Interval Predictor Model for the Survival Signature Using Monotone Radial Basis Functions

Abstract

This research describes a novel method for approximating the survival signature for very large systems. In recent years, the survival signature has emerged as a capable tool for the reliability analysis of critical infrastructure systems. In comparison with traditional approaches, it allows for complex modeling of dependencies, common causes of failures, as well as imprecision. However, while it enables the consideration of these effects, as an inherently combinatorial method, the survival signature suffers greatly from the curse of dimensionality. Critical infrastructures typically involve upward of hundreds of nodes. At this scale analytical computation of the survival signature is impossible using current computing capabilities. Instead of performing the full analytical computation of the survival signature, some studies have focused on approximating it using Monte Carlo simulation. While this reduces the numerical demand and allows for larger systems to be analyzed, these approaches will also quickly reach their limits with growing network size and complexity. Here, instead of approximating the full survival signature, we build a surrogate model based on normalized radial basis functions where the data points required to fit the model are approximated by Monte Carlo simulation. The resulting uncertainty from the simulation is then used to build an interval predictor model (IPM) that estimates intervals where the remaining survival signature values are expected to fall. By applying this imprecise survival signature, we can obtain bounds on the reliability. Because a low number of data points is sufficient to build the IPM, this presents a significant reduction in numerical demand and allows for very large systems to be considered.