Resists require higher resolution, lower line-edge roughness (LER) (or line-width roughness (LWR)), and improved sensitivity. However, those characteristics have an uncertain triangular relation and require trade-off. In this paper, a molecular-scale Monte Carlo simulation of the master equations is described. The master equations are proven analytically to be the rate equations of the chemically-amplified resist (CAR). The impact of various parameters, the aerial image contrast, the photoacid generator, the acid diffusion length, the quencher, the acid, the quencher diffusion coefficients, and the polymer size, on the LER in a CAR is analyzed with the Taguchi method and the spatial scaling metrics of CAR-induced LER. Simulation results for the 3 sigma LER agree with the experimental results, so a molecular-scale simulator can predict the dependence of the LER on the material properties and the process conditions. The HHCF (Height-height correction function) of spatial scaling metrics for the resist characterization and the Taguchi method for the LER minimization are discussed.