Fast statistical analysis of rare circuit failure events via subset simulation in high-dimensional variation space

In this paper, we propose a novel subset simulation (SUS) technique to efficiently estimate the rare failure rate for nanoscale circuit blocks (e.g., SRAM, DFF, etc.) in high-dimensional variation space. The key idea of SUS is to express the rare failure probability of a given circuit as the product of several large conditional probabilities by introducing a number of intermediate failure events. These conditional probabilities can be efficiently estimated with a set of Markov chain Monte Carlo samples generated by a modified Metropolis algorithm, and then used to calculate the rare failure rate of the circuit. To quantitatively assess the accuracy of SUS, a statistical methodology is further proposed to accurately estimate the confidence interval of SUS based on the theory of Markov chain Monte Carlo simulation. Our experimental results of two nanoscale circuit examples demonstrate that SUS achieves significantly enhanced accuracy over other traditional techniques when the dimensionality of the variation space is more than a few hundred.