## 4 Method for Optimizing Measurement Uncertainty  
### Secondary Optimal Evaluation of Uncertainty Components  
The uncertainty component features \"overestimation\" in time of quantization, which is the possible upper bound of the uncertainty component under worse conditions to ensure the safety and reliability of the evaluation results. Referring to the new generation of GPS uncertainty evaluation theory, develop an uncertainty management program as shown in Figure 2 for a given task-oriented measurement process [34]. In this management program, the measurement tasks, conditions and methods, etc. as well as relevant matters related to the measurement process are given, so its core task is to optimize the estimation of the measurement uncertainty.  
From the initial evaluation of the measurement uncertainty, we can find the dominant contribution factors to uncertainty, redesign the scheme for quantization of the dominant uncertainty component, make it more close to the actual situation of the uncertainty component and avoid the influence of excessive estimation. However, such an uncertainty component will somewhat increase the measurement time and economic costs during secondary optimal evaluation, and the surveyors should make corresponding improvements according to their own measurement needs. The optimal evaluation of the uncertainty components described in this section mainly cover the uncertainty components introduced by indication errors and reproducibility.  
The uncertainty component caused by the indication errors as described in Section 3 is estimated according to the CMM maximum permissible error, i.e. the error limit. During secondary evaluation, physical standards similar to the object under test or calibrated workpiece can be adopted to calibrate the indication errors and thus to obtain a more accurate upper bound estimation of the indication error. See Table 1 for CMM \(E_{\text{L}=60,\text{MPE}}\) and \(\text{MPE}_{p}\) calibration results by using standard gauge blocks and master balls with calibration uncertainty able to be neglected. It is shown that the uncertainty component introduced by the indication errors after secondary evaluation has been significantly reduced compared with the initial evaluation.  
The uncertainty component caused by reproducibility depends on the operation difference of the surveyor. The greater uncertainty component of reproducibility indicates that the operation  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Error** & **Error Limit** & **Uncertainty Component** \\ \hline \(E_{\text{L}=60,\text{MPE}}\) & 3.24 \(\mu\)m (\(L=60\) mm) & 1.87 \(\mu\)m \\ \(E_{\text{L}=60}\) & 1.4 \(\mu\)m (\(L=60\) mm) & 0.81 \(\mu\)m \\ \hline \(\text{MPE}_{p}\) & 3.5 \(\mu\)m & 2.02 \(\mu\)m \\ \(P\) & 1.2 \(\mu\)m & 0.69 \(\mu\)m \\ \hline \hline \end{tabular}
\end{table}
Table 1: Calibration results of indication error and probing error of CMM.  
Figure 2: Management program of task-oriented uncertainty by definitized measurement process.  
of the surveyor has a significant impact on the measurement results, and a more normalized and standardized measurement program file should be formulated to reasonably reduce the impacts on the evaluation results of reproducibility. For example, the secondary evaluation of the uncertainty component introduced by sampling strategy: When more prior information of the measurement task is available, reasonably and properly reduce the change range of sampling points; use spectral analysis to determine the best sampling strategy and estimate the changes of the measurement results from the difference between the actual measurement points and the optimal sampling points to evaluate the uncertainty caused by the sampling strategy. When the number of optimal sampling points is known, the influence of uncertainty introduced by this factor can be ignored.