Bound for Trivariate Integrals in System Bound

Abstract

The reliability of a structure with many potential failure modes is usually assessed by evaluating an upper bound and a lower bound on the failure probability of the structure. Although it is known that a better estimate of the failure probability can be obtained with third‐order linear bounds, the excessive computational requirement of trivariate integrals (trisections) has so far restricted their use in normal practice. In this paper a nonlinear bound for trisections in terms of bisections (bivariate integrals) is presented with examples. Furthermore, the bound developed for the trisections has been used in the third‐order linear bound to produce a better second‐order lower bound (nonlinear) for the reliability of structures, and the results are compared with other published results.