Combined Uncertainty

From CheLabWiki

Jump to: navigation, search

…from CheLabWiki, an online resource for chemical-engineering laboratories located at www.chelabwiki.org; Site Revision #419; 6 January 2009.

Community Portal → Data Analysis → Combined Uncertainty


Figure 1. The total uncertainty for a measured quantity is given by the root sum of squares of the type A and type B uncertainties.
Figure 1. The total uncertainty for a measured quantity is given by the root sum of squares of the type A and type B uncertainties.

Once we have determined estimates of the type A and type B uncertainties for a measured quantity, then we must combine them to obtain the total or combined uncertainty u. We assume type A and type B uncertainties are independent, so the total uncertainty is computed by[1][2]


(1)
u \ = \ \sqrt{u_A^2 + u_B^2}


This calculation is illustrated in Figure 1. To have a numerical example, consider the flow-rate data in Table 1. For these data we have found the type A uncertainty to be uA = 0.051 gpm and we found the type B uncertainty to be uB = 0.12 gpm. Using these values in (1) gives the value for the total uncertainty as


Table 1. Ten measured values for flow rate of water through a pipe.
Run # Flow Rate Run # Flow Rate
1 5.5 6 5.6
2 5.85 7 5.75
3 5.55 8 5.65
4 5.8 9 5.4
5 5.9 10 5.7
(2)
u \ = \ \sqrt{(0.051)^2 + (0.12)^2} \ = \ 0.13 \, \mbox{gpm}


Note that the estimate given by (1) is somewhat smaller than the value that would be obtained if we had simply added the type A and type B uncertainties. When reporting total uncertainties, we usually keep only one significant figure. However, an exception occurs when the first significant digit is unity; then we may include one additional figure.

Once we have a value for the combined (total) uncertainty, we may want to attach a level of confidence to it. We do this by computing an expanded uncertainty.

References

  1. ↑ U. S. Guide to the Expression of Uncertainty in Measurement, ANSI/NCSL Z540-2-1997, American National Standards Institute, NCSL International, Boulder, CO, 1997.
  2. ↑ J. R. Taylor, An Introduction to Error Analysis, University Science Books, Mill Valley, CA, 1982.
Retrieved from "http://www.chelabwiki.org/wiki/Combined_Uncertainty"
Personal tools