Let us consider a case of measurement of mass of a 1 kg mass standard. Observations after applying buoyancy and other corrections are given in Table below
Different parameters are as follows:
Best estimate of the mass of the kilogram is 1000.000072g
The information about degrees of freedom is required to estimate the extended uncertainty of the mean with given confidence level for a single input quantity and also for the estimation of effective degrees of freedom veff for several input quantities.
Here we see that to have a reasonable estimate of Type A uncertainty, a good number of observations need to be taken. In a calibrating laboratory to take such a large number of observations at one calibration point is not feasible. Normally fewer observations say 3 or maximum 5 are taken. In such case the uncertainty uA is full of statistical fluctuations. The author suggested a method to smooth out these statistical fluctuations. The method is of pooling a larger number of variances of the instrument or of the procedure of measurement. The method is described in the following post.
Source: measurement uncertainty
