In this paper, a complete SSTA scheme is proposed to calculate the output waveform of a logic cell on any random selected point in the process variational space, or the mean value and variance of the output signal with very high accuracy and acceptable CPU cost. At first, Miller capacitances between the input nodes and internal nodes of a logic cell are introduced to construct the improved MCSM model so as to improve the modeling accuracy. Secondly, the stochastic collocation method jointed with the Modified Nested Sparse Grid technique is adopted for SSTA procedure to avoid the exponential increase of the collocation points number caused by tensor product. Thirdly, a Nominal waveform based Fast Simulation Method is developed to speedup the simulation on each collocation point. At last, Automatic Waveform Construction Technique is developed to construct the output waveform with the approximation points as little as possible to decrease the computational cost while guaranteeing high accuracy. Numerical results are also given to demonstrate the efficiency of the proposed algorithm.