## 4 Case Study
### System Failure Consequence Analysis
#### 4.5.3 Determination of the Possibilities of Conditioning Events with/without Safety Barriers  
As shown in Table 19, the experts' opinions on the possibilities of conditioning events in the ET were obtained. Then, they were converted into the corresponding IVIFNs (see Table 20) according to Table 3. Subsequently, these IVFFNs were aggregated and defuzzified into crisp values using Equations (15) and (17).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**C\(m\)** & **C1** & **C2** & **C3** & **C4** \\ \hline C1 & ([0.38, 0.42], [0.07, 0.47], [0.29, 0.41], [0.32, 0.58]) & [0.13, 0.53]) & [0.12, 0.58]) & [0.08, 0.38]) \\ C2 & ([0.13, 0.53], [0.38, 0.42], [0.32, 0.62], [0.32, 0.62], [0.3819, 0.6828]) & CO3 & ([0.2189, 0.4218], [0.3002, 0.5782]) \\ C3 & ([0.21, 0.58], [0.08, 0.38], [0.38, 0.42], [0.38, 0.42], [0.38, 0.42], [0.38, 0.47], [0.22, 0.58]) \\ C4 & ([0.32, 0.62]) & [0.52, 0.72]) & [0.03, 0.47]) & [0.22, 0.58]) \\ \hline \hline \end{tabular}
\end{table}
Table 16: IVFFNs of comparison judgment matrix for criteria from Expert No.3.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Failure** & \multicolumn{4}{c}{**Expert No.1**} & \multicolumn{4}{c}{**Expert No.2**} & \multicolumn{4}{c}{**Expert No.3**} \\ \cline{2-11}
**Outcomes** & **C1** & **C2** & **C3** & **C4** & **C1** & **C2** & **C3** & **C4** & **C1** & **C2** & **C3** & **C4** \\ \hline CO1 & H & VH & H & H & H & VH & H & H & H & H & H & VH \\ CO2 & VH & VH & VH & VH & VH & H & H & VH & VH & H & VH & H \\ CO3 & L & M & L & VL & L & L & L & VL & VL & M & L & VL \\ CO4 & H & H & H & H & H & VH & M & VH & M & H & H & H \\ CO5 & VL & VL & VL & L & L & VL & VL & VL & VL & VL & VL & VL \\ CO6 & VH & VH & VH & VH & VH & VH & VH & VH & VH & VH & VH & VH \\ \hline \hline \end{tabular}
\end{table}
Table 17: Experts’ linguistic judgments on the effect of each failure outcome on different consequence severity types.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Failure Outcomes** & **Severity Index (SJ)** & **Failure Outcomes** & **Severity Index (SJ)** \\ \hline CO1 & ([0.6194, 0.8226], [0, 0.1774]) & CO4 & ([0.5937, 0.8012], [0, 0.1988]) \\ CO2 & ([0.6876, 0.88897], [0, 0.1103]) & CO5 & ([0.1169, 0.3172], [0.3819, 0.6828]) \\ CO3 & ([0.2189, 0.4218], [0.3002, 0.5782]) & CO6 & ([0.7, 0.9], [0, 0.1]) \\ \hline \hline \end{tabular}
\end{table}
Table 18: The severity indexes of different failure outcomes.  
4.5.4. Computation of the Failure Consequence Severity with/without Safety Barriers  
Using Equation (32), the detailed Formulas (53)-(58) for calculating the probability of each failure outcome were obtained. Using these formulas and Equation (33), the failure consequence severity with/without the SBs of the storage tank was calculated, and the calculation results are shown in Figure 8. As can be seen in Figure 7, the probability of critical events only decreases when preventive SBs are set. As shown in Figure 8, the failure consequence severity is reduced only when protective SBs are used. Thus, it is obvious that preventive SBs only have an effect on the probability of critical event occurrence, while protective SBs only affect the failure consequence severity.  
\[P_{\text{CO1}}=P_{EV1} \tag{53}\]  
\[P_{\text{CO2}}=(1-P_{EV1})\times P_{EV2}\times P_{EV3}\times P_{EV4} \tag{54}\]  
\[P_{\text{CO3}}=(1-P_{EV1})\times P_{EV2}\times P_{EV3}\times(1-P_{EV4}) \tag{55}\]  
\[P_{\text{CO4}}=(1-P_{EV1})\times P_{EV2}\times(1-P_{EV3})\times P_{EV4}+(1-P_{ EV1})\times(1-P_{EV2})\times(1-P_{EV3})\times P_{EV4} \tag{56}\]  
\[P_{\text{CO5}}=(1-P_{EV1})\times P_{EV2}\times(1-P_{EV3})\times(1-P_{EV4})+(1- P_{EV1})\times(1-P_{EV2})\times P_{EV3}\times(1-P_{EV4}) \tag{57}\]  
\[+(1-P_{EV1})\times(1-P_{EV2})\times(