# Research on the Reliability of Bridge Structure Construction Process System Based on Copula Theory
## 4 Conclusions  
In this paper, based on an in-depth study of the existing relevant reference, a method of using Copula theory for structural system reliability analysis in the construction phase of bridge projects was proposed, and the study mainly achieved the following conclusions.  
Figure 4: The influence of the change of the Kendall rank correlation coefficient on the reliability index of the system when the change range of the Kendall rank correlation coefficient is 0.8–1.0.  
Figure 3: Effect of the change of the failure modes combination correlation coefficient on the reliability index of the system.  
(1) The theory and method of calculating the reliability of the traditional system of bridge structures were summarized in the light of the existing research, and the shortcomings of the traditional theory in calculating the reliability of the system were analyzed. The idea of using Copula theory to establish the correlation between failure modes was proposed. (2) The basic contents of Copula theory were introduced in detail, and the Copula theory was extended to the field of reliability calculation of bridge structural systems. (3) The method proposed in this paper was used to calculate the examples in reference [34], and the formula of Copula theory was appropriately improved according to the calculation results. After comparing the results with the original reference, it was concluded that the improved Copula theory for calculating the reliability of the bridge structure system overcomes the problem of safety bias of the traditional Copula theory, and can be used with the traditional \"interval estimation method\", which is simple to calculate, easy to understand, is suitable for large and complex bridges, and has a certain guiding effect on engineering practice. (4) Finally, the sensitivity analysis was carried out from two aspects, and the results showed that the influence of the correlation between the failure modes on the failure probability of the structural system must not be ignored in engineering.  
This paper has achieved milestones in the study of the reliability of bridge structure construction process system using Copula theory, but there are still areas that need to be considered and improved. Based on the research process and results of this paper, the general directions of the subsequent research are as follows. (1) In this paper, only the correlation between two failure modes was established, and the analysis was carried out from the perspective of two-dimensional Copula function, which is not closely enough connected with the actual engineering. The Copula function with a higher dimension should be used for calculation as much as possible so as to improve the connection with the actual project. (2) In this paper, only a coefficient was generalized into the improvement of the calculation theory to weaken the situation that the same failure mode appears many times in the calculation, and this calculation is not accurate enough. The weights of all failure modes and their combinations should be calculated and the weights brought into the calculation theory as coefficients so as to further improve the accuracy of the calculation results.  
Conceptualization, Q.L.; methodology, T.Z.; validation, T.Z.; formal analysis, Q.L.; resources, Q.L.; data curation, T.Z.; writing--original draft preparation, T.Z.; writing--review and editing, Q.L.; supervision, Q.L. All authors have read and agreed to the published version of the manuscript. This research received no external funding. This study did not require ethical approval. This study did not involve humans. This study did not involve humans.  
All the data used in this study can be found in the article. The authors declare no conflict of interest.