## 5 Discussion
### Theoretical Contributions  
Our work has two main contributions. First, we showed the benefit of applying MCS to PdM. In this case, we show the importance of understanding and modeling interdependencies. In particular, we demonstrated that _time from last replacement of component_ is a valuable feature to quantify interdependencies between components. Second, we illustrated that visual approaches and XAI could identify and explain interdependencies.  
Regarding our first contribution, we demonstrate the positive impact of interdependencies on predictive models by comparing the trained model with/without taking the  
Figure 7: Model explainability for every single component using SHAP. The results show the presence of interdependencies between components altogether with the positive/negative impact with respect to the value magnitude. For instance, concering the component 1 failure prediction (section **(a)**) it is visible that that an worn out of component 2 contributed more on prediction of the failures, respectively a newly changed component 2 contributed otherwise.  
interdependencies into account. To the best of our knowledge, we are the first to demonstrate how modeling interdependencies within a predictive model could facilitate prediction quality. Last but not least, we demonstrated that _time from last replacement of components_ provides valuable information to quantify the interdependencies between components. In future research, we plan to explore other valuable features, respectively, the aggregation of this information with other features aiming to encode interdependencies between components. Data-driven PdM is a complex framework consisting of five consecutive steps, as shown in the background section. In this work, maintenance scheduling which includes planning, scheduling, and decision-making, is not considered; thus, we focused only on the facilitation of the predictive results with respect to the interdependencies knowledge. In the future, we plan to build a complete data-driven PdM process and evaluate it on a real use case that could help understand the real impact in the field of the MCS perspective.  
Regarding our second contribution, we showed that the identification of interdependencies requires a certain level of domain knowledge, and thus visual and XAI approaches are suitable. We showed that the multi-line approach as visual inspection helps to identify interdependencies between components. An advantage of this approach is that it provides a faster and better way of understanding data [49]. The previous studies aiming to improve maintenance scheduling in the context of MCS showed that the interdependencies between components within a system could be found [2; 4]. Similarly, we demonstrate the existence of interdependencies between components, e.g., between components 1 and 2, which was not obvious in the initial research work [10]. Moreover, we demonstrate that SHAP is a valuable tool to identify and analyze interdependencies. Employment of SHAP in the context of MCSs is a novel application. In literature, the main intuition behind the description of interdependencies within an MCS is that the worn-out component will accelerate the wear rate of other components that are interacting with each other [2; 4; 3]. Similarly, we demonstrate the same effect (e.g., see Figure 7-Component 1 in section A) using the SHAP results. However, we plan to explore other XAI approaches aiming to explain feature interaction analysis, respectively, feature contribution concerning the RUL.