# Analyzing the Factors Influencing Time Delays in Korean Railroad Accidents
## 6 Discussion  
This study focuses on identifying key factors influencing the likelihood of time delays in railroad events, utilizing comprehensive historical data from 2001 to 2022 in Korea. The dataset is divided into two categories: accidents with a significant impact on human life or property and incidents leading to time delays. Over the years (2001-2022), there is a substantial decline in both accidents and incidents, with an AGR of approximately \(-9.9\%\) for accidents and \(-3.7\%\) for incidents. Adoption of advanced safety systems and technological innovations, such as automatic train control, contributes to the reduction in accidents. The study aims to measure time delays caused by accidents or incidents, considering factors like season, train operator size, railroad type, accident cause, and location. A total of 14,771 accidents and incidents occurred, with only 38.3% having time delay records on average over 22 years. Reporting of accidents and incidents aligns with guidelines established under the Railway Safety Act from November 2007; therefore, the study used the data for the analysis starting from 2008. The total number of events used for human factors is 3244, and is 3350 for technical factors. The average delay time due to human factors ranges from 14.8 to 48.0 min, with an overall average of 27.2 min, while the average delay time due to technical factors ranges from 28.9 to 51.0 min, with an overall average of 34.3 min. There are variations in the annual average delay times, emphasizing the need for a dynamic and context-specific approach to address the causes of delays in the railway system. The overall decrease in the total number of events indicates positive trends in railway safety, but the varying delay times highlight the importance of understanding the specific factors contributing to delays for effective mitigation strategies. To address excess zeros in the data, two approaches are employed: a two-stage model involving binary logit and NB models, and a ZINB model, offering a more accurate representation. The article further introduces the mathematical formulations of these models and their parameters. Additionally, ANNs are explored as an alternative method, mimicking human brain processes for non-linear pattern recognition. The structure and components of ANNs, along with the backpropagation algorithm for training, are explained. The study aims to provide insights into predicting delayed time in railway accidents, considering both traditional regression models and advanced ANN methods. The study investigates time delays resulting from human-related and technical factors by dividing the dataset for model estimation and testing. Statistical tests indicate no significant difference in the frequency distribution of time delays between the two \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**Training Data**} & \multicolumn{3}{c}{**Testing Data**} \\ \cline{2-7}  & \(\mathbf{R^{2}}\) & **MSE** & **RMSE** & \(\mathbf{R^{2}}\) & **MSE** & **RMSE** \\ \hline Two-stage & 0.197 & 13.338 & 3.652 & 0.101 & 15.522 & 3.940 \\ ZINB & 0.209 & 13.140 & 3.625 & 0.124 & 14.048 & 3.748 \\ ANN & 0.300 & 11.626 & 3.410 & 0.183 & 12.416 & 3.524 \\ ANN/TWO & 52.3\% & \(-12.8\%\) & \(-6.6\%\) & 81.2\% & \(-20.0\%\) & \(-10.6\%\) \\ ANN/ZINB & 43.5\% & \(-11.5\%\) & \(-5.9\%\) & 47.6\% & \(-11.6\%\) & \(-6.0\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Model performance comparison for the technical-related factors. subsets. Modeling outputs, particularly from the Two-stage and ZINB models, consistently demonstrate trends in the likelihood and duration of delays associated with various factors. Human-related delays, influenced by event types, seasons, and passenger categories, show nuanced impacts. An ANN model is configured with optimal parameters, and its performance is compared to regression models, indicating that the ANN model provides superior predictions for human-related factors.