Learning a Kernel-Based Beran Estimator Using Nearest-Neighbours and Its Application to Reliability Analysis

Abstract

Reliability analysis plays a crucial role in various domains for modeling time-to-event data; however, traditional approaches often struggle with complex and nonlinear data distributions. Among the nonparametric methods, the Beran estimator stands out as a robust method employed for estimating the reliability of equipment in industrial environments. Built upon it, the Beran estimator with Neural Kernels (BENK) aims to address some limitations its counterpart faces, albeit at the cost of careful hyperparameter fine-tuning, particularly the number of neural subnetworks that implement the neural kernels, which can be addressed by using simpler methods, like the k-nearest neighbors algorithm. Although widely used, finding suitable values for the neighborhood’s size is not straightforward. This work introduces a parameterless k-Nearest Neighbors algorithm to the context of kernel-based estimators, particularly the Beran estimator, and evaluates it in reliability analysis for downhole safety valves, an essential device concerning security issues in oil wells. We demonstrate that our parameterless approach maintains or surpasses the predictive capability of survival functions compared to traditional hyperparameter-dependent methods, providing a robust and adaptable tool for reliability analysis that effectively handles complex, nonlinear data distributions without requiring dataset-specific calibration.