Efficient Statistical Analysis for Correlated Rare Failure Events

To estimate the overall rare probability of correlated failure events for complex system containing a large number of replicated cells, we summarize two novel techniques in this paper. First, Asymptotic Probability Approximation (APA) method is introduced to capture the correlations among the failures of different cells by exploring a series of carefully defined partial failure events. Next, the entire system failure rate can be approximated by using a linear function of the total number of cells. Second, to further improve the estimation accuracy, we present the Asymptotic Probability Evaluation (APE) approach. The key idea of APE is to approximate the failure rate of the entire system by solving a set of nonlinear equations derived from a general analytical model. The numerical experiments demonstrate that APA and APE can accurately and efficiently estimates the overall failure rate of correlated rare failure events.