The big challenge that we face today for designing resilient memories is the huge number of simulations needed to arrive at a good estimate of memory's yield. A lot of work has come up recently focusing on the reduction of these simulations. The majority of these methods have focused on using different Markov Chain Monte Carlo (MCMC) methods, most notably Importance Sampling. SRAMs, though, have an interesting property of failure monotonicity which implies that given a known failure point in SRAM's parameter space all points with larger variations will also be failure points. Our work REEM (Region Estimation by Exploiting Monotonicity), thus, focuses on exploiting the SRAM's failure monotonicity property for faster estimation of the Failure/Non-Failure regions. The usual MCMC methods can then be used without needing actual spice simulations. Our results show that using our method we can achieve an overall 10x reduction in simulations compared to traditional Importance Sampling methods.