# A Formal Model of the Exploitation Process for Railway Signalling Devices
## 6 Verification of the Modelling Method  
The verification of the method consisted of examining the discrepancies between the data obtained from modelling and the data from the real system. The method of modelling the exploitation process for signalling devices proposed in this paper allows for calculating the exploitation parameters of these devices using statistical analysis and simulating future exploitation states. Real data, for one year, were acquired from part of the E-65 railroad line of the PKP PLK S.A. network. The group of railway signalling systems studied comprised three basic types of subsystems:  
1. Computer-based interlocking;
2. Automatic block signalling system;
3. Level crossing system. These consist of the following types of elements:  
1. Railway signal;  
Figure 9: Mathematica software window; limiting probabilities for the model railway signalling system from the graph in Figure 8: after implementation (**a**) and after simplifications (**b**). 2. Railway switch;
3. Track section;
4. Level crossing. Next, a comparison was made between the results of the modelling exploitation process and the real exploitation data for the studied section of the railroad line. The results of the conducted verification are shown in Tables 1 and 2. In the results presented in Tables 1 and 2, there is a gap in values between the estimated data and the real exploitation data. It could be caused by the limited sample size of identified computerised railway signalling system failures occurring on the studied section of the E-65 railroad line and, consequently, the low saturation of the railway signalling system model with failures and renewal, which results in limited model stability over the observation period (the real exploitation data were acquired for 1 year, and the railroad selected for analysis was equipped with modern and relatively new railway signalling systems). The authors' simulation tool provides information on the failures and renewals, and the reliability parameters presented in Tables 1 and 2 are the results of statistical analysis of such occurrences. The consistency of the obtained results may also be impacted by other factors, such as the credibility of collected failure data, the skills and experience of the employees \begin{table}
\begin{tabular}{c c c} \hline
**Reliability Parameters** & **Real Exploitation Data** & **Estimated Data** \\ \hline \multicolumn{3}{c}{computer-based interlocking} \\ \hline Mean Time between Failure (MTBF) (h) & 690.6075 & 501.3801 \\ Mean Time to Repair (MTTR) (h) & 2.4473 & 2.4016 \\ Availability & 0.9965 & 0.9952 \\ \multicolumn{3}{c}{automatic block signalling system} \\ Mean Time between Failure (MTBF) (h) & 1042.0946 & 859.2450 \\ Mean Time to Repair (MTTR) (h) & 2.0219 & 2.4064 \\ Availability & 0.9981 & 0.9933 \\ \multicolumn{3}{c}{level crossing system} \\ Mean Time between Failure (MTBF) (h) & 570.3957 & 391.5000 \\ Mean Time to Repair (MTTR) (h) & 2.3864 & 2.4127 \\ Availability & 0.9958 & 0.9939 \\ \hline \end{tabular}
\end{table} 
Table 1: Observed and estimated reliability parameters for selected signalling subsystems. \begin{table}
\begin{tabular}{c c c} \hline
**Reliability Parameters** & **Real Exploitation Data** & **Estimated Data** \\ \hline \multicolumn{3}{c}{railway signal} \\ \hline Mean Time between Failure (MTBF) (h) & 236.7954 & 272.1535 \\ Mean Time to Repair (MTTR) (h) & 1.9404 & 2.2913 \\ Availability & 0.9860 & 0.9917 \\ \multicolumn{3}{c}{railway switch} \\ Mean Time between Failure (MTBF) (h) & 659.3533 & 895.5731 \\ Mean Time to Repair (MTTR) (h) & 2.3172 & 2.4450 \\ Availability & 0.9950 & 0.9978 \\ \multicolumn{3}{c}{track section} \\ Mean Time between Failure (MTBF) (h) & 679.5923 & 968.3691 \\ Mean Time to Repair (MTTR) (h) & 1.6750 & 2.4030 \\ Availability & 0.9965 & 0.9973 \\ \multicolumn{3}{c}{level crossing} \\ Mean Time between Failure (MTBF) (h) & 133.3635 & 167.4408 \\ Mean Time to Repair (MTTR) (h) & 2.3247 & 2.4792 \\ Availability & 0.9829 & 0.9854 \\ \hline \end{tabular}
\end{table}