## 3 Case Research
### Bayesian Network Construction
#### 3.2.2 Intermediate Event Probability Analysis  
Through the logical connections between events, we can gradually determine the probabilities of intermediate occurrences using the FBN model and associated probability computation techniques. The FTA model can be converted to the FBN model through logical gates such as OR gates or AND gates. According to the reasoning logic of the FBN, we will proceed with the relevant calculations.  
(1) OR Gate. According to Table 6 and Figure 4, the conditional probability table for intermediate event C1 corresponding to basic events X\({}_{26}\), X\({}_{27}\), and X\({}_{28}\) is obtained, as shown in Table 8. The terms \"Yes\" and \"No\" are used to indicate whether event C1 occurs or not. The GeNle (4.1.4190.0) software is utilized to compute the probability of intermediate events.  
(2) AND Gate. According to Table 6 and Figure 4, the conditional probability table for intermediate event N1 corresponding to basic events X\({}_{1}\), X\({}_{2}\), and X\({}_{3}\) is obtained, as shown in Table 9. The terms \"Yes\" and \"No\" are used to indicate whether event B1 occurs or not. The GeNle (4.1.4190.0) software is utilized to compute the probability of intermediate events.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Basic Events** & **Probabilities** & **Basic Events** & **Probabilities** & **Basic Events** & **Probabilities** \\ \hline X\({}_{1}\) & \(3.105\times 10^{-3}\) & X\({}_{12}\) & \(3.826\times 10^{-2}\) & X\({}_{23}\) & \(1.907\times 10^{-2}\) \\ X\({}_{2}\) & \(2.233\times 10^{-3}\) & X\({}_{13}\) & \(3.507\times 10^{-4}\) & X\({}_{24}\) & \(5.477\times 10^{-3}\) \\ X\({}_{3}\) & \(6.141\times 10^{-4}\) & X\({}_{14}\) & \(3.507\times 10^{-4}\) & X\({}_{25}\) & \(7.524\times 10^{-2}\) \\ X\({}_{4}\) & \(5.33\times 10^{-2}\) & X\({}_{15}\) & \(3.507\times 10^{-4}\) & X\({}_{26}\) & \(2.307\times 10^{-2}\) \\ X\({}_{5}\) & \(2.873\times 10^{-2}\) & X\({}_{16}\) & \(8.264\times 10^{-3}\) & X\({}_{27}\) & \(1.136\times 10^{-2}\) \\ X\({}_{6}\) & \(3.685\times 10^{-2}\) & X\({}_{17}\) & \(8.264\times 10^{-3}\) & X\({}_{28}\) & \(2.804\times 10^{-2}\) \\ X\({}_{7}\) & \(2.804\times 10^{-2}\) & X\({}_{18}\) & \(2.307\times 10^{-2}\) & X\({}_{29}\) & \(7.514\times 10^{-2}\) \\ X\({}_{8}\) & \(3.018\times 10^{-3}\) & X\({}_{19}\) & \(2.091\times 10^{-2}\) & X\({}_{30}\) & \(5.282\times 10^{-2}\) \\ X\({}_{9}\) & \(2.523\times 10^{-2}\) & X\({}_{20}\) & \(1.576\times 10^{-3}\) & X\({}_{31}\) & \(7.529\times 10^{-2}\) \\ X\({}_{10}\) & \(3.267\times 10^{-3}\) & X\({}_{21}\) & \(2.523\times 10^{-3}\) & X\({}_{32}\) & \(6.19\times 10^{-3}\) \\ X\({}_{11}\) & \(3.453\times 10^{-3}\) & X\({}_{22}\) & \(9.973\times 10^{-5}\) & & \\ \hline \hline \end{tabular}
\end{table}
Table 7: Prior probability values of root nodes.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline Notation & & & & & & & \\ \hline X\({}_{26}\) & & & 0 & & & 1 & & \\ X\({}_{27}\) & 0 & & & 1 & & 0 & 1 & \\ X\({}_{28}\) & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 1 \\ C\({}_{1}\) (Yes) & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ C\({}_{1}\) (No) & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Conditional probabilities for C1.