## 8 Conclusions  
Scheduling maintenance actions is a complex task, and the most suitable policy depends on the specific use case. A policy based on PdM is the optimal choice for reducing maintenance-associated costs; however, developing monitoring systems and RUL prognostic models for all components may not be feasible. In such cases, an alternative approach based on periodic maintenance actions may be a viable option to mitigate costs associated with equipment failures. Some of the most widely used PM approaches in industry often employ static values for the time between replacements, which could be based on the MTBF calculated from historical data or overlying conservative values to prevent all failures. Such inflexible approaches can lead to sub-optimal cost-effectiveness, as maintenance costs may vary over time, affecting the compromise between asset lifetime exploitation and minimizing failures to obtain an optimal solution. Moreover, the time between failures and, consequently, the MTBF may dynamically change due to shifting working conditions or the degradation of other components within the system. In this work, we propose two distinct maintenance policies: (1) The PMD, designed for scenarios where no RUL prognostic model is available. It dynamically calculates the time between interventions based on the occurrence of failures within the set of the last replaced components. (2) The PdMI policy, which leverages the RUL predictions and the failure probability estimated by the k-LSTM-GFT model to calculate a dynamic safety factor to account for the uncertainty of RUL predictions. This approach mitigates the impact of imperfect RUL predictions based on the estimated failure probability, which allows for the dynamic calculation of the safety factors. The maintenance policies were tested on two distinct realistic use cases: one to highlight a scenario where sensor data are available and safety is a major concern (aircraft  
Figure 11: Number of working cycles and failures obtained with each policy. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Engine ID** & **Actual RUL** & \(RUL_{e}\) & \(RUL_{s}\) & \(F_{p}\) & \(t_{p}\) & **Flights** &
\begin{tabular}{c} **Maintenance** \\ **Slot (\(d_{s}\))** \\ \end{tabular} \\ \hline... &... &... &... &... &... &... &... \\
100 & 12 & 17.2 & 14.81 & 0.845 & 0.82 & 187 & No \\
100 & 11 & 14.69 & 12.65 & 0.845 & 0.82 & 188 & No \\
100 & 10 & 12.80 & 9.80 & 0.862 & 0.82 & 189 & No \\
100 & 9 & 10.56 & 8.10 & 0.862 & 0.82 & 190 & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Scenario for the engine with ID = 100 with the proposed PdMI policy. engines), and another where failures are allowed but no sensor data are available (friction welding use case). In the first use case, the proposed PdMI achieved a very good performance, achieving costs only 3-5% higher than the perfect maintenance plan, which is not achievable in practice since there is no perfect RUL prognostic model. Moreover, the PdMI approach successfully avoids failures, a crucial requirement for critical systems where safety is a crucial requirement. In cases where an RUL prognostic model is not feasible, we employ the proposed PMD policy. The results demonstrate that this approach outperforms static PM policies in the friction welding use case in both cases, A and B, where the costs of maintenance actions are different. The improvement was 51.8% and 19.5%, respectively, for Cases A and B. In addition to being more cost-effective than traditional PM approaches, the PMD policy offers flexibility to adapt to changes that may affect the distribution of the time between failures, which may occur due to varying working conditions or the degradation of other components within the system. The proposed maintenance approach aims to be deployed in a real industrial environment for future work. This deployment will involve integrating the company's data, including the availability of resources for maintenance actions.