Taylor Expansion of Series System Reliability

Abstract

Series systems with correlated random safety margins distributed according to the normal distribution play an important role in recent developments of methods of structural reliability theory. These methods require calculation of values of n‐dimensional normal distribution functions. The paper points at a surprisingly accurate rule of thumb calculation method based on a modified second order Taylor expansion in terms of the correlation coefficients and with equicorrelation as expansion point. The equieorrelation coefficient to be used in the method is determined such that the first differential of the distribution function vanishes. The modification is simply to omit the coefficient 1/2 on the second differential in the expansion.