Abstract
As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the number of 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 for non-repairable and repairable components, demonstrating 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, or where the desired precision is lower.
Highlights
It can prove to be computationally intractable to perform classical reliability analysis of very large engineered systems when the number of cut sets grows combinatorially
We have presented an exciting new application for the Multilevel paradigm for estimating the reliability of systems, which speeds up traditional Monte Carlo estimation of system lifetimes and provides a approach which can generalise to other reliability problems which involve cut sets
We have demonstrated that the proposed approach to using Multilevel Monte Carlo (MLMC) in reliability problems achieves the strong mean and variance decay required to enable truncation of the number of levels which must be simulated
Summary
It can prove to be computationally intractable to perform classical reliability analysis of very large engineered systems when the number of cut (path) sets grows combinatorially. For simplicity of exposition we consider the canonical problem of estimating the expectation of a functional of system lifetime both with and without a component repair process, showing the approach developed is generalised to other reliability problems which depend on cut (path) sets for the analysis. Note that interest may not be in the reliability at a particular fixed mission time, but instead in: some expectation of a functional of system lifetime; or in ascertaining a quantile of system lifetime (i.e. the time to which one is 99.9% certain the system will survive); or in estimation of the entire system lifetime distribution In these situations Monte Carlo methods are typically the only tractable approach.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
