## 4 Experimentation and Results
### Statistical Analysis
#### 4.5.5 Performance Stability and Variability  
To guarantee the resilience and dependability of our findings, we carried out several extra tests that concentrated on the performance stability of the used algorithms. Ten runs of each method were conducted under uniform circumstances to evaluate the variation in the accuracy metrics derived by the DeepSORT and YOLOv5 models.  
This method enables us to comprehend both the average performance and the constancy of the outcomes over several executions. We computed the average accuracy, precision, and recall metrics for these ten runs for the training, validation, and test datasets. We also calculated the standard deviation for every indicator, which shed light on the models' performance's stability and variability.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Subset** & \begin{tabular}{c} **Percentage of** \\ **Total Data** \\ \end{tabular} & **Number of Images** & **Purpose** \\ \hline Training Set & 70\% & 653 & \begin{tabular}{c} Used for training the model \\ and learning patterns. \\ \end{tabular} \\ \hline Validation Set & 20\% & 200 & \
\begin{tabular}{c} Used for hyperparameter \\ tuning and preventing \\ overfitting. \\ \end{tabular} \\ \hline Test Set & 10\% & 150 &
\begin{tabular}{c} Used for final evaluation \\ and simulating real-world \\ scenarios. \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 10: Dataset sampling mechanism overview.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Accuracy** & **Precision** & **Recall** \\ \hline Training Set & 84.22\% \(\pm\) 2.14\% & 91.67\% \(\pm\) 1.85\% & 84.23\% \(\pm\) 2.10\% \\ Validation Set & 85.00\% \(\pm\) 1.89\% & 89.47\% \(\pm\) 2.00\% & 85.00\% \(\pm\) 1.95\% \\ Test Set & 84.67\% \(\pm\) 2.01\% & 89.44\% \(\pm\) 1.98\% & 84.65\% \(\pm\) 2.05\% \\ \hline \hline \end{tabular}
\end{table}
Table 11: The 95% confidence intervals for key performance metrics.  
The computed mean and standard deviation data are essential for analyzing the models' performance. High stability, indicated by a low standard deviation relative to the mean, suggests that the model performs consistently across runs. A high standard deviation, on the other hand, might indicate potential issues with the model's resilience or sensitivity to changes in the input data.  
The YOLOv5 model's findings from 10 executions are shown in Table 12. According to calculations, the model's mean accuracy is 84.91% with a standard deviation of 1.23%. The constant performance throughout several runs confirms the model's dependability under different situations.  
Figure 15 shows the accuracy of the YOLOv5 model over ten executions with error bars indicating the standard deviation for each run. Each point represents the accuracy achieved in a specific execution. The red dashed line represents the model's overall stability, indicating the mean accuracy at approximately 84.91%. The YOLOv5 model's dependability is demonstrated by the slight variations in accuracy, suggesting that it detects products consistently. The standard deviation indicates that the model's accuracy is not significantly influenced by variation between executions.