Multilevel Monte Carlo for Reliability Theory

TL;DR

This paper applies Multilevel Monte Carlo methods to reliability theory, demonstrating significant computational efficiency improvements over classical Monte Carlo in estimating system lifetime expectations for large, complex systems.

Contribution

It introduces the use of MLMC in reliability problems, showing how to control bias-variance tradeoff and achieve computational advantages.

Findings

MLMC reduces computational complexity by orders of magnitude for large systems.

MLMC effectively estimates expectations of system lifetime functions.

The approach outperforms classical Monte Carlo in complex reliability scenarios.

Abstract

As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - a simulation approach which is typically used for stochastic differential equation models - can be applied in reliability problems by carefully controlling the bias-variance tradeoff in approximating large system behaviour. In this first exposition of MLMC methods in reliability problems we address the canonical problem of estimating the expectation of a functional of system lifetime and show the computational advantages compared to classical Monte Carlo methods. The difference in computational complexity can be orders of magnitude for very large or complicated system structures.