Fast Statistical Analysis of Rare Failure Events with Truncated Normal Distribution in High-Dimensional Variation Space

In this paper, to accurately estimate the rare failure rates for large-scale circuits (e.g., SRAM) where process variations are modeled as truncated normal distributions in high-dimensional space, we propose a novel truncated scaled-sigma sampling (T-SSS) method. Similar to scaled-sigma sampling (SSS), T-SSS distorts the truncated normal distributions by a scaling factor, resulting in an analytical model for failure rate estimation. By drawing random samples from the distorted distribution and estimating a sequence of scaled failure rates, we can solve all unknown model coefficients and predict the original failure rate by extrapolation. The accuracy of T-SSS is further assessed by estimating its confidence interval (CI) based on re-sampling. Our numerical results demonstrate that the proposed T-SSS method can achieve superior accuracy over the state-of-the-art method without increasing the computational cost.