Subset Simulation Method for Rare Event Estimation: An Introduction

TL;DR

This paper introduces Subset Simulation, an advanced stochastic method for efficiently estimating very small probabilities of rare failure events, with detailed explanation, implementation guidance, and illustrative examples.

Contribution

It provides a clear, intuitive derivation and MATLAB implementation of Subset Simulation, making it accessible for practitioners to estimate rare event probabilities.

Findings

Effective estimation of small failure probabilities demonstrated

Method's simplicity and intuitive derivation highlighted

Examples with MATLAB code facilitate practical understanding

Abstract

This paper provides a detailed introductory description of Subset Simulation, an advanced stochastic simulation method for estimation of small probabilities of rare failure events. A simple and intuitive derivation of the method is given along with the discussion on its implementation. The method is illustrated with several easy-to-understand examples. For demonstration purposes, the MATLAB code for the considered examples is provided. The reader is assumed to be familiar only with elementary probability theory and statistics.