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.