Manufacturing process variations and environmental effects (such as temperature) result in the variations of the values of circuit elements and parameters. Statistical methods of circuit design optimization take those variations into account and apply statistical (or statistical/deterministic) optimization techniques to obtain an “optimal” design. A broad class of problems exists in this area: statistical analysis involves studying the effects of element variations on circuit performance. It applies statistical techniques, such as Monte Carlo simulation and the variance propagation method, to estimate variability of performances. Parametric circuit performance is a measure of circuit quality and is represented by measurable performance functions such as gain, delay, bandwidth, etc., constituting the y-parameter vector. The major feature of statistical yield optimization methods, referred to as statistical design centering, is statistical sampling in either θ-space only or in both θ and x spaces.