2.
Measurement Process Characterization
2.5. Uncertainty analysis


Case study showing uncertainty budget  Uncertainty components are listed in a table along with their corresponding sensitivity coefficients, standard deviations and degrees of freedom. A table of typical entries illustrates the concept. 
Typical budget of type A and type B uncertainty components


 
Sensitivity coefficients show how components are related to result 
The sensitivity coefficient shows the relationship of the individual
uncertainty component to the standard deviation of the reported value
for a test item. The sensitivity coefficient relates to the result
that is being reported and not to the method of estimating uncertainty
components where the uncertainty, \(u\), is
$$ u = \sqrt{\sum_{i=1}^R a_i^2 s_i^2} $$ 
Sensitivity coefficients for type A components of uncertainty 
This section defines sensitivity coefficients that are appropriate
for type A components estimated from repeated measurements. The
pages on type A evaluations, particularly the
pages related to estimation of repeatability and
reproducibility components, should be reviewed before continuing on
this page. The convention for the notation for sensitivity
coefficients for this section is that:

Note on longterm errors  Even if no daytoday nor runtorun measurements were made in determining the reported value, the sensitivity coefficient is nonzero if that standard deviation proved to be significant in the analysis of data. 
Sensitivity coefficients for other type A components of random error  Procedures for estimating differences among instruments, operators, etc., which are treated as random components of uncertainty in the laboratory, show how to estimate the standard deviations so that the sensitivity coefficients = 1. 
Sensitivity coefficients for type A components for bias  This Handbook follows the ISO guidelines in that biases are corrected (correction may be zero), and the uncertainty component is the standard deviation of the correction. Procedures for dealing with biases show how to estimate the standard deviation of the correction so that the sensitivity coefficients are equal to one. 
Sensitivity coefficients for specific applications 
The following pages outline methods for computing sensitivity
coefficients where the components of uncertainty are derived in the
following manner:

Sensitivity coefficients for type B evaluations  The majority of sensitivity coefficients for type B evaluations will be one with a few exceptions. The sensitivity coefficient for the uncertainty of a reference standard is the nominal value of the test item divided by the nominal value of the reference standard. 
Case studysensitivity coefficients for propagation of error  If the uncertainty of the reported value is calculated from propagation of error, the sensitivity coefficients are the multipliers of the individual variance terms in the propagation of error formula. Formulas are given for selected functions of: 