## 5 Conclusions  
The system reliability evaluation results of the bridge structure by considering only a single failure criterion cannot objectively and accurately reflect the actual condition of the bridge system. The aim of the paper was to propose a novel method to evaluate bridge system reliability by considering multiple failure criteria based on multivariate copulas and the AHP-EW method. Bridge structures are complex structures composed of multiple components. Considering the joint failure of multiple components, the multivariate copula functions were constructed. Then, the system reliability under each failure criterion was obtained based on different copulas. According to the AHP-EW method and the system reliability evaluation results of each failure criterion, the system reliability obtained by considering multiple failure criteria was evaluated. The numerical example of the simply supported RC hollow slab bridge was used for the process of system reliability evaluation by considering multiple failure criteria. The method proposed in this paper is not only applicable to the numerical example, but it can also be a utility method for the technical community to evaluate the system reliability of structures with multiple components like the numerical example. The following conclusions were drawn:  
* Copulas provided an effective tool for constructing the joint distribution of multiple failure modes in the system reliability evaluation of a bridge structure. The binary copulas and ternary copulas were constructed to calculate the system failure probability of each failure criterion. * According to the three failure criteria proposed by the previous research, the copula functions were used to calculate the bridge system failure probability. The results showed that the greater the number of any adjacent failed slab segments, the smaller the system failure probability, namely \(P_{f_{1}}(1.099\times 10^{-4})>P_{f_{1}}(1.049\times 10^{-5})>P_{f_{11}}(4.356 \times 10^{-6})\). This law was consistent with the objective facts, and proved the applicability of the copula function in the bridge system reliability evaluation once again. * It is important to select the best-fitting copula from the candidate copulas. By comparison, different system reliability evaluation results will be obtained based on different copulas. Compared with the system reliability evaluation results of three failure criteria based on the most suitable Gaussian copula, the system reliability evaluation results obtained based on the Clayton copula were the closest, and the system reliability evaluation results obtained based on the Frank copula were the most different. * Among the subjective weights, the weight of failure criterion II (0.3849) was the largest and the weight of failure criterion III(0.2536) was the smallest. Among the objective weights, the weight of failure criterion I (0.4100) was the largest and the weight of failure criterion II (0.1919) was the smallest. The comprehensive weight of each failure criterion obtained using the AHP-EW method avoided the deviation caused by the subjective weighting method and the absolutization caused by the objective weighting method, and overcame the shortcomings of the single-weight method. The comprehensive weights of the three failure criteria were 0.4588, 0.2287, and 0.3125, respectively. \begin{table}
\begin{tabular}{c c c c} \hline
**Index Layer** & **Subjective Weight** & **Objective Weight** & **Comprehensive Weight** \\ \hline Failure Criterion I & 0.3615 & 0.4100 & 0.4588 \\ Failure Criterion II & 0.3849 & 0.1919 & 0.2287 \\ Failure Criterion III & 0.2536 & 0.3981 & 0.3125 \\ \hline \end{tabular}
\end{table} 
Table 14: The evaluation indexes of bridge system reliability and the weights of indexes.