ML20069M716
| ML20069M716 | |
| Person / Time | |
|---|---|
| Site: | Crystal River  |
| Issue date: | 03/25/1994 |
| From: | Mccurdy H MPR ASSOCIATES, INC. |
| To: | |
| Shared Package | |
| ML20069M635 | List: |
| References | |
| 102-071-HWM3, 102-071-HWM3-R00, 102-71-HWM3, 102-71-HWM3-R, NUDOCS 9406220106 | |
| Download: ML20069M716 (7) | |
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924 563 4575 FAR 25. 1994 1:47PM 4383 P,29 E,$:Y NUR EG/CR-0277 1
PNL 2684 R5 STEAM GENERATOR TUBE INTEGRITY PROGRAM Annual Progress Report January 1 - December 31,197/
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i M. Vagins J. M. Alzheirner R. L. England C. J. Morris R. A. Clark I
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Manuscript Completed: June 1978 Data Published: August 1978 y:\\
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904 563 4575 MAR 25. 1994 1:48PM 4383 P.12 a
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Steam Generator Tu 3e Integrity Program / Steam Generator Group Project Final Project Summary Report Manuscript Completed: April 1990 Date Published: May 1990 Prepared by R. J. Kurtz R. A. Clark, E. R. Bradley, W. M. Bowen, P. G. Doctor, R. H. Ferris, F. A. Simonen I
Pacine Northwest Laboratory Richland, WA 99352 Prepared for Division of Engineering Office of Nuclear Regulatory Research l
U.S. Nuclear Regulatory Commission Washington, DC 20555 NRC FIN B2097
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i APPENDIX F 95% CONFIDENCE LEVEL CALCULATION FOR FIGURE 18 l
l
4
+18048320520 5 62 FROJECT ENG.
095 P02 AFR 07 '94 10:33
)
(12) From: JW Pegram at NEFS1 4/7/94 10:55AM (1697 bytes: 37 in)
Priority: Urgent To: JC Brown at SGE-BWNS Rsceipt Requested
Subject:
PREDICTION LIMITS FOR SIMPLE LINEAR REGRESSION
-- ------ - - - - ------- -- -- --- ---- Me s s a g e C o n t e nt s - -- - ----- ------- -- -- --- -- -- -- -.
If the fitted model ir yhat = a + h
- x,
4 given a true model Y = A + B*x +?
]
and you knows n (sample size used in fitting),
xbar = average of x's used in fitting i
SUMXSQ = sum of (x(i) -xbar) * (x (i) -xhar)) over i= 1 to n then the basic formula for a prediction limit, at a 95% level, is l
yhat + t*s*sqrt{(1 + 1/n + ((x(p) -xbar)*(x(p)-xbar))/SUMXsQ))
WHERE t is from Student's t (also called just the t distribution) for j
the 954 percentile, and for n-2 degrees of freedom; and e is the i
standard error from the regression fit.
x(p) is the particular value 1
of the independent variable of interest.
A prediction limit is used to estimate a bound on a value of the dependent variable at some value of x.
The only difference between the computation of a 95% upper confidence s
limit on the average value vs the prediction limit, is that in the 95%
upper confidence case, the 1 is omitted from the square root.
This makes the interval smaller, of course.
The difference is caused by the fact that for the prediction interval estimate, the random element of the model is an additional source of
)
uncertainty.
d If your customer has a statistics book, this would be in the simple I
linear regression chapter, probably under the heading of something like I
" prediction of an individual Ya or so.
Questions, please call.
Jim Fee cn c" * *** * " " * ' (* * "
t
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098 P06 4:R 07 '94 13:57
+18048220520 3/G FROJECT ENG.
KENJ1'S CURVE FIT VALUES PREDICTED 95% CONFIDENCE VALUES
?
400 KHZ DE PREDICTED 95% CONF.
DELTA 1
X^2 VMAX
%7W V(P)
%TW UP BOUND U.B. - PRED.
1 0.25 0.50 53 0.00 31.7 41.5 9.9 0.04 0.19 34 0.25 36.7 46.3 9.6 O.04 0.19 33 0.50 41.7 51.3 9.6 0.17 0.41 45 0.75 46.7 56.3 9.6 1.08 1.04 54 1.00 51.7 61.5 9.8 0.6' O.82 46 1.25 56.7 66.8 10.1 1.66 1.29 54 1.50 61.7 72.2 10.5 0.08 0.28 29 1.75 66.8 77.7 11.0 0.12 0 34 40 2.00 71.8 83.3 11.6 0.08 0.29 36 2.25 76.8 89.0 12.2 2.50 81.8 94.7 13.0 2.73 86.3 100.0 13.7 3.00 91.8 106.4 14.6 3.25 96.8 112.2 15.4 4
3.50 1 01.8 118.1 16.3 3.75 106.8 124.1 17.2 4.00 111.8 130.0 18.2 i
XBAR =
0.535 SUMX SQR 4.1865 i
s i
Regression Output:
Constant 31.67777988 i
Std Err of Y Est 5.640231774 R Squared 0.676376252 No.of Observations 10 8
Degrees of Freedom X Coefficient (s) 20.04153 Std Err of Coef.
4.901308
EPRIVOLTAGE TO %TW CORRELATION 95% PREDICTION UPPER UMIT,400 KHZ DIF
/
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-*- PREDICTIOt4 FROM FIT 95% UPPER UMIT l
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2 APPENDlX G i
i CRYSTAL RIVER UNIT 3 EDDY CURRENT DATA ANALYSIS GUIDELINES DRAFT REVISION i
l i
i 1
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