## 4 Reference Scenario
### Data Analysis for Process Modeling Accuracy  
Cycle times related to each process activity were collected through eight iterations conducted in the field. The results of these iterations were subjected to rigorous statistical tests for compliance with three basic criteria: randomness (independence among observed events), homogeneity (uniformity of the data population), and goodness of fit (alignment with the theoretical distribution model). The results of these analyses are shown in Tables 3-5.  
Statistical analysis of the cycle times of process activities provided insight into the nature of the data and their distribution, giving useful indications for accurate modeling of the processes analyzed.  
Regarding independence, Runs Test confirmed that the \"Structure\", \"Doors\", \"Cover\", and \"Cabinet\" streams are random, highlighting the absence of sequential dependencies. Values of p above the significance level support the hypothesis of independence of the data, ensuring that there are no repetitive patterns or hidden structures.  
Homogeneity among the streams was tested using the Levene's Test and the Kruskal-Wallis Test, the results of which show that the variances and distributions of the data are homogeneous. The absence of significant differences confirms that the streams share similar statistical characteristics, allowing them to be considered as belonging to a single coherent system.  
Finally, the Kolmogorov-Smirnov Test showed that all streams follow a uniform distribution. High \(p\)-values for \"Structure\", \"Doors\", \"Cover\", and \"Cabinet\" indicate that the data are well distributed over a uniform range, confirming a good statistical representation of the observed behavior.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test** & **Flow** & **F-Value** & \(p\)**-Value** & **Conclusion** \\ \hline Levene’s Test (Variance) & All Flow & 2.782 & 0.058 & \
\begin{tabular}{c} Homogeneous \\ variances \\ \end{tabular} \\ \hline Kruskal–Wallis Test (Distribution) & All Flow & 7.564 & 0.056 &
\begin{tabular}{c} Homogeneous \\ distributions \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 4: Results of tests of homogeneity.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test** & **Flow** & **K** & \(p\)**-Value** & **Conclusion** \\ \hline \multirow{4}{*}{Runs Test (Randomness)} & Structure & \(-0.573\) & 0.567 & Random \\ \cline{2-5}  & Doors & \(-1.909\) & 0.056 & Random \\ \cline{1-1} \cline{2-5}  & Cover & \(-0.382\) & 0.703 & Random \\ \cline{1-1} \cline{2-5}  & Cabinet & \(-0.206\) & 0.837 & Random \\ \hline \hline \end{tabular}
\end{table}
Table 3: Results of tests of randomness.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test** & **Flow** & **K** & \(p\)**-Value** & **Conclusion** \\ \hline \multirow{4}{*}{Kolmogorov–Smirnov Test (Uniformity)} & Structure & \(-0.573\) & 0.567 & Random \\ \cline{2-5}  & Doors & \(-1.909\) & 0.056 & Random \\ \cline{1-1} \cline{2-5}  & Cover & \(-0.382\) & 0.703 & Random \\ \cline{1-1} \cline{2-5}  & Cabinet & \(-0.206\) & 0.837 & Random \\ \hline \hline \end{tabular}
\end{table}
Table 3: Results of tests of randomness.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Test** & **Flow** & \
\begin{tabular}{c} **Min** \\ **Value** \\ \end{tabular} &
\begin{tabular}{c} **Max** \\ **Value** \\ \end{tabular} & \(p\)**-Value** & **Conclusion** \\ \hline \multirow{4}{*}{Kolmogorov–Smirnov Test (Uniformity)} & Structure & 9 & 12 & 0.124 & Uniform \\ \cline{1-1} \cline{2-5}  & Doors & 5 & 10 & 0.212 & Uniform \\ \cline{1-1} \cline{2-5}  & Cover & 8 & 11 & 0.748 & Uniform \\ \cline{1-1} \cline{2-5}  & Cabinet & 10 & 13 & 0.424 & Uniform \\ \hline \hline \end{tabular}
\end{table}
Table 5: Results of tests of goodness of fit.  
These results provide a solid basis for further analysis and intervention, ensuring that the conclusions drawn are robust and reliable.