The Nanopositioning- and Nanomeasurement machine is one at the TU Ilmenau developed machine that measures in a
volume of . Through a special order of the Laserinterferometer, it has succeeded to enforce the measurements abbé-
error-free. This is applied for the three coordinate-directions. If a measurement is enforced, measurement errors are
originated. The reasons therefore must be quantified and localized exactly as possible. For that it is necessary to
describe the measurement in a model. The model should comprise all possible influences on the measurement
uncertainty and the measurement result. In this work, the length measurement with the Nanopositioning - and
Nanomeasurement machine is described through a difference-model. The influences on the measurement result are
expressed through the individual components. The touching-point, the framework, the interferometer reference- and
interferometer measurement component, the cosine-total- and abbé-error on the basis of the angle tilting of the
leadership-tracks and the lateral disalignment of the interferometer, the mirror-error-component and the alteration of
the initially-point of the measurement during the measurement. The given information of the measurement uncertainty
doesn't take place like until now usually through the given information of the singles measurement uncertainties in the
three coordinate-directions but also through the information of the entire measurement uncertainty. The model as well
as the model equation has partially non-linear behaviour through it. The absolutely acknowledged and in the practice
taken procedures of the GUM pushes with the treatment of non-linear models at its borders. Even if it is possibly to get
the measurement uncertainty of a result-size of such models with the GUM, the mathematical expenditure is difficult
and complicate. It must be looked for other procedures. A possible alternative represents the Monte Carlo method. This
procedure is based on the variation of random numbers. In contrast to the GUM, no uncertainties but probability
distributions will be propagated. The so originated probability distributions of the result must be evaluated. The
arithmetic mean is the best estimated value and the standard deviation shows his uncertainty. While the GUM says,
that the originated distribution of the result is symmetrical and therefore forms the interval of the widened
measurement uncertainty about the best estimated value symmetrically, also non-symmetrical distributions are
evaluated precisely with the Monte Carlo method. The widened measurement uncertainty in this case doesn't lie about
the best-estimated value symmetrically - After the preparation of the metrological model, it must be simulated. This
happens with the program MATLAB. In order to assess the quality of the simulation, it must be compared with the
result of the GUM Workbench. The evaluation has shown that the Monte Carlo method absolutely represents an
alternative to the procedure of the GUM.