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With aggressive scaling down of feature sizes in VLSI fabrication, process variation has become a critical issue in designs. We show that two necessary conditions for the ldquomaxrdquo operation are actually not satisfied in the moment matching based statistical timing analysis approaches. We propose two correlation-aware block-based statistical timing analysis approaches that keep these necessary conditions, and show that our approaches always achieve the lower bound and the upper bound on the timing yield. Our approach combining with moment-matching based statistical static timing analysis (SSTA) approaches can efficiently estimate the maximal possible errors of moment-matching-based SSTA approaches.