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

Formulas for functions of one variable

Case: Y=f(X,Z) Standard deviations of reported values that are functions of a single variable are reproduced from a paper by H. Ku (Ku).

The reported value, Y, is a function of the average of N measurements on a single variable.

Function Y of Xbar

Xbaris an average of N measurements

Standard deviation of Y

s(x) = standard deviation of X.

Y = Xbar
Y = Xbar/(1 + Xbar)
s(x)/{SQRT(N)*(1 + Xbar)**2}
Y = (Xbar)**2
Y = SQRT(Xbar)
Y = LN(Xbar)
Approximation could be seriously in error if n is small--
Y = EXP(Xbar)
Not directly derived from the formulas
Y = 100*s(x)/Xbar

Note: we need to assume that the original data follow an approximately normal distribution.

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