# Joint Maintenance Strategy Optimization for Railway
## 2 Problem Statement
\begin{table}
\begin{tabular}{c c} \hline \hline
**Items** & **The Limit** \\ \hline Wheel diameter & 790–860 mm \\ Wheel flange height & 28–33 mm \\ Wheel flange thickness & 26–32 mm \\ \(\mathbb{Q}\)r value & 6.5–12.7 mm \\ Inside distance of wheelset & 1353 (+3, –2) mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Standard dimensions for the use of wheelsets. Figure 3: Effects of reprofiling on the wheelset’s profile, flange thickness and diameter. Figure 2: The profile and main parameters of the wheel. accuracy. Maintenance can improve a wheelset's condition, but it is difficult to restore the wheelset to the same condition as a new one, so the effect of reprofiling is assumed to be imperfect. In recent times, according to maintenance regulations [39], the wheel mainly adopts daily inspection and periodic inspection. During daily inspection, also known as patrol inspection, the tread surface damage is checked when the train returns to the depot. Periodic inspection cleans and measures the main parameters of the wheel. The wheel is reprofiled if the flange thickness is less than the specified limit or if the train runs to a specified mileage. This maintenance strategy ensures the normal operation of the wheelset. However, the service life of the wheel can be reduced by frequent reprofiling. Based on the periodic inspection mode, reprofiling is implemented according to the status of the wheel. The maintenance strategy of periodic inspection and preventive maintenance is as follows. 1. The wheelset is inspected daily to check its surface. If there is damage exceeding the limit on the tread, the wheel is reprofiled to eliminate surface damage and to recover the thickness of the flange to \(Sd_{H}\), where \(Sd_{H}\) is the wheel flange thickness threshold after reprofiling. 2. The wheelset is periodically cleaned, measured and maintained. If the wheel flange thickness is greater than \(Sd_{L}\), normal maintenance is performed to remove defects on the flange and tread, such as burrs and sharp edges, where \(Sd_{L}\) is the wheel flange thickness threshold to trigger preventive reprofiling. If the thickness of the flange is less than \(Sd_{L}\), preventive reprofiling is carried out to restore the thickness of the flange to \(Sd_{H}\). 3. If it is found that the wheel diameter is less than the threshold during periodic inspection, the wheel is replaced. These two maintenance strategies are compared in Table 2.  
In the joint maintenance strategy, the states of the wheel are working mode, daily inspection, periodic inspection, corrective maintenance, preventive maintenance and replacement. The events experienced by the wheel from the beginning to the end are shown in Figure 4, with details as follows:  
1. Working event \(o\): The wheel is in normal working condition. 2. Daily inspection event \(x\): The vehicle returns to the depot, and the wheel surfaces are inspected for damages. 3. Periodic inspection event \(s\): The wheel is periodically cleaned, maintenance is performed and the main parameters of the wheel are measured. 4. Corrective maintenance event \(c\): When it is found that the wheel tread damage or wear exceeds the limit during daily inspection, reprofiling is carried out to eliminate the surface damage. 5. Preventive maintenance event \(r\): If the thickness of the wheel flange is below \(Sd_{L}\), reprofiling is implemented to restore the thickness of the flange to \(Sd_{H}\). 6. Replacement event \(g\): When the wheel diameter reaches the use limit, the wheelset is replaced.