A high-dimensional variable selection unit determines a list of critical parameters from sensor data and parametric tool measurements from a semiconductor manufacturing tool, such as a semiconductor inspection tool or other types of semiconductor manufacturing tools. The high-dimensional variable selection model can be, for example, elastic net, forward-stagewise regression, or least angle regression. The list of critical parameters may be used to design a next generation semiconductor manufacturing tool, to bring the semiconductor manufacturing tool back to a normal status, to match a semiconductor manufacturing tool's results with that of another semiconductor manufacturing tool, or to develop a specification for the semiconductor manufacturing tool.