## 4 Simulation Analysis and Verification
### Simulation Results and Analysis  
The Monte Carlo method was used to simulate the operation scenario of low-voltage circuit breaker overload protection, and the service state of low-voltage circuit breaker overload protection action characteristics was simulated and analyzed according to the degradation rate parameter and the distribution parameter at different reliability levels and under different operating conditions. The transfer analysis of different service states of low-voltage circuit breaker overload protection action characteristics was carried out with class I products under good operating conditions as an example. The results are shown in Figure 8.  
From the figure, it can be seen that the overload protection of low-voltage circuit breakers shifts between five states: a healthy state, a mildly degraded state, a heavily degraded state, a general fault state, and a severe fault state. In the absence of maintenance, with an increase in service time the number of circuit breakers in the same batch in the healthy state gradually decreases and the number of circuit breakers in the severe fault state continues to increase. In addition, the mild degradation, severe degradation, and general failure states are transition states; however, the laws presented are basically the same, all of which increase first, then decrease, and eventually transfer to the severe failure state. Analyzing the transfer of the service states of class I products under three operating conditions, the results are shown in Figure 9. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Action Time** & **Circuit Breaker Reliability Level and** & **Distribution** \\
**Parameter** & **Operating Conditions** & **Parameters** \\ \hline \multirow{2}{*}{Initial value \(t\)} & Product I & \(t_{d0}^{*}\sim N(0.5,0.059^{2})\) \\  & Product II & \(t_{d0}^{*}\sim N(0.5,0.027^{2})\) \\ \hline \multirow{4}{*}{Degradation rate \(\beta^{*}\)} & Good operating conditions & Product I & \(\beta^{*}\sim N(0,0.0481^{2})\) \\  & Conditions & Product II & \(\beta^{*}\sim N(0,0.3730^{2})\) \\ \cline{2-4}  & General operating conditions & Product I & \(\beta^{*}\sim N(0,0.0641^{2})\) \\ \cline{2-4}  & Severe operating conditions & Product I & \(\beta^{*}\sim N(0,0.0481^{2})\) \\ \cline{2-4}  & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \\ \cline{2-4}  & Severe operating conditions & Product II & \(\beta^{*}\sim N(0,0.1000^{2})\) \\ \cline{2-4}  & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \\ \cline{2-4}  & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \\ \end{tabular}
\end{table} 
Table 1: Overload protection action time degradation distribution parameters. Figure 8: Circuit breaker overload protection state transfer probability diagram. From the figure, it can be seen that the service state transfer law of low-voltage circuit breaker overload protection action characteristics under different operating conditions is consistent. When comparing good operating conditions with poor operating conditions, the same level of reliability for the low-voltage circuit breaker overload protection in a healthy state of probability is higher and the transition to the probability of heavy failure is lower; the state transfer rate between the service state is also low and the general operating conditions of the circuit breaker service state is between the two. This is also consistent with the fact that, in practice, circuit breakers are more susceptible to damage under poorer operating conditions. The transfer of the service state of the overload protection action characteristics of circuit breakers with different reliability levels during service is shown in Figure 10. From the figure, it can be seen that the service state transfer law of the overload protection action characteristics of low-voltage circuit breakers under different circuit breaker reliability levels is consistent.