A new simulation approach to estimating expected values of functions of Bernoulli random variables under certain types of dependencies

Abstract

Consider an n-component system, where each component either works or is failed. With X _i equal to one if component i works and zero otherwise, a new simulation approach is presented that is based on an innovative use of stratified sampling, for estimating E[h(X ₁, …, X _n )], when h is a monotone function and the vector X ₁, …, X _n is exchangeable. It is shown how to extend the proposed approach to the case where there is a random environmental parameter Θ such that, conditional on Θ = θ, the components act independently, with component i working with probability θ p _i . Improvements in the method when the components are independent are also indicated.

Keywords:

• Simulation
• variance reduction
• stratification

Acknowledgements

This research was supported by the United States Department of Homeland Security through the Center for Risk and Economic Analysis of Terrorism Events (CREATE), grant number EMW-2004-GR-0112. However, any opinions, findings, and conclusions or recommendations in this document are those of the author and do not necessarily reflect views of the United States Department of Homeland Security.