# A Robust Conformal Framework for IoT-Based Predictive Maintenance
## 5 Robust Conformal Prognostic for Reliable Predictive Maintenance
### Uncertainty Quantification Methodologies in Predictive Maintenance  
Bayesian models (e.g., Bayesian Neural Network, Prophet) assume that errors or residuals follow a specified distribution (e.g., normal distribution), and when the underlying degradation process is oversimplified assumptions (e.g., using the piecewise linear model as in Section 4), these models assume and leverage a pattern that does not match the true variability and complexity of the data, delivering inaccurate results when used for test inference.  
Figure 7 represents the problem of leveraging the FD2 dataset from the CMAPSS data collection. The prophet algorithm, introduced in Section 3.1, overfits the data distributions and produces statistically coherent \"probabilistic gaps\" that fail to capture the actual sensor-based dynamics. Overestimating the piecewise linear trend imposed in the RUL extraction phase can make an impractical strategy for real-world applications where degradation does not strictly follow a piecewise linear path.  
Conversely, CP, introduced in Section 3.2, provides a more flexible and distribution-free CI adapted to the actual degradation pattern inherent in the data, permitting practitioners to apply a UQ strategy to independently evaluate the modeling and the CI estimation. Despite the advantages of the CP approach for time series analysis, it necessitates regulation for real PdM applications since it does not inherently embed maintenance domain knowledge, such as the physical requirement that RUL must decrease over time. In fact, if not adequately regulated, the conformal intervals can fluctuate in response to short-term sensor noise, causing large, erratic swings in the predicted intervals and making this practice unfeasible for effective maintenance planning. This tension between purely probabilistic modeling and the need for physically coherent forecasts highlights the motivation for a robust CP framework that regulates prediction and the CI intervals, supporting a rational application to IoT-enabled PdM.  
This methodology is the most embodied core of this work. Firstly, it enforces the monotonicity in the predicted RUL sequence (e.g., preventing any non-decreasing segments),  
Figure 7: Example of UQ methodology using Unit 260 of CMAPSS: Probabilistic Model (Prophet) and Conformal Predictions via BiLSTM.  
which aligns with the real-world nature of degradation processes. After that, to refine the conformal intervals by comparing multiple margin estimators, such as naive quantile, exponential weighting, or bootstrap--and selecting the methodology with the largest coverage. This methodological application ensures that while the coverage guarantees of CP are maintained, it will strengthen predictive margins through a conservative approach. The final intervals remain physically plausible, respecting the PdM practice. Practically, this regulated CP strategy is found especially valuable for PdM decision-making, as it yields intervals that are both statistically valid. To reflect the true component wear while permitting optimized scheduled interventions aiming to preserve the estimation confidence through a more refined CI. Leveraging this tool, a maintenance engineer can combine domain knowledge and a data-driven approach. Looking at both RUL prediction and interval estimation and applying maintenance strategies that reduce unexpected failures to optimize resource allocation and productivity in industrial environments.