## 6 Data-Driven DES
### Forecast Study  
Figure 12 shows the distributions for the expected construction time for the three volumes of data considered, along with the actual duration of the pile production. Figure 13 shows their cumulative durations. The average predicted total durations are presented in Table 5 as a function of the construction progress.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Process** & **Parameter** & **25\%** & **50\%** & **75\%** \\ \hline \multirow{4}{*}{Drill} & Mu & \(-5.33\times 10^{-12}\) & \(7.21\times 10^{-12}\) & \(-2.17\times 10^{-12}\) \\  & Sigma & 7995.83 & 7787.97 & 7090.17 \\ \cline{2-5}  & Slope & 1211.12 & 1216.27 & 1173.93 \\  & Intercept & \(-16\),781.52 & \(-17\),638.90 & \(-17\),837.04 \\ \hline \multirow{4}{*}{Idle 1} & Mu & \(2.82\times 10^{-13}\) & \(-7.37\times 10^{-13}\) & \(-5.02\times 10^{-13}\) \\  & Sigma & 3619.61 & 4555.91 & 5119.83 \\ \cline{2-5}  & Slope & \(-163.18\) & \(-26.71\) & \(-32.85\) \\  & Intercept & 12,496.47 & 7209.08 & 7381.52 \\ \hline \multirow{4}{*}{Reinforce} & Mu & \(7.84\times 10^{-15}\) & \(-3.18\times 10^{-13}\) & \(-6.27\times 10^{-13}\) \\  & Sigma & 500.08 & 581.13 & 545.05 \\ \cline{2-5}  & Slope & 105.71 & 83.95 & 75.64 \\  & Intercept & \(-2299.57\) & \(-1480.55\) & \(-1184.78\) \\ \hline \multirow{4}{*}{Idle 2} & Mu & \(1.39\times 10^{-13}\) & \(3.4\times 10^{-13}\) & \(1.36\times 10^{-13}\) \\  & Sigma & 762.92 & 1869.31 & 1636.55 \\ \cline{2-5}  & Slope & \(-45.05\) & \(-41.68\) & \(-20.96\) \\  & Intercept & 2596.29 & 2519.07 & 1639.18 \\ \hline \multirow{4}{*}{Install contractor pipe} & Mu & \(-2.59\times 10^{-13}\) & \(-3.72\times 10^{-13}\) & \(-3.55\times 10^{-13}\) \\  & Sigma & \(785\times 10^{-1}\) & 691.22 & 650.05 \\ \cline{2-5}  & Slope & 72.25 & 58.94 & 56.68 \\  & Intercept & \(-1039.17\) & \(-494.96\) & \(-301.61\) \\ \hline \multirow{4}{*}{Idle 3} & Mu & \(6.27\times 10^{-14}\) & \(-1.09\times 10^{-12}\) & \(-3.35\times 10^{-13}\) \\  & Sigma & 2238.13 & 2218.63 & 27,756.29 \\ \cline{2-5}  & Slope & \(-30.32\) & 89.56 & 129.42 \\ \cline{2-5}  & Intercept & 3359.87 & \(-266.50\) & \(-1134.46\) \\ \hline \multirow{4}{*}{Concrete} & Mu & 0 & \(-1.11\times 10^{-12}\) & \(-2.7\times 10^{-12}\) \\  & Sigma & 1407.71 & 1534.68 & 1448.72 \\ \cline{2-5}  & Slope & 267.39 & 415.97 & 436.95 \\ \cline{1-1}  & Intercept & 1505.92 & \(-3429.70\) & \(-4101.32\) \\ \hline \end{tabular}
\end{table}
Table 4: Parameters for the linear regression and residuals depending on the process.  
\begin{table}
\begin{tabular}{c c c} \hline
**Project Completion:** & **Prediction of Total Pile Production:** \\
**Ratio of as-Built Data** & **Mean** & **Standard Deviation** \\ \hline
25\% & 128.2 days (+7.76\%) & 1.4 days \\
50\% & 127.5 days (+7.14\%) & 1.2 days \\
75\% & 123.6 days (+3.86\%) & 0.8 days \\
100\% & 119.0 days & - \\ \hline \end{tabular}
\end{table}
Table 5: Results of simulation study compared to actual duration of pile production.  
As the construction process progresses, the amount of as-built data used as simulation input could be increased (25%, 50%, to 75%). As a result, the distributions of the predictions get closer to the actual duration. The results in Table 5 show that, at 25% construction progress, the simulated data deviated only about 9 days from the as-built duration. At 50%, this deviation became smaller. At 75%, it decreased to about 5 days. Furthermore, uncertainty decreases with continuous updating of the data. The standard deviation around the mean of the predicted value decreased from 1.4 days at 25% of construction progress to 0.8 days at 75%.