2.3.3. Implementation of ISO 15530-3 Technical Specification

As previously stated, the uncertainty assessment method suggested in this article is based on the ISO 15530-3 technical specification application backed by the ISO 15530-4 technical specification, through which the task-specific uncertainty assessment for the calibrated values (*ucal)* is realised.

According to the ISO 15530-3 technical specification, the uncertainty of the systematic error b (*ub*) is assessed by the difference between the average value obtained during the measurement process variability (*up*) parameter assessment and the indicated value of the CMM. However, according to the GUM recommendation, the measurement results should be corrected by the amount of systematic effect. Thus, if the measurement result is not corrected by the systematic error, the error fully contributes to the uncertainty budget; thus, (*ub*) = b.

The uncertainty budget presented here comprises the uncertainty contributors *ub*, *up* and *ucal*, whereas *uw* is negligible because of the lack of variation between the calibrated and measured dummy. The same physical dummy part is used during the calibration and measurement processes.

Other potential uncertainty sources, such as the measuring system resolution or any divergence between the master and measured dummy parts, were discarded because of their negligible effect on the uncertainty budget.

Equation (4) shows the combined standard uncertainty, *u*, which is given by the quadrature sum of each uncertainty contributor. Equation (1) shows the expanded measurement uncertainty U determined with a coverage factor *k* = 2 for an approximated coverage probability of 95%.

$$
\mu = \sqrt{\mu\_p^2 + \mu\_{cal}^2 + \mu\_w^2 + \mu\_b^2} \tag{4}
$$

wherein:

*uw*: standard uncertainty associated with material and manufacturing variations. This was negligible in this case.

*ucal*: standard uncertainty associated with the uncertainty of the MMC calibration (task-specific uncertainty value of each GD&T estimated by ZEISS VCMM™)

*ub*: standard uncertainty associated with systematic errors in the measurement process. It was assessed by the difference between the average value obtained during the measurement process variability (*up*) parameter assessment and the indicated value of the CMM.

*up*: to the standard uncertainty associated with the measurement process variability. The standard deviation of the ten-3D point cloud measurement repetitions was considered for each GD&T.

*k*: confidence interval: defines an interval with a level of confidence of approximately 95% (*k* = 2) with a normal distribution

U: expanded uncertainty for each GD&T comprising all the uncertainty error sources and their propagation with a confidence interval of 95% (*k* = 2).

Other uncertainty sources, such as thermal effects, measuring process drift, or the interaction between the light and the part surface, have not been considered separately within the uncertainty budget, as it is assumed that they contribute to (*up*) the standard uncertainty associated with the measurement process variability.

#### **3. Results**

This section describes the results obtained during the experimental implementation of the proposed uncertainty assessment method. For the sake of understanding, the experimental results are presented in such a way that every uncertainty contributor can be explained in detail. First, the standard uncertainty results associated with the measurement process variability (*up*) are presented. Then, the standard uncertainty results associated with the uncertainty of the MMC calibration (*ucal*) are presented, along with the values indicated by the ZEISS CMM for each evaluated GD&T. Subsequently, the standard uncertainty results associated with the systematic error of the measurement process (*ub*) are presented. Finally, the uncertainty budget for the 3D point cloud task-specific measurement uncertainty assessment is presented, where the expanded measurement uncertainty U is obtained for each GD&T element.
