In this paper, we propose an efficient statistical analysis method for analyzing on-chip power grids. The new method, called SN-SOR (and its faster version, PSN-SOR), is based on a novel localized relaxed iterative approach and it can perform variational analysis on one node at a time. PSN-SOR further speeds up the analysis by using a refined conditioner, where the initial solution of SN-SOR is used as the pre-conditioner for the later iterations. Experimental results show that PSN-SOR is about two orders of magnitude faster than Monte-Carlo method with small errors and is about one order magnitude faster than general global successive over relaxation (SOR) method. PSN-SOR is more accurate and efficient than the recently proposed random walk method for localized statistical analysis.