## 4 Simulation Analysis and Verification  
### Analog Simulation Analysis Process  
In order to simulate the impact of product quality and the operating environment on reliability, two products with different reliability levels and three different performance degradation rates were used to analyze the operating state of circuit breaker overload protection in service. The Monte Carlo method was used to simulate the circuit breaker overload protection operation scenario and analyze the transfer of each state during the service process of the circuit breaker; the simulation flow of the reliability of the low-voltage circuit breaker overload protection based on the linear degradation of the performance of the thermal cutoff is shown in Figure 7. The simulation parameter setting includes the setting of parameters such as simulation years, upper and lower action time limits, and action time cloth parameters. Figure 7: Simulation process of the reliability of circuit breaker overload protection based on linear degradation. In order to facilitate the simulation and simulation analysis, the circuit breaker operating conditions are assumed [20], and the simulation and analysis process is as follows:  
(1) The larger the number of samples, the closer it is to reality. In this paper, the number of samples of low-voltage circuit breakers was selected as \(n=\) 10,000 and the simulation period was selected as 20 years. (2) Low-voltage circuit breaker overload protection action time standardization. The upper limit of the standard action time \(t_{\max}\) was standardized as 1, the lower limit of the standard action time \(t_{min}\) was standardized as 0, and the initial circuit breaker action time \(t_{d0}\) was standardized as 0.5. (3) Low-voltage circuit breaker overload protection action time degradation may be increased or decreased, assuming that the overload protection action time increase and decrease probabilities are the same but the action time dispersion of different batches of products by different operating conditions and reliability levels are different. Without maintenance [37], it is assumed that 40% and 50% of the circuit breaker overload protection action times for Product I and Product II meet the requirements after 20 years of service under good operating conditions, that it is 30% and 40% under normal operating conditions, and that it is 20% and 30% under severe operating conditions. Based on the above assumptions, the annual degradation rate of LV circuit breakers under different operating conditions and different reliability levels is calculated (\(\beta\)); the calculation process is as follows:  
\[p_{i}=P_{i}(0\leq\mu_{d0}^{*}+20\beta\leq 1),i=1\sim 6 \tag{17}\]  
where \(\mu_{d0}^{*}=0.5\). \(p_{1}\) and \(p_{2}\), \(p_{3}\) and \(p_{4}\), and \(p_{5}\) and \(p_{6}\) correspond to the probability that the overload protection action time of the two products in service for 20 years under good, general, and poor operating conditions is within the required range, \(p_{i}=\) (0.40, 0.50, 0.30, 0.40, 0.20, 0.30). Transform Equation (17) into a standard normal distribution:  
\[\Phi(\frac{0.025-\mu_{\beta i}^{*}}{\sigma_{\beta i}^{*}})-\Phi(\frac{-0.025- \mu_{\beta i}^{*}}{\sigma_{\beta i}^{*}})=p_{i},i=1\sim 6 \tag{18}\]  
where \(\mu_{\beta i}^{*}=0\). Utilize the properties of the normal distribution:  
\[\Phi(\frac{0.025-\mu_{\beta i}^{*}}{\sigma_{\beta i}^{*}})+\Phi(\frac{-0.025- \mu_{\beta i}^{*}}{\sigma_{\beta i}^{*}})=1,i=1\sim 6 \tag{19}\]  
We can obtain:  
\[\Phi(\frac{0.025-\mu_{\beta i}^{*}}{\sigma_{\beta i}^{*}})=\frac{1+p_{i}}{2},i=1\sim 6 \tag{20}\]  
Through Equation (20), the variance in the degradation rate of the overload protection action time of LV circuit breakers under different operating conditions and different reliability levels can be obtained by using the standard normal distribution table. (4) Through Equation (21), the probability values for different service states of LV circuit breaker overload protection at a certain moment are counted.