Input measurand: , i=1..N

Output measurand:

Estimate of :

Standard uncertainty of :

Estimate of Y:

Combined standard uncertainty, GUM order 1, uncorrelated input quantities

Estimate of standard uncertainty of Y=

combined standard uncertainty:

With : sensitivity coefficient

Combined variance:

Combined standard uncertainty, GUM order 1, correlated input quantities

where is the estimated correlation coefficient between et : where is the estimated covariance associated with and .

Combined standard uncertainty, GUM second order, uncorrelated input quantities

-Useful in case of significant non linearity. Every distribution is supposed normal and only most important term is retained.

-Estimate of standard uncertainty of Y:

With

Remark:

Each measurand can eventually be affected by many error source:

, where the error has zero average and

standard uncertainty

The standard uncertainty foris