## 2 Materials and Methods
### Validation and Performance Assessment  
To address the limitations imposed by the small sample size, Leave-One-Out Cross-Validation (LOOCV) was adopted as the primary validation strategy. Unlike traditional k-fold cross-validation, which can suffer from high variance and unstable validation splits in low-data contexts, LOOCV maximizes the use of available samples by iteratively training on all data points except one (Figure 3). This method offers a nearly unbiased estimate of model generalization ability, ensuring that every observation contributes to both training and validation phases. While more computationally intensive, the small dataset size made LOOCV computationally feasible in this case. Figure 3: Leave-One-Out Cross-Validation strategy. Following model training, the focus moved to validation, where three standard metrics were used to assess performance:  
* R2 (coefficient of determination) to measure the proportion of variance explained by the model. * MAE (Mean Absolute Error) to evaluate average prediction error in absolute terms. * RMSE (Root Mean Squared Error) to penalize large deviations more strongly, thus capturing the overall prediction robustness. The mathematical formulations of these evaluation metrics are defined as follows:  
\[R^{2}=1-\frac{\sum_{i=1}^{n}\left(y_{i}-\hat{y}_{i}\right)^{2}}{\sum_{i=1}^{n} \left(y_{i}-\overline{y}\right)^{2}}\]  
\[MAE=\frac{1}{n}*\sum_{i=1}^{n}\lvert y_{i}-\hat{y}_{i}\rvert\]  
\[RMSE=\sqrt{\frac{1}{n}*\sum_{i=1}^{n}\left(y_{i}-\hat{y}_{i}\right)^{2}}\]  
In addition to numerical metrics, visual diagnostic tools were employed to analyze model behavior. Scatter plots of predicted versus actual values provided an intuitive measure of alignment with the ground truth, while residual plots were used to detect potential patterns or systematic biases in the prediction errors. Once the model demonstrated acceptable performance during the validation phase, a final training step was carried out using the entire initial dataset (i.e., all data from the first month and a half). This process aimed to maximize the model's learning potential by incorporating the full range of observed operating conditions. The resulting model serves as the production version, to be used in subsequent evaluations and operational testing. Feature Importance and Model Interpretability  
Model interpretability plays a crucial role in predictive maintenance applications, as it enables understanding and trust in the model's decisions. Given the variety of algorithms proposed in this study, each model requires a specific interpretability approach aligned with its intrinsic nature. For Linear Regression and Ridge Regression, interpretability is intrinsic and based on the analysis of learned coefficients. When input features are scaled, using RobustScaler in this case, the sign and magnitude of each coefficient indicate the direction and strength of its effect on the target. A positive value implies that increasing the feature raises the predicted duration, while a negative one implies the opposite. Feature relevance can be assessed by comparing the absolute values of these coefficients. In contrast, Decision Tree models offer interpretability through their hierarchical structure. In this work, tree depth was deliberately limited to reduce overfitting, which also enhances clarity. The model's logic can be illustrated through tree diagrams that highlight the sequence of decisions based on feature thresholds or alternatively expressed as simplified, human-readable rules (e.g., \"If the fuel intensity index is below 0.3, the expected time in Zone 3 is under 1 h\"). Additionally, feature importance scores extracted from the model summarize each variable's impact on predictions. Finally, for K-Nearest Neighbors, which lacks internal model coefficients or rules, a model-agnostic approach was required. In this case, permutation importance was used to assess each feature's relevance by measuring the decrease in R2 when the values of a feature are randomly permuted in the test set.