A Statistical Maximum Algorithm for Gaussian Mixture Models Considering the Cumulative Distribution Function Curve

The statistical static timing analysis has been studied intensively in the last decade so as to deal with the process variability, and various techniques to represent distributions of timing information, such as a gate delay, a signal arrival time, and a slack, have been proposed. Among them, the Gaussian mixture model is distinguished from the others in that it can handle various correlations, non-Gaussian distributions, and slew distributions easily. However, the previous algorithm of computing the statistical maximum for Gaussian mixture models, which is one of key operations in the statistical static timing analysis, has a defect such that it produces a distribution similar to Gaussian in a certain case, although the correct distribution is far from Gaussian. In this paper, we propose a new algorithm for statistical maximum (minimum) operation for Gaussian mixture models. It takes the cumulative distribution function curve into consideration so as to compute accurate criticalities (probabilities of timing violation), which is important for detecting delay faults and circuit optimization with the use of statistical approaches. We also show some experimental results to evaluate the performance of the proposed method.