Narrow Reliability Bounds for Structural Systems

TLDR

Reliability analysis of structural systems with multiple possible failure modes is simplified by using upper and lower bound techniques. When single‑mode limit surfaces are hyperplanes and the basic variables are jointly normally distributed, a simple geometric interpretation of mode safety margins and reliability indices enables straightforward calculation of system reliability bounds. The authors establish general bounds based on single‑mode and pairwise intersection failure probabilities, showing that these bounds are very narrow and almost coincident in high‑reliability regimes.

Abstract

ABSTRACT For structural systems that may fail in any one of several possible modes, reliability analysis is greatly simplified by use of upper and lower bound techniques. General bounds based on all the single mode failure probabilities and all the pairwise mode intersection failure probabilities are established. For systems where the single mode limit state surfaces are hyperplanes in the space of basic variables, a simple geometrical interpretation of the correlation between mode safety margins combined with a well-known geometrical interpretation of the single mode reliability index makes the practical calculation of the system reliability bounds easy. This is particularly true when the set of basic variables is jointly normally distributed. Examples show very narrow bounds which, in the practically important domain of high reliability, are almost coincident.