combined in quadrature

English translation: square root of the sum of the squares

GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)

English term or phrase:	combined in quadrature
Selected answer:	square root of the sum of the squares
Entered by:	Jörgen Slet

19:26 Nov 3, 2007

English language (monolingual) [PRO]
Science - Mathematics & Statistics / uncertainty calculation

English term or phrase: combined in quadrature

"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 ? :)

Jörgen Slet KudoZ activity Questions: 132 (3 open) (30 without valid answers) (6 closed without grading) Answers: 99 Estonia
Local time: 11:40

square root of the sum of the squares

Explanation:
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_...

Selected response from:

JohnGBell
Local time: 11:40

Grading comment

Makes sense, uncertainty should be additive, thank you
4 KudoZ points were awarded for this answer

SUMMARY OF ALL EXPLANATIONS PROVIDED

4 +1

square_root(a-squared times b-squared)/2

Alexander Demyanov

4 +1

square root of the sum of the squares

JohnGBell

Answers

23 mins confidence:

peer agreement (net): +1

square_root(a-squared times b-squared)/2

Explanation:
...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.

Alexander Demyanov
Local time: 04:40
Works in field
Native speaker of:

Russian

Notes to answerer

Asker: yes, it is a loose expression indeed :)

Peer comments on this answer (and responses from the answerer)

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

-> 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.

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

-> 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.

2 hrs confidence:

peer agreement (net): +1

square root of the sum of the squares

JohnGBell
Local time: 11:40
Native speaker of:

English
PRO pts in category: 4

Grading comment

Makes sense, uncertainty should be additive, thank you

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