An improved method and apparatus for controlling the depth of removal by a chemical mechanical polishing of a selected material on a supporting semiconductor underlayer where it is desired to terminate removal of the selected material, such as silicon oxide, at a specified depth. In accordance with this novel method and system, the selected material such as a surface oxidization layer is polished to initiate removal thereof in the direction of the material-underlayer interface. This system includes three primary components: a chemical mechanical wafer polishing machine, a semiconductor thin film thickness measurement device, and statistical signal process algorithm and its associated computer system provides a chemical mechanical polishing system control by analysis and prediction of the current and future removal rates based on performance of past ratios for the before and after semiconductor thin film thickness measurements.