# Failure Trends of High-Voltage Porcelain Insulators Depending on the Constituents of the Porcelain
## 1 Introduction
Figure 2 shows change in the trend of K of the porcelain insulators for samples manufactured in 1975, 1995, and 2005. Further, the hardness was evaluated to confirm the trend of the mechanical strength increase by implementing the HRB hardness test. Figure 3 shows the results of the HRB hardness test. The average result of the HRB test for the collected samples was calculated to be 119.8, 119.4, and 121.8 for samples produced in 1975, 1995, and 2005, respectively. The standard deviation was calculated and plotted in Figure 2 to check the distance of each data point from the mean hardness values observed. Figure 2 shows that the standard deviation decreased in samples manufactured later compared to earlier insulators. It can be deduced from the above experiments that the mechanical and electrical properties were enhanced with the increasing year of production. Further, XRF and SEM were performed to study the elemental composition change and microstructural condition in the porcelain insulators with increasing years to investigate the reason for the improvement in electrical and mechanical properties. The XRF results are shown in Table 3 for the collected samples. Microstructural analysis performed using SEM, as shown in Figure 4, depicts a huge porosity in sample A, which enhanced the tendency for cracking in these porcelain insulators. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Insulator ID**} & \multicolumn{6}{c}{**Failure Load (lbs)**} \\ \cline{2-7}  & **Sample A (1975)** & **Remarks** & **Sample B (1995)** & **Remarks** & **Sample C (2005)** & **Remarks** \\ \hline
1 & 21,020 & Neck & 22,450 & Pin & 22,740 & Pin \\
2 & 19,080 & Neck & 22,180 & Pin & 22,490 & Pin \\
3 & 22,250 & Pin & 22,530 & Pin & 22,380 & Neck \\
4 & 19,910 & Neck & 21,780 & Pin & 22,580 & Pin \\
5 & 20,750 & Neck & 22,140 & Pin & 22,940 & Pin \\
6 & 22,220 & Pin & 22,710 & Pin & 21,200 & Pin \\
7 & 14,250 & Neck & 19,780 & Pin & 22,880 & Pin \\
8 & 15,300 & Neck & 21,640 & Pin & 23,120 & Pin \\
9 & 19,070 & Neck & 22,240 & Pin & 21,790 & Pin \\
10 & 22,710 & Neck & 22,420 & Pin & 22,580 & Pin \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Details of the thermal and mechanical (T&M) load test results. Figure 2: Results of the HRB hardness test and Quality factor of load test on porcelain insulator samples. Figure 4: Microstructure of insulator sample A depicting a high porosity of the porcelain body. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Constituents (wt.\%)** & **1975** & **1995** & **2005** \\ \hline SiO\({}_{2}\) & 64.82 & 58.77 & 59.03 \\ Al\({}_{2}\)O\({}_{3}\) & 30.56 & 35.22 & 35.52 \\ CaO & 0.76 & 0.25 & 0.54 \\ MgO & 0.25 & 1.01 & 0.98 \\ Fe\({}_{2}\)O\({}_{3}\) & 0.82 & 0.33 & 0.22 \\ TiO\({}_{2}\) & 0.45 & 0.17 & 0.41 \\ Na\({}_{2}\)O & 1.56 & 1.87 & 1.76 \\ K\({}_{2}\)O & 1.83 & 1.96 & 1.54 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: X-ray fluorescence (XRF) studies of the porcelain body of porcelain insulators. Figure 3: Results of the hardness test for (**a**) sample A, (**b**) sample B, and (**c**) sample C.  
Statistical Analysis of the Constituents of Porcelain and the Probability of Failure of Porcelain Insulators  
Among all statistical techniques, the Weibull distribution is popular for analyzing the failure probability with fewer data points. In this case, 10 samples were considered for studying the failure probability of the porcelain insulators. The Weibull distribution has the potential to provide an accurate failure analysis with a low number of samples (n < 20) [15, 16, 17, 18, 19, 20, 21]. Another advantage identified with Weibull analysis is that it provides a logical and effortless graphical plot of the required lifetime expectancy. The graphical plot analysis is quite significant for researchers. The two most significant parameters in the case of a Weibull distribution are the shape (\(\alpha\)) and the scale factor (\(\beta\)). Here, a two-parameter Weibull distribution was used to predict the lifetime of the porcelain insulators.