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This communication presents a new approach to the statistical analysis of linear circuits. The method is based on a two-stage sampling scheme in which random directions are first generated in multiparameter component space, and then sample points are selected in each direction, the points being generated according to a modified probability density function within the tolerance region. An efficient tracking-sensitivity algorithm based on a matrix series expansion is utilized to approximate the circuit response values at the sample points. A technique for reducing the variance associated with the yield estimate is also discussed. The results are compared with those obtained by conventional Monte Carlo methods for a test example. Considerable savings in computational effort have been observed.