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Variance analysis is used for the estimation of how random device parameter variation effects the behavior of analog integrated circuits. This method is very effective if the random parameter deviations can be assumed to be normally distributed and statistically independent and if the nonlinear dependence of the circuit characteristics can be linearized around the nominal (mean) parameter values. It is shown under which conditions the nonlinear dependencies of the system characteristics on the parameters have to be taken into account and how this can improve the accuracy of statistical analysis. This is illustrated with two examples: a transconductance amplifier and an analog filter.