The influence of failure mode order on structural system reliability

The failure probability of a structural system solved by O'Ditilevsen's narrow bound method or Y.S. Feng's high accuracy method is influenced by the orders of the failure modes. In this paper, the O'Ditilevsen minimal upper bound and maximal lower bound can be solved by using a max-tree finding algorithm in a correlative weighted graph and an optimality criterion respectively, so that the interval width between the upper and lower bounds becomes more narrow. Using an optimality criterion similar to the above-mentioned one, the maximum failure probability of a structural system combined with the high accuracy method can be obtained. Two examples are given to illustrate the effectiveness of the method presented in this paper.