First-order second moment method (FOSM)

This method is also referred to as mean value first-order second moment (MVFOSM) method, and it is based on the first order Taylor series approximation of the performance function linearized at the mean values of the random variables. It uses only secondmoment statistics (mean and variance) of the random variables. Originally, Cornell (1969) used the simple two variable approaches. On the basic assumption that the resulting probability of Z is a normal distribution, by some relevant virtue of the central limit theorem, Cornell (1969) defined the reliability index as the ratio of the expected value of Z over its standard deviation. The Cornell reliability index (βc) is the absolute value of the ordinate of the point corresponding to Z = 0 on the standardized normal probability plot as given in Figure 4 and equation.