Glossary entry (derived from question below)
English term or phrase:
combined in quadrature
English answer:
square root of the sum of the squares
Added to glossary by
Jörgen Slet
Nov 3, 2007 19:26
16 yrs ago
1 viewer *
English term
Estonia
19 years of biomedical translation
Native in: Estonian 
Works in: English to Estonian, Estonian to English
combined in quadrature
English
Science
Mathematics & Statistics
uncertainty calculation
"As set out in 5.1, the average flow is controlled to within ± 2%, while the flow meter is calibrated against a transfer standard with an uncertainty of less than 2%. These figures have been combined in quadrature to give an effective contribution in Table 1, for the uncertainty contribution to flow not covered by the field tests, of 3%."
(EN 14907)
Could somebody explain this expression please ? :)
(EN 14907)
Could somebody explain this expression please ? :)
Responses
+1
2 hrs
Selected
square root of the sum of the squares
i.e. using something similar to Pythagoras.
Thus in your example, a system error of 2% and a flow error of 2% combined in quadrature give an error of 2.818%
e.g.
a) dosimeter calibration uncertainty, scal
b) dose mapping uncertainty, smap
c) dosimeter reproducibility, srep
d) machine variability, smach.
stotal = sqrt(scal^2 + smap^2 + srep^2 + smach^2)
http://www.irradiationpanel.org/docs/publications/Panel_SPC_...
Thus in your example, a system error of 2% and a flow error of 2% combined in quadrature give an error of 2.818%
e.g.
a) dosimeter calibration uncertainty, scal
b) dose mapping uncertainty, smap
c) dosimeter reproducibility, srep
d) machine variability, smach.
stotal = sqrt(scal^2 + smap^2 + srep^2 + smach^2)
http://www.irradiationpanel.org/docs/publications/Panel_SPC_...
4 KudoZ points awarded for this answer.
Comment: "Makes sense, uncertainty should be additive, thank you"
+1
23 mins
Alexander Demyanov
Works in field
Software Engineering background
Native in: Russian
Works in: English, Russian, Russian to English, and 1 more.
square_root(a-squared times b-squared)/2
...where a and b are your "these figures"
Alternatively, it may mean that each individual measured value is squared, the results added to each other, the sq. root of the sum is taken and then divided by the number of values measured.
c.err : Rate errors combined in quadrature, i.e., it's sqrt{\sum{err^2}}/N, where N is the number of points in a given bin. Only calculate if err is input ...
space.mit.edu/CXC/analysis/SITAR/functs_reb.html - 12k
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Note added at 24 mins (2007-11-03 19:50:13 GMT)
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SOOORRRY!!!!! "plus", not "times"
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Note added at 29 mins (2007-11-03 19:55:15 GMT)
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Also, it appears that the "combined in quadrature" expression is a bit more loose and there can be other techniques for calculating the combination.
Alternatively, it may mean that each individual measured value is squared, the results added to each other, the sq. root of the sum is taken and then divided by the number of values measured.
c.err : Rate errors combined in quadrature, i.e., it's sqrt{\sum{err^2}}/N, where N is the number of points in a given bin. Only calculate if err is input ...
space.mit.edu/CXC/analysis/SITAR/functs_reb.html - 12k
--------------------------------------------------
Note added at 24 mins (2007-11-03 19:50:13 GMT)
--------------------------------------------------
SOOORRRY!!!!! "plus", not "times"
--------------------------------------------------
Note added at 29 mins (2007-11-03 19:55:15 GMT)
--------------------------------------------------
Also, it appears that the "combined in quadrature" expression is a bit more loose and there can be other techniques for calculating the combination.
Note from asker:
| yes, it is a loose expression indeed :) |
Peer comment(s):
| agree |
Nik-On/Off
: It seems that the square root of the sums of the squares should not be divided by two// http://tinyurl.com/yrha99
21 mins
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Thanks, Dmitrii!//Then it wouldn't be "combined". What if we had 10000 values? Right, as e.g. combining forces at 90 deg. (the more forces you combine the greater is the resulting force). Like I said, the expression may be somewhat loose.
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| neutral |
Ken Cox
: with Nik-On/Off -- the formula you give is for calculating a form of mean error, but here the objective is to calculate the total error. (In the example, 3 is the approximate square root of 4 plus 4).
1 hr
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Thanks, Ken! As seen in the responses above, I don't insist on /N. I'm not 100% sure whether "eff. contribution" here should be a quadr-ed sum or quadr-ed mean. Unfortunately, I didn't make up the formula: got it at the mit.edu site.
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