The invention provides a method for performing statistical static timing analysis using a novel on-chip variation model, referred to as Sensitivity-based Complex Statistical On-Chip Variation (SCS-OCV). SCS-OCV introduces complex variation concept to resolve the blocking technical issue of combining local random variations, enabling accurate calculation of statistical variations with correlations, such as common-path pessimism removal (CPPR). SCS-OCV proposes practical statistical min/max operations for random variations that can guarantee pessimism at nominal and targeted N-sigma corner, and extends the method to handle complex variations, enabling graph-based full arrival/required time propagation under variable compaction. SCS-OCV provides a statistical corner evaluation method for complex random variables that can transform vector-based parametric timing information to the single-value corner-based timing report, and based on the method derives equations to bridge POCV/SSTA with LOCV. This significantly reduces the learning curve and increases the usage of the technology, being more easily adopted by the industry.