The measuring accuracy of coordinate measuring machines (CMMs) will be affected by the different geometrical and dynamic errors, including the deviations associated to the axis displacement, the working table and the part to be measured. This work is focused on the analysis of the influence of the position errors, repeatability errors and reversibility errors in 3-axis FXYZ coordinate measuring machines, and it will be developed by a numerical model that is known as EE-based stochastic model. This model implements a new error index that is named equivalent error (EE), which will integrate the totality of machine errors of the CMMs and will allow a global description of all these error sources by means of a unique error parameter. The results obtained by this numerical model have been compared with the application of a traditional method, and it was probed that the EE-based model makes possible an increase of a 13.29% in the linear modelling of the performance of CMMs from the machine errors considered in this work, which implies a relevant improvement for the analysis and description of the effect of the distinct error sources on the achievable measuring accuracy of CMMs. For this reason, the EE-based model will be of special interest for industrial applications such as the quality control to be applied inside the production systems dedicated to manufacture mechanical components of high dimensional accuracy.