ML19337A532
| ML19337A532 | |
| Person / Time | |
|---|---|
| Issue date: | 06/23/1980 |
| From: | Abramson L NRC OFFICE OF MANAGEMENT AND PROGRAM ANALYSIS (MPA) |
| To: | Kopp L Office of Nuclear Reactor Regulation |
| References | |
| NUDOCS 8009290207 | |
| Download: ML19337A532 (3) | |
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JUN 2 31980 8
MEMORANDUM FOR: Laurence I Kopp, Core Performance Branch, Division of Systems Safety,.NRR-FROM:
. Lee RJ Abramson, Acting Chief, Applied Statistics Branch, MPA
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SUBJECT:
EXXOff-NUCLEAR RESPONSE-TO NRC REQUEST FOR INFORMATI0fl CN
" UNCERTAINTY ANALYSIS FOR THE MEASURED REi.ATIVE POWER DISTRIBUTION",'XN-NF-79-6(P),
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I have reviewed Exxon's response to my preliminary review of the subject docu-ment (memo to Bob Schemel, January 7,1980) and find that they have missed the point. Exxon argues that the test for normality is carried out simply to con-firm the model assumption of normality, whose validity they see no reason to question. While a model assumption of overall a'pproximate normality (nothing in the real world is exactly normal) may or may not be reasonable, it is the nomality of 'the tails which is at issue. The desired tolerance limits refer to the behavior in the tail of the distribution, and this might differ signifi-cantly from normality, even if the distribution as a whcle passes a test for normality. For exampic, from Table 4.5 of XN-fiF-76-6(P), there are.19 obser-
.vations greater than 4.0, as ennpared with an expected number of about 14. The possible significance of this result is. swamped by the good fit of the remainder
-of the observations.. What is needed here is a method of calculating tolerance limits which will not be invali' dated by departures from normality in the tails *.
It is for this reason;that.I suggested using nonparametric ~ tolerance limits.
Another ' potential problem which was not. addressed in my preliminary review
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relates to the pooling of data. From Table 4.11 of XN-NF-79-6(P), the degrees of freedom associated with the estimates of the relative standard deviations are quite large. This suggests that data:from a number of experiments was.
pooled to arrive at each of the estimates. 'If this was the case, then the pooling must be justified, ;1.e., it, must be shown that the data from the various experiments being pooled mustia11f have.approximately the same distribution.
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- See James V. Bradley, Distributton - Free Stattstical Tests, Prentice-Hall,1968, for a Monte Carlo investigatica of distributions which are nomal except for a
, slight departure from normality in the tafis'. Bradley shows that the results of
.J. normal-based statistical" tests of such slightly contaminated distributions can lead to unpredictable gross errors.
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Laurence~I. Kopp M 0 31980
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' pecific coments on the Exxon responses are as follows.
S It is not ' minor point to make a distinctio'n between mathematical equality A2_.
a and an approximation.
If an approx 1 ration is being used, then it is essen-tial to verify that the eiror in the approximation is not so large as to invalidate' the approximation. This is best done by carrying an. error term along in the calculations and then using a bounding argument to show that the error is sufficiently small.
The point about a' mathematical model being'only an approximation to the real world is irrelevant. What is being discussed here is the proper analysis of the mathematical model.
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What Its needed here, and what is meant by a detailed mathematical model,
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is an explicit representation of the "true" values, the measured values and the relations among them.
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A4. The Exxon assertion about the normality of a mixture *s incorrect for the ~
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case at hand. In order for a mixture of normals with clxed means and with the same variance'to be normal, they must all have the same mean. If the mean of e'ach subpopulation is itself an observation on a nonnal distribution and if there is only one observation on each subpopulation,'then the resul-tant mixture is again normal. However, if there is more.than one observa-tion on any subpopulation, which is certainly the case here, then the re-sultant mixture is not nonnal.
Furthermore, I question the appropriateness of considering the means of the subpopulations as random variables.' If the means correspond to different~
reactors or different fuel regions,- f t is not clear that it is appropriate to average over the reactors or the fuel regions, which is what the model-ing of the means ~as random. variables-is tantamount to.
The Exxon response and the unresolved' questions which it raises are an excellent example of the confusion that can result in the absence of an explicit model.
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A_6,Page 26. -Exxon's coments are correct. 'Q6 should have.re~ferred to,Page 3 x
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.m A7., For the reasons-discuss,ed above, I; consider any normal-based tolerance limits-as unjustifiedi It is essential that nonparametric tolerance s
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l Laurence I. Kopp EN : 31980_
Please call me at x27806 if you have any questions.
WsM s ned br e
Lee R. Abramson, Acting Chief Applied Statistics Branch Office of Msnagement' and Program Analysis m.
cc:
H. S. Bassett, PFA
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l N. M. Haller, MPA
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R. Schemel,.NRR '
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