## 5 Results  
Goodness-of-fit statistics were computed for each condition to assess the suitability of the test data for a specific statistical distribution. The K-S statistic was excluded owing to its limitation in evaluating the overall trend of the dataset, as it assesses only a single numerical value with the highest deviation from the trend line. The LKV test was also omitted, because it may be biased by certain values when the number of observed data points is small. The AIC and BIC were considered unsuitable for assessing goodness of fit as they evaluate the number of parameters in a statistical model and are not well suited for comparing the fit between different statistical distributions. R\({}^{2}\) and MD values were employed to evaluate the goodness of fit, considering the entire dataset and accounting for biases in the data. In this study, five statistical distributions (log-normal, exponential-1P, exponential-2P, Weibull-2P, and Weibull-3P) were assessed using R\({}^{2}\) and MD values. Tables 3 and 4 present the R\({}^{2}\) and MD values, respectively, for each statistical distribution under different degradation conditions. Figures 3-6 depict the results of specimens after 960 h at 130 \({}^{\circ}\)C and before and after degradation as various statistical functions. The vertical axis in the figures represents the unreliability function. Three functions--log-normal, exponential, and Weibull--were used in the analysis. Figures 3 and 4 illustrate unreliability functions as exp-1P and log-normal functions using the BD before degradation. Visually, exp-1P appears unsuitable for modeling BD data before degradation (R\({}^{2}\) = 0.465), while the log-normal function provides a good fit (R\({}^{2}\) = 0.955). \begin{table}
\begin{tabular}{c c c} \hline
**Item** & & **Contents** \\ \hline \multirow{5}{*}{Testing condition} & Maximum voltage & 60 [KV] \\  & Applied voltage & AC ramp \\  & Ramp rate & 1 [KV/s] \\  & Material of electrode & Stainless steel \\  & Electrode type & McKeown (sphere to sphere) \\  & Electrode size & 10 \(\Phi\) \\ \hline \multirow{2}{*}{Specimen} & Material & PP \\  & Size & 8 \(\Phi\) \\  & Thickness & 120 \(\pm\) 8 [\(\mu\)m] \\ \hline \multirow{2}{*}{Environmental condition} & Temperature & 20 [\({}^{\circ}\)C] \\  & Relative humidity & 35 [\%] \\ \hline \end{tabular}
\end{table} 
Table 2: AC BD test conditions. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Degradation Condition** & & \multicolumn{5}{c}{**Coefficient of Determination**} \\ \hline
**Temp. ** [\({}^{\circ}\)**C] & **Time [h]** & **Log-Normal** & **Exp-1P** & **Exp-2P** & **Weibull-2P** & **Weibull-3P** \\ \hline - & 0 & 0.955 & 0.465 & 0.726 & 0.912 & 0.953 \\ \hline \multirow{5}{*}{110} & 72 & 0.966 & 0.469 & 0.771 & 0.937 & 0.964 \\  & 240 & 0.815 & 0.520 & 0.629 & 0.872 & 0.863 \\  & 480 & 0.960  
Figure 4: Unreliability plot before thermal degradation of log-normal distribution. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multicolumn{2}{c}{**Degradation Condition**} & \multicolumn{5}{c}{**Mean Difference**} \\ \hline
**Temp.** [°C] & **Time [h]** & **Log-Normal** & **Exp-1P** & **Exp-2P** & **Weibull-2P** & **Weibull-3P** \\ \hline - & 0 & 5.3 & 24.2 & 10.1 & 6.1 & 5.2 \\ \hline \multirow{5}{*}{\(110\)} & 72 & 4.4 & 25.7 & 8.5 & 3.8 & 3.8 \\  & 240 & 10.3 & 27.1 & 22.6 & 8.4 & - \\  & 480 & 3.8 & 29.1 & 8.8 & 6.2 & 3.6 \\  & 720 & 13.8 & 26.3 & - & 11.8 & - \\  & 960 & 3.0 & 29.3 & 18.3 & 2.4 & 2.1 \\ \hline \multirow{5}{*}{\(130\)} & 72 & 4.0 & 23.4 & 2.9 & 6.7 & 2.5 \\  & 240 & 3.0 & 27.2 & 15.9 & 3.5 & 3.2 \\ \cline{1-1}  & 480 & 3.7 & 29.6 & 14.8 & 2.5 & 3.2 \\ \cline{1-1}  & 720 & 5.2 & 28.6 & 16.5 & 3.1 & 2.6 \\ \cline{1-1}  & 960 & 7.4 & 31.3 & 20.7 & 4.8 & - \\ \hline \end{tabular}
\end{table} 
Table 4: Mean differences according to statistical distribution and degradation conditions. Figure 3: Unreliability plot before thermal degradation of exponential-\(1\)P distribution.