# Fuzzy Preference Programming Framework for Functional Assessment of Subway Networks
## 3 Methodology and Implementation
### Failure Impacts Module
#### 3.1.3. Compute the Severity Scores (S\({}_{\text{i}}\))
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Failure Impact**} & \multirow{2}{*}{**Attribute**} & \multirow{2}{*}{**Definition**} & \multicolumn{2}{c}{**Score**} \\ \cline{3-5}  & & & **Maximum** & **Minimum** \\ \hline \multirow{3}{*}{Financial} & Replacement/repair cost & Direct cost for replacement/repair of the failed component & Replacement cost/element & Repair cost/element \\ \cline{2-5}  & Loss of revenue & Profit loss due to service interruption, factor of user traffic frequency, time to repair and fare & 100\% & 0\% \\ \hline \multirow{3}{*}{Operational} & Ease of providing alternative & Measured by the decision maker based on the available bus stations per area & Normalized based on maximum and minimum number of bus stops/station/network \\ \cline{2-5}  & Time to repair & Required time to return the failed component to a full functioning state & 365 days & 0 days \\ \hline \multirow{3}{*}{Social} & User Traffic Frequency & The number of users accessing station and affected by the service interruption & Normalized based on maximum ridership per network \\ \cline{2-5}  & & Defined by the decision maker as the maximum allowable number of interruptions per year & 6 & 0 \\ \cline{1-1} \cline{2-5}  & & Estimated based on element configuration and decision maker & Full interruption = 100\% & No interruption = 0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Failure impacts Definition and Scales. where the interruptions were considered in weekends only. Since STA4 had a higher probability of failure, it was assumed the time to repair will be longer with a value proportional to the difference in probabilituy of failure values calculated. The fourth action of Major Rehabilitation was used as the scores input for STA4 and STA6 in the failure impacts module calculations. User traffic frequency for all stations was obtained from online data available and normalized based upon the total ridership of the network under study. Calculations for computing failure impacts criteria scores and normalizing them is presented in Table 5 for financial impacts of failure. The actual value for revenue loss per station and the expected repair cost are shown. Normalized values for each of the financial impacts sub-attributes are also presented. Calculations are done using MS Excel(r) workbook where the entire framework calculations is located. Scores for social impacts of failure are presented in Table 6. For each station, the service continuation value is assigned based upon the M&R scenario selected. In our case study segment, STA4 and STA6 required rehabilitation. Since STA6 is currently under rehabilitation, the actual rehabilitation value was used. STA6 is undergoing rehabilitation actions only on weekends to minimize the service disruption. Consequently, time to repair is calculated only on weekends for every given week, giving an overall service continuation percentage of 2/7 = 0.285. While the rehabilitation actions were performed, a whole service disruption is expected and the entire station is closed, thus the interruption rate is total (1.0) for weekend rehabilitation activities. Operational impacts of failure scores are presented in Table 7.  
Ease of providing alternative is calculated based upon the number of bus stops surrounding the metro station and normalized based upon the maximum number of stops available per station per study segment. Time to repair is the actual time required to return the failed component to a full functioning state. Time to repair of STA4 and STA6 are assumed proportional to their PoF values.