Statistical Data Analysis. Prof. Terry A. Ring, Ph. D. Dept. Chemical & Fuels Engineering University of Utah. http://www.che.utah.edu/~geoff/writing/index.html. Making Measurements. Choice of Measurement Equipment Accuracy – systematic error associated with measurement.
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This approach applies no matter how large the uncertainties (Lyons, 1991).
(i) Set all xi equal to their measured values and calculate f. Call this fo.
(ii) Find the n values of f defined by
fi = f(x1,x2,...,xi+si,...,xn) (11)
(iii) Obtain sf from
If the uncertainties are small this should give the same result as (10). If the uncertainties are large, this numerical approach will provide a more realistic estimate of the uncertainty in f. The numerical approach may also be used to estimate the upper and lower values for the uncertainty in f because the fi in (11) can also be calculated with xi+ replaced by xi-.
(12) with +
(12) with -
Now try the same calculation using the spread sheet method. The dimensionless form of (12) is (after taking the square root)
The propagated fractional uncertainties using (15) and (17) are compared in Table 4.
A further advantage of the numerical approach is that it can be used with simulations. In other words, the function f in (12) could be a complex mathematical model of a distillation column and f might be the mole fraction or flow rate of the light component in the distillate.
Table 4. Uncertainties in Gas Velocity Calculated from (15) and (17)
See web page with sample calculation done with Excel
Linearized Eq. Fit