An assessment of high-order bounds for structural reliability

Second-order bounds are often used to estimate the reliability of series structural systems. However, the quality of second-order bounds is poor when the failure modes are highly correlated. This paper examines the merit of third and higher-order bounds. First, the general form of the nth-order upper and lower bounds is derived. Second, an efficient algorithm for computing the n-dimensional multinormal integral is presented. Finally, the performance of the third and fourth-order bounds is examined in three numerical examples. These bounds can provide significant improvement over the second-order bounds, particularly when the number of significant failure modes is small (less than 20) or when the correlations between modes are somewhat localized.