# Dynamic Railway Derailment Risk Analysis with Text-Data-Based Bayesian Network
## 4 Case Study and Experimental Results
### Quantitative Safety Assessment of the Railway System Using a Bayesian Network
#### 4.2.1 The Probabilities of Train Derailment  
A train derailment refers to the occurrence of a derailment accident. The train derailment and failure probabilities of the safety layers are calculated using the established BN model depicted in Figure 8, and the results are provided in rows 2 and 5-7 of Table 5. Table 5 indicates the failure probabilities of the safety layers. Referring to the assessment criteria, we find that in Situation 3, high probabilities are attained that are mainly caused by the high failure probabilities in the first stage. In contrast, in Situation 2, the lowest success probabilities occur because both the first and second stages have low failure probabilities. It should be noted that the prior probabilities of the barriers originate from the text records, in contrast to the majority of previous works, which obtained prior probabilities from expert experience, thus resulting in uncertainty; this should be further examined.  
It is worth mentioning that the probabilities in Table 5 are conditional probabilities, under the precondition that the derailment accident occurred through the train process. A comparison of the results under the different accident scenarios in Table 5 reveals the importance of considering the various potential derailment risks in the safety assessment process. If a safety manager focuses only on the prevention of the first stage, the safety level is considered acceptable (**Assessment criteria for the safety level** in Table 6) with a train derailment probability of \(2.24\times 10^{-4}\).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Code** & **Definition** & **Count** & **Prior Probabilities** \\ \hline T110 & \begin{tabular}{c} Rack, Roadbed and Structures; Wide gage \\ (due to defective or missing crossties) \\ \end{tabular} & 1309 & 0.1645\% \\ \hline H702 & Switch improperly lined & 1355 & 0.1703\% \\ \hline T314 & Switch point worn or broken & 600 & 0.0754\% \\ \hline T207 & \
\begin{tabular}{c} Broken Rail—Detail fracture from shelling \\ or head check \\ \end{tabular} & 542 & 0.0681\% \\ \hline H307 &
\begin{tabular}{c} Shoving movement, man on or at leading \\ end of movement, failure to control \\ \end{tabular} & 524 & 0.0646\% \\ \hline... &... &... &... \\ \hline \hline \end{tabular}
\end{table}
Table 4: Prior probabilities of the basic events.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **1** & **2** & **3** \\ \hline Prior probabilities of successful derailment & \(3.00\times 10^{-3}\) & \(1.31\times 10^{-1}\) & \(3.06\times 10^{-2}\) \\ Posterior probabilities of successful derailment (give successful safety barriers) & \(4.00\times 10^{-3}\) & \(1.30\times 10^{-2}\) & \(-\) \\ Failure probabilities of first stage & \(2.71\times 10^{-1}\) & \(1.30\times 10^{-2}\) & \(2.71\times 10^{-2}\) \\ Failure probabilities of second stage & \(1.30\times 10^{-2}\) & 1.00 & \(1.31\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: The probabilities of actual accidents and safety layer failure.