## 4 Experimental Data
### Summary Statistics  
The summary statistics of the collected data are presented in Table 4. \begin{table}
\begin{tabular}{c c} \hline
**Collected Data** & **Description** \\ \hline plasma & Plasma intensity levels \\ Flow rate in/out: & The flow rate of gases entering and leaving the system. \\ Conc in/out & Concentration of gases entering and leaving the system. \\ Volume flow rate in/out & In and out of the system. \\  & the proportion of gas consumed \\ Ui & during the semiconductor manufacturing process \\  & The proportion of gas\({}_{\text{i}}\) not utilized in the process, \\
1-Ui & representing the fraction of total gas\({}_{\text{i}}\) that is either unconsumed, lost, or \\  & left over at the end of the manufacturing process \\ \hline \end{tabular}
\end{table} 
Table 3: Descriptions of collected data. Figure 7 shows the distributions of the variables presented in Table 2, including plasma intensity measurements and 1-Ui. The standard deviations in Table 2 help assess the measurement precision of each variable. For instance, the standard deviation of 1-Ui is 0.23, indicating moderate variability relative to its mean value of 0.30. Among the continuous columns, the \"conc out\" and \"volume flow out\" are skewed right, but the \"flow late out\" is skewed left. Plasma intensity values were found to be widely spread, ranging from 40 to 3000. In this experiment, seven gases that had undergone various semiconductor production processes were used. Since plasma levels vary depending on the process, the range was substantial, from 40 to 3000. The flow rates of gases entering and leaving the system (flow rates (in/out)) were relatively consistent, as indicated by the marginal differences between the flow rates in and \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & **Plasma** & **Flow Late in** & **Flow Late Out** & **Con In** & **Con Out** & **Volume Flow** & **Volume Flow** & **1-Ui** \\  & **(W)** & **(LPM)** & **(LPM)** & **(ppm)** & **(ppm)** & **Rate In** & **Rate Out** & **1-Ui** \\ \hline count & 8324 & 8324 & 8324 & 8324 & 8324 & 8324 & 8324 & 8324 \\ mean & 1209.55 & 62.69 & 61.88 & 979.90 & 295.42 & 61,810.41 & 18,657.99 & 0.30 \\ std & 974.72 & 2.33 & 6.43 & 367.56 & 248.87 & 23,674.80 & 16,640.30 & 0.23 \\ min & 40.00 & 57.04 & 45.07 & 478.07 & 0.00 & 27,270.65 & 0.00 & 0.00 \\ Q1 & 500 & 62.48 & 55.65 & 608.07 & 143.27 & 37,991.50 & 8833.04 & 0.11 \\ Q2 & 1000 & 63.62 & 63.96 & 820.78 & 223.07 & 52,841.82 & 14,102.37 & 0.32 \\ Q3 & 2000 & 64.38 & 65.70 & 1324.66 & 379.91 & 84,269.48 & 24,444.16 & 0.47 \\ max & 3000 & 64.38 & 89.76 & 1525.78 & 1129.21 & 95,407.02 & 76,205.57 & 1.04 \\ \hline \end{tabular}
\end{table} 
Table 4: Summary statistics. Figure 7: Distribution of each collected data. out (mean inflow rate: 62.69; mean outflow rate: 61.88). The standard deviation in flow rates, especially \"flow late out\" (6.43), suggests some variability but not extreme. The concentration values (concentration (in/out)) exhibited a wide range, particularly \"conc out\", with a mean of 295.42 and a high standard deviation of 248.87. This variability reflects differences in gas behavior after processing under varying plasma intensities. The distribution of 1-Ui (remaining gas rate) showed moderate variability with a mean of 0.3045 and a standard deviation of 0.2259. The distribution may be right-skewed, reflecting cases with higher remaining gas values. Definition of 1-Ui is given in Equation (7):  
\[1-\mathrm{U_{i}}=1-\frac{volume\;out}{volume\;in} \tag{7}\]  
In the formula, volume in represents the volumetric flow rate entering the system, calculated as the product of the input flow rate and the input concentration, and volume out represents the volumetric flow rate leaving the system, calculated as the product of the output flow rate and the output concentration. In Table 5, the correlation coefficient between the \"plasma\" and \"1-Ui\" columns in the dataset was approximately \(-\)0.016.