So what is the separative power of the IR-1 centrifuge, really? We’ve touched on this question before, sometimes in connection with Natanz breakout scenarios. Lately, it’s come up in connection with the Qom facility, a.k.a. Fordow (see: Iran: Compliance in Defiance?, December 1, 2009). But simple answers are not forthcoming.
If you follow this blog, you’re probably already aware of the running exchange between Ivan Oelrich and Ivanka Barzashka of FAS on one hand, and David Albright and Paul Brannan of ISIS on the other. If not, see the FAS article in the Bulletin, the response by ISIS, the reply by FAS, and the rebuttal by ISIS.
This dispute, whose technicalities I won’t presume to referee, mainly underscores that estimates of the separative power of the IR-1 centrifuge are sensitive to a variety of assumptions. Open-source data do not suffice to provide a single, authoritative answer to the question, “How many kg SWU per annum?”
If You Don’t Know, Say So
When experts disagree, we can think of the answer as a range that indicates some uncertainty. (I’ve taken this approach before.) But what’s the right range?
Starting from Table 1 in the new FAS paper Calculating the Capacity of Fordow, we can assemble a collection of informed judgments. Then we can do something mildly controversial: we can average them and derive confidence intervals in the usual manner. Voilà! An instant range of IR-1 separative power estimates.
The rationale for averaging was aptly described in James Surowiecki’s 2004 book The Wisdom of Crowds. Each estimate “has two components: information and error. Subtract the error, and you’re left with the information.” The process of averaging “subtracts” the error because, if the individual errors are randomly distributed, they will largely cancel each other out.
Careful readers will notice that this requires that estimates be mutually independent. (Correlated errors are not random.) In that spirit, I’ve weeded the FAS table of all estimates that appear to be replications of earlier figures. I’ve used only the most recent estimate available from each expert, and have added a couple of estimates not included in the FAS table. I’ve taken the trouble to re-check the sources, too.
This exercise produces a table of nine opinions. Two were given as ranges rather than point estimates; in these two cases, I’ve used the average of each range as the estimate. There are good reasons for excluding three of these opinions (Hibbs, Persbo, and Salehi) as being related to the nominal performance of the IR-1 on paper (or the performance of its predecessors), not its actual performance.
[Update | Dec. 7, 2009. I’ve added a 10th opinion, that of Houston Wood as related by Scott Kemp, to the bottom of the table. Notice that it’s a nominal estimate, a calculation of the “maximum performance of a P-1,” the immediate predecessor of the IR-1.]
|Hibbs* in Nuclear Fuel||2||Jan. 31, 2005|
|Lewis & “Feynman” at ACW||1.46||May 16, 2006|
|Garwin at BAS||1.362||Jan. 17, 2008|
|Persbo* at vThoughts||2.2||Feb. 27, 2009|
|Salehi* in Fars News||2.1||Sep. 22, 2009|
|Oelrich & Barzashka at FAS||0.5||Sep. 25, 2009|
|Wisconsin Project||0.5||Nov. 16, 2009|
|Albright & Brannan at ISIS||1.0 to 1.5||Nov. 30, 2009|
|Kemp at ACW||0.6 to 0.9||Dec. 1, 2009|
|Wood* via Kemp at ACW||2.1 to 2.2||Dec. 1, 2009|
*Estimates of nominal performance
(I’m assuming that the Wisconsin Project’s figure was derived independently of FAS’s.)
Some Findings (Provisionally Speaking)
First, a caveat: I’ve used ye olde normal distribution to demonstrate the concept, which seems problematic when considering the lower range of the intervals it produces in this instance. A more sophisticated iteration might involve another distribution. Math wonks are encouraged to engage directly with the data table.
Excluding the three nominal figures provides a mean estimate of 0.97 kg SWU/yr, +/-0.86 with 95% confidence. The resulting interval is 0.11 to 1.83 kg SWU/yr. (You see the problem with the lower end of the range.)
At 68% confidence – corresponding to one standard deviation – the result is 0.97 +/-0.44, with a resulting interval of 0.53 to 1.41 kg SWU/yr.
The technique demonstrated here makes the latest ISIS estimate (1.0 to 1.5 kg SWU/yr) look pretty good. It’s more or less coterminous with the upper half of the first standard deviation.
But this is not the whole story. Even within the trimmed-down data table above, a decline in estimates is apparent over time. The larger FAS table shows a sustained decline; a few years ago, estimates of 2 or 3 kg SWU/yr. were common, in ISIS papers and elsewhere. As mentioned earlier here, as new information about the performance of the IR-1 at Natanz has become available, it keeps driving down estimates of what the machine can do (see: Why Iran’s Clock Keeps Resetting, August 19, 2009). So it is not entirely surprising to see expert judgments converging somewhat south of the figures given here.
So what happens if we drop the first [remaining] estimate from the table above [i.e., Lewis & “Feynman”], on the grounds that it was produced before operations commenced at the FEP at Natanz? The result at 95% confidence is 0.87 +/-0.80, or 0.07 to 1.68 kg SWU. (There’s that sticky lower end again.) The result at 68% confidence is 0.87 +/-0.41, or 0.46 to 1.28 kg SWU/yr. From the perspective of a “moving average,” then, the central estimates of FAS and ISIS — respectively at 0.5 and 1.25 — just about bracket the first standard deviation. Statistically speaking, the truth is probably somewhere between them.
Update. See the comments for further elaboration, in which the Poisson distribution and the bootstrap raise their heads. Fun times.