In this paper, we present an approach to the tolerance analysis of non-linear, time-invariant systems depending on statistical distributed parameters. The approach is based on an approximation of the performance function over the parameter domain which allows the determination of statistical properties of this function and provides appropriate information for the design adjustment. We show that parameter sensitivities and even higher order Taylor expansions of the performance function are not applicable in general, and propose an interpolation approach using power series. Finally, we give some remarks on the incorporation of our method in numerical simulation programs (e.g. spice), especially we discuss the reduction of computational efforts to outperform the Monte Carlo method, even for a larger number of parameters.