*X3}+17.00\,\,\text{X2*X3}-0.4000\,\,\text{X1*X2*X3}\]  
where,  
X1: Arrival time  
X2: Capacity of the CNC turning process  
X3: Capacity in the inspection station  
Table 8 illustrate the high and low values of the above mentioned factors in the study, while Table 9 shows the results of the interaction of all variables at all levels.  
The Pareto chart in Figure 8 shows that none of the factors or interactions were statistically significant at the 0.05 level, as no effect exceeded the reference line of 33.88. However, the interaction between factors A and B (AB) and the main effects of B and A showed relatively larger influences on the output, with AB being the highest. Factor C and its interactions (AC, BC, and ABC) had minimal effects. For practical improvement, focus should be placed on factors A, B, and C, and their interaction.  
Figure 9 shows the plot of the output's main effects, illustrating the variation in the mean output with varying quantities of variables X1, X2, and X3. As each element increased from its lowest to its highest level, the graph shows that output fell. After X1 and X3, factor X2 had the sharpest slope, indicating that it had the greatest effect on production. For example, when X1 was at 35, X2 was at level 1, and X3 was at level 1, the greatest mean output was recorded. Setting the process at the lowest levels of all three factors, we found that X2 will particularly optimize production.  
\begin{table}
\begin{tabular}{c c c c} \hline  & & **Low** & **High** \\ \hline Arrival time & X1 & 35 & 40 \\ \hline Capacity of the CNC turning process & X2 & 1 & 2 \\ \hline Capacity in the inspection station & X3 & 1 & 2 \\ \hline \end{tabular}
\end{table}
Table 8: High and low values of the factors in the study.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **X1** & **X2** & **X3** & **Output** & **High Queue** & **High Utilization** \\ \hline
1 & 35 & 1 & 1 & 141 & 0.75 & 77\% \\ \hline
2 & 40 & 1 & 1 & 124 & 0.4596 & 67\% \\ \hline
3 & 35 & 2 & 1 & 116 & 0.38 & 62\% \\ \hline
4 & 40 & 2 & 1 & 125 & 0.5956 & 71\% \\ \hline
5 & 35 & 1 & 2 & 136 & 0.88 & 72\% \\ \hline
6 & 40 & 1 & 2 & 115 & 0.38 & 61\% \\ \hline
7 & 35 & 2 & 2 & 114 & 0.2564 & 46\% \\ \hline
8 & 40 & 2 & 2 & 117 & 0.4776 & 48\% \\ \hline \end{tabular}
\end{table}
Table 9: Results values at all level of interaction of the factors in the study.  
Figure 10 illustrates the design of experiments (DOE). This interaction plot illustrates how three parameters (X1, X2, and X3) affect the results. The non-parallel and intersecting lines suggest that the X1, X2 interaction is significant, indicating that the level of X2 influences the effect of X1. The relatively parallel lines in X1, X3, and X2*X3 graphs suggest minimal interaction between these factor pairings. The notable interaction between X1 and X2 indicates that they should be analyzed together rather than separately. This figure assists in identifying important element combinations for optimizing process output.  
Optimal factor levels from the regression equation:  
X1 = 37.22, X2 = 4.21, and X3 = 7.37  
Figure 8: Interaction factors significance at 0.05 level.  
Figure 9: Output’s main effects results.