## 2 Background
### Visual Analytics and XAI  
Visual analytics is an important method to explore data-sets in an easy and faster way. Hence, this method helps identify hidden patterns and analyze the root cause of failures and faults. Recently, visual analytics has been applied in many complex industrial settings [32], such as PdM, condition monitoring, anomaly, or fault detection, where the aim  
Figure 1: In section A, the intrinsic interdependencies on the components are shown. This type of interdependencies is assumed and taken into account in referenced research work [10]. Whereby, in section B, along with intrinsic interdependencies, also interdependencies with other components and system state and its condition are shown. is to explore and understand large data-sets [33; 34]. In particular, visual analytics shows promising results when combining machine intelligence with human intelligence aiming to gain new insights from data, thus, performing informed decision-making support in complex scenarios [32]. In general, visual analytics for MCS as a complex topic is less explored. However, [PERSON] et al. [9] evaluated different visualization approaches aiming to identify interdependencies using a crowd-sourced study. As a result, the multi-line approach outperformed other approaches in this regard. A drawback of this study is that the methods were evaluated using synthetic data. Therefore, we aim to use and analyze this approach using data from a real industrial use case. The identified interdependencies can be considered new knowledge that can be used as an input for the predictive models. This could help to enhance the PdM process further. However, the lack of transparency of predictive models, e.g., black-boxes, is a growing concern that requires to be handled. As a result, XAI as a new approach was introduced in 2004 [35], which helps to make black-box models understandable and interpretable. Current works in XAI focuses on two perspectives aiming for explainability: (1) global interpretability and (2) local interpretability [36]. The former focuses on explaining the model behavior, thus, extracting the whole logic of the model. The latter aims to understand the model's decision-making on specific instances, i.e., predictions. XAI has shown good results so far in different application domains, such as healthcare [37; 38], legal [39], or defect prediction [40]. Recently, extensive research on the topic of global interpretation has been conducted. Usually, the interpretation of models within this topic is performed either by ranking the model features (e.g., permutation feature importance) based on prediction importance or by analyzing the interdependencies between features (e.g., partial dependency plot). In contrast, SHAP approach [41] based on game theoretical optimal Shapely Values [42] estimates feature importance and interaction between features, as well as the feature contribution toward prediction using Shapely values. Moreover, SHAP is the only XAI method based on solid theory (Shapely value). Initially, SHAP explains the prediction of a specific instance by estimating the contribution of each feature using Shapley values from coalitional game theory [42]. Shapley value is a method to estimate each player's contribution in a coalition game. In particular, players corporate on a coalition and receive a certain profit from this cooperation. In the case of ML, the game is the prediction task, whereby the profit is the actual prediction minus the average prediction for all instances. The players are the feature values of the instance. The feature ranking is estimated as the absolute average of features across the data, formally stated as \(\sum_{j=1}^{N}|\phi_{i}^{(j)}|\)[43] where \(\phi\) represents each contribution (noted as \(j\)) of feature \(i\) whereas \(N\) denotes the number of all instance values of the feature \(i\). The global impact of the features can be estimated for all predicted classes as shown in Figure 6, with the features at the top being the most important.