RE: Why Monte Carlo? Re: Calculation of uncertainty in EU determination

["Bradshaw, Keith" <Keith.Bradshaw@nnc.co.uk>]

Dear Radsafers interested in uranium enrichment uncertainty propagation
problem.

Suppose you have an alpha spec measurement of the 238U/235U activity ratio,
then according to Rucker and Johnson Jr:

log(wt%235U) = 1.065 - 0.7317(log(238U/235U act ratio)) - 0.129(log238U/235U
act ratio)^2

The activity ratio will have an uncertainty due to counting statistics.  In
practice, I suspect this will be by far the largest uncertainty for alpha
spec measurement and is random in nature.  For mass spec measurements,
things like mass fractionation uncertainty may be relatively more important.
Still, the same arguments may apply if you convert the equation from
activity ratio to atom% for mass spec.

Anyway, say you get a 238U/235U activity ratio of 10.86 +/- 0.74 (95%
confidence).  Then simply plug in to the equation the activity ratios (10.86
- 0.74) and (10.86 + 0.74) and see what you get for wt% 235U.  That will
give you the 95% confidence range for wt% 235U.

This works out to a 235U of 1.47 wt% with a 95% confidence range of 1.380 to
1.582 wt%.

Unfortunately, we aren't given the uncertainty on their fitted line by
Rucker and Johnson Jr.  In principle this should also be included.

In my previous message  I was worried about the summing to 100% problem and
whether you could use the usual laws of error propagation.  But in the
above, both 238U and 234U remain undefined.  What's important is the
uncertainty on 235U content only.  It's probably only if you have to give a
complete isotopic composition (ie give atom% for all three isotopes) that it
starts to get metaphysical.

What do you think?

REFERENCE

	'Relationship between isotopic uranium activities and total uranium
at various uranium enrichments', by Rucker and Johnson Jr, J. of
Radioanalytical and Nuclear Chemistry, Vol 235 1-2 (1998) pp47-52.


	Regards

	keith.bradshaw@nnc.co.uk






	END




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