## 6 Conclusions  
In the framework of the GPS standard system, the CMM task-oriented uncertainty evaluation has been studied. The main content is as follows:  
(1) The difficulty of uncertainty evaluation for CMM measurement tasks oriented at dimensional and geometric errors has been solved systematically. Based on the systematic analysis of the CMM task-oriented uncertainty sources, a model for evaluating the CMM task-oriented measurement uncertainty based on the measurement system analysis has been proposed. Starting from the statistical  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Uncertainty Components** & **Initial Evaluation** & \multicolumn{3}{c}{**Optimized Evaluation Results**} \\ \hline
**Symbol** & **Sources** & **Results** & **Workpiece A** & **Workpiece B** & **Workpiece C** \\ \hline \(u_{\text{E}}\) & Indication error & 2.021 \(\mu\)m & 0.69 \(\mu\)m & 0.69 \(\mu\)m & 0.69 \(\mu\)m \\ \(u_{\text{r}}\) & Repeatability & 0.357 \(\mu\)m & 0.339 \(\mu\)m & 0.323 \(\mu\)m & 0.309 \(\mu\)m \\ \(u_{\text{R}}\) & Reproducibility & 0.915 \(\mu\)m & 0.518 \(\mu\)m & 0.518 \(\mu\)m & 0.518 \(\mu\)m \\ \hline Standard uncertainty \(\text{u}_{\text{c}}\) & 2.3 \(\mu\)m & 0.9 \(\mu\)m & 0.9 \(\mu\)m & 0.9 \(\mu\)m \\ \hline Expanded uncertainty \(\text{U}\) (p = 95\%) & 4.6 \(\mu\)m & 1.8 \(\mu\)m & 1.8 \(\mu\)m & 1.8 \(\mu\)m \\ Comparison with target & \multirow{2}{*}{Excess} & \multirow{2}{*}{Less} & \multirow{2}{*}{Less} & \multirow{2}{*}{Less} \\ uncertainty \(\text{U}_{\text{o}}\) = 2.0 \(\mu\)m & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 12: The uncertainty budget of optimized evaluation for flatness measurement.  
Figure 5: Comparison of measurement uncertainty before and after optimization.  
characteristic indexes of the measurement results, this model has somewhat comprehensively reflected the impact of the CMM measuring system uncertainty sources on measurement results.  
(2) The quantization method and evaluation model for uncertainty components of such three different measurement tasks of the CMM as dimensions, geometrical errors have been studied. The uncertainty components caused by the indication errors of CMM different measurement tasks are quite different, and especially the form error and some position errors reflect the relative changes in the micro-sized space. The linear influence should be neglected when the uncertainty components are quantified. Moreover, the indication bias introduced by the residual system errors of the measuring instrument should also be quantified and characterized by reasonably selecting the error indicators according to the specific measurement tasks.  
(3) The optimal evaluation of the CMM task-oriented uncertainty has been studied. The target uncertainty of geometric parameter detection must satisfy the requirements of the design tolerance. In order to ensure the safety and reliability of the evaluation results, there is an \"excessive estimation\" in the CMM task-oriented uncertainty evaluation, which has the evaluation results of uncertainty possibly not meet the requirements for measurement accuracy. At this time, the secondary optimal evaluation of the measurement uncertainty should be extremely important. The uncertainty source information of the measurement process should be further grasped by means of experiments and other prior information, as well as each uncertainty component should be re-quantified reasonably; thus the combined standard uncertainty would be reduced.  
Conceived the Method and Wrote the Paper, Y.C.; Data curation, H.L. and Y.L.; Performed some Confirmatory Experiments, Y.C., H.L. and H.W.; Resources, Z.W. and X.C.; Edited the Manuscript, Z.W.  
This research was supported by National Key Research and Development Plan of China, Grant Number 2016 YFF0203801; Fujian Province Public Scientific Research Institute Special Program of China, Grant Number 2018R1033-6; Natural Science Foundation of China, Grant Number 515/5032.  
The authors declare no conflict of interest.