Determination of the uncertainty of length measurement with a three-coordinate measuring device

• The paper presents a new methodology for evaluating the calibration of a coordinate measuring machine (CMM) using a polynomial calibration curve and a confidence interval. • The paper also introduces a method for assessing measurements performed by a CMM using an established calibration curve and compares the results with the current approach based on the Maximum Permissible Error (MPE). The article presents an alternative method for evaluating the calibration of a coordinate measuring machine (CMM) using a polynomial calibration curve, including its confidence interval, and its subsequent use in evaluating measurements. The methodology, based on the OEFPIL (Optimal Estimation of Functional Parameters by Iterated Linearization) algorithm and GUM principles, enables a more comprehensive and statistically sound evaluation of measurements using CMM. The procedure was applied to measurements along three coordinate axes and four diagonal directions, with confidence intervals set at a minimum coverage probability of 95 %. The proposed procedure allows for a more accurate and traceable determination of measurement uncertainty and provides a significant improvement over conventional MPE-based evaluation under conditions close to calibration. The paper presents quantitative results for a specific calibration and measurement case.