A Study of Stratified Sampling in Variance Reduction Techniques for Parametric Yield Estimation

The Monte Carlo method exhibits generality and insensitivity to the number of stochastic variables, but is expensive for accurate yield estimation of electronic circuits. In the literature, several variance reduction techniques have been described, e.g., stratified sampling. In this contribution the theoretical aspects of the partitioning scheme of the tolerance region in stratified sampling is presented. Furthermore, a theorem about the efficiency of this estimator over the Primitive Monte Carlo (PMC) estimator vs. sample size is given. To the best of our knowledge, this problem was not previously studied in parametric yield estimation. In this method we suppose that the components of parameter disturbance space are independent or can be transformed to an independent basis. The application of this approach to a numerical example (Rosenbrock’s curved-valley function) and a circuit example (Sallen-Key low pass filter) are given.