# A Data-Driven Fault Tree for a Time Causality Analysis in an Aging System
## 5 Conclusions  
This paper has proposed an interpretable time causality analysis (ITCA) methodology for aging systems. The ITCA model represents the fault hierarchy causality by using the logic of the graphical fault tree and the knowledge discovery in the dataset. The obtained tree models the effect of the system's aging on the changes in the fault causality structure over time to better achieve fault prognosis. The illustrated case study demonstrates its usefulness and ability to discover only the relevant root cause that impacts the fault behaviour. Based on the model's interpretability, the expert is able to use the time causality structure of the turbofan HPC degradant performance to support his decision. Thus, the ITCA model provides the expert with the deep causality knowledge that explains the fault evolution over time. Unlocking the data-driven model's complexity by providing an interpretable graphical model, in addition to summarizing the evolution of the fault over time in one interpretable model are the two major contributions of the ITCA model over the current time causality data-driven models for fault prognosis. The ITCA model takes a further step towards reinforcing the link between experts and data-driven models. Such a model will help experts elucidate and implement the maintenance decision-making process.  
Our next research work will be to assist the expert by better optimizing the system performance through a set of control actions to maximize the RUL. We hope to allow our future ITCA model to demonstrate the system's reaction regarding a set of proposed control actions based on its causality rules and link the impact of a given proposed action to the RUL. The expert still needs to observe this system's reaction, represented by the new fault causality structure that reflects the system's response to the causality rule control actions that are taken, and note how this improves the RUL. Therefore, the future ITCA model must include different scenarios for fault causality structures that reflect the impact of the different combinations of control actions based on the derived causality rules.  
K.W.: Methodology, Data curation, Formal Analysis, Validation, Investigation, Software, Writing--Original draft preparation. M.-S.O.: Conceptualization, Formal Analysis, Writing--Reviewing and Editing, Supervision, Resources, Funding. All authors have read and agreed to the published version of the manuscript.  
The Natural Sciences and Engineering Research Council of Canada [grant number 231695] supported this work.  
Not applicable.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & NC & NRc & htlBleed & W31 & W32 \\ \hline T24 & \(-0.159\) & \(-0.502\) & \(0.595\) & \(-0.629\) & \(-0.614\) \\ \hline T30 & \(-0.211\) & \(-0.459\) & \(0.534\) & \(-0.543\) & \(-0.582\) \\ \hline T50 & \(-0.153\) & \(-0.548\) & \(0.644\) & \(-0.727\) & \(-0.699\) \\ \hline P15 & \(-0.001\) & \(-0.014\) & \(0.065\) & \(-0.059\) & \(-0.107\) \\ \hline P30 & \(\mathbf{0.175}\) & \(0.588\) & \(-0.651\) & \(0.718\) & \(0.739\) \\ \hline Nf & \(-0.167\) & \(-0.594\) & \(0.707\) & \(-0.750\) & \(-0.743\) \\ \hline Ps30 & \(-0.171\) & \(-0.594\) & \(0.689\) & \(\mathbf{-0.761}\) & \(\mathbf{-0.742}\) \\ \hline phi & \(0.158\) & \(\mathbf{0.616}\) & \(-0.688\) & \(0.722\) & \(0.721\) \\ \hline NRF & \(-0.169\) & \(-0.582\) & \(\mathbf{0.708}\) & \(-0.746\) & \(-0.715\) \\ \hline BPR & \(-0.184\) & \(-0.575\) & \(0.605\) & \(-0.663\) & \(-0.714\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Correlation matrix. The bold cell shows the maximum correlation value.