Abstract: A new mixed-sensitivity index is proposed by combining the derivative based the local sensitivity of failure probability with the moment independent global sensitivity. The mixed-sensitivity index inherits the advantages of the traditional moment independent sensitivity, and it reflects the intrinsic relationship between the moment independent sensitivity and the variance based one. For solving the large computational cost, the proposed index is first transformed into the variance based mixed-sensitivity, then the high efficient state dependent parameter (SDP) method for the calculation of the conditional moments can be employed to calculate it efficiently. To further improve the computational efficiency, the importance sampling based SDP method and the truncated importance sampling based SDP method are proposed respectively. Several examples are employed to illustrate the reasonability of the proposed index and the accuracy of the proposed method.