###### Abstract
Their statistical analysis revealed that in most cases, the Weibull distribution fit the data better. Similarly, [PERSON] et al. [16] analyzed the probabilities of Weibull and normal distributions for the results of AC breakdown experiments performed on ester synthesized with fullerene and graphene nanofluids. In the research of [PERSON] et al. [17], the study focused on investigating the effect of moisture accumulation on surface flashover performance in high-voltage insulation systems. They measured the flashover voltage under conditions where moisture was evenly or unevenly distributed on the insulator surface and used statistical techniques to analyze the flashover data under different conditions. In that study, log-normal and gamma distributions were also employed for statistical analysis. In previous studies [15; 16; 17], Weibull distribution analysis was conducted using the Anderson-Darling (A-D) statistic and \(p\)-values [18]. The normal distribution analysis, on the other hand, was verified using the Shapiro-Wilk method [19]. Although several distribution models (e.g., Weibull and normal distribution) have been generally considered as a representative distribution model for statistical processing of electrical breakdown data, it is necessary to validate such an approach based on statistical analysis tools, as to be shown later in this paper. This paper studied the electrical insulation performance of epoxy/Al2O3 micro-composites. In order to characterize the specimen, measurement of dielectric properties (i.e., permittivity and loss tangent) and electrical breakdown experiments were performed. From the experiment data, it was possible to characterize the dielectric properties and electrical BDS of epoxy/Al2O3 micro-composites. Furthermore, statistical analysis was performed on the data to gain insights on the measurement results and material performance. From such analysis, in particular, the dependence of the specimen permittivity on temperature was observed, and the conformity of electrical breakdown data to several parametric distribution models was observed. In this study, the conformity of the AC-BDS measurement results of epoxy/Al2O3 micro-composites to the laws of normal and Weibull distributions was verified. The Weibull distribution analysis was conducted using the method proposed in [18]. For the normal distribution analysis, four different methods were employed: Shapiro-Wilk (statistic: W) [19], Anderson-Darling (statistic: A-D) [20], Ryan-Joiner (statistic: R-J) [21], and Kolmogorov-Smirnov (statistic: K-S) [22]. The \(p\)-values obtained from these methods were used to confirm whether the AC-BDS of epoxy/Al2O3 micro-composites satisfied normality. Furthermore, the skewness and kurtosis of the AC-BDS data were analyzed to verify if the shape of the distribution resembled that of a normal distribution. Meanwhile, in the statistical analysis of failure data for insulating materials, distributions such as Weibull, Gumbel, and log-normal are commonly used [23]. Moreover, other distributions, such as Gaussian normal, double-exponential, Wohlmuth's two-limit, and gamma, have also been considered for processing high-voltage experiment data [24]. Therefore, the effectiveness of the distribution models of log-normal, exponential, and gamma for modeling AC-BDS experiment data of epoxy/Al2O3 micro-composites were also studied in this paper. The best-fitting distribution for analyzing the AC-BDS of the epoxy/Al2O3 micro-composites was selected using the A-D statistics obtained from the distribution analyses. The remainder of this paper is organized as follows. In Section 2, the AC-BDS measurement method is presented. Details on the test sample configuration and measurements of the permittivity and the loss tangent are also introduced. Section 3 introduces the normal distribution and Weibull distribution methods, along with distribution fitting techniques, for statistically analyzing BDS. Experiment results of the dielectric properties and electrical breakdown tests are provided in Section 4.