## 4 RAM analysis of EPBM
### Reliability and Maintainability Analysis of Line 1  
First, the database's trend and serial correlation tests are carried out. As shown in Figure 6, if the data follow a trend, then the NHPP method should be used; otherwise, the serial correlation test should be performed to determine whether the data are dependent or independent. If the data are dependent, the HPP method is used; otherwise, a renewal process (RP) is used based on the probability density function with continuous distribution. Following the determination of the TBFs and TTRs for each subsystem, the two mentioned tests can be performed as presented in [28]. The Trend test is performed by analyzing the data and calculating the statistical value, \(U\), using the following equation:  
\[U=2\sum_{i=1}^{n-1}\ln\frac{T_{n}}{T_{i}} \tag{24}\]  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameters** & & **Values** \\ \hline P\({}_{0}\) & EPBM Availability & 0.45 \\ P\({}_{\text{E}}\) & Electrical subsystem Unavailability & 0.03 \\ P\({}_{\text{M}}\) & Mechanical subsystem Unavailability & 0.15 \\ P\({}_{\text{C}}\) & Cutterhead subsystem Unavailability & 0.37 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Availability of EPBM in Line 1 using the Markov method.  
Figure 5: The TBF and TTR of the machine for the whole system.  
where, \(n\) is the total number of failures, \(T_{n}\) is the time of the (\(n\))th failure, and \(T_{i}\) is the time of the (\(i\))th failure.  
Under the null hypothesis of no trend, the test statistic \(U\) is chi-squared distributed with \(2(n-1)\) degrees of freedom (the number of independent grids in the system). A null hypothesis is not rejected if the test statistic \(U\) is located between the values of Chi\({}^{2}\) in lower and upper levels of significance [29]. Serial correlation tests are performed by plotting the (\(i\))th TBF or TTR against the (\(i-1\))th TBF or TTR. If the plotted points are scattered with no apparent pattern, the TBFs or TTRs are independent, and have no serial correlation [30,31].  
The trend test results are shown in Table 6, which indicates that the electrical and mechanical subsystem has no trend, but the cutterhead subsystem has a trend. Figure 6 shows the results of the serial correlation test, which indicates that there is no serial correlation between TBFs and TTRs of each subsystem. Therefore, the renewal process is used for the electrical and mechanical subsystems, and the cutterhead subsystem uses the NHPP. The best fit results to determine the theoretical probability distribution for the TBF and TTR data are presented in Table 7.  
Figure 6: Serial correlation test on TBFs and TTRs of electrical and mechanical EPBM subsystems.  
Table 7 shows that the probability distribution is not exponential in all subsystems. In other words, \(\lambda(t)\) and \(\mu(t)\) are not constant in all subsystems. This suggests that the Markov method cannot always be used for R(t) and M(t), which is contrary to the conclusions presented by [4]. The analysis of each subsystem has been determined based on the tests' results. Subsequently, reliability and maintainability diagrams for each subsystem and the EPBM have been produced, as presented in Figures 7 and 8. As seen in Figure 7, the reliability of the whole system is close to that of the mechanical subsystem, indicating that by performing scheduled repair and maintenance on the mechanical subsystem, the reliability of the entire system will also improve. Figure 8 suggests that the maintainability of the whole system significantly depends on the maintainability of the cutterhead.