2. Measurement Process Characterization
2.5. Uncertainty analysis
2.5.5. Propagation of error considerations

2.5.5.2.

Formulas for functions of two variables

Case: Y=f(X,Z)

Standard deviations of reported values that are functions of measurements on two variables are reproduced from a paper by H. Ku (Ku).

The reported value, Y is a function of averages of N measurements on two variables.

Function of , and are averages of N measurements	Standard deviation of = standard dev of X; = standard dev of Z; = covariance of X,Z Note: Covariance term is to be included only if there is a reliable estimate
	Note: this is an approximation. The exact result could be obtained starting from the exact formula for the standard deviation of a product derived by Goodman (1960).