## 7 Conclusions  
In this paper, a novel method for the reliability estimation of probabilistic and non-probabilistic hybrid structural systems is proposed and numerically validated. Differing from those methods that produce an interval of the failure probability prediction, the proposed method yields a single value reliability prediction that is sufficiently accurate. In addition, the following conclusions are drawn:  
1. The decorrelation between the random variables and the interval variables decreases the influence of the interval variables' distributions on the system's failure probability;
2. The proposed method is robust against the change of variable distributions; and  
\begin{table}
\begin{tabular}{c c c c} \hline  & **Parameter 1** & **Parameter 2** & **Variables Type** \\ \hline Width of main arch ring \(b(\text{m})\) & 10 & 0.0067 & Normal distribution \\ Thickness of main arch ring \(h_{1}(\text{m})\) & 0.606 & 0.004 & Normal distribution \\ Pavement thickness \(h_{2}(\text{m})\) & 0.25 & 0.003 & Normal distribution \\ Elastic modulus of concrete \(E_{5}(\text{MPa})\) & 3.25 \(\times\) 10\({}^{4}\) & 1.08 \(\times\) 10\({}^{3}\) & Normal distribution \\ Reinforcement area \(A_{5}(\text{m}^{2})\) & 7.126 \(\times\) 10\({}^{-3}\) & 2.380 \(\times\) 10\({}^{-4}\) & Normal distribution \\ Thickness of protective layer \(a_{5}(\text{m})\) & 0.05 & 0.003 & Normal distribution \\ Concrete unit weight \(\gamma_{1}(\text{kN}/\text{m}^{3})\) & 25 & 1.25 & Interval distribution \\ Packing unit weight \(\gamma_{2}(\text{kN}/\text{m}^{3})\) & 18 & 0.9 & Interval distribution \\ Pavement unit weight \(\gamma_{3}(\text{kN}/\text{m}^{3})\) & 24 & 1.2 & Interval distribution \\ Vehicle load \(F(\text{kN})\) & 300 & 15 & Interval distribution \\ Tensile strength of reinforcement \(f_{sd}(\text{MPa})\) & 3.20 \(\times\) 10\({}^{5}\) & 1.60 \(\times\) 10\({}^{4}\) & Interval distribution \\ \hline \end{tabular} For the normal distribution, parameters 1 and 2 represent the mean and standard deviation, respectively, and for the interval distribution, parameters 1 and 2 represent the midpoint and radius, respectively.  
\end{table}
Table 8: Values of the basic parameters in Section 6.1.  
3. The error of failure probability estimation produced by the proposed method decreases as the failure probability decreases, demonstrating its promising engineering potential.  
Conceptualization, Y.P. and Z.X.; methodology, Y.P. and Z.X.; software, Y.P.; validation, X.C. and Z.X.; formal analysis, X.C. and Q.W.; investigation, Y.P. and Z.X.; resources, X.C.; data curation, Y.P. and Z.X.; writing--original draft preparation, Y.P. and Z.X.; writing--review and editing, Y.P. and Z.X.; visualization, Y.P. and Q.W.; supervision, X.C. and Q.W.; project administration, X.C. and Z.X.; funding acquisition, X.C. and Z.X. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (No. 52178301) and the Science Research Foundation of Wuhan Institute of Technology (No. K2021030).  
Not applicable.  
Data Availability Statement: Data sharing is not applicable to this article.  
The authors declare that they have no conflict of interest with respect to the study, authorship, or publication of this article.