Uncertainty Assessment in Measurement Results Using Coordinate Measurement Systems

Coordinate measurement systems are commonly used to perform dimensional inspection of discrete-product part nowadays. They include coordinate measuring machines (CMMs), vision systems, and theodolites. It is desirable to express uncertainties associated with fitted measurement results due to inherent measurement uncertainties in coordinate measurement processes. A method is described in this paper for assessing uncertainties in coordinate measurement results. The method is based on first-order Taylor series approximation of data analysis algorithms in coordinate measurement processes. Use of the method has been illustrated using examples, and the results of which have been validated by comparing the assessed uncertainties with uncertainties obtained using Monte Carlo simulations. The method is applicable to linear and nonlinear fitting algorithms and is independent of the CMMs algorithms. It is advantageous since the algorithms are black boxes to most CMM users and the method can be easily applied to the calculation of sensitivity coefficients without the knowledge of the CMMs fitting algorithms. Another advantage of this method is the significant reduction of number of fitting times compared with that of the simulation method. The method presented in this paper can assist in evaluating sampling strategies by taking into consideration the measurement uncertainties in the measuring process. The assessed uncertainties can be used as an evaluation tool to ensure the selection of an appropriate sampling strategy in coordinate measurements by expressing uncertainties associated with fitted parameters. The method can also be used in selecting measuring instruments since uncertainties in measurement results are one of the critical factors in instrument selection. This method may be used to assist evaluation of tolerance zone of the feature, which defines the primary quality of the part features.