Much design principles are based on “a chain is as strong as its weakest link”. However, engineering systems are typically not in the form of the chain but complicated networks and individual safety of components matters as well as the structure of the system. While we can increase by improving all components this might not be cost-effective. This work will give a better understanding how the reliability of individual components affects the overall reliability, and this shall improve the safety of the person and property.
As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the increasing number of ways a system can fail. In this research, 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.
Part of The Alan Turing Institute-Lloyd’s Register Foundation Programme for Data-Centric Engineering.