Estimating Failure Probabilities

Abstract

System failure describes an undesired configuration of an engineering device, possibly leading to the destruction of material or a significant loss of performance and a consequent loss of yield. For systems subject to uncertainties, failure probabilities express the probability of this undesired configuration to take place. The accurate computation of failure probabilities, however, can be very difficult in practice. It may also become very costly, because of the many Monte Carlo samples that have to be taken, which may involve time consuming evaluations. In this chapter we present an overview of techniques to realistically estimate the amount of Monte Carlo runs that are needed to guarantee sharp bounds for relative errors of failure probabilities. They are presented for Monte Carlo sampling and for Importance Sampling. These error estimates apply to both non-parametric and parametric sampling. In the case of parametric sampling we propose a hybrid algorithm that combines simulations of full models and approximating response surface models. We illustrate this hybrid algorithm with a computation of bond wire fusing probabilities.