Degradation model selection using depth function: A comparative analysis of median and outlier of functional data

In industrial systems such as wind turbines, accurately predicting component failure times is critical to ensure cost-effective maintenance and avoid catastrophic breakdowns. For predicting failure times and ensuring the reliable maintenance of complex systems, selecting an appropriate degradation model is essential. However, traditional model selection techniques often rely on the assumption of independent and identically distributed (i.i.d.) data—an assumption frequently violated in real-world applications with heterogeneous environments or small sample sizes. These violations can lead to poor model selection and inaccurate First Hitting Time (FHT) or Remaining Useful Life (RUL) estimates. This study introduces a novel methodology for degradation model selection based on functional data depth, a statistical tool that treats entire degradation trajectories as functional objects. By quantifying the centrality and extremeness of functional data, we develop a depth-based criterion for evaluating candidate stochastic models. To ensure robustness and predictive performance, we incorporate first-hitting time distributions as a validation mechanism. Our approach explicitly accounts for functional variability and temporal structure. The proposed method addresses key limitations of traditional model selection techniques, including sensitivity to non-i.i.d. data and neglect of temporal dependence. Numerical experiments and a case study on wind turbine degradation show that the approach effectively discriminates between competing models, providing a robust foundation for improved failure time estimation in complex systems.