## 3 Results and Discussion
### System Reliability

Table 9: The minimum reliability index of each slab segment under different damage cases of hinge joints. \[\beta_{5-case8} =0.1136\times 4.253+0.0606\times 4.616+0.3721\times 4.470+0.3084 \times 4.481+0.1454\times 4.235=4.424.\] \[\beta_{5-case9} =0.1055\times 4.250+0.1020\times 4.587+0.5851\times 4.317+0.1020 \times 4.587+0.1055\times 4.250=4.357.\]  
In order to verify the applicability of the proposed system reliability evaluation method, the system reliability indexes were also calculated by traditional methods under different damage cases of hinge joints according to Equations (5) and (6). The results are shown in Table 10.  
Then, the calculation results of the proposed method in this paper and the traditional methods are compared with the target reliability index, as shown in Figure 6. At present, the system reliability does not have a specified target reliability index. Therefore, the target reliability index of the component is adopted as the evaluation criteria. In accordance with the standard [39], the target reliability index is chosen for the RC2 reliability class, \(\beta_{\rm T}=4.2\). As can be seen form Table 10 and Figure 6, the average values of the system reliability indexes calculated by the series method are mostly less than the target reliability index (4.2). In particular, when the hinge joints are intact, the system reliability index is already close to the target reliability index (4.2). When the reliability index is less than the target reliability index, it means that the structure has failed. Obviously, the calculation results of the series method are too conservative and may result in an unreasonable allocation of maintenance funds in maintenance management. The lower bound value of \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Case Number**} & \multicolumn{2}{c}{**Series Method**} & \multicolumn{2}{c}{**Parallel Method**} \\ \cline{2-5}  & **Lower Bound** & **Upper Bound** & **Lower Bound** & **Upper Bound** \\ \hline Intact & 4.104 & 4.314 & 4.698 & \(+\infty\) \\ Case 1 & 4.038 & 4.232 & 4.673 & \(+\infty\) \\ Case 2 & 3.992 & 4.176 & 4.612 & \(+\infty\) \\ Case 3 & 3.986 & 4.176 & 4.633 & \(+\infty\) \\ Case 4 & 4.007 & 4.238 & 4.608 & \(+\infty\) \\ Case 5 & 4.023 & 4.251 & 4.567 & \(+\infty\) \\ Case 6 & 3.988 & 4.254 & 4.594 & \(+\infty\) \\ Case 7 & 3.986 & 4.248 & 4.594 & \(+\infty\) \\ Case 8 & 4.000 & 4.235 & 4.616 & \(+\infty\) \\ Case 9 & 3.985 & 4.250 & 4.587 & \(+\infty\) \\ \hline \hline \end{tabular}
\end{table} 
Table 10: System reliability indexes obtained by traditional methods. Figure 6: Comparisons of system reliability indexes calculated by different methods. the system reliability index calculated by the parallel method is the maximum reliability index of all slab segments under different damage cases, and the upper bound value is infinite. The results may overestimate the reliability level of the structure and cannot objectively evaluate the actual structural performance, which will result in potential security risks in the structure. The calculation results of the method proposed in this paper are larger than the average values of the series method and smaller than the lower bound values of the parallel method. It shows that the method proposed in this paper is more reasonable and accurate than the traditional methods. In addition, as the number of damaged hinge joints increases, the system reliability indexes show a declining trend, but it is not a linear changing process. Comparing different damage cases of hinge joints, it can be inferred that the influence of hinge joint 1 or 2 on the system reliability is greater than that of hinge joint 3 or 4 on the system reliability.