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An announcement. (Sound of a fork tapping a glass.) Ladies and gentlemen — may I have your attention?

Ladies and gentlemen, although there were no armistice talks, the SWU Wars have ended in a truce. The experts have reached a consensus, roughly speaking, about the actual separative power of Iran’s IR-1 gas centrifuges — the devices enriching uranium at the Natanz Fuel Enrichment Plant (FEP) and Pilot Fuel Enrichment Plant (PFEP). (The latter facility has been in the news lately.)

It looks like this:

Perhaps you’d like more explanation than that?

Faithful readers will recall that this subject has been covered here previously (see: Estimating SWU with Expert Opinion, December 6, 2009, and IR-1 Estimates Revisited, January 18, 2010). The discussions summarized therein involved some disagreements — strong ones, at times.

But now, way down in Section 10 of a new ISIS paper dated February 11, 2010, Iran’s Gas Centrifuge Program: Taking Stock, David Albright and Christina Walrond conclude that “the average separative capacity” of an individual IR-1 at the FEP in Natanz is between 0.5 and 1.0 kg SWU/yr.

As a result, the experts’ estimates, depicted in the figure above, now largely overlap.

(There’s no significance to how high or low each estimate is placed in the histogram — that’s purely an aesthetic choice.)

In effect, we’ve just seen a slow-motion, public version of a “behavioral” approach to expert consensus: the question is argued until the participants converge, or as much as they’re willing. This is probably not the ideal approach, as there is evidence that a purely mathematical combination of initial estimates produces a better result. On the other hand, what happened is what happened. And, despite my original take, it seems better not to try to aggregate numbers when none of the experts has stated the level of confidence surrounding their estimates (e.g., 90%, 95%, or 99%). With that caveat, though, there’s no reason not to draw a picture like the one above.

So here are the estimates that are represented visually above.

Author(s)	Data source(s)	kg SWU/yr	Date
Persbo	Cascades operating between 27 and 36% of total capacity (based on 2.2 kg SWU/yr. nominal)	0.59 to 0.79	2/27/09
Wisconsin Project	IAEA reports	0.5	11/16/09
Oelrich & Barzashka (FAS)	IAEA reports	0.44 to 0.88 (0.88 is highly unlikely)	12/1/09
Kemp	IAEA reports	0.6 to 0.9	12/1/09
Albright & Walrond (ISIS)	Multiple sources	0.5 to 1.0	2/11/10

A final caveat: Consensus is in the eye of the beholder, and not everyone involved in this debate would necessarily agree that it has concluded, or concluded appropriately. (See also the view of Ivan Oelrich and Ivanka Barzashka of FAS.) I could certainly imagine ways to do this better.

But for now, it will do. On to the IR-3 and IR-4, should they ever go beyond testing:

Interviewer: “P2 centrifuges?”

Ali-Akbar Salehi: “P3, P4, Allah willing. We will announce this in two months’ time.”

Interviewer: “Iran is currently enriching uranium using P1 centrifuges, but it announced that it began experimenting with P2. Has Iran actually begun enriching uranium using the P2 centrifuges?”

Ali-Akbar Salehi: “Not yet. But Allah willing, in two months, we will experiment with P3 and P4, and after that, we will announce the steps we will take.”

So far, at least, the new machines are just spin jobs…

Update | Feb. 17. The latest from Iranian President Ahmadinejad:

We’ve tested the new generation of our centrifuges whose capacity is five times that of the current centrifuges. We’ll run them in the near future in order to supply fuel to our power plants and reactors. We keep our 20% production until our needs are met. The IAEA inspectors are well aware of our work.

Comment [15]

[Update | Feb. 11, 2010. Estimates from the new ISIS analysis by David Albright and Christina Walrond, “Iran’s Gas Centrifuge Program: Taking Stock,” now appear at the end of the table. The paper contains a number of different estimates derived from different sources; the summary in the last two lines of the table doesn’t fully do them justice. So read it for yourself.]

Note: Two previously overlooked estimates have been added to the data table, and the “observations” section updated accordingly.

Last week, at an event sponsored by AAAS (depicted above*), I had the privilege of giving a presentation on “Expert Opinion on Iran’s IR-1 Centrifuge.” The session was off the record, but I can share with you, Dear Reader, a data table assembled for the occasion, along with a few observations.

This table is an amended version of the data previously assembled by the Federation of American Scientists (see Table 1 in this report). I’ve tinkered with this dataset before (see: Estimating SWU with Expert Opinion, December 6, 2009). The amended table covers every published estimate of the separative power of the IR-1 centrifuge that I could find, running from March 2003 to December 2009. Explicit repetitions of previous estimates [or estimates explictly derived from earlier estimates] are not included.

(N.B. “Actual” indicates the mean performance of actual devices. “Nominal” indicates the maximum power of the device on paper. Despite some ambiguities, it’s usually apparent from context which type of estimate is intended, when not stated directly. For example, I’ve tagged as “nominal” those estimates that relate to the machines believed by different experts at various points to be ancestors of the IR-1.)

There are 29 31 now 33 estimates, although some of the “nominal” estimates from ISIS appear to be repetitions. (More on this point in a few moments.) Here it is: the whole megillah.

Note: Thanks to Scott Kemp for the clarification on his 5/27/08 estimate, which was actually two estimates. Thanks also to Andreas Persbo for the similar observation about his estimate of 2/27/09. I’ve corrected the table to reflect both of these inputs. I’ve also corrected a few minor errors and inconsistencies.

Author(s)	Data source(s)	kg SWU/yr	Estimate of	Date
Hibbs	Official sources	7 to 15	Actual	3/13/03
Hibbs	IAEA sources	12 to 14	Actual	5/12/03
Hibbs	AEOI data	6 to 7	Actual	5/12/03
Albright & Hinderstein (ISIS)	Senior Western officials	2	Actual	9/1/03
Albright & Hinderstein (ISIS)	Senior IAEA officials (stated subsequently)	3	Nominal (based on 4M)	3/1/04
Gilinsky, Miller, & Hubbard	Unclassified sources (and educated guesses)	1 to 3	Actual	10/22/04
Hibbs	IAEA and Western governments	2	Nominal (based on SNOR & CNOR)	1/31/05
Glaser	(not stated)	2	Nominal (estimate of P-1)	6/14/05
Lewis	Rademaker (USDOS) statement	2 < and < 3, closer to 2	Actual	4/15/06
Lewis	Aghazadeh (AEOI) statement	2.3	Actual	4/18/06
“Feynman” via Lewis	Aghazadeh (AEOI) statement	1.46	Actual	5/12/06
“Feynman” via Lewis	Aghazadeh (AEOI) statement	2.3	Nominal	5/12/06
Albright (ISIS)	Aghazadeh (AEOI) statement	1.4 to 2.7	Actual	5/17/06
Albright (ISIS)	(not stated)	2.5 to 3	“the high end of the possible”	7/1/06
Albright & Shire (ISIS)	Level Pakistan is said to have achieved	2	Actual of P-1	11/1/07
Garwin	Aghazadeh (AEOI) statement	1.362	Actual	1/17/08
Glaser	(not stated)	2.5	Nominal (hypothetical max. of P-1)	4/16/08
Kemp via Lewis	Observed efficiency of 42%	1	Actual	5/27/08
Kemp via Lewis	(not stated)	2.5	Nominal	5/27/08
ISIS NuclearIran FAQ	(not stated)	1 to 2	Actual	~9/1/08 (n.d.)
ISIS NuclearIran FAQ	(not stated)	3	Nominal	~9/1/08 (n.d.)
Persbo	Cascades operating between 27 and 36% of total capacity	0.59 to 0.79	Actual	2/27/09
Persbo	(not stated)	2.2	Nominal (based on SNOR)	2/27/09
Salehi (AEOI)	(not stated)	2.1	Unclear; nominal?	9/22/09
Oelrich & Barzashka (FAS)	IAEA reports	0.5	Actual	9/25/09; see also 11/23/09
Wisconsin Project	IAEA reports	0.5	Actual	11/16/09
Albright & Brannan (ISIS)	IAEA reports	1.0 to 1.5	Actual	11/30/09
Albright & Brannan (ISIS)	(not stated)	3	Nominal	11/30/09
Oelrich & Barzashka (FAS)	IAEA reports	0.44 to 0.88 (0.88 is highly unlikely)	Actual	12/1/09
Kemp	IAEA reports	0.6 to 0.9	Actual	12/1/09
Wood via Kemp	Max. of P-1 based on validated hydrodynamic codes from the U.S. program	2.1 to 2.2	Nominal (max. of P-1)	12/1/09
Albright & Walrond (ISIS)	Multiple sources	0.5 to 1.0	Actual	2/11/10
Albright & Walrond (ISIS)	Multiple sources	1.60 to 3.76	Nominal	2/11/10

Four Observations

First, as noted previously, the trend of the estimates declines with time. This effect only becomes more pronounced with the inclusion of the estimates reported by Mark Hibbs in NuclearFuel and Nucleonics Week in early 2003: now the trend of the decline is follows an exponential curve. These reports appeared when IAEA inspectors had just put eyes on the IR-1 (then called the P-1 in IAEA reports) for the first time. Their initial frame of reference presumably involved more up-to-date machines, rather than centrifuges whose design heritage extends back to the 1960s.

[Update | 22:54. See Mark Hibbs’ account in the comments below.]

Second, the decline comes in bursts, coinciding with the availability of new information. This effect is loosely similar to the influence of news on stock prices, as documented in event studies. The effect tends to be prompt in finance; a bit less so here.

• From mid-2003 into 2005, which covers the first period of centrifuge operations at PFEP in Natanz, we see the gradual sorting-out of the design heritage of the IR-1.
• The next wave comes in mid-2006, right after AEOI chief Gholamreza Aghazadeh gave some detailed figures during an interview with Iranian TV. Here we start to see some divergence between “actual” and “nominal” estimates, with “actual” figures falling below 2 kg SWU/yr.
• Next come the estimates of late 2007 to early 2009 2008, after the commencement of enrichment work at the FEP in Natanz, whose results were periodically documented in IAEA reports.

• A final burst of estimates, explicitly derived from the ever-accumulating IAEA reports, takes place in late 2009. Here, “actual” estimates fall below 1 kg SWU/yr.

Third, in most cases, a “new entrant” tends to lead the way in pushing “actual” estimates down. That is, someone who wasn’t previously in the game seems to take hold of the new information and bring it to light, with the rest shortly catching up. In 2003 and 2004, it was David Albright and Corey Hinderstein of ISIS. In 2006, it was Jeffrey Lewis and a pseudonymous correspondent here at ACW. In 2009, it was Ivan Oelrich and Ivanka Barzashka of FAS.

[Update | 23:51. In hindsight, Andreas Persbo was the first to present an “actual” estimate below 1, using recent IAEA reports. This contribution may have been overlooked because it was couched as a range of percentages of a nominal figure.]

Fourth, there are lingering differences between experts in both “actual” and “nominal” figures. Much of the basis of the “actual” differences was laid bare in the FAS-ISIS debate of late 2009. The “nominal” differences seem to originate with early reports about the design heritage of the IR-1. In March 2004, ISIS related that the IR-1 was copied from URENCO’s 4M centrifuge; both designs have four aluminum tube rotor segments. In January 2005, Hibbs reported that the IR-1 was derived from URENCO’s SNOR and CNOR machines.

Both 4M and CNOR are said to have been capable of about 3 kg SWU/yr. The CNOR had six segments, each responsible for about 0.5 kg SWU/yr, according to Hibbs. Since the Pakistani P-1 and the Iranian IR-1 have four segments, their nominal output, if they are understood to be CNOR derivatives, is about 2 — or, according to some recent figures, 2.1 or 2.2. Most experts seem to agree with Hibbs, or wind up close to his figure. But Albright and colleagues persist in viewing 3 as the real ceiling.

Should you, Dear Reader, notice any other subtle patterns in the data, well, that’s what the comments feature is for!

*Actually, the picture at the top of this post does not show me giving a presentation.

Comment [11]

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.]

Source	kg SWU/yr	Date
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.

Comment [23]