## 3 Results and Discussion
### Analysis of Features
#### 3.3.2 ANOVA Analysis
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**H-C \({}^{*}\)** & **Cases** & **SS \({}^{*}\)** & **df** & **MS \({}^{*}\)** & **\(F\)** & **\(p\)** & **VS-MPR \({}^{*}\)** & **\(\eta^{2}\) \({}^{*}\)** & **\(\eta^{2}\) \({}^{*}\)** & **\(\omega^{2}\) \({}^{*}\)** \\ \hline \multirow{2}{*}{None} & MDS\_Coded & \(6.002\times 10^{6}\) & 4 & \(1.501\times 10^{6}\) & 2.861 & 0.027 & 3.778 & 0.097 & 0.097 & 0.063 \\  & Residuals & \(5.560\times 10^{7}\) & 106 & 524,565.039 & & & & & & \\ BF \({}^{*}\) & MDS\_Coded & \(6.002\times 10^{6}\) & 4 & \(1.501\times 10^{6}\) & 3.347 & 0.014 & 6.248 & 0.097 & 0.097 & 0.063 \\  & Residuals & \(5.560\times 10^{7}\) & 81.283 & 684,075.358 & & & & & & \\ Welch & MDS\_Coded & \(6.002\times 10^{6}\) & 4 & \(1.501\times 10^{6}\) & 3.850 & 0.010 & 7.697 & 0.097 & 0.097 & 0.063 \\  & Residuals & \(5.560\times 10^{7}\) & 36.127 & \(1.539\times 10^{6}\) & & & & & & \\ \hline \hline \end{tabular} \({}^{*}\)H-C = Homogeneity Correction; SS = Sum of Squares; MS = Mean Square; BF = Brown–Forsythe VSMPR = Vovk-Selke Maximum p-Ratio. \(\eta^{2}\) = the effect size that indicates the proportion of total variance in the dependent variable attributed to an independent variable; \(\eta^{2}p\) = similar to \(\eta^{2}\) but adjusted for other effects; \(\omega^{2}\) = the measure of an effect size adjusted for bias.  
\end{table} 
Table 10: ANOVA analysis MAP and MTBF. Figure 8: The distributions with point estimate results of the ANOVA considering (**a**) MAP (1 = None, 2 = Visual Inspection, 3 = Contamination Control, 4 = LCM, 5 = Contamination Control and PHM) categorical predictors (\(y\)-axis) and MTBF_Est (\(x\)-axis); and (**b**) Quantile–Qunatile plot of residuals. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Comparison** & \(z\) & \(W_{i}\) & \(W_{\text{j}}\) & \(p\) & \(p_{\text{bonf}}\) & \(p_{\text{holm}}\) \\ \hline
1–2 & \(-1.509\) & 42.480 & 55.083 & 0.131 & 1.000 & 0.788 \\
1–3 & \(-3.843\) & 42.480 & 69.741 & \(<\)0.001 *** & 0.001 ** & 0.001 ** \\
1–4 & \(-3.815\) & 42.480 & 82.650 & \(<\)0.001 *** & 0.001 ** & 0.001 ** \\
1–5 & \(-1.291\) & 42.480 & 62.875 & 0.197 & 1.000 & 0.983 \\
2–3 & \(-1.607\) & 55.083 & 69.741 & 0.108 & 1.000 & 0.756 \\
2–4 & \(-2.300\) & 55.083 & 82.650 & 0.021 \({}^{*}\) & 0.215 & 0.172 \\
2–5 & \(-0.464\) & 55.083 & 62.875 & 0.643 & 1.000 & 1.000 \\
3–4 & \(-1.158\) & 69.741 & 82.650 & 0.247 & 1.000 & 0.987 \\
3–5 & 0.424 & 69.741 & 62.875 & 0.672 & 1.000 & 1.000 \\
4–5 & 1.100 & 82.650 & 62.875 & 0.271 & 1.000 & 0.987 \\ \hline \hline \end{tabular} \({}^{*}\)_p \(<\) 0.05, **\(p\) \(<\) 0.01, ***\({}^{*}\)_p \(<\) 0.001._  
\end{table} 
Table 9: Post hoc pairwise comparison. MAP5 categories regarding the performance of MTBF (\(t=-2.823\), \(p=0.044\); \(z=-2.822\), \(p=0.005\)). After using Bonferroni correction on a post hoc [PERSON]'s test, the results report statistically significant results with a large effect size (\(p=0.048\), RBC \(=-0.721\)). However, [PERSON]'s test also suggests a significant difference between MAP1 and MAP4 (\(p=0.014\)); however, after subjecting the \(p\)-value to Bonferroni correction, the results are not (\(p=0.141\)). In sum, using advanced maintenance analysis programs, such as contamination control and prognostics and health management [46; 47], the MTBF will significantly rise, improving the operational availability of fluid power systems. Lastly, the analysis of CMS and MTBF_Est (Table 12) and the ANOVA analysis, suggests the presence of significant findings (\(F=4.369\), \(\eta^{2}=0.109\)). At the same time, CMS did not have an apparent effect on WOM and MTTR performance metrics. After performing the normality analysis, the distributions of CMS categories (Figure 9a) and the QQ plot (Figure 9b) suggest that normality was not violated. Next, the analysis of [PERSON]'s test (\(p=0.897\)) suggests homogeneity of variances. Consequently, a [PERSON] post hoc pairwise comparison is performed (Table 13).