## 3 Materials and Methods  
### Data Set and Problem Definition  
The availability of public data-sets suitable for MCS analysis is very scarce due to the level of detail required to explain an MCS and the sensitivity of the data or business competitiveness. This work is an extension of the results shown in [10], where the aim is to predict component failures based on various data sources, such as condition monitoring and maintenance logs. In this work, [10], a comprehensive public data-set provided by Microsoft [44] is used to apply the PdM concept in terms of ML. This data-set is collected in the semi-conductor industry [16] and is suitable for the MCS topic and consists of the following data sources: machine conditions and usage data (telemetry records), error logs, maintenance logs, failure logs, and machine metadata. Machine conditions and usage data (i.e., telemetry data) include sensor data, such as voltage, rotation, pressure, and vibration from 100 machines aggregated on an hourly basis (see Table 1). This data are collected in the year 2015 and included 8761 records. Furthermore, 761 failures of the components were collected within the corresponding year. A failure leads to a crash of the component. Additionally, error logs and maintenance data are collected. An error presence does not cause a crash or force the machine to stop, therefore errors are not considered as failure. Maintenance data includes all the maintenance activities on the components. These different types of data are described in Table 2. Information concerning components and errors is anonymized by data-set's publisher and is therefore not available. It is important to note that feature engineering is also conducted, where statistical features are estimated from telemetry data by aggregating the data into 3 and 24 h to catch both short-term and long-term knowledge. Moreover, the categorical error data are transformed to numerical values by counting the errors for the time window of 3 h. Finally, the usage time of the each component is extracted from maintenance data, thus extracting the information concerning the _time from the last replacement_ for the corresponding components. In general, the data-set description and the feature engineering/selection process are completely replicated based on the previous research works [10; 44]; therefore details are not included in this section to avoid redundancy. This research works is based and extends the previous research work [10], which considers the intrinsic dependency as important information to improve predictive results. However, current research work demonstrates that intrinsic dependency is important information; however, the interdependencies between components is another information that is actually impacting the predictive results significantly. The relation to the previous research work and the focus of current research work is highlighted in Figure 2. In the aforementioned referenced work [10], _time from last replacement_ of the corresponding component is considered as valuable information to improve predictive results of the component failures. This information was considered and modeled based on the assumption that the usage time of each component helps to predict failures of this component, i.e., intrinsic dependency (see Figure 1-Section A). Consequently, the interdependencies between components are not taken into account in the referenced work [10]. Therefore, in this work, we aim to demonstrate that along with intrinsic dependency, the interdependencies between components can be used to improve predictive models. Building on the previous works with this data-set also allows us to compare the results of our MCS model with the SCS-models other scholars used.