###### Abstract  
Thanks to the performance improvement introduced by micro sized functional fillers, application of epoxy composites for electrical insulation purposes has become popular. This paper investigates the dielectric properties of epoxy micro-composites filled with alumina (Al\({}_{2}\)O\({}_{3}\)). In particular, measurements of relative permittivity, dissipation factor, and electrical breakdown are performed, and a comprehensive statistical analysis on dielectric properties was conducted. AC breakdown strength (AC-BDS) was analyzed for normal distribution using four methods (Anderson-Darling, Shapiro-Wilk, Ryan-Joiner, and Kolmogorov-Smirnov). In addition, the AC-BDS was analyzed at risk probabilities of 1%, 5%, 10%, and 50% using Weibull distribution functions. Both normal and Weibull distributions were evaluated using the Anderson-Darling (A-D) statistic and \(p\)-value. Additionally, the log-normal, gamma, and exponential distributions of AC-BDS were examined by A-D goodness-of-fit test. The hypothesis test results of AC-BDS were fit by normal and Weibull distributions, and the compliance was evaluated by \(p\)-value and each method statistics. In addition, the experimental results of AC-BDS were fit by log-normal and gamma distributions, and the goodness-of-fit was evaluated by \(p\)-value and A-D testing. On the other hand, exponential distribution was not suitable for \(p\)-value and A-D testing. The results showed that the distributions of AC-BDS were the best using log-normal distribution. Meanwhile, statistical analysis results verified the apparent effect of temperature on dielectric properties using a paired \(t\)-test. The analysis results of this paper not only contribute to better characterization of epoxy/Al\({}_{2}\)O\({}_{3}\) micro-composites but also introduce a comprehensive approach for performing statistical analysis for electrical insulation materials. epoxy/Al\({}_{2}\)O\({}_{3}\) micro-composites; breakdown strength; statistical analysis; Weibull distribution; normal distribution; goodness-of-fit test +
Footnote †: journal: applied sciences  
obtained by adding a smaller amount of filler compared to epoxy micro-composites, epoxy nano-composites have received attention. According to [3], nano-sized silica particles contribute to increased performance of thermal conductivity, insulation strength, and PD resistance of epoxy-based insulation materials. Thanks to such improvement, the effectiveness of SiO\({}_{2}\)/epoxy nano-composites for applications that involve high level of electrical stress (e.g., HVAC power cables and insulation of electric machines) were studied. In addition, nano-sized alumina fillers improve PD resistance and are mainly applied for miniaturization in rotating machines and winding insulation. Alumina fillers are also known for enhancing mechanical properties. As a result, alumina fillers are applied in gas-insulated switchgear (GIS) spacers, playing a critical role in high-voltage system insulation and providing mechanical support for power equipment [4]. Further research on epoxy-alumina nano-composites has been performed as follows. [PERSON] et al. [5] investigated the influence of interfacial polarization between the polymer and nano particles on the dielectric properties, highlighting its critical role in dielectric relaxation mechanisms. [PERSON] and [PERSON] [6] evaluated the AC breakdown properties of epoxy nano-composites by assessing the insulation durability with varying concentrations of alumina nano-fillers. Furthermore, [PERSON] and [PERSON] [7] emphasized the impact of field treeing degradation mechanisms on the electrical performance of epoxy-alumina nano-composites using electroluminescence techniques. Despite the advantages of nano sized fillers in improving electrical, mechanical, and thermal properties, micro sized fillers are preferred in actual power equipment insulation design due to economic considerations, ease of processing, and reliability.