A general robust reliability index

Three available robust reliability indexes include the robust reliability index based on interval analysis, the robust reliability index based on expansion function, and the robust reliability index based on infinite norm. The characteristics of these indexes are discussed in detail, and the advantage and disadvantage of them are demonstrated. To solve the existing problem, a general robust reliability index is set up, which may be applied to linear system and nonlinear system including various uncertainty convexes. In process of solving the proposed index, the multiple size parameters of many various uncertainty convexes are transform into the single size of a general uncertainty convex which includes all of the basic variables, then the lower limit of the single size, which makes the general convex overlap with failure set, is taken as the robust reliability index η. The proposed index shows the safety degree of linear system and nonlinear system definitely in the current conditions. η<1 shows that the system failure is possible in the current uncertainty condition of basic variables. η>1 shows that the system failure is impossible in the current uncertainty condition of basic variables, and that the system is in critical condition of safety and possible failure when the size parameter of the current uncertainty convex is multiplied by η. And the solving of the robust reliability index η is transformed into an optimization problem, which can be solved by the simulated method. Finally, the results of illustrations show the rationality and wide applicability of the presented method.