## 4 Results and Discussion
### Analysis of Independence Between BEs  
In this section, the effect of independence between basic events on the quantitative analysis of storage tank probability is analyzed, and the prediction results of the constructed ANN model are compared with the TE failure probability derived from the traditional DFT calculation method. The comparison results show that the average error of the failure probability of the top event predicted by the ANN model is 2.14%. Compared with the 3.44% of the traditional DFT method, the performance of the ANN model is improved by 38%. This performance enhancement may be attributed to the unknown dependencies between BEs in DFT, which are often ignored in traditional methods. The advantage of the ANN model is its ability to capture and account for these interdependencies between input variables, thus outperforming the traditional fault tree computation methods in terms of prediction accuracy. Furthermore, this property of ANN models is particularly important when performing probabilistic calculations for complex systems. Since real-world systems often involve multiple interdependent variables, ANN models can model these complex interactions more accurately, providing a more accurate tool for probabilistic failure calculations. This section analyzes the impact of the independence between basic events on the quantitative probability analysis of storage tanks and compares the predicted results of the constructed artificial neural network (ANN) model with the failure probabilities obtained using the traditional DFT calculation method. The results of the output set of the test dataset, as shown in Figure 7, are used to calculate the average error of the top event for both models using the following formula and to make a comparison [17]. \[T=\frac{\sum\limits_{i=1}^{30}P_{i}/30}{\textit{Top event probability}} \tag{10}\]  
where \(T\) is the calculated average error, \(\sum\limits_{i=1}^{30}P_{i}/30\) is the sum of the top event results for the two models' test datasets, consisting of 30 datasets, with the denominator being the failure probability of the top event, 0.04255. By substituting both datasets into the formula and comparing the results, it was found that the average error of the top event failure probability predicted by the ANN model is 2.14%. Compared to 3.44% for the traditional DFT method, the ANN model's performance improved by 38%. This improvement in performance may be due to the unknown \begin{table}
\begin{tabular}{c c c c c c} \hline
**Rank \#** & **Contribution Factor** & **BEs \#** & **Rank \#** & **Contribution Factor** & **BEs \#** \\ \hline
1 & 0.08399 & X4 & 12 & 0.011869 & X21 \\
2 & 0.059301 & X22 & 13 & 0.002327 & X3 \\
3 & 0.026236 & X20 & 14 & 0.010162 & X6 \\
4 & 0.100024 & X19 & 15 & 0.017152 & X9 \\
5 & 0.073867 & X1 & 16 & 0.008302 & X15 \\
6 & 0.02441 & X10 & 17 & 0.047656 & X11 \\
7 & 0.049332 & X5 & 18 & 0.064706 & X12 \\
8 & 0.011497 & X18 & 19 & 0.084544 & X8 \\
9 & 0.019861 & X2 & 20 & 0.084576 & X14 \\
10 & 0.083958 & X7 & 21 & 0.034478 & X16 \\
11 & 0.014578 & X17 & 22 & 0.087173 & X13 \\ \hline \end{tabular} Note: The contribution factor is calculated to determine the contribution of each basic event to the top event failure by calculating the ratio of the failure probability of the basic event to the failure probability of the top event and normalizing the result [17].  
\end{table} 
Table 9: Ranking of contributions by BEs to TE. dependencies between basic events in the model design, which are often overlooked in traditional methods. The advantage of the ANN model is that it can capture and explain the interdependencies between input variables, making it superior to traditional fault tree calculation methods in terms of prediction accuracy. Additionally, this characteristic of the ANN model is especially important when performing probabilistic calculations for complex systems.