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With technology scaling into nanometer regime, rampant process variations impact visible influences on leakage power estimation of very large scale integrations (VLSIs). In order to deal with the case of large inter- and intra-die variations, we induce a novel theory prototype of the statistical leakage power analysis (SLPA) for function blocks. Because inter-die variations can be pinned down into a small range but the number of gates in function blocks is large(>1000), we continue to simplify the prototype. At last, we induce the efficient methodology of SLPA. The method can save much running time for SLPA in the low power design since it is of the local-updating advantage. A large number of experimental data show that the method only takes feasible running time (0.32 s) to obtain accurate results (3 σ-error <0.5% on maximum) as function block circuits simultaneous suffer from 7.5%(3σ/mean)inter-die and 7.5% intra-die length variations, which demonstrates that our method is suitable for statistical leakage power analysis of VLSIs under rampant process variations.