# Failure Mode and Effect Analysis for Cyber-Physical Systems
## 4 New RPN Criteria and Formula
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Level** & **Description** & **Criteria** \\ \hline \multirow{3}{*}{4} & \multirow{3}{*}{Moderate} & High number of light injuries \\  & & Reduced number of serious injuries \\  & & LI \(\geqslant\) 30 \\  & & 1 \(\leqslant\) SI \(\leqslant\) 10 \\  & & 773,400 € \(\leqslant\) C \(\leqslant\) 1,203,000 € \\ \hline \multirow{3}{*}{5} & \multirow{3}{*}{Moderate} & High number of light injuries \\  & & Moderate number of serious injuries \\  & & LI \(>\) 30 \\  & & 10 \(<\) SI \(\leqslant\) 30 \\  & & 1,203,000 € \(\leqslant\) C \(\leqslant\) 3,331,000 € \\ \hline \multirow{3}{*}{6} & \multirow{3}{*}{Moderate} & High number of light injuries and serious injuries \\  & & LI \(>\) 30 \\  & & CI \(>\) 30 \\  & & C \(>\) 3,444,000 € \\ \hline \multirow{3}{*}{7} & \multirow{3}{*}{High} & Reduced number of serious injuries and fatalities \\  & & 1 \(\leqslant\) SI \(\leqslant\) 10 \\  & & 1 \(\leqslant\) F \(\leqslant\) 10 \\  & & 910,000 € \(\leqslant\) C \(\leqslant\) 11,252,000 € \\ \hline \multirow{3}{*}{8} & \multirow{3}{*}{High} & Moderate number of serious injuries and fatalities \\  & & 10 \(<\) SI \(\leqslant\) 30 \\  & & 10 \(\leqslant\) F \(\leqslant\) 30 \\  & & 8,137,400 € \(\leqslant\) C \(\leqslant\) 27,312,000 € \\ \hline \multirow{3}{*}{9} & \multirow{3}{*}{Catastrophic} & High number of fatalities \\  & & F \(>\) 30 \\  & & C \(>\) 24,090,000 € \\ \hline \multirow{3}{*}{10} & \multirow{3}{*}{Catastrophic} & High number of serious injuries and fatalities \\  & & SI \(>\) 30 \\  & & F \(>\) 30 \\  & & C \(>\) 27,312,000 € \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c} \hline \hline
**Level** & **Description** & **Criteria** \\ \hline \multirow{3}{*}{1} & \multirow{3}{*}{Low} & Low damage to the railway track (\(\leqslant\) 1000 m) \\  & & 0 \(<\) C \(\leqslant\) 250,000 € \\ \hline \multirow{3}{*}{2} & \multirow{3}{*}{Low} & Low damage to 1 or more bogies \\  & & 250,000 € \(<\) C \(\leqslant\) 500,000 € \\ \hline \multirow{3}{*}{3} & \multirow{3}{*}{Low} & Low damage to the railway track and 1 or more bogies \\  & & 500,000 € \(<\) C \(\leqslant\) 750,000 € \\ \hline \multirow{3}{*}{4} & \multirow{3}{*}{Moderate} & 1 or more bogies derailment \\  & & 750,000 € \(<\) C \(\leqslant\) 1,250,000 € \\ \hline \multirow{3}{*}{5} & \multirow{3}{*}{Moderate} & 1 or more bogies derailment and access points destruction \\  & & 1 250,000 € \(<\) C \(\leqslant\) 1,750,000 € \\ \hline \multirow{3}{*}{6} & \multirow{3}{*}{Moderate} & Serious damage to the railway track (\(>\) 1000 m) \\  & & 1 or more bogies derailment and access points destruction \\  & & 750,000 € \(<\) C \(\leqslant\) 2,250,000 € \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Evaluation criteria to assess infrastructure impact. Table 5 displays the environmental costs where we considered carbon dioxide (CO\({}_{2}\)) emissions from fires. Our parameterization is based on the Sustainable Structural Design Methodology (SSD) formula RSSD (CO\({}_{2}\)) = PCO\({}_{2}\)\(\times\) QCO\({}_{2}\), where RSSD (CO\({}_{2}\)) is the result of the financial value of environmental impacts, PCO\({}_{2}\) is the carbon price of a ton of CO\({}_{2}\) emissions in euro/ton and QCO\({}_{2}\) is the total CO\({}_{2}\) equivalent emissions developed from the Life Cycle Assessment (LCA) analysis, declared in tons [20]. To calculate the total cost, we used the 2019 OCDE CO\({}_{2}\) emission tax for Portugal [21], which is 25 E/ tonne (t) CO\({}_{2}\) and the formula already mentioned. Table 5 shows our categorization for environmental costs, classified from 1 to 10, where 1 corresponds to Low and 10 to Catastrophic. While we used Portuguese data to develop our RPN criteria, it can apply to railway systems in other countries or even to other systems. However, for this purpose, our categorization will have to be adapted to the country's socio-economic context or the system's requirements. To a final risk estimation, we propose five different categories.