## 3 Case Study
### Distribution Parameters and Condition Data Estimations
Next, the individual condition parameters data for the next 10 years were computed while using the estimated distribution parameter through ICDF, as in Equations (19) and (20) for validation purpose. Figure 6 presents the predicted and computed individual condition parameters data over the transformer age band. Based on Table 2 in [16], the predicted dielectric breakdown voltage is quite close to the computed dielectric breakdown voltage, whereby it stays in \"very good\" condition for 25 years, as shown in Figure 6a. Most of the predicted water content shows reasonable agreement with the computed water content throughout the transformer age period, as in Figure 6b. An apparent deviation is found between predicted and computed water content for year 8-10 and year 25. The predicted and computed water content remain in \"very good\" condition for 25 years. The predicted interfacial tension shows a clear deviation from the computed interfacial tension, as seen in Figure 6c. The predicted interfacial tension is in \"very good\" condition throughout the first seven years. From year 8 to 15, it is in \"good\" condition and ends up in \"fair\" condition after year 15. Meanwhile, the computed interfacial tension is in \"very good\" condition during the first four years. It fluctuates among \"very good\", \"good\", and \"fair\"  
Figure 5: Parameters estimation for acidity based on Weibull distribution model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Transformer Age**} & \multicolumn{2}{c}{**Dielectric Breakdown Voltage**} & \multicolumn{2}{c}{**Acidity**} \\ \cline{2-5}  & \(\mu\) & \(\sigma\) & \(\alpha\) & \(\beta\) \\ \hline
16 & 43.877 & 20.170 & 0.0719 & 1.2458 \\
17 & 42.790 & 19.970 & 0.0779 & 1.2175 \\
18 & 41.729 & 19.771 & 0.0844 & 1.1898 \\
19 & 40.695 & 19.574 & 0.0914 & 1.1627 \\
20 & 39.686 & 19.379 & 0.0991 & 1.1363 \\
21 & 38.702 & 19.187 & 0.1073 & 1.1105 \\
22 & 37.743 & 18.996 & 0.1163 & 1.0852 \\
23 & 36.807 & 18.807 & 0.1259 & 1.0605 \\
24 & 35.895 & 18.619 & 0.1364 & 1.0364 \\
25 & 35.005 & 18.434 & 0.1478 & 1.0129 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Estimated distribution parameters for dielectric breakdown voltage and acidity. conditions between year 5 and 9. It enters a \"good\" condition after year 9 and then transits to \"fair\" condition between year 17 and 21. After year 21, it fluctuates between the \"very good\" and \"good\" conditions. The predicted color is close to the computed color throughout the first 23 years, as shown in Figure 6d. It deviates from the computed color after 23 years. The predicted color is in \"very good\" condition throughout the first eight years and then transits to \"good\" condition from year 9 to 11. The predicted color enters a \"fair\" condition between year 12 and 15. After 15 years, it ends up in a \"poor\" condition. Meanwhile, the computed color is in \"very good\" condition during the seven years and it transits to \"good\" condition from year 8 to 10 and then enters \"fair\" conditions in year 11. Between year 12 and 13, the computed color reinstates to a \"good\" condition. It enters the \"fair\" condition between year 14 and 16, and later ends up in \"poor\" condition. There are deviations between predicted and computed acidities between year 7-12, 16-18, and 22-24, as shown in Figure 6e. The predicted acidity is in a \"very good\" condition during the first 15 years. It ends up in \"good\" condition after year 15. The computed acidity is in \"very good\" during the first six years. Between year 7 and 9, it fluctuates between \"very good\" and \"good\" conditions. After year 9, the computed acidity remains in \"good\" condition. The predicted 2-furfurraldehyde remains close to the computed 2-furfurraldehyde during the first 15 years, as shown in Figure 6f. Most of the predicted 2-FAL is lower than the computed 2-furfurraldehyde after year 10. The predicted and computed 2-FAL are in THE \"very good\" condition during the first five years. Between year 6 and 15, the predicted 2-FAL is in \"good\" condition.