Uncertainty of flatness least-square verification

The least-square method is commonly employed to verify the flatness in actual three-dimensional measuring process, but the uncertainty of the verification result is usually not given by the coordinate measuring machines. According to the basic principle of flatness least-square verification and the uncertainty propagation formula given by ISO 14253-2, a method for calculating the uncertainty of flatness least-square verification is proposed. By this method, the coefficients of the plane equation are regarded as a statistical vector, so that the plane equation, the result of the. flatness verification and the uncertainty of the result can be obtained after the expected value and covariance matrix of the vector are determined.. The method can not only ensure the integrity of the verification results but also conform to the requirement. of the new generation of GPS standards, which can improve the veracity of verification. Experimental results indicate that based on the result of flatness least square verification and the uncertainty, the plane can be accepted or rejected quantitatively in accordance with the decision rules given by ISO 14253-1.