Correlated Rare Failure Analysis via Asymptotic Probability Evaluation

Abstract

In this article, a novel asymptotic probability evaluation (APE) method is proposed to estimate the probability of correlated rare failure events for complex integrated systems containing a large number of replicated cells. The key idea is to approximate the failure rate of the entire system by solving a set of nonlinear equations derived from a general analytical model. An error refinement method based on look-up table is further developed to improve numerical stability and, hence, reduce estimation error. Furthermore, a statistical algorithm based on resampling is developed to accurately estimate the confidence interval of APE. Our numerical experiments demonstrate that compared to the state-of-the-art method, APE can reduce the estimation error by up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$30\times $ </tex-math></inline-formula> without increasing the computational cost.