## 3 Results and Discussion
### Model Validation  
For the validation, the paired \(t\)-test was applied to the model. This was performed to verify the results obtained from the simulation with real data using the time it takes to produce 120 batches, which is 24,000 capsules. The following working hypothesis was tested:  
\(X\) = _The time in minutes it takes to produce 120 batches (24,000 capsules) in the real process._  
\(Y\) = _The time in minutes it takes to produce 120 batches (24,000 capsules) in the created simulation model._  
The results of the 2-week, 10-day runs are shown in Table 3, for which a 95% confidence interval was considered for Z where ZJ = XJ - YJ. A 95% confidence interval was considered for Z where ZJ = XJ - YJ. Applying the formulas described in the previous section for the paired \(t\)-test, the results are shown in Table 3.  
### Model Validation  
For the validation, the paired \(t\)-test was applied to the model. This was performed to verify the results obtained from the simulation with real data using the time it takes to produce 120 batches, which is 24,000 capsules. The following working hypothesis was tested:  
\(X\) = _The time in minutes it takes to produce 120 batches (24,000 capsules) in the real process._  
\(Y\) = _The time in minutes it takes to produce 120 batches (24,000 capsules) in the created simulation model._  
The results of the 2-week, 10-day runs are shown in Table 3, for which a 95% confidence interval was considered for Z where ZJ = XJ - YJ. A 95% confidence interval was considered for Z where ZJ = XJ - YJ. Applying the formulas described in the previous section for the paired \(t\)-test, the results are shown in Table 3.  
\(Yar[Z(n)]=\frac{\sum_{i=1}^{15}\left[z_{i}-\overline{z}_{(15)}\right]^{2}}{15 (15-1)}=\frac{4805.43}{(15)(14)}=22.88\)  
\(Z_{(n)}\pm t_{n-1,1-a/2}\sqrt{\hat{V}ar\left(\overline{Z}_{(n)}\right)}\)  
\(-5.40\pm t_{14,0.975}\sqrt{22.88}\) \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Measures of**} & \multicolumn{6}{c}{**Test Statistic**} & \multicolumn{6}{c}{**Theoretical Distribution**} \\ \multirow{2}{*}{**Process Stage**} & \multicolumn{2}{c}{**Central**} & \multicolumn{2}{c}{**Kolmogorov–Smirnov**} & \multicolumn{2}{c}{**Anderson–Darling**} & \multirow{2}{*}{**Data Distribution**} & \multicolumn{2}{c}{**Statistics.**} \\  & \multicolumn{2}{c}{**Tendency (min)**} & & \multicolumn{2}{c}{**Kolmogorov–Smirnov**} & \multicolumn{2}{c}{**Anderson–Darling**} & \multirow{2}{*}{**Fit**} & \multicolumn{2}{c}{**Minimum**} & \multirow{2}{*}{**\(\mu\)} & \multirow{2}{*}{\(\sigma\)**} \\  & \multicolumn{2}{c}{**X**} & \multicolumn{2}{c}{**s**} & & & & & & & & & & \\ \hline Raw Material & 39.99 & 3.663 & 0.116 & 0.005 & 0.477 & 1.3 & 0.005 & 0.232 & Log normal & 30 & 2.25 & 0.395 \\ Reception & 3.78 & 0.310 & 0.137 & 0.005 & 0.275 & 1.99 & 0.005 & 0.934 & Log normal & 3 & \(-0.320\) & 0.496 \\ Leaf Selection & 58.87 & 0.583 & 0.131 & 0.005 & 0.329 & 1.51 & 0.005 & 0.174 & Uniform & 58.02 & & \\ Basic SetFiltration & 4.79 & 0.116 & 0.125 & 0.005 & 0.382 & 0.73 & 0.005 & 0.534 & Log normal & 4.49 & \(-2.23\) & 0.14 \\ Cushing & 39.02 & 2.66 & 0.158 & 0.005 & 0.145 & 2.18 & 0.005 & 0.073 & Log normal & 33.895 & 1.66 & 0.582 \\ Pulverization & 40.00 & 3.94 & 0.175 & 0.005 & 0.008 & 2.25 & 0.005 & 0.004 & Log normal & 30 & 2.23 & 0.51 \\ Secondary & 120.12 & 0.142 & 0.102 & 0.005 & 0.635 & 0.427 & 0.005 & 0.821 & Log normal & 119.81 & 0.0097 & 0.129 \\ Sterilization & 21.84 & 1.55 & 0.00973 & 0.005 & 0.694 & 0.418 & 0.005 & 0.831 & Log normal & 19.49 & 0.907 & 0.540 \\ Business Labeling & 4.51 & 0.570 & 0.168 & 0.005 & 0.106 & 1.44 & 0.005 & 0.192 & Log normal & 3.45 & 0.329 & 0.441 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Data obtained from the goodness fit test of observed data from the production process. It is observed that the resulting interval includes zero; therefore, the null hypothesis cannot be rejected. Thus, it is concluded that with a 95% confidence level, the model is valid and representative of the real system.