The experimental design technique in the literature, which has been limited only to normally distributed random variables, is extended to handle non-normal cases. It is easy to implement and provides good results for the moments of system response functions compared with other traditional methods. It is based on the three-level Taguchi method, and optimum levels and weights to handle non-normal distributions are derived. A systematic procedure for tolerance analysis is then proposed by using the Pearson system. Numerical results for non-linear examples are shown to be very accurate in comparison with those from Monte Carlo simulations and the first-order reliability method.