A Method for Estimating the Probability of Extremely Rare Accidents in Complex Systems

TL;DR

This paper introduces a novel method combining Interacting Particles System and DIRECT algorithms to estimate extremely rare accident probabilities in complex systems, especially with autonomous agents and human interactions.

Contribution

It presents a new approach that effectively estimates very low failure probabilities and identifies key intermediate events in complex, multi-agent systems.

Findings

Significantly improved estimation accuracy for rare events.

Ability to identify critical intermediate events.

Enhanced sensitivity analysis of system parameters.

Abstract

Estimating the probability of failures or accidents with aerospace systems is often necessary when new concepts or designs are introduced, as it is being done for Autonomous Aircraft. If the design is safe, as it is supposed to be, accident cases are hard to find. Such analysis needs some variance reduction technique and several algorithms exist for that, however specific model features may cause difficulties in practice, such as the case of system models where independent agents have to autonomously accomplish missions within finite time, and likely with the presence of human agents. For handling these scenarios, this paper presents a novel estimation approach, based on the combination of the well-established variation reduction technique of Interacting Particles System (IPS) with the long-standing optimization algorithm denominated DIviding RECTangles (DIRECT). When combined, these two techniques yield statistically significant results for extremely low probabilities. In addition, this novel approach allows the identification of intermediate events and simplifies the evaluation of sensitivity of the estimated probabilities to certain system parameters.