## 4 Experiment Results
### Breakdown Strength Analysis
#### 4.2.2 Weibull Distribution  
Figure 9 presents the Weibull distribution graph for the AC-BDS of epoxy/Al2O3 micro-composites, based on different voltage application methods (RT and ST). In the case of Figure 9a, statistical processing was performed on the electric field (AC-BDS), while in Figure 9b, statistical processing was conducted on the voltage (AC-BDV). Both graphs are accompanied by key parameters characterizing the Weibull distribution, including the shape parameter (which indicates the slope of the graph line), the scale parameter (which represents the dispersion and failure level of the data), and the A-D statistic and \(p\)-value. The \(p\)-value of the experimental data and the compliance with the Weibull distribution are summarized in Table 5 for AC-BDS and Table 6 for AC-BDV. In the case of Table 5, ST-BDS indicates that the data follow this probability distribution law because the \(p\)-values is greater than 0.05. On the other hand, RT-BDS shows the \(p\)-value less than 0.01, indicating that is does not follow the Weibull distribution law. To analyze the cause of this result, additional statistical analysis was performed on AC-BDV, unlike the normal distribution. The results of both experiments (ST and RT) indicate that the data follow this probability distribution law, as the \(p\)-value is greater than 0.05 in Table 6. Given that RT-BDV follows the Weibull distribution well, the reason why RT-BDS does not follow the Weibull distribution can be attributed to a thickness of the epoxy/Al2O3 micro-composites. This is due to RT-BDS being calculated as the RT-BDV value divided by the specimen thickness. Although the average thickness of epoxy/Al2O3 micro-composites was introduced as 1.05 mm in Section 2.1, the actual thickness of each specimen showed a variation between 0.99 and 1.11 mm. Thus, the influence of specimen thickness cannot be ignored as a factor that prevents RT-BDS from following the Weibull distribution. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Test Method** & **Skewness** & **Kurtosis** \\ \hline Ramp Test & \(+0.75\) & \(+0.80\) \\
60 s Step-up Test & \(-0.19\) & \(-0.79\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Skewness and kurtosis values with normal distribution of AC-BDS. Figure 8: Histogram of epoxy/Al2O3 micro-composites: (**a**) RT-BDS; (**b**) ST-BDS. Table 7 summarizes the AC-BDS at 1% cumulative probability, which is one of the critical parameters from a practical perspective, particularly when designing insulating components [33]. It also includes the AC-BDS at 5%, 10%, and 50% probabilities. This allows for a comparison of the AC-BDS for the micro-composites at each probability level. The RT-BDS and ST-BDS showed differences in growth rates according to the failure probability of the Weibull distribution. Based on a 1% cumulative failure probability, as the cumulative probabilities increased to 5%, 10%, and 50%, RT-BDS increased by approximately 8.8%, 12.9%, and 24.5%, respectively. Additionally, as ST-BDS increased with each cumulative probability, it rose by about 5.0%, 7.3%, and 13.62%, respectively. Overall, as the cumulative probability increased, the growth rate of RT-BDS was greater than that of ST-BDS. This is presumed to be the result of a difference of approximately 0.31 at the lowest 1% cumulative probability for RT-BDS and ST-BDS, respectively. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Test Method** & \(p\)**-Value** &
\begin{tabular}{c} **Conformity to Weibull** \\ **Distribution** \\ \end{tabular} \\ \hline Ramp Test & \textgreater{}0.250 & Accepted \\
60 s Step-up Test & 0.091 & Accepted \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Hypothesis test of compliance with Weibull distribution of AC-BDV.