# Minimization of Material Waste Through Maintenance Interval Optimization in Transport Systems
## 3 Materials and Methods
### Example Requirements According to the Tsi/dsu  
The EN57/EN57 AL rail vehicle is a three-car, bidirectional electric multiple unit, produced from 1961 to 1993. It is designed for regional passenger service. The EN57 consists of three cars: two end driving cars (ra and rb) that are equipped with driver's cabins, and a middle motor car(s). The cars are connected by passenger passages and short couplings (without a head), ensuring a reliable connection during operation. The vehicles are capable of operating in multiple-unit mode with other units of the same series as well as with EN71 and ED72 vehicles. The vehicle's steel structure (cars) is mounted on six running bogies, with two trailing bogies under each end driving car, and two powered bogies under the middle motor car. Table 1 presents the assumptions of the maintenance cycle, while Figure 1 shows the schematic diagram of the maintenance cycle for the EN57 vehicle based on the maintenance system documentation (DSU). Determining the Expected Technical Review Date Based on Actual Mileage and the Technical Review Interval  
The mileage at the time of the last technical review at a given level (P1 to P5) or based on the last known mileage and its recorded date (e.g., through automatic reading from the vehicle's diagnostic system) is used. Additionally, the maximum mileage until the next technical review at the same level specified in the DSU and the planned mileage for the vehicle, calculated based on the algorithm presented later in the article, are also taken into account. By knowing the mileage required for the next technical review, the date when this mileage will be reached can be determined. This will indicate the next technical review date. The calculation of the predicted technical review/repair date based on time is determined by the date and time of the last technical review and the required interval to the next technical review as specified in the DSU. To mathematically determine the date of the next technical review, we use the expected mileage \(\hat{M}(t)\) of the vehicle as a function of time. Assuming the current mileage of the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type of Service (Maintenance Level)** & **Frequency [days]** & **Mileage [km]** \\ \hline P1 & 5 & 2500 \\ \hline P2 & 45 & 25,000 \\ \hline P3 * & 912 & 250,000 \\ \hline P4 * & 1825 & 500,000 \\ \hline P5 * & 10,950 & 3,200,000 \\ \hline \hline \end{tabular}  
*—depending on what comes first (days/mileage).  
\end{table} 
Table 1: Assumptions of the EZT EN57 service cycle—input data structure. Figure 1: EZT EN57 service cycle diagram. vehicle is \(M_{0}\) and the average daily mileage is \(\overline{M}_{daily}\), the future mileage of the vehicle after \(t\) days can be defined by:  
\[\hat{M}(t)=M_{0}+\overline{M}_{daily}\cdot t \tag{1}\]  
The next technical review should occur after reaching a defined mileage threshold \(M_{review}\), leading to the determination of the time \(T_{servis}\):  
\[T_{servis}=\frac{M_{review}-M_{0}}{\overline{M}_{daily}} \tag{2}\]  
If we know today's date \(T_{0}\), the predicted review date \(T_{next}\) can be expressed as:  
\[T_{next}=T_{0}+T_{servis} \tag{3}\]  
This approach allows us to accurately estimate the date when the vehicle will need maintenance based on its current mileage and planned daily distance. Instead of using the average daily mileage \(\overline{M}_{daily}\), other more advanced approaches can be applied to calculate the predicted mileage \(\hat{M}(t)\), allowing for a better representation of the variable nature of actual vehicle usage. Below are some alternative methods:  
1. Daily Mileage Update  
The predicted vehicle mileage \(\hat{M}(t)\) can be updated daily based on actual daily data obtained from the vehicle's monitoring system. In this case, the predicted mileage can be expressed as the sum of previous daily mileages:  
\[\hat{M}(t)=M_{0}+\sum_{i=1}^{t}M_{i} \tag{4}\]  
where \(M\) represents the actual mileage on day \(i\).