## 1 Introduction
[23] proposed a method for the system reliability analysis of engineering structures by considering multiple dependent failure modes based on a copula and introduced copula functions into the narrow bounds theory. [PERSON] et al. [24] applied a copula technique to describe the nonlinear dependence among typical component seismic demands of the commonly used concrete continuous girder bridge style and analyzed the influence of the real dependence among components on the seismic reliability. [PERSON] et al. [25] used a copula function to model the dependency between two degradation processes in a bivariate degradation model of a coherent system. [PERSON] et al. [26] proposed a system reliability evaluation method based on non-parametric copulas and utilized four examples to illustrate the feasibility and efficiency of the proposed method. Significant studies have been devoted to the reliability evaluation of complex systems based on copula functions. However, most studies only use the binary copula function to consider the case where two failure modes occur together. For a bridge structure composed of multiple components, the system reliability evaluation may consider the occurrence of multiple failure modes simultaneously. Therefore, a multivariate copula function needs to be constructed. In order to evaluate the bridge system reliability, the relationship between individual components and the overall system should be identified first, such as a series system, parallel system, and series-parallel system. This relationship is also called the failure criterion of the bridge system. [PERSON] et al. [PERSON] et al. (2020) proposed a failure criterion where the failure of any two adjacent components would cause the entire system to fail and calculated the system reliability using a simple supported hollow slab beam as an example. [PERSON] et al. [PERSON] et al. (2020) assumed that the failure of any three adjacent beams would lead to the destruction of the entire structure and calculated the system reliability of a widened T-girder bridge using the proposed failure criterion. [PERSON] et al. [PERSON] et al. (2020) proposed a semi-analytical method to assess the time-dependent reliability of an aging series system subjected to non-stationary loads and considered that the failure of any single component would cause the entire system to fail. However, the selection of the failure criterion is ambiguous in the system reliability evaluation of the bridge structure. There are no rules for determining which failure criterion should be chosen. Therefore, multiple failure criteria should be comprehensively considered to make the evaluation result more reasonable. The AHP-EW method is introduced to solve this problem, which can obtain the comprehensive weight of the subjective weight and the objective weight of each evaluation index. The analytic hierarchy process entropy weight (AHP-EW) method is gradually being accepted and recognized in various research fields [PERSON] et al. (2020); [PERSON] et al. (2020); [PERSON] et al. (2020). This paper develops a novel method that can be used to evaluate the system reliability of the bridge structure by considering multiple failure criteria based on copulas and the AHP-EW method. In order to obtain accurate evaluation results, the system reliability evaluation under each failure criterion was used to adapt the copula theory. By considering the joint failure of multiple components, the multivariate copula functions were constructed. The AHP-EW method was used to comprehensively consider the subjective and objective weights of each failure criterion in the system reliability evaluation and construct the analytic hierarchy model. The specific process of the system reliability evaluation using the method proposed in this paper is shown in Figure 1. Then, a simply supported RC hollow slab bridge composed of nine slab segments was selected as the numerical example to illustrate the applicability of the proposed method.