# Optimizing Replaced Nozzle Diameter of Abrasive Blasting Systems Using Experiment Technique Design
## 4 Results and Discussions  
### The Influence of Main Parameters and Their Interactions  
The single influence of each input parameter on the response, the initial optimum diameter \(d_{op}\), is graphically presented in Figure 6 (main effects plot). It is obvious that the initial nozzle diameter \(d_{N0}\) has the strongest impact on the response, which is the positive impact, i.e., \(d_{op}\) increases with increase in \(d_{N0}\) value from 5 to 12.5. Additionally, the parameters of \(C_{n,p}\) (F), **WR** (B), and \(t_{\mathbf{\alpha}}\) (C) also have positive effects. On the contrary, \(\mathbf{P_{c}}\) (D), \(\mathbf{C_{s}}\) (G), and \(\mathbf{C_{m,h}}\) (E) negatively impact the response. In terms of quantification, the influence of input parameters on the response are in the order of \(d_{N0}\), \(\mathbf{P_{c}}\), \(\mathbf{C_{n,p}}\), \(\mathbf{C_{s}}\), \(\mathbf{C_{m,h}}\), \(\mathbf{WR}\), and \(\mathbf{t_{\mathbf{\alpha}}}\). Nevertheless, it is difficult to distinguish these influences, hence a normal plot and a Pareto chart of the standardized effects can give more details about this. The Pareto chart of the standardized effects is shown in Figure 7, where the influence of each single input parameter is orderly arranged. In this case, a given input parameter is considered as statistically significant to the response at the level of 0.05. Again, the dominant impact of the initial nozzle diameter on the optimum initial nozzle diameter is apparently noticed. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Real Factor** & **Minitab®19** & **Name** & **Unit** & **Low** & **High** \\ \hline Initial nozzle diameter & A & \(d_{N0}\) & mm & 5 & 12.5 \\ Nozzle wear rate per hour & B & \(WR\) & \(10^{-3}\) mm/h & 1 & 2 \\ Time for changing a nozzle & C & \(t_{\mathbf{\alpha}}\) & min & 1 & 15 \\ Compressor power & D & \(P_{c}\) & kW & 4 & 80 \\ Machine cost per hour & E & \(C_{m,h}\) & USD/h & 5 & 30 \\ Nozzle cost per piece & F & \(C_{m,p}\) & USD/piece & 20 & 120 \\ Cost of sand & K & \(C_{s}\) & USD/kg & 0.06 & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Input parameters. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Run Order** & **CenterPt** & **Blocks** & \(d_{N0}\) & \(WR\) & \(t_{\mathbf{\alpha}}\) & \(P_{c}\) & \(C_{m,h}\) & \(C_{n,p}\) & \(C_{s}\) & \(d_{op}\) \\ \hline
1 & 1 & 1 & 5 & 1 & 15 & 80 & 100 & 50 & 0.4 & 5.03 \\
2 & 1 & 1 & 12.5 & 1 & 15 & 4 & 100 & 300 & 4.5 & 12.58 \\
3 & 1 & 1 The influencing degree on the response progressively descends, as documented above: initial nozzle diameter (\(\mathbf{d}_{n0}\)), compressor power (\(\mathbf{P}_{c}\)), nozzle cost per piece (\(\mathbf{C}_{n,p}\)), cost of sand (\(\mathbf{C}_{s}\)), machine cost per hour (\(\mathbf{C}_{m,h}\)), nozzle wear rate per hour (\(\mathbf{W}\)R), and time for changing a nozzle (\(\mathbf{t}_{cn}\)). However, it is comprehended that the impact levels of the last six parameters are minor. Only two parameters are counted as varying, while five remaining are constantly fixed. Regarding the evolution in Figure 8a in which five ranges of colors exhibit correspondingly five different values of the response. It is observed that when Pc increases, the response decreases, a positive influence. In case of Cn,p, an increase in Cn,p leads to increase in the response, corresponding to a negative impact. However, it is noticed that the increment value of the response between colors are minor. This means that the Cn,p and Fc factors have little influence on the response which is previously presented in Figure 6. The minor impacts of input parameters on the response can be similarly seen in Figure 8b-e. However, the influence of dN0 on the response is huge and can be profoundly observed in Figure 8f. In this situation the color ranges are bigger than previous ones and value corresponding to each range is higher also.