## 6 Results: Application of the Sensitivity Analysis on the \"Traffic Jam Chauffeur\"
### Comparing Our Results with Those of an Expert  
In order to evaluate the relevance of the proposed sensitivity assessment method, we decided to compare our sensitivity results (Table 12) obtained in Section 6.1 with the opinion of an expert. To do that, we asked an expert to classify the same logical situations (all described in Table 4) from the most critical to the least critical. The classification is performed using the pairwise comparison with the analogy of the well-known multi-criteria decision-making approach called Analytic Hierarchy Process (AHP). This approach aims to compare criteria and their importance. In our work, the aim is to compare situations according to their criticality. The question is: which criterion (resp. situation) is more important (resp. critical), and how much more on a scale of 1-9? The scale is as follows: 1--Equal Importance, 3--Moderate importance, 5--Strong importance, 7--Very strong importance, 9--Extreme importance. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & **Lane Changing Left** & **GiveBack** \\ \cline{2-4} Functional Situation of “Car Following” & Event impacting functional situation & e\({}_{8.7}=\Delta\)(A1\_1, A1\_0) & e\({}_{8.9}=\Delta\)(A5\_1, A5\_2) \\ \cline{2-4}  & Sensitivity & S(e\({}_{8.7})=1 & S(e\({}_{8.8})=1\) \\ \cline{2-4}  & the event & S(e\({}_{8.8})=1\) & S(e\({}_{8.9})=1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Sensitivities of events impacting the functional level for Y8. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{Events} & e\({}_{8.1}\) = & e\({}_{8.2}\) = & e\({}_{8.3}\) = & e\({}_{8.4}\) = & e\({}_{8.5}\) = & e\({}_{8.6}\) = & e\({}_{8.7}\) = & e\({}_{8.8}\) = & e\({}_{8.9}\) = \\  & \(\Delta\)(A1\_2) & \(\Delta\)(A2\_2) & \(\Delta\)(A4\_2) & \(\Delta\)(A1\_1) & \(\Delta\)(A4\_2) & \(\Delta\)(A2\_2) & \(\Delta\)(A1\_1, & \(\Delta\)(A1\_2, & \(\Delta\)(A5\_1, \\ & & & & A1\_1) & A4\_1) & A2\_1) & A1\_0) & A1\_0) & A5\_2) \\ \hline \multirow{2}{*}{Sensitivity values} & S(e\({}_{8.1}\)) & S(e\({}_{8.2}\)) & S(e\({}_{8.3}\)) & S(e\({}_{8.4}\)) & S(e\({}_{8.5}\)) & S(e\({}_{8.6}\)) & S(e\({}_{8.7}\)) & S(e\({}_{8.8}\)) & E(e\({}_{8.9}\)) \\  & \(=1.4\) & \(=0.4\) & \(=1.6\) & \(=1\) &As we can observe, these results give a four-level classification (rank 1 for S\({}_{8}\), rank 2 for S\({}_{7}\), S\({}_{6}\) and S\({}_{4}\), rank 5 for S\({}_{5}\), S\({}_{3}\) and S\({}_{2}\), rank 8 for S\({}_{1}\)) which is totally different from our classification results as mentioned in Table 12. Even if the consistency ratio of the expert is quite good as we obtain 1.6% (0.016 \(<\) 0.1), the problem with such a logic is that the differences between the impact degrees of the ranges are not taken into account: two different ranges affecting the same technology or component are considered as having the same risk level. Thus, we proposed that another classification be made, but considering the fact that the ranges of values have their proper degree of impact on the sensor technologies or on decision and actuation components. Therefore, the new principle used by the expert is that \"A situation is more critical than another if the number of sensor technologies, decision and actuation components that are sensitive to value ranges is more important\". Figure 4 shows the resulting classification. \begin{table}
\begin{tabular}{c c c} \hline
**Sensitivity Distribution** & **Priority/Rank** & **Logical Situations** \\ \hline
0 & 5 & Y\({}_{1}\) \\ \hline
3.45 \(\times\) 10\({}^{-2}\) & 4 & Y\({}_{2}\) \\ \hline
12.07 \(\times\) 10\({}^{-2}\) & 3 & Y\({}_{6}\), Y\({}_{5}\) \\ \hline
13.79 \(\times\) 10\({}^{-2}\) & 2 & Y\({}_{4}\), Y\({}_{3}\) \\ \hline
22.41 \(\times\) 10\({}^{-2}\) & 1 & Y\({}_{8}\), Y\({}_{7}\) \\ \hline \end{tabular}
\end{table} 
Table 12: Summary of the sensitivity results obtained with the eight logical situations described in Section 6.1. Figure 3: The expert’s classification of the logical situations using the first principle.