6. Type B evaluations

6. Type B evaluations
Type B evaluations can apply to both random error and bias. The distinguishing feature is that the calculation of the uncertainty component is not based on a statistical analysis of data.
Some examples of sources of uncertainty that lead to type B evaluations are: Reference standards calibrated by another laboratory Physical constants used in the calculation of the reported value Environmental effects which cannot be sampled Possible configuration/geometry misalignment in the instrument Lack of resolution of the instrument
Documented sources of uncertainty, such as calibration reports for reference standards or published reports of uncertainties for physical constants, pose no difficulties in the analysis. The uncertainty will usually be reported as an expanded uncertainty, U, which is converted to the standard uncertainty, u = U/k. If the k factor is not known or documented, it is probably conservative to assume that k = 2.
Sources of uncertainty which are local to the measurement process but which cannot be adequately sampled to allow a statistical analysis require type B evaluations. One technique, which is widely used, is to estimate the worst-case effect, a, from: experience scientific judgment scant data
The GUM guidelines require that worst-case estimates of bias be converted to equivalent standard deviations. The mechanism is to consider that any error or bias, for the situation at hand is a random draw from a known statistical distribution. Then the standard deviation is calculated from known (or assumed) characteristics of the distribution. The methods are based on assumptions which may, or may not, be valid and require the experimenter to consider the effect of the assumptions on the final uncertainty. Three of the distributions that can be considered are: Uniform Triangular Normal (Gaussian)
Among these three, the uniform distribution leads to the most conservative estimate of uncertainty; i.e., it gives the largest standard deviation. The calculation of the standard deviation is based on the assumption that the end-points, ± a, of the distribution are known. It also embodies the assumption that all effects on the reported value, between -a and +a, are equally likely for the particular source of uncertainty. The degrees of freedom are usually assumed to be infinite although this is not a requirement.
The triangular distribution gives a less conservative estimate of uncertainty; i.e., it leads to a smaller standard deviation than the uniform distribution. The calculation of the standard deviation is based on the assumption that the end-points, ± a, of the distribution are known. The degrees of freedom are usually assumed to be infinite although this is not a requirement.
Of the three distribution listed above, the normal distribution leads to the least conservative estimate of uncertainty; i.e., it gives the smallest standard deviation. The calculation of the standard deviation is based on the assumption that the end-points, ± a, encompass 99.7 percent of the distribution. The degrees of freedom are usually assumed to be infinite although this is not a requirement.