Employing Scaled Sigma Sampling for Efficient Estimation of Rare Event Probabilities in the Absence of Input Domain Mapping

Traditional techniques for statistical analysis of rare events require a good understanding of the dependence of the outputs on the independent input variables. This can sometimes be an insurmountable challenge, especially when the dimensionality of the input variation space is high. In this paper, we present an innovative scaled sigma sampling (SSS) technique that is able to obtain an accurate quantification of the low probability tails without requiring visibility to the failure regions or their input dimensionality. SSS leverages the probability density differences produced by process sigma scale factors to uncover the nature of the population redistribution induced by the circuit. This understanding is used to construct an efficient transform for the circuit metric, one that has the same sigma scale factor dependency of the cumulative probabilities as the SPICE simulations. This transform is then used to obtain the low probability tails corresponding to the original process distribution. We present representative circuit applications to illustrate the large savings in computational costs that one can achieve with SSS and the transparency and accuracy of this approach.