## 4 Experimental Results
### Interdependencies Exploration Using SHAP  
Interdependencies exploration based on feature importance with feature effects on prediction of all component failures using SHAP is shown in Figure 6. In particular, we focus on the features containing information about the time from the last replacement of specific components, e.g., comp1_change, comp2_change, comp3_change, comp4_change. Interestingly, the contribution on failure prediction of component 1 from other components, e.g., comp2_change, comp3_change, and comp4_change, is obvious (as shown in Figure 6-section A, B, and E). On the other hand, component 1 shows no significant contribution toward the prediction of the failure of other components (e.g., Figure 6-section D). In addition, the contribution toward the prediction of component 3 failure from component 4 is recognized as shown in Figure 6-section C. In general, the results indicate no interdependencies effect on the prediction of failures for components 2 and 4. These results  
Figure 5: Estimation of interdependencies effect between components through comparison of predictive results. In purple are shown predictive results including interdependencies. Whereby, in green the predictive results excluding interdependencies are presented. Significant interdependencies are visible in components 1 and 3.  
explain and provide valuable insights regarding the prediction outcome shown in the previous section.  
For a better overview, global interpretation based on SHAP for every target value (component) is shown in Figure 7. The features are ordered by feature importance, with the most important features being listed first. For each feature, the contribution based on the Shapley value estimated for every instance is shown on the x-axis. Whereby a higher Shapley value indicates a more substantial contribution toward the prediction of the component failure. Moreover, the raw value of the instances is colored from red to blue, whereby red represents the highest value and blue represents the lowest value. Every plot of SHAP visualization represents the results for a specific component.  
The results show that features representing the time from the last replacement (e.g., comp1_change) for components are especially important while predicting single components. For instance, Figure 7a-Component 1 shows that the time from the last replacement of component 2 is especially important for the prediction of component 1 failures. The importance of this information provides a good basis to prove that the deterioration process of a specific component depends not only on the current state of the component and the operation conditions of the system but also on the current state of other components that are interacting with it. Moreover, based on the color of Shapley values, we can see that the contribution toward predicting the failures of component 1 is higher while the usage time of other components increases (see Figure 7a-Component 1 in section A, B, and C). This fits perfectly with the intuition behind the description of interdependencies within an MCS, where a worn-out component will accelerate the wear rate of other components that it is interacting with. Moreover, the interdependencies of component 1 with components 4 and 3 are also obvious based on these results. In general, similar behavior is present in the results shown in the analyzes of component 3 ( see Figure 7c).  
Figure 6: Estimation of feature importance with feature effects on prediction of all components ordered by feature importance in the y-axis and on the x-axis by Shapley value. Features _comp1_change_, _comp2_change_, _comp3_change_, _comp4_change_ show the contribution of corresponding _time from last change of these components_ on the prediction of components failures (e.g., blue color shows the contribution of this feature on prediction of the failures for component 1).