The second order moment method was used to derive the analytical formulas for both beam waist and the position of the waist of the focused elegant sin Gaussian beam.

Fuzzy reliability analysis based on the FOSM method;

Based on First-order Second-moment Method(FOSM),a formula for calculating t.

Reliability analysis using First Order Second Moment(FOSM)is important for structural probability design,in which process demands the derivative operation.

Using the JC method and the first order second moment method, the crack exceedance probability of aircraft wheel hubs under various cycle index number of cycles is calculat.

The first-order second-moment method is employed to calculate the reliability of girders,and to evaluate whether the carrying capacity is safe or not.

Based on the foregoing work, the parameters of soil are considered as random variables and by using of the first-order second-moment method and Monte Carlo method, the calculating method of static earth pressure by reliability theory is presented.

Based on the limit state equation and the first order second moment(FOSM)method,the process of solving the Psfs at the target reliability is simulated.

The result obtained has been compared with the one obtained by first order second moment (FOSM) method expanded about mean value.