## 5 Case of Establishing an Operational Risk Assessment Model
### Brake System Performance under a Single Overhaul Interval  
We calculated the variation of the train braking safety index over time for a single overhaul interval. The input parameters are shown in Table 1. In Figure 3, we can see the safety index decreases over time during operation, while it gradually increases during maintenance time. The upper bound of the curve over time is the safety index at the beginning of every day, that is, the safety index at the initial state and the state after each daily maintenance. Accordingly, the lower boundary of the curve is the safety index at the end of every day's work before daily maintenance has begun.  
Figure 3: Braking distance verified in one overhaul interval.  
Figure 2: Results obtained from 10,000 simulations.  
To compare the impact of daily maintenance and overhaul, different daily maintenance rates and overhaul interval values with the same average safety index at a single cycle are put under one curve for comparison. The input parameters are the same as in Table 1 except for the daily maintenance rate and overhaul interval. In Figure 4, we can find that as the routine maintenance repair rate increases, the minimum overhaul interval of the required maintenance strategy becomes longer and longer while meeting the safety level requirements. Similarly, the longer the overhaul interval is scheduled, the higher the required routine maintenance rate will be, but eventually, it will gradually stabilize. This is because as the condition stabilizes, the safety level of the brake system will also stabilize during the overhaul interval.  
Then, we compared the variation of braking distance with time for a train under three specified load conditions in a single cycle. The input parameters are the same as in Table 1 except for the load. In Figure 5, it can be seen that as the trainload increases, the braking distance becomes correspondingly longer, and the fluctuation range of the braking distance between the upper and lower bound becomes larger. The braking distance of the subway train at the load at full load and full load conditions meet the requirements of safe braking distance regulations. While in the overload condition, the braking distance cannot meet the requirements of the safe braking distance regulations.  
To compare the effects of daily maintenance rate and failure rate on braking distance, we calculated the variation of the average braking distance in one cycle with the motor failure rate \(\lambda\) and daily maintenance repair rate \(\mu\) for metro trains under three different loads. The input parameters are the same as in Table 1 except for the load, \(\lambda\), and \(\mu\). The results are shown in Figure 6. It can be seen that the effect of routine maintenance repair rate on the average braking distance is significantly higher than the effect of motor failure rate on the average braking distance.  
Figure 4: Variation of daily maintenance rate and overhaul interval with the same average safety index.  
To compare the effect of brake motors with different failure rates and different installation numbers on the braking distance, we calculated the average braking distance within a single overhaul interval for three different failure rates and different installation numbers. The input parameters are the same as in Table 1 except for the number of motors and \(\lambda\). In Figure 7, we can see that the number of motors required to meet the safe braking distance will also be higher when motors with higher failure rates are selected.  
Figure 5: Braking distance under different loads during an overhaul interval.  
Figure 6: Average braking distance in one overhaul interval verified with the different parameters of motors: (**a**) braking distance verified with \(\lambda\); (**b**) braking distance verified with \(\lambda\).