Corner-based Timing Analysis (CTA) becomes more and more pessimistic as feature size shrinks. This trend has motivated the development of Statistical Static Timing Analysis (SSTA). In this paper, we propose a new path-based SSTA framework that allows the estimation of path delay distributions and delay correlations by propagating iteratively mean and variance of cell delay. These moments, conditioned on input slope and output load values, are pre-characterized by an improved method: log-logistic distribution based input signals and inverters as output load. In applications, the delay gains of this SSTA framework with respect to CTA are shown to be significant. It is also highlighted that the discrepancy of critical paths orderings obtained by SSTA and CTA depends on two factors: cell-to-cell delay correlation and standard deviation of cell delay.