Improved Reliability Bounds of Structural Systems

Abstract

A set of generalized and improved reliability bounds is developed to obtain very narrow upper and lower limits of the probability of failure of a structural system with known performance functions and basic variables. It is assumed that the basic variables are distributed normally due to the central limit theorem. The improved bounds are compared with second‐order and Monte Carlo solutions. The amount of calculations involved is the same as in second‐order bounds. The developed technique requires the evaluation of joint failure probabilities as required in second‐order bound. However, unlike in second‐order bound, the technique takes into account the effect of intersection of joint failure probabilities. The degree of improvement over second‐order bound seems to depend on correlation among failure modes as well as the absolute value of the probability of failure. The developed method can also be applied to other systems, provided the performance functions are known and the central limit theorem is applicable to the basic variables.