Abstract: The following points are proved in this paper: (1) Non-probabilistic reliability index of an arbitrary structure merely exists at one of the crossing points at which standard failure surface of the structure intersects the straight lines passing through both origin of a standard infinite space and vertices of holohedric convex polyhedron centered at the origin, and (2) The non-probabilistic reliability index equals to the absolute value of the coordinate of one of the crossing points. Based on the reduction of feasible region from the standard infinite space to finite crossing points within the standard infinite space, a one-dimensional optimization algorithm for non-probabilistic reliability index is developed to replace the interval algorithm and multi-variable optimization approach. The algorithm is reliable and efficient in arithmetic operations.