Second‐Order Upper Bounds on Probability of Intersection of Failure Events

The estimation of structural‐system reliability often requires the computation of the intersection probability of multiple‐failure events. Bounds on this joint probability may be less time‐consuming to compute and have adequate accuracy for some practical problems compared with approximate numerical solutions. This technical note compares the accuracy among different second‐order upper bounds on the probability of intersection of multiple‐failure events. An upper bound has been derived in the literature from the Ditlevsen lower bound on the probability of union of multiple‐failure events; the equivalence of its different expressions commonly used in literature is explained, and its accuracy is numerically investigated and compared with other possible second‐order upper bounds. The accuracy of this upper bound reduces to the joint failure probability of the two least probable events for practical problems. The different bounds are ranked in terms of computational effort and accuracy.