# Machine Failure Prediction Using Survival Analysis
## 5 Results
### COX and RSF Feature Analysis  
For the selection of the most important features, a set of feature selection and feature analysis techniques were used. These results were then compared and the features that prevailed were applied to the RSF model for training. The features were also ranked for each of the machine failure types mentioned in Section 4.3.  
The COX and RSF methods in the feature ranking section showed that the most important features in terms of machine failure were torque, rpm, and air temperature, as shown in Figure 2 and Table 2. Specifically, in the figure and table, the ranking of the characteristics is shown for the type of machine failure. In the COX results, the values that have a negative value indicate low correlation with machine failure, while positive values indicate an increased probability of machine failure. In contrast, in the RSF results, negative values indicate that the characteristic reduces the predictive ability of the model, i.e., in this specific case, the correlation of the characteristic with a low risk of machine failure. In the case of RNF prediction, all characteristics have negative values, indicating that they are all related to a low risk of machine failure. Although this complicates the model prediction, including the context of machine failure, i.e., a random factor, it is somewhat logical.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Feature** & **Machine** & **HDF** & **OSF** & **PWF** & **RNF** & **TWF** \\ \hline Rotational speed [rpm] & 0.1173 & 0.0850 & 0.1594 & 0.0047 & \(-\)0.1413 & 0.1377 \\ Torque & 0.0678 & \(-\)0.0008 & 0.0028 & 0.2343 & \(-\)0.1162 & 0.1041 \\ Air temperature [K] & 0.0480 & 0.0731 & (\(\sim\))\(-\)0.00  
The ranking of the features in the various techniques differed slightly, but the characteristics were consistently among the top-ranked features. Specifically, the features of torque and rpm were consistently ranked among the top three features.  
Figure 2: _Cont._  
For the COX results shown in Figure 2, we can observe that in the case of all the failed machines, the COX diagram showed a strong correlation between the machine failure risk and the failure risk. The results show that the proposed method is able to predict the risk of the failure risk.  
Figure 2: (**a**) Cox feature analysis results for RNF and TWF; (**b**) OSF and PWF; (**c**) and for machine failure and HDF.  
and the increase in the air temperature. Moreover, the torque feature seems to have a correlation with the failure of the machine but to a smaller degree. The rest of the features in the diagram seem to have either no impact (rotational speed) or are associated with a lowered risk of the failure of the machine. Similar results are shown in the HDF failure type on the COX diagram where the air temperature seems to have the highest correlation to the risk of machine failure, while the increase values in other features seem to have a lower risk. For the OSF, RNF, PWF, and TWF failure types, all the features seem to have a small correlation with the event we aimed to capture, so using the other metrics in combination with the COX diagram is needed to better evaluate the features. The small correlation is noticed because of the small values of the positive and negative rankings, which means that most of the features are closer to 0.