2ND-ORDER UPPER-BOUNDS ON PROBABILITY OF INTERSECTION OF FAILURE EVENTS

The estimation of structural-system reliability often requires the com putation of the intersection probability of multiple-failure events. B ounds on this joint probability may be less time-consuming to compute and have adequate accuracy for some practical problems compared with a pproximate numerical solutions. This technical note compares the accur acy among different second-order upper bounds on the probability of in tersection of multiple-failure events. An upper bound has been derived in the literature from the Ditlevsen lower bound on the probability o f union of multiple-failure events; the equivalence of its different e xpressions commonly used in literature is explained, and its accuracy is numerically investigated and compared with other possible second-or der upper bounds. The accuracy of this upper bound reduces to the join t failure probability of the two least probable events for practical p roblems. The different bounds are ranked in terms of computational eff ort and accuracy.