## 3 Case Study
### Distribution Parameters and Condition Data Estimations
It ends up in \"fair\" condition after year 15. The computed 2-FAL is in \"good\" between year 8 and 13. After year 13, it enters \"fair\" conditions. It is in \"poor\" condition between year 18 and 19, and it reinstates to \"good\" condition between year 20 and 22. After 22 years, it remains in a \"fair\" condition. Table 4 summarizes the representative distribution models for each condition parameters data in oil quality and furanic compound analyses. The dielectric breakdown voltage, color, and 2-FAL can be represented by the normal distribution, whereas interfacial tension, acidity, and water content are suitable to be represented by Weibull distribution. Color has the highest \(R^{2}\) with 0.9044, and interfacial tension has the lowest \(R^{2}\) with 0.3602. The exponential-based model was chosen for the curve fitting process for dielectric breakdown, water content, and interfacial. Whereas, color, acidity, and 2-FAL could be curve fitted by the power-based model. These models are chosen, since the highest \(R^{2}\) is obtained when compared to other models besides these curves depict the closest generic trends of oil quality and furanic compound analyses parameters data. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Fitted Distribution** & **Master Curve Equation** & \(R^{2}\) \\ \hline Dielectric breakdown voltage & Normal & y = exp(4.204 \(-\) 0.026x + 0.0001x\({}^{2}\)) & 0.8379 \\ Water content & Weibull & y = exp(2.181 + 0.423x \(-\) 0.0004x\({}^{2}\)) & 0.6167 \\ Interfacial tension & Weibull & y = exp(3.468 \(-\) 0.056x + 0.002x\({}^{2}\)) & 0.3602 \\ Color & Normal & y = 0.321(1 + x)\({}^{0.727}\) & 0.9044 \\ Acidity & Weibull & y = 0.015(1 + x)\({}^{0.531}\) & 0.6224 \\
2-FAL & Normal & y = 9.088x\({}^{1.459}\) & 0.4674 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The representative distribution for oil quality and furtar analyses. Figure 6: Comparison between computed and predicted (**a**) dielectric breakdown voltage; (**b**) water content; (**c**) interfacial tension; (**d**) color; (**e**) acidity; and, (**f**) 2-furfurraldehyde. Most of the predicted dissolved gases show deviation with the computed dissolved gases, as shown in Figure 7. Based on Table 1 in [16], the predicted H\({}_{2}\) deviates from the computed H\({}_{2}\) during the first two years, between year 4-7 and 17-21, as shown in Figure 7a. Both of the predicted and computed H\({}_{2}\) maintain in \"very good\" condition for 25 years. The predicted CH\({}_{4}\) still follows the decrement trend of the computed CH\({}_{4}\), regardless of the deviation, as seen in Figure 7b. The predicted and computed CH\({}_{4}\) remains in \"very good\" condition for 25 years. A few of the predicted CO show reasonable agreement with the computed CO between year 4 and 23, as shown in Figure 7c. The deviation between the predicted and computed CO occurs between year 1-3 and year 24-25. The predicted CO maintains in \"very good\" condition during the first seven years and later transits to the \"good\" condition. The computed CO maintains in \"very good\" during the first six years. Between year 7 and 23, it is in \"good\" condition. The computed CO reinstates to the \"very good\" condition after 23 years. The majority of the predicted CO\({}_{2}\) deviates from the computed CO\({}_{2}\), as shown in Figure 7d. The predicted CO\({}_{2}\) is in \"very good\" condition during the first two years. It is in a \"good\" condition between year 3 and 7. After seven years, the predicted CO\({}_{2}\) remains in a \"fair\" condition. The computed CO\({}_{2}\) is in \"very good\" condition during the first three years. From year 4 to 6, the computed CO\({}_{2}\) is in \"good\" condition. It enters a \"fair\" condition after year 6. It reinstates to \"good\" condition between year 21 and 23, and later transits to \"very good\" condition. The predicted C\({}_{2}\)H\({}_{4}\) is close to computed C\({}_{2}\)H\({}_{4}\) during the first 24 years, as shown in Figure 7e. It deviates from computed C\({}_{2}\)H\({}_{4}\) at year 25.