## 3 Materials and Methods
### Data Set and Problem Definition
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Datetime** & **machineID** & **Volt** & **Rotate** & **Pressure** & **Vibration** \\ \hline
1 January 2015 06:00 & 1 & 176.22 & 418.5 & 113.08 & 45.09 \\
1 January 2015 07:00 & 1 & 162.88 & 402.75 & 95.46 & 43.41 \\
1 January 2015 08:00 & 1 & 170.99 & 527.35 & 75.24 & 34.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: An example of machine conditions and usage date i.e., telemetry which includes information about time (“Datetime”), machine (“machineID”), and the sensors data consisting of voltage (“Volt”), rotation (“Rotate”), pressure (“Pressure”) and vibration (“Vibration”). In this work, we focus only on the Random Forest (RF) classifier, which is ranked as one of the best models in the aforementioned reference work [10]. In our case, the focus is to explore and show the importance of interdependencies rather than to compare various ML models. Therefore, considering only the RF model is sufficient to accomplish our experiments. RF is an ensembled method based on decision tree (DT) approach. To be more accurate, RF generate multiple uncorrelated DT models. This models usually consider different subsets of features selected in a random way. Finally, all this models are used for prediction/classification and a majority voting is used to decide the outcome. The advantage of operating as a committee helps to outperform any of the individual models (e.g., DT). A critical challenge within this use case is imbalanced data. In addition to suitable scores for imbalance data provided in reference work [10], we employed the SMOTEENN approach [45], which is a hybrid approach. This approach takes advantage of both under-sampling and over-sampling techniques. In other words, under-sampling method is used to remove redundant records in the majority class aiming to balance the data distribution over the classes. On the other hand, over-sampling method aims to generate new records on the minority class aiming to balance the distribution of these classes. As a results SMOTEENN combines this two techniques to balance the distribution of the data. To be more accurate, Synthetic Minority Over-sampling Technique (SMOTE) [46] is the over-sampling method and Edited Nearest Neighbours (ENN) [47] is used to remove/clean redundant records in the majority class. Finally, by considering the aforementioned methods, we were able to replicate predictive results successfully, as shown in Table 3. Moreover, we employed the 3-Fold time series cross-validator introduced in [48]. This approach is valuable to avoid over-fitting in time-series data while evaluating ML models. \begin{table}
\begin{tabular}{c c c} \hline \hline _Data Types_ & _Nr. of Records_ & _Features_ \\ \hline
**Machine conditions and** & & \\
**usage data** & 8761 & datetime, voltage, rotation, pressure, vibration \\
**failure logs** & 761 & datetime, machineID, failure \\
**error logs** & 3919 & datetime, machineID, errorID \\
**maintenance logs** & 3286 & datetime, machineID, comp \\
**machine metadata** & 100 & machineID, Model, Age \\ \hline \hline \end{tabular}
\end{table} 
Table 2: This table describes the considered dataset to conduct the experiments within this research work. For more details concerning data engineering/selection process, please refer to previous research work [10]. Figure 2: This Figure shows the relation of this research to the previous research work, which considers intrinsic (self-dependency) interdependencies. Furthermore, it highlights the focus of this research work which in addition to intrinsic dependency, demonstrates also the impact of interdependencies between components (i.e., MCS interdependencies).