Based on the variance-based global reliability sensitivity index, new regional and parametric sensitivity indices were defined respectively to measure how the sensitivity indices of the whole inputs change when the distribution range of one input is changed or its variance is decreased. Then these two proposed indices were described by PCC (Pearson correlation coefficient) between the unconditional failure indicator and its pick-frozen replication. Based on the transformation, two methods based on PCC were proposed to compute the proposed regional and parametric sensitivity indices. One method was based on Monte Carlo method and iterating sampling, whereas the other one was based on IS (importance sampling) and reusing the samples without extra computational cost, so the computational efficiency of the second method was much higher. The feasibility of the proposed regional and parametric indices, the accuracy and high efficiency of the proposed methods were demonstrated by the results of several examples.