This second simplification enables, firstly, the approximate models to be specified by a small number of statistical parameters and, secondly, the sensitivity of the points coordinates with respect to the modelled kinematic and probing errors to be calculated using simple formulae involving the statistical parameters. Using the approximate models, the uncertainty behaviour of a CMM for a range of influence factors considered in this paper can be specified in terms of the 12 statistical parameters listed in Table 1 and defined in Sections 4 and 5. The methods described in this paper represent an attempt to achieve a functionality as close as possible to that of a VCMM capability but using models that are as simple as possible but no simpler. The GUM differentiates between two methodologies, Type A and Type B, for associating uncertainties with effects. A Type A approach, usually applied to repeated measurements, involves a statistical analysis of the data in order to assign an uncertainty, e.g., derived from the standard deviation of repeated measurements. A Type A approach can be regarded as an _a posteriori_ approach. According to the GUM, a Type B approach involves assigning uncertainties to influence factors using other information, such as previous measurements, manufacturer's specifications, experience or expert judgement. As such, a Type B evaluation can be thought of as an _a priori_ approach, as these assignments can be made before measurements are made. The approach described in this paper largely follows a Type B approach and addresses uncertainty evaluation on the basis of information that is available a priori. This prior information is encoded in the values of statistical hyper-parameters associated with the various influence factors considered. These parameters can be thought of as specifying a population of CMMs that are consistent with the parameter values, e.g., CMMs that have squareness errors in a plausible range, etc. If we draw a number of CMMs from this population and use them to perform a particular measurement task, such as measure the length of a gauge block, we will obtain a range of measurement results. The uncertainty evaluation methodology described attempts to provide a statistical characterisation, in terms of uncertainties, of what that range would be if we were able to perform these experiments. Many of the influence factors, such as a squareness error associated with CMM measurements, can be thought of as systematic in that they persist and stay approximately constant in the time taken to perform a measurement task. The GUM Type B methodology enables the uncertainty contribution associated with these systematic effects to be evaluated. The remainder of this paper is organised as follows. The application of the GUM methodology to point cloud data is discussed in Section 2. Although this paper is mainly concerned with CMM length measuring capability, Section 3 discusses CMM length measuring capability in the context of three-dimensional measurement capability, showing that the length measuring capability can only partially characterise CMM performance. Point cloud uncertainty evaluation for repeatability effects, probe qualification effects and scale and squareness effects are discussed in Section 4. Section 5 discusses Gaussian process models to represent kinematic errors, such as straightness, roll, pitch and yaw, and probing errors and how these models can be used to evaluate point cloud uncertainties. Section 6 describes how the uncertainties associated with the influence factors propagate through to uncertainties associated with length measurement. The section also discusses how a statement of length measuring capability such as maximum permissible error can be used to guide the assignment of the statistical parameters for the influence factors. Section 7 illustrates the uncertainty evaluation methodologies related to the measurement of a step gauge artefact. Our concluding remarks are given in Section 8.