Response surface augmented moment method for efficient reliability analysis

The reliability analysis procedure based on design of experiment (DOE) is combined with the response surface method (RSM) for numerical efficiency. Instead of using the inefficient full factorial DOE, a response surface is constructed initially based on the data on the axial experimental points and updated successively by adding one more experimental point selected using an influence index, until the probability is converged. It is calculated using the Pearson system and the four statistical moments obtained from the experimental data complemented by the response surface. During the update of a response surface, cross product terms can be added into the formulation. The number of updating steps is finite, since the points to be added are selected among the set of points of full factorial design. The performance of the proposed method is tested with several examples containing various types of distributions. It is shown that the probability converges early in the process and thus the amount of calculation is only a small fraction of that of a full factorial design. This is comparable or even better than any other methods including FORM for a moderate number of random variables tested.