A consideration of the reliability index of the second moment method.

This paper is concerned with the reliability index of the second moment method for structural reliability analysis. The first problem considered is whether μ/σz is invariant, where μz and σ2z are the mean and variance of the function z=G(X1, X2, …, Xn) and G≦0 represents the failure state. Xi(i=1n) are the failure governing random variables. It is shown that μz/σz is not invariant. This result reveals the essential cause as being that βFOSM lacks invariance, where βFOSM is the reliability index of the FOSM (First-Order-Second-Moment) method. Hence, if invariance is the indispensable requirement for the measure of reliability, μz/σz is not adequate as a basis of such measure. The second problem considered is the relation between βAFOSM and μz/σz, where βAFOSM is the reliability index of the AFOSM (Advanced-First-Order-Second-Moment) method. Since βAFOSM is invariant whereas μz/σz is not invariant, βAFOSM may not be a good approximation of μz/σz . Numerical comparison of μz/σz, βFOSM, βAFOSM< reveals that βAFOSM is not a better approximation of μz/σz than βFOSM is. Hence, βAFOSM is better interpretted as the shortest distance from the origin to the surface G(X1, X2, …Xn)=0 in the space of the normalized variables than as an approximate value of μz/σz.