## 2 Background  
### Predictive Maintenance  
Recently, with the emergence of Industry 4.0, PdM has become one of the most effective solutions to address smart manufacturing and industrial big data with respect to fault diagnosis and remaining life assessment [11]. Maintenance management approaches in manufacturing can be grouped into three main categories: corrective maintenance or run-to-failure, preventive maintenance, and PdM [11; 12; 13]. First, corrective maintenance considers the maintenance performed only after the occurrence of failures. In other words, corrective maintenance is a reactive approach. Second, preventive maintenance goes a step further and aims to react proactively. In this case, the maintenance is performed according to a planned schedule based on time or process iterations. The advantage of this approach is that failures are usually avoided. However, unnecessary maintenance often is performed due to planned actions. Third, PdM is a proactive approach, which performs maintenance based on the monitoring status of the system and components. In this approach, the core aspect needed for decision-making is the estimation of the system's health status or components. This can be performed due to the available historical data of the machines and ML or statistical approaches [14]. The process of data-driven PdM can be divided into five stages: (1) operational assessment, (2) data acquisition, (3) feature engineering, (4) modeling, and (5) maintenance scheduling [8; 11; 15]. PdM is effectively applied in a wide range of different topics, such as bearings, blades, or driving motors [13]. This indicates that the PdM is focused on different fields of manufacturing, such as the electronics industry, semiconductors manufacturing [16], or additive manufacturing [17]. Furthermore, the health state of the system/components is successfully evaluated in different types of sensors, such as vibration [16; 18] temperature [13], electrical signal [13], or even from log data [19]. For instance, vibration analysis can be used for the detection and identifying problems that are directly related to the vibration patterns of the health system [20]. Last but not least, both ML and deep learning approaches are widely applied for PdM solutions [17]. For instance, [PERSON] and [PERSON] [21] introduced a novel dynamic data-driven PdM framework based on the LSTM approach. This framework covers the entire PdM process, from data-driven prognosis using the LSTM to maintenance decisions. The LSTM model is trained using multivariate time series data to predict the probability of system failure. This work also discusses the impact of imperfect prognosis information on maintenance decisions. On the other hand, [PERSON] et al., [22] proposed an enhanced dynamic PdM framework based on LSTM, which aims to predict failure moments and to determine the exact timing for long-term reliable maintenance decision-making. In the digital age, PdM approaches are widely applied in manufacturing. However, predicting failures or maintenance actions of MCS can be very challenging due to the complexity of these systems as a result of the existence of interdependencies and the influence of other environmental conditions [2; 3]. For instance, a complex system consists of components that last up to some years and components that have a shorter lifespan. In this context, components with a shorter lifespan will be replaced more often, leading to the scenario where newly replaced components are coupled with old worn-out components. The old worn-out component might affect the deterioration rate of the new component, leading to the accelerated rate of the new component and the whole system. Therefore, the lifespan of the newly replaced component and the system may not fit the exact description provided in the equipment manual. Hence, PdM approaches neglecting interdependencies can lead to imprecise or even erroneous estimation or predictive results, as well as reliable decision support in such a complex system [23; 24].