Abstract: The characteristics of system failure boundaries are studied with different distribution of design points of failure modes. It explains why a failure boundary is possibly non-smooth with multiple failure modes. Moreover, the applicability of the Gauss-Hermite integration method is analyzed for solution of system failure probability. Then, an improved method is proposed to calculate the system failure probability with dimension reduction and trapezium integral techniques based on theses characteristics. The examples show that the proposed method is accurate and efficient.