2. Measurement Process Characterization 2.5. Uncertainty analysis 2.5.6. Uncertainty budgets and sensitivity coefficients 2.5.6.3. Sensitivity coefficients for measurements from a 2level design 

Sensitivity coefficients from a 2level design 
If the temporal components are estimated from
a 2level nested design,
and the reported value for a test item is an average over
 
Problem with estimating degrees of freedom  If degrees of freedom are required for the uncertainty of the reported value, the formula above cannot be used directly and must be rewritten in terms of the standard deviations, \(s_1\) and \(s_2\). $$ s_{reported \, value} = \sqrt{\frac{1}{M}s_2^2 + \frac{JN}{MNJ} s_1^2} $$  
Sensitivity coefficients 
The sensitivity coefficients are:
\(a_1 = \sqrt{\frac{(JN)}{MNJ}} ; \, a_2 = \sqrt{\frac{1}{M}} \).
Specific sensitivity coefficients are shown in the table below for selections of \(N, \, M\). 

Sensitivity coefficients for two components of uncertainty
