## 4 Results and Analysis
### Weight Variation  
The main and interaction effects plots for the standard deviation of the weight of a single jetted dot are shown in Figures 9 and 10, respectively. As shown in Figure 9, all four parameters exhibit steep slopes, and thus it appears that all parameters significantly affect the weight variation of a single jetted dot. The six interaction effects for the four parameters, AB, AC, AD, BC, BD, and CD, are plotted in Figure 10. As shown in Figure 10, the stroke-open time, rising time-open time, and rising time-cooling pressure significantly affect the weight variation. The Pareto chart of the standard deviation of the weight is shown in Figure 11. However, it is observed from the Pareto chart that only the needle stroke and the open time are the main effective parameters, and the stroke-open time is the only effective interaction parameter. These results are verified in the table of the effects and estimated coefficients for the standard deviation, as shown in Table 9. The effective parameters include the needle stroke, the open time, and the stroke-open time with a \(p\)-value lower than 0.1 and are denoted by a shaded background. The results in Figure 11 and Table 9 indicate that the interaction of the needle stroke-open time displays the highest effect on the variation of the weight of a single jetted dot. With respect to the low needle stroke and low open time, the run orders of 1, 2, 5, and 6 in Table 6 display a lower standard deviation value when compared with the other run orders. With respect to the higher open time, the standard deviations for the run orders 3, 4, 7, and 8 rapidly increase. However, with respect to a higher needle stroke, the standard deviations for the run orders 9, 10, 13, and 14 are unchanged compared to those of the run orders 1, 2, 5, and 6 with the exception of the run order 9. These results are also observed in the interaction effects plot in Figure 10. The variation is reanalyzed with only the effective parameters, and the result is shown in Table 10. A regression model is constructed to estimate the standard deviation of the average weight of a single jetted dot as follows, by using the coefficients in the third column in Table 10.  
\[ \begin{split} Y_{\text{variation\_weight}}&=0.05-0.02 \times\text{A(Stroke)}+0.022\times\text{C(Open Time)}\\ -0.034\times\text{A(Stroke)}\cdot\text{C(Open Time)}\end{split}  \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Effect** & **Coeff. ** & **SE Coeff. ** & \(\mathbf{t}\) & \(\mathbf{p}\) \\ \hline Const. & - & 4.01406 & 0.01075 & 373.52 & 0.000 \\ \hline A &  
Figure 11: Pareto chart for the variation in weight. Figure 10: Interaction effects plot for the variation in weight. Figure 9: Main effects plot for the variation in weight. This is similar to the conclusions for the average weight, and it is concluded that the reduction of the needle stroke and the open time is the most effective method to minimize the variation in the weight of a single jetted dot. Among the 16 parameter sets, the optimal operating parameters to minimize both the average weight and the standard deviation of the weight of a single jetted dot are obtained and shown in Figure 12. It is observed that an 80% needle stroke, 2 ms rising time, 2 ms open time, and 138 kPa cooling pressure are selected as the optimal operating parameters for the minimum average weight and minimum variation with respect to the weight of a single jetted dot. However, it is observed that the average weight and standard deviation for the run order 1 in Table 6 (the operating parameters are the same as the optimal parameters) are small but not minimum. The values for the run orders 2, 5, and 6, with different rising time and cooling pressure, are lower than those for the run order 1. It is concluded that the average weight and the variation of the weight of a single jetted dot are mainly affected by parameters such as the needle stroke and the open time and not affected by parameters such as the rising time and the cooling pressure.