# Enhancing Reliability Analysis with Multisource Data:
## 2 Proposed Method to Mitigate Adverse Selection in Bridge Monitoring and MRR
### Procedure for Determining a Reliability Index to Close the Information Gap  
A reliability analysis uses WIM data and quantifies the risk of live loads exceeding structural load carrying capacities of bridges by calculating a reliability index. Therefore, the analysis outcome should provide decision-makers with a quantitative metrics regarding the associated risk for each bridge in Georgia and enable decision makers to mitigate overconfidence problems in measuring the bridge capacity or posting bridges due to conservativeness in LR. Furthermore, it should reduce the miscalculated risk which hinges on incomplete information resulting from uncertainties in predicting the rate of vehicle growth and bridge deterioration, ultimately reducing the likelihood of adverse selection problems.  
The limit state function, g, that forms the basis for a reliability analysis is defined by Equation (1), where the strength of a bridge and load effect is represented by \(R\) and \(Q\), respectively. It is noted that both \(R\) and \(Q\) are random variables, and thus it is assumed that their true value cannot be determined with absolute certainty.  
\[g=R-Q \tag{1}\]  
Structural behavior is considered as satisfactory if the limit state, g, is greater than 0 or (\(R-Q\)) > 0, and unacceptable when (\(R-Q\)) \(\leq\) 0. Since the probabilistic distribution of R and Q is not precisely known, a method known as the First Order Second Moment (FOSM) probabilistic analysis [26; 27] is used employing the mean and standard deviation, R and Q, respectively. In the FOSM analysis, the probability of failure (\(p_{f}\)) is calculated by Equation (2), where \(\mu\) and \(\sigma\) are the mean and standard deviation. \(\mu_{R}\) is the mean resistance of bridges and \(\mu_{Q}\) is the mean WIM load. Similarly, \(\sigma_{R}\) is the standard deviation of bridge resistance and \(\sigma_{Q}\) is the standard deviation of a WIM load distribution. The reliability Index (\(\beta\)) is determined by Equation (3), and \(\phi^{-1}\) is the inverse normal distribution function.  
\[p_{f}=\phi\left(-\frac{\mu_{R}-\mu_{Q}}{\sqrt{{\sigma_{R}}^{2}+{\sigma_{Q}}^{ 2}}}\right) \tag{2}\]  
\[\beta=\phi^{-1}\left(1-p_{f}\right) \tag{3}\]  
In this study, we assume that WIM truck weights and NBI capacities are random quantities, and a normal distribution is used to represent the weight data. A probabilistic distribution representing the capacity is determined by taking the operating LR as the mean of the distribution, and the standard deviation (\(\sigma_{R}\)) is assumed to be within 10 percent of the mean value (\(\mu_{R}\)) [14; 27]. This is a fairly conservative approach but recognizes that the load rating provided in the NBI is not an absolute measure but is expected to vary due to uncertainties associated with parameters used for bridge load rating.  
Lastly, in this study, two main approaches are used for selecting bridges for a reliability analysis. In the first approach, each of 12 selected WIM sites is associated with interstate highway bridges along each of 4 selected routes (I-75, I-95, I-16, and I-20). In the second approach, a group of bridges in the vicinity of the Atlanta area is analyzed with WIM data obtained from each of 7 selected WIM sites. Additionally, a group of bridges in the vicinity of the Savannah area is analyzed with WIM data from each of 5 selected WIM sites.