## 6 Conclusions  
This study analyzed the AC-BDS and dielectric properties of epoxy/Al2O3 micro-composites and verified the experimental data using various statistical methods. The analysis of dielectric properties showed a trend of increasing relative permittivity and dissipation factor with rising temperatures, and the \(t\)-test confirmed that these changes were statistically significant. This emphasizes that the insulation performance is sensitive to temperature changes and provides important insights for predicting the behavior of insulating materials in high-temperature environments.  
The AC-BDS of the micro-composites was measured using the ramp test (RT) and 60 s step-up test (ST), and the data were analyzed using various statistical distribution models, including normal and Weibull distributions. ST-BDS data fit well with the Weibull distribution, confirmed by \(p\)-values greater than 0.05. On the other hand, RT-BDS showed results that were inconsistent with the Weibull distribution, with a \(p\)-value of less than 0.05. However, the breakdown voltage values obtained from RT showed good agreement with the Weibull distribution. This is thought to be due to the standard deviation of the thickness of the epoxy/Al2O3 micro-composites. The normal distribution also provided a good fit for the experimental data, with all \(p\)-values exceeding the 0.05 threshold. Additionally, the results of the goodness-of-fit test showed that both the log-normal and gamma distributions had \(p\)-values greater than the significance level (5%) and exhibited a high degree of fit with low A-D statistics. However, the exponential distribution showed poor conformity, as indicated by higher A-D statistics and \(p\)-values lower than 0.05.  
In conclusion, the study has provided valuable insights into the breakdown characteristics and dielectric behavior of epoxy/Al2O3 micro-composites. Regarding the dielectric properties, the temperature dependence of both the relative permittivity and the dissipation factor were verified using a statistical analysis approach. The statistical analysis confirmed that the Weibull and normal distributions are appropriate for analyzing the AC-BDS of these materials, while the exponential distribution was found to be less suitable. In addition, the goodness-of-fit test results comparing A-D values revealed that the experimental data (AC-BDS of epoxy/Al2O3 micro-composites) of this research best fits the log-normal distribution. Given that the log-normal distribution is one of the distributions used in the high-voltage field, our research suggests that it may, as in this study's findings, be more suitable than the normal or Weibull distributions. Further research is planned to explore the behavior of these materials under higher temperatures to ensure reliability in high-voltage insulation applications. Additionally, various statistical analyses will be conducted to assess the lifetime of these materials over extended testing durations.  
Conceptualization, C.C.; methodology, C.C.; data analysis, C.C. and D.S.; formal analysis, C.C. and D.S.; investigation, C.C.; data curation, C.C.; writing--original draft preparation, C.C.; writing--review and editing, M.K.; supervision, M.K. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education (No. 2020R1A6A1A12047945).  
The authors declare no conflicts of interest.