For timing analysis, each flip-flop and latch in a standard library is characterized for two constraints: setup time and hold time constraints. These constraints need to be characterized for their sensitivities to the variation parameters in order to perform statistical timing analysis. Several approaches have been proposed to perform statistical characterization of delays. However, the predominant computation time requirements during statistical characterization are for constraint sensitivity characterization. In this paper we propose a new delay-based approach for statistical characterization of constraint sensitivities. We show that the sensitivities obtained using such an approach on an average result in $150X$ runtime improvement comparing with traditional approaches, without significant loss of accuracy.