NUREG-1477, Discusses Technical Concerns W/Changes to Draft NUREG-1477 Re Probability of Leakage Curves
| ML20149E925 | |
| Person / Time | |
|---|---|
| Issue date: | 02/22/1994 |
| From: | Buslik A NRC OFFICE OF NUCLEAR REGULATORY RESEARCH (RES) |
| To: | Tim Reed Office of Nuclear Reactor Regulation |
| References | |
| RTR-NUREG-1477 NUDOCS 9408080207 | |
| Download: ML20149E925 (3) | |
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- a February 22, 1994 NOTE TO: Tim Reed, NRR/PDII-1 FROM: Arthur Buslik, RES/PRAB 4/
SUBJECT:
TECHNICAL CONCERNS WITH CHANGES TO ORAFT NUREG-1477, PROBABILITY OF LEAKAGE CURVES I disagree with the proposed conclusion that only the log-logistic probability of leakage curve should be used, for the reasons outlined below, and supported in the enclosed documents. I believe other f amilies of probability of leakage curves should also be used. (I use here the term log-logistic curve to identify the logistic function with the argument a linear function of the eddy current voltage.)
One reason for the proposed conclusion that only the log-logistic curve should be used is apparently that the logistic function is appropriate for a dichotomous population. There is no theoretical reason for choosing the logistic function for a probability of leakage curve over other curves such as the Cauchy or normal. The selection of the appropriate function is purely empirical. The same statement holds for the argument of the probability of leakage function, whether it is a linear function of the logarithm of the eddy current voltage (V) or a linear function of the voltage itself, except that, .
since one knows that there is a non-zero probability of leakage for a zero measure voltage, the use of the linear function of logV seems inappropriate.
Of course, there is no reason to restrict oneself to these two possibilities
- for the argument of the probability of leakage function. The enclosed note to fou dated January 5, 1994, indicates that there canno_t be any theoretical reason for the choice of the logistic function. Aside from measurement error, the probability of leakage at voltage V is the ratio of the probability of crack morphologies which lead to a leak and which give a voltage V to the probability of all crack morphologies which lead to a voltage V. There is just no way of deriving a log-logistic probability of leakage curve froa the g
physics of the situation.
N Q Moreover, there is no empirical basis for choosing the log-logistic o probability of leakage curve over the normal, log-normal, logistic, Cauchy, or
& log Cauchy curves. An empirical basis would be present if the goodness of fit g
of the log-logistic curve were significantly better than that of the other oW curves. This is not the case, as I showed by extensive calculation in the enclosed document I wrote entitled , "Model and Parameter Uncertainty in the U Estimation of Steam Generator Tube Leakage Probability as a Function of Eddy Current Voltage". In point of fact (see p. 15 9f the document), the hR log-logistic model of Westinghouse is in no way distinguished with respect to
<"$e goodness-of-fit: it gave the worst fit as measured by the Hosmer-Lemeshow index, and the next to worst fit as measured by the deviance, for the data set used in the Catawba report.
c ._ y Uuv,. u"# Note that it is insufficient to say that log-logistic curve gives s good fit to the data--all the models did, and most betterBecause than thethe log-logistic log-logisticfit, although the differenca may not be significant.
curve is not any better than the others studied with respect to goodness fit, there is no empirical basis for the use of the log-logistic curve.
QO
The usual reason given for the use of the logistic regression curve is that in many problems it does not make much difference which model is used. This is frequently the case when the region of interest is between the 20% probability and 80% probability (of response) points. However, here we are interested in the low probability tail.
I showed in the enclosed document (see Table 7 of that document) that the maximum likelihood estimate of the probability of leakage can vary by a factor of 8, from .004 to .032, at one volt, for the 3/4 inch tube data considered. Thus, despite the fact that all the curves fit the data well (and most better than the log-logistic curve of Westinghouse), there are significant differences in their predictions.
The suggetted resolution of this issue states that the parametric uncertainty in the j: rot >.bility of leakage curve should be accounted for. This is certainly tne case, but including the parametric uncertainty in no way makes up for not including the model uncertainty. Both uncertainties must be included.
I believe that several different families of b'aary response regression curves should be used, such as the Cauchy, normal and logistic, with arguments that are linear in the voltage, and linear in the log of the voltage. The uncertainties arising from the use of the different models should be incorporated into the overall estimates of the uncertainties. Whether the decision as to how many tubes should be plugged should be based on the most conservative of these models, or, say, from a mean value weighting all of the models equally, or some other way, would have to be a staff decision. One notes that there is very little basis for choosing one model over another.
The quotation from Feller given in the enclosed January 5,1994 note from me to you is highly relevant.
" ..not only the logistic distribution, but also the normal, the Cauchy, and other distributions can be fitted to the same material with the same or better goodness of fit. In this competition the logistic distribution plays no distinguished role Ghatever; most contradictory theoretical models can be supported by the same observational material."
Feller was referring to the use of the logistic distribution function to describe growth precesser, but the quotation applies here as well.
C c A w /.' /] 4 .r b M
REFERENCES
- 1. 0.R. Cox, "The Analysis of Binary Data", Methuen & Co. Ltd, London, 1970. (This is the first edition).
- 2. W. Feller, "An Introduction to Probability Theory and its Applications",-
Second Edition, John Wiley & Sons, Inc., 1971. See pp 52-53.
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