2.
Measurement Process Characterization
2.5. Uncertainty analysis 2.5.7. Standard and expanded uncertainties


Degrees of freedom for individual components of uncertainty 
Degrees of freedom for type A uncertainties are
the degrees of freedom for the respective standard deviations.
Degrees of freedom for Type B evaluations may be available from
published reports or calibration certificates. Special cases
where the standard deviation must be estimated from fragmentary
data or scientific judgment are assumed to have infinite degrees of
freedom; for example,


Degrees of freedom for the standard uncertainty  Degrees of freedom for the standard uncertainty, \(u\), which may be a combination of many standard deviations, is not generally known. This is particularly troublesome if there are large components of uncertainty with small degrees of freedom. In this case, the degrees of freedom is approximated by the WelchSatterthwaite formula (Brownlee). $$ {\large \nu = \frac{u^4}{\sum_{i=1}^R \frac{a_i^4 s_i^4}{\nu_i}} }$$  
Case study: Uncertainty and degrees of freedom  A case study of type A uncertainty analysis shows the computations of temporal components of uncertainty; instrument bias; geometrical bias; standard uncertainty; degrees of freedom; and expanded uncertainty. 