# Resilience Assessment of Beijing Subway Lines under Extreme Precipitation Weather
## 4 Case Study
### Risk Analysis of Changping Line
#### 4.2.2 Probability of Failure Mode  
According to the method in Section 2.3, the failure probability of the failure modes caused by extreme rainfall can be calculated as shown in the following steps.  
First, count the data of extreme rainfall days from 2018 to 2022. Here, rainfall in a single day exceeding 10 mm is considered extreme rainfall; therefore, there are 96 days of extreme rainfall in total.  
Second, combined with the failure data of 5 years, the number of failures in extreme rainfall days in the Changping Line can be obtained.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**First Level Subsystem** & **Failure Mode** & **Failure Cause** & **Secondary Sub-Function** \\ \hline \multirow{8}{*}{**Electromechanical system**} & \multirow{2}{*}{Environment control failure} & Extreme rainfall & Environment and equipment monitoring system \\ \cline{3-4}  & & Extreme rainfall & Integrated monitoring system \\ \cline{2-4}  & & Extreme rainfall & \begin{tabular}{c} Escalators, moving walks, and \\ barrier-free access \\ \end{tabular} \\ \cline{2-4}  & & \begin{tabular}{c} Lighting failure \\ Fire alarm failure \\ \end{tabular} & Extreme rainfall & \begin{tabular}{c} Low-voltage lighting \\ Automatic fire alarm system \\ \end{tabular} \\ \cline{2-4}  & & \begin{tabular}{c} Failure of fire extinguishing \\ equipment \\ \end{tabular} & Extreme rainfall & \begin{tabular}{c} Water supply and drainage \\ and fire extinguishing system \\ \end{tabular} \\ \cline{2-4}  & & \begin{tabular}{c} Platform door failure \\ Water supply and drainage \\ failure \\ \end{tabular} & Extreme rainfall & \begin{tabular}{c} Platform door \\ Access control system \\ \end{tabular} \\ \cline{2-4}  & & \
\begin{tabular}{c} HVAC equipment failure \\ \end{tabular} & Extreme rainfall &
\begin{tabular}{c} Ventilation air conditioning \\ and heating \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 4: The relationship of failure modes, failure causes, and sub-functions of the electromechanical system—examples.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**First Level Subsystem** & **Secondary Sub-Function** & **Expert Score** \\ \hline \multirow{8}{*}{**Electromechanical system**} & Environment and equipment monitoring system & 9 \\ \cline{2-3}  & Integrated monitoring system & 10 \\ \cline{2-3}  & Escalators, moving walks, and barrier-free access & 6 \\ \cline{2-3}  & Low-voltage lighting & 8 \\ \cline{2-3}  & Automatic fire alarm system & 9 \\ \cline{2-3}  & Water supply and drainage and fire extinguishing system & 9 \\ \cline{2-3}  & Platform door & 10 \\ \cline{2-3}  & Access control system & 8 \\ \cline{2-3}  & Ventilation air conditioning and heating & 8 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The importance evaluation results of the electromechanical system—examples.  
Third, according to the failure data, the failure probability of each failure mode can be calculated by the following equation:  
\[P_{failure}=\left(\begin{array}{c}\frac{\text{number of failures in rainy days}}{ \text{number of rainy days}\times\text{number of line stations}}\\ -\frac{\text{number of failures in normal weather}}{\text{number of normal days}\times\text{number of line stations}}\end{array}\right)\times 100\% \tag{4}\]  
According to Equation (4), the failure probability of the Changping Line can be calculated as shown in Table 6. The rest of the failure probability results are shown in Appendix A.  
Based on the above results, we can divide the failure probability of failure modes into five categories as shown in Table 7.