Evaluation of measurement uncertainty based on grey system theory for small samples from an unknown distribution

To evaluate measurement uncertainty for small sample size and measurement data from an unknown distribution, we propose a grey evaluation method of measurement uncertainty based on the grey relation coefficient. The uncertainty of measurement is analyzed using grey system theory, and the defects of the grey evaluation model of measurement uncertainty （GEMU） are studied. We then establish an improved grey evaluation model of measurement uncertainty （IGEMU）. Simulations show that the precision of IGEMU is greater than that of GEMU, and that sample size has only a small effect on the precision of IGEVU. In particular, IGEMU is applied to evaluating measurement uncertainty for small sample size and measurement data from an unknown distribution. The measurement uncertainty of total profile deviation, which is measured by the CNC gear measuring center, can be evaluated by a combination of IGEMU and the Monte Carlo method.