This thesis presents a method for estimating transmitted variance to enable robust parameter design in computer simulations. This method is based on the Hermite-Gaussian quadrature for a single input. It is extended to multiple variables, in which case, for simulations with n randomly varying inputs, the method requires 4n + 1 samples. For situations in which the polynomial response is separable, it is proven that 1) the method gives exact transmitted variance if the response is up to a fourth-order separable polynomial response and 2) the error of the transmitted variance estimated by the method is smaller than zero if the response is a fifth-order separable polynomial response. For situations in which the polynomial response is not separable, two probability models based on the effect hierarchy principle are used to generate a large number of polynomial response functions. The proposed method and alternative methods are applied to these polynomial response functions to investigate accuracy. For typical populations of problems, it is shown that the method has good accuracy, providing less than 5% error in 90% of cases.
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