## 1 Introduction  
Numerous methods, including tan delta testing, partial discharge testing, leakage current testing, dielectric breakdown (BD) strength testing, tensile strength testing, elongation testing, differential scanning calorimetry, oxidative induction time testing, the thermogravimetric analysis, and Fourier transform infrared spectroscopy, have been utilized to assess the properties of insulating materials [1, 2].  
Dielectric BD strength testing is a valuable technique for evaluating insulation properties and changes due to the aging of insulating materials. The results of dielectric BD strength testing are variable and influenced by environmental conditions, the applied voltage, and electrode shape. Consequently, this method was employed for understanding characteristics through relative comparisons under identical test conditions and should be conducted in accordance with specified considerations [3]. The selection of an appropriate statistical distribution is crucial for the reliable interpretation of BD strength data. While various statistical distributions are generally used for analyzing BD strength in insulation materials, the appropriateness of the acquired data and statistical distribution have not been adequately investigated [4, 5, 6, 7]. This gap renders it challenging to identify errors between data and statistical distributions, posing a risk to the performance of power systems designed based on BD strength. This study aimed to investigate the correlation between dielectric BD strength data and statistical distribution, with the primary objectives of determining the suitability of various statistical distributions for BD strength data analysis and establishing a highly reliable statistical distribution using the coefficient of determination. In this study, PP insulation materials underwent thermal degradation at a maximum of 130 \({}^{\circ}\)C for 960 h, and the alternating current (AC) BD test was conducted to assess degradation characteristics. Additionally, a coefficient of determination was employed to identify a statistical distribution suitable for the acquired BD strength data. The findings indicate that log-normal and Weibull distributions were suitable when analyzing the BD strength of insulation before and after deterioration.  
The novelty of this study lies in its establishment of a suitable statistical distribution by using the coefficient of determination before analyzing the BD strength data of insulation materials, differentiating it from previous research. Unlike other works, statistical distribution can be selected in consideration of suitability, not just the Weibull distribution function, for the interpretation of breakdown strength. This contribution can lead to lower errors in the power system design process, enhancing reliability when analyzing the BD strength data of insulation materials.  
The rest of this paper is organized as follows. Section 2 provides the mathematical expressions and definitions of various statistical distributions for interpreting dielectric BD strength. Additionally, equations related to correlations are compiled to derive an appropriate statistical distribution. Section 3 describes the testing and setup required to obtain dielectric BD strength data. Section 4 presents an evaluation of the reliability of various statistical distributions based on the acquired data and determines the appropriate statistical distribution. Sections 5 and 6 present the Results and Discussion, respectively.