Abstract
To assess the reliability of micro-nano coordinate measuring machines (CMMs) for sphericity measurement, the Monte Carlo method (MCM) is applied to quantify the associated measurement uncertainty. A random forest regression model is further employed to construct a nonlinear mapping that links sphericity error to various uncertainty sources, such as measurement repeatability, probe wear, inter-axis crosstalk force of the CMM probe, and temperature. Using random-forest-derived metrics (out-of-bag error and increase of out-of-bag error), the relative impact of each error source on sphericity error is quantitatively analyzed. Through the integration of MCM with the random forest approach, this work not only demonstrates the reliability of sphericity measurements performed by micro-nano CMMs but also provides a quantitative breakdown of the contributions from individual uncertainty components. These findings offer considerable engineering value for enhancing the accuracy and trustworthiness of ultra-precision manufacturing measurements.