## 2 Evaluation Method  
### Source Analysis of Uncertainty  
During CMM measurement, all relevant factors may have an impact on the measurement results. The sources of uncertainty in the coordinate measuring system can be divided into five categories according to the analysis method of \"personnel, machine, object, method and environment\" commonly used in product quality management as shown in Figure 1: Uncertainty caused by CMM instrument's own errors, measured workpiece, surveyors, measuring method, and external environment. Figure 1: The uncertainty sources of the measurement system. EN: European Norm; ASME: American Society of Mechanical Engineers; GB: Chinese National Standards. (1) Uncertainty caused by surveyors  
In addition to professional qualities, the uncertainty caused by surveyors is mainly characterized by the differences of the measurement strategies caused by different understandings of the measurement specifications, such as clamping positioning, coordinate system establishment, sampling strategy, and probe configuration. (2) Uncertainty caused by the instrumental errors  
This refers to the uncertainty component produced by the deviation of the CMM's own metering characteristics from the ideal characteristics, including the uncertainty caused by design, standard quantity, detection system, dynamic characteristics, fitting and evaluation algorithm, and other factors, mainly including the impacts of 21 items of CMM mechanism errors and probe system errors, etc. on the measurement results [30]. Usually, CMM can correct 21 items of mechanism errors and calibrate the probe system. The CMM's own errors are reflected in the influence of residual system errors after correction and calibration. To ensure that the CMM measurement accuracy meets the relevant requirements, it is usually necessary to carry out acceptance and re-inspection testing of the CMM measuring characteristics by means of the measurement calibration programs. In the GPS ISO10360 series standards [26; 27], the CMM performance evaluation has been defined and relevant performance parameters and evaluation methods of the measuring instrument have been given, such as the indication, detection and scanning detection errors of the dimensional measurement as well as the dimensional and geometrical errors of the universal detection system. The technical parameters corresponding to the above-mentioned performance parameters are generally given before CMM is delivered, that is, the maximum permissible errors. In practical measurement, the Maximum Permissible Indication Error (\(E_{\text{L, MPE}}\)) is mainly related to the errors of the distance and other dimensional elements, and the MPE\({}_{P}\) indicates the error of the whole measurement system in a very small test space, generally affecting the form measurement. (3) Uncertainty caused by measured workpiece  
The geometric and physical characteristics of the workpiece itself will affect the measurement results, for example, the form, surface waviness and surface roughness of the measured elements have impacts on the measurement results together with the sampling strategy and probe configurations; the thermal expansion coefficient of the workpiece and its changes produce uncertainty in the temperature compensation; the force deformation is also affected by the workpiece positioning and clamping mode. Therefore, it is necessary to combine the specific measurement tasks to evaluate the uncertainty introduced by the measured workpiece. (4) Uncertainty caused by measurement methods  
In the actual measurement, measurement specifications only give general guidance and constraints for the measurement process, resulting in a certain degree of randomness in measurement methods. If currently there are no standards or specifications to clearly and meticulously stipulate the choice of the CMM sampling strategy and probe configurations, different sampling strategies and probe configurations will result in inconsistency of the measurement results.