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Registered Member #190
Joined: Fri Feb 17 2006, 12:00AM
Location:
Posts: 1567
I have seen different methods for multiplication/division which includes the simple addition of the fractional error to quadratures.
Here is a reference:
Which is it?
If I have A = 2 +/- 0.05 and B = 1 +/- 0.01 A*B is easy as it is dA/A + dB/B
or, I have seen it as error = sqrt(sqr(dA/A) + sqr(dB/B))
Which is it?
Finally, the reference states the error for division is dA/A - dB/B For my example this gives an error of +/- 0.015 (.05/2 - 0.01/1) However, if I do a maximum error analysis:
Registered Member #2529
Joined: Thu Dec 10 2009, 02:43AM
Location:
Posts: 600
I can't remember the correct way to do this; I know how to do addition, but not multiplication.
But I certainly don't think your 'maximum error analysis' is legitimate.
Don't forget these are standard deviations not maximums.
If you do that kind of calculation you do then you're kind of assuming worse case for both; which rarely happens; it's not a statistically valid step, you're giving the unlikely case too much weight.
Registered Member #162
Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3140
For a true mathematical answer, wait for someone else to reply, and don't expect to understand it from the document pointed to, for typical electronics calculations, the precision commonly achievable is such that 'errors in errors' (propagation of errors) is a vanishingly small number, usually well below any achievable noise floor, or transducer/sensor error, so it is fairly safe to say that percentile errors just add together, e.g. three multipliers of 0.1% error gives 0.3% error, the rest is buried in noise.
P.S if you have many stages multiplying errors then; . the above is over-simplified . the methodology wasn't thought through rigorously
Registered Member #1526
Joined: Mon Jun 09 2008, 12:56AM
Location: UK
Posts: 216
Ahhhh, I love the smell of error analysis in the morning...
Errors are just small changes in the output of a function in respect of small changes in the input variables. More usefully, the partial derivative of your function, taken in respect of one of its variables and multiplied by the error in that variable equals that variable`s absolute contribution to the output error, as per ordinary calculus.
If you add the contributions from each variable together in quadrature then you`ll have the error in the result.
That`s all of error analysis - if you can differentiate then you can do any errors ever ever
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propagation of errors
