## 4 Results and Discussion
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**Parameters Used in Survival Analysis, Equations (4) through (9)**} \\ \hline
**Type of Superstructure** & **Steel** & **Concrete** & **Combined** \\ \hline
**Parameter “Type\"** & **1** & **0** & **2** \\ \hline \(\alpha\) & \(5.80\times 10^{-04}\) & \(5.80\times 10^{-04}\) & \(5.40\times 10^{-04}\) \\ \(\beta\) & \(2.12\times 10^{+00}\) & \(2.12\times 10^{+00}\) & \(2.09\times 10^{+00}\) \\ \(c\) & \(3.74\times 10^{-03}\) & \(3.74\times 10^{-03}\) & \(3.37\times 10^{-03}\) \\ \(d\) & \(6.28\times 10^{-06}\) & \(6.28\times 10^{-06}\) & \(8.31\times 10^{-06}\) \\ \(h\) & \(-1.50\times 10^{-01}\) & \(-1.50\times 10^{-01}\) & \(0.00\times 10^{+00}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Reliability and failure rate parameters. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Estimate** & **Standard Error** & **Wald** & **\(p\)-Value** \\ \hline \(\alpha\) & \(5.80\times 10^{-04}\) & \(1.17\times 10^{-04}\) & 24.68 & \(6.76\times 10^{-07}\) \\ \(\beta\) & \(2.12\times 10^{+00}\) & \(5.35\times 10^{-02}\) & 1566.19 & \(1.63\times 10^{-342}\) \\ Type & \(-1.50\times 10^{-01}\) & \(2.25\times 10^{-02}\) & 44.26 & \(2.88\times 10^{-11}\) \\ MSL & \(3.75\times 10^{-03}\) & \(6.61\times 10^{-04}\) & 32.09 & \(1.47\times 10^{-08}\) \\ ADT & \(6.28\times 10^{-06}\) & \(1.16\times 10^{-06}\) & 29.17 & \(6.62\times 10^{-08}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameter and standard error estimates for the Hypertabastic accelerated failure time model. Based on the results shown in Figure 2, the reliability (survival) of steel superstructures is slightly higher than concrete superstructures in Wisconsin. Reliability starts from a value of 1 or 100% at the beginning of the service life and decreases as the age increases. At 75 years of age, the reliability of Wisconsin bridges with steel, concrete, and combined superstructures is 0.23, 0.11, and 0.18, respectively (when covariates are held at Wisconsin's mean values). It should be noted that this observation does not necessarily indicate superiority of one system over the other. This comparison does not address initial and long-term costs, and has not been consistently preferential to one superstructure system in different states in a similar study on bridge deck reliability [20]. To investigate the effect of MSL on the reliability and failure rate of superstructures, various maximum span lengths ranging from 10 m to 50 m were analysed for all superstructure types while holding ADT at a constant level of 5000. Results are shown in Figure 3. As the maximum span length increases, the reliability of superstructure decreases, and the failure rate increases at a given age. As shown in Figure 3, the slope of failure rate remains approximately constant after the age of 40. This slope is estimated here as 0.0014 per year for MSL of 50 m and 0.0011 per year for MSL of 10 m. Figure 4 shows plots of reliability and failure rate as a function of ADT for steel and concrete superstructures at a bridge age of 50 years. Figure 2: Hypertabastic reliability and hazard rate curves for bridge superstructures with covariates at their mean values (ADT = 4872 and MSL = 18.5 m). As expected, at the age of 50 years, superstructure reliability decreases rapidly as ADT increases. Similarly, increasing ADT increases the failure rate. Increasing ADT indicates increased frequency of load application. Higher ADT may also lead to an increase in deicing salt usage during the winter (chloride exposure). The reinforcing steel bars embedded in concrete may thus be at increased risk of chloride-induced corrosion. Figure 4 shows superstructure reliability curves that cover a wide range of values from 0.66 to 0.09 (at age 50), depending on the ADT and MSL. Figure 3: Superstructure reliability and hazard rate versus age at different maximum span lengths for ADT of 5000 (All superstructure types).