## 4 Results and Discussion  
Statistical information on various parameters and superstructure types (steel, concrete or combined) for the data used in the analyses is shown in Table 3. These parameters were calculated for bridges in the State of Wisconsin. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{Wisconsin Bridge with Superstructure Rating of 5} & \multicolumn{4}{c}{All Wisconsin} \\ \cline{2-10}
**Statistical** & \multicolumn{2}{c}{**Steel Superstructure**} & \multicolumn{2}{c}{**Concrete Superstructure**} & \multicolumn{2}{c}{**Both Superstructure Types**} & \multicolumn{2}{c}{**Bridges Combined \({}^{\star}\)**} \\ \cline{2-10}
**Parameter** & **ADT** & **MSL** & **Age** & **ADT** & **MSL** & **Age** & **ADT** & **MSL** & **Age** & **MSL** \\ \hline Mean & 1911 & 14.0 & 61.8 & 6014 & 14.5 & 50.9 & 3879 & 14.2 & 56.6 & 4872 & 18.5 \\ Median & 210 & 9.8 & 60.0 & 1200 & 12.8 & 47.0 & 450 & 11.9 & 52.0 & 690 & 14.9 \\ Standard deviation & 4971 & 13.0 & 17.0 & 1103.5 & 8.4 & 21 & 8682 & 11.0 & 19.6 & 9699 & 11.5 \\ No. of bridges & 472 & 435 & & & & & & & & & 9835 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical information on the Wisconsin NBI data used in the analyses. The calculated parameters for Equations (4) through (6) are shown in Table 4. In Table 4, the parameters \(\alpha\), \(\beta\), \(c\), \(d\), and \(h\) are identical for steel and concrete superstructures. The value of the parameter \"Type\" (0 or 1) describes the difference between the two superstructure types. Calculated \(p\)-values are shown in Table 5. Smaller \(p\)-values indicate that the effect of that parameter is statistically significant. The \(p\)-values in Table 5 indicate that covariates Type, MSL and ADT are all statistically significant parameters affecting superstructure reliability. Using Equations (4) and (5), the developed Hypertabastic survival model can estimate the reliability and failure rates at any age as a function of Type, ADT and MSL. The estimated bridge age corresponding to a reliability of 0.5 (50%) at the end of service life for steel and concrete superstructures was 57 and 49 years, respectively, when mean values of covariates ADT and MSL were used in the equations. Table 6 shows percentiles for age at the end of service life when either mean or median values of covariates (ADT and MSL) were used for concrete and steel bridges. Plots of reliability and failure rate associated with steel, concrete, and combined superstructures are shown as a function of age in Figure 2. In these curves, the ADT and MSL are assumed to be at their mean values for Wisconsin (ADT = 4872 and MSL = 18.5 m). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Percentile**} & \multicolumn{2}{c}{**Mean (ADT and MSL)**} & \multicolumn{2}{c}{**Median (ADT and MSL)**} \\ \cline{2-5}  & **Concrete (years)** & **Steel (years)** & **Concrete (years)** & **Steel (years)** \\ \hline
0.1 & 73 & 85 & 76 & 88 \\
0.2 & 64 & 74 & 67 & 78 \\
0.3 & 58 & 68 & 61 & 70 \\
0.4 & 53 & 62 & 56 & 65 \\
0.5 & 49 & 57 & 51 & 60 \\
0.6 & 46 & 53 & 47 & 55 \\
0.7 & 41 & 48 & 43 & 50 \\
0.8 & 36 & 42 & 38 & 44 \\
0.9 & 30 & 35 & 31 & 37 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Deciles for estimated age at the end of service Life using Hypertabastic accelerated failure time model.