An algorithm for circuits yield estimation and optimization is described.To obtain the first and secondderivatives of yield with respect to center and obtain maximum production yield,Monte Carlo analysis(MCA)and Newton method are employed.By using“fail”samples and rearrange frequences in order ofnonincreasing weights,the estimator is improved and the number of circuit analysis is reduced.Boththeoretical analysis and calculation examples show that the estimator is correct and the proposed algorithmperforms well and can be used for middle-scale circuit design.No matter the region of acceptability is convexononconvex,the circuit is linear or nonlinear,the algorithm is available. An algorithm for circuits yield estimation and optimization is described. To obtain the first and second derivatives of yield with respect to center and obtain maximum production yield, Monte Carlo analysis (MCA) and Newton method are employed. By using “fail” samples and rearrange frequences in order ofnonincreasing weights, the estimator is improved and the number of circuit analysis is reduced. Theothooretical analysis and calculation examples show that the estimator is correct and the proposed algorithmperforms well and can be used for middle-scale circuit design. No matter the region of acceptability is convexonconvex, the circuit is linear or nonlinear, the algorithm is available.