## 4 Results
### Illustrative Study
#### 4.1.1 Update of Input Parameters  
For the three update steps after 10%, 25%, and 50% of the project progress, the input data for the core processes, ringbuild and advance, were adjusted as described in the following:  
Process Duration of Ringbuild  
The duration of the ringbuild essentially depends on the experience and degree of familiarization of the personnel and on project-specific boundary conditions such as the number and size of the segments per ring or the precision and speed of the erector [7]. The project-specific factors are constant within a project. However, the degree of familiarization changes as the project progresses and must be taken into account during an update. Depending on the degree of familiarization, the current actual data must be filtered and adjusted accordingly.  
In this case, the familiarization effect is analyzed with the help of trend analysis, as described in Section 3.1.2. For the individual update steps, the actual data available at the respective point in time were cleaned, the respective learning curve was identified, and the ringbuild data were normalized. Subsequently, new distribution functions were adapted to the current actual data (Table 2) at each update step, and goodness-of-fit tests were performed (Chi\({}^{2}\) test, Kolmogorov-Smirnov test, Anderson-Darling test). Figure 10 shows the probability density functions of the adjusted distributions for the update steps 1, 2, and 3 in comparison to the actual data and the original distribution function from planning.  
\begin{table}
\begin{tabular}{c c c} \hline
**Update Step** & **Distribution** & **Parameters** \\ \hline Planning phase & Triangular & Min = 20; mean = 45; max = 60 \\ \hline Update 1 (200 m) & Log-Logistic (E) & loc = 14.133222; \(\alpha\) = 20.054445; \(\beta\) = 2.869374 \\ \hline Update 2 (500 m) & Log-Logistic (E) & loc = 14.679972; \(\alpha\) = 14.623870; \(\beta\) = 2.242208 \\ \hline Update 3 (1000 m) & Pearson Type V (E) & loc = 9.790273; \(\alpha\) = 3.345234; \(\beta\) = 0.017947 \\ \hline \end{tabular}
\end{table}
Table 2: Probability density functions for the update steps of the ringbuild duration [min] input parameter [34].  
Process Duration of Advance  
The advance speed is significantly influenced by the geological boundary conditions and the encountered ground conditions. The advance speed must therefore be adjusted for each geotechnical section of the tunnel drive.  
In this example, comparable ground conditions are assumed for the tunnel sections between the stations (A). However, a considerable reduction in the advance speed is prescribed for the excavation of the stations (B). Therefore, two different distributions of the advance speed are assumed for this project.  
Equivalent to the procedure for adjusting the duration of ringbuild parameter, current actual data are divided into the areas A and B, and the distribution functions for the advance speed are updated according to the known construction progress. The updated distribution functions are presented in Table 3. Figure 11 shows the improvement in the probability density functions for the advance speed input parameter within the update steps compared to the actual data and planned input parameters.