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A new and efficient algorithm is described for selecting the most economic set of component tolerances for a mass-produced electronic circuit, and is illustrated by application to two filter circuits. The algorithm is based on a statistical sampling of component space, and its efficiency is a consequence of using inexpensive sensitivity information to calculate response from a truncated Taylor-series approximation. The algorithm extends, to tolerance space, the familiar concept of undertaking exploratory random perturbations in order to seek an optimum design. The computational cost of the algorithm is shown to be reasonable: moreover, theoretical considerations and experimental evidence indicate the likelihood of further considerable reduction in the computational cost of tolerance assignment.