## 2 Background
### Multi Component Systems  
Machines are complex systems that consist of a variety of sub-systems and components. Furthermore, the sub-systems and components are required to interact with each other to provide smooth operation of these machines. Moreover, the environmental conditions and context highly affect the machine operation state and production results. All these factors directly influence the deterioration rate of machines, sub-systems, and components (see Figure 1-Section B). In literature, MCS models focus exactly on these challenges as they consider a higher degree of complexity and dynamic behavior of the environment. An MCS is defined as a system that consists of multiple components, and these components strongly interact with each other [25; 26]. In other words, dependencies between sub-systems or components can be modeled and considered for analytical tasks.  
In existing research work, interdependencies are grouped into four categories: economic, structural, stochastic, and resource-based interdependencies [5; 27; 28; 29]. Economicinterdependencies focus on the cost relationships between components. The main assumption is that the maintenance of a group of components at once leads to different costs compared to separate maintenance for each component [5]. Structural dependencies focus on the structural dependency between components, which could impact the maintenance process in a way that maintenance on failed components implies maintenance on the components that structurally are dependent [5]. Third, stochastic interdependencies consider the deterioration process of one component, which is possibly influenced by the deterioration state of other components, or other way around [5]. In particular, the condition state of a component depends not only on the current state of the system and its operating conditions but also on the current state of other components that interact with it [2; 3; 4]. Finally, resource-based interdependencies [4; 30] model the dependency between components and required resources for maintenance of, e.g., spare parts. Maintenance workers are also considered within this group. This research work focuses only on stochastic interdependencies or deterioration influences between components rather than economic or structural interdependencies.  
Components within an MCS are subject to continuous deterioration, depending on the past deterioration, which is described as an intrinsic effect in literature [2]. The intrinsic dependency is depicted in Figure 1-Section A. However, the deterioration state of a component within an MCS depends not only on intrinsic dependency but also on the system operation state and the deterioration state of other components that are interacting with, i.e., stochastic interdependencies (see Figure 1-Section B). Modeling stochastic interdependencies provides many advantages in practice: the opportunity to understand better and explain the dynamic system behavior, provide more accurate Remaining Useful Life (RUL) predictions, and thus more reliable decision support and maintenance scheduling results. In the current age of the manufacturing industry, the system is becoming more complex due to the need for high customization to fit specific expectations. Moreover, various components with mostly different purposes and life spans are coupled together within a system. These challenges make the identification of the model health indicators more challenging. However, these indicators are crucial to build reliable predictive models and thus are mandatory input [31]. Therefore, modeling stochastic interdependencies seems promising to tackle these effects, thus, providing more reliable results.