ML20236K869
| ML20236K869 | |
| Person / Time | |
|---|---|
| Issue date: | 04/15/1998 |
| From: | Howe A NRC OFFICE OF NUCLEAR MATERIAL SAFETY & SAFEGUARDS (NMSS) |
| To: | Battige C NRC OFFICE OF NUCLEAR MATERIAL SAFETY & SAFEGUARDS (NMSS) |
| Shared Package | |
| ML20236K829 | List:
|
| References | |
| FOIA-98-188 NUDOCS 9807100115 | |
| Download: ML20236K869 (1) | |
Text
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.a 4'
- From: Allen Howe pgsJ To: ckb1 g ga b; 4/15/98 6:48am
Subject:
Evaluation of NDE capability for Storage Casks. -Forwarded l
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'9807100115 990630 ..
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From: "Heasier, Patrick G' < patrick.heasierepn!. gov >
To: AGH10nrc. gov <AGH10 nrc. gov >
Date: 4/13/98 4:09pm
Subject:
Evaluation of NDE capability for Storage Casks, i To: Allen Howe I have reviewed the material you put together, and as I said in the phone conversation, your strategy for evaluating sizing capability is sound, it simply needs to be extended a bit. The prediction interval that you have calculated (which is on measured size), can be used to produce an interval for true size.
The methodology for converting the predictied intervals on measured size to true size is quite simple, if you do it graphically.
This prediction interval can be used to determine if the sizing results are
" good enough." If the sizing error is too large or the calibration curve slope is too shallow, the prediction interval for true size will be infinite; this is a clear case when the sizing results are inadequate. Also, one would judge the sizing measurements to be inadequate if this prediction interval was so large that it covered most of the possible range of flaw sizes.
The prediction interval should also be used to introduce a ' safety factor' for sizing error when determining the size of a rejectable flaw. For example, suppose some sort of fracture mechanics analysis deterrnined an 80% through wall flaw would be of safety concem. Suppose further that the regression analysis of a particular set of sizing results showed that the half-width of the prediction interval was about 20% in through-wall units. Then one would use a flaw rejection threshold of 80%-20%=60% in actualinspection with this technique.
1.0 Formulas for a Prediction Interval The memo that Allen Howe put together on prediction formulas is correct, and all the formulas he presents are complete. I had remarked that the definitions for some of the terms he used in the formulas were missing, but I had not looked at the last page, and thsy are defined there.
These formulas should be easy to construct in Excell. It is all simple algebra except the t-value, which is available as a statistical function in Excell.
Realize that the formulas presented in Howe's memo are for a new Y value. Since Y in this regression represents measured size, they don't directly produce a confidence bound on the corresponding X-value (which is true size). However, one can accomplish this task by calculating upper and lower prediction bounds on Y for a large number of values of X, say 500. This will produce upper and lower bound curves, call them U(x) and L(x). If one obtains a new NDE measurement, Y.new, then bounds on the true measurement are given by X. low and X. upper, which must satisfy U(X. low)=Y.new and L(X. upper)=Y.new.
I This is easier to understand graphically. Plot the predicted regression line, and surround the line by the upper and lower prediction bounds, U(x), and L(x). {
. Plot the new measured value, Y.new, on the Y axis, and extend a horizontal line u-__ _____' N' - - -
v
. from this point until it intersects with U(x) and L(x). X. low will be at the point this line intersects with U(x), while X. upper will be at the point that it intersects with L(x). ,
it should be remarked that the prediction interval presented in your memo is not
~the only prediction interval that could be calculated. One could also calculate l a multiple prediction interval, which attempts to account for misclassification
, error when one calibration experiment is used repeatedly. One could also j formulate this problem in terms of tolerance intervals, which attempts to account for calibration error in a different manner than measurement error.
l 1 mention these other altematives, so that you know they exist. However, I would consider your formulation to be entirely adequate.
2.0 Use of Prediction Intervals for APC in Steam Generators.
You had asked if anyone else uses this methodology. This methodology is used all the time on instruments that use some sort of experimentally determined l calibration curve. For example, almost any chemistry lab will make extensive use of these bounds. A good analytic chemistry book would have a description of this procedure or some slight variant of it. -
The example that closest to home that I can site is the work that industry has been doing for the inspection of ODSCC cracking in steam generators. To evaluate ODSCC, they record oddy current voltages on tubes and compare these voltage
. measurements to a plugging threshold.
. How have they determined the plugging threshold? They have conducted two calibration experiments that relate the measured voltages to tube burst pressure and leak rates respectively. These calibration curves allow them to produce
, regression curves that relate burst pressures and leak rates to voltage. They l have specific burst pressure and leak rate thresholds that the tubes are l supposed to meet, and use prediction bounds on these regression curves to l translate these pressure and leak-rate thresholds into voltage thresholds.
There are several reports that describe this methodology, one that you might j find most accessible is 'PWR Steam Generator Tube Repair Limits - Technical '
Support Document for Outside Diameter Stress Corrosion Cracking at Tube Support Plates," TR-100407 by EPRI.
i
( CC: ' Doctor, Steven R' < steven.doctorepnl. gov >
)
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From: 'Hessler, Patrick G' < patrick.heasierOpnl. gov >
Subject:
Evaluation of NDE capability for Storage Casks.
To: "'AGH1 O nrc. gov" <AGH1 O nrc. gov >
Cc: " Doctor, Steven R' < steven.doctorOpnl. gov >
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Subject:
Evaluation of NDE capability for Stcrage Casks. -Forwarded Creation Date: 4/15/98 6:48am
~ From: Allen Howe Created By: WND1.WNP7:AGH1 I
Recipients Action Date & Time Post Office WND1.WNP7 ckb1 (Charles (Ken) Battige)
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From: " Doctor, Steven R' < steven.doctorOpnl. gov >
To: AGH10 nrc. gov" <AGH10nrc. gov >, DAJ10 nrc. gov" ... d OO W##
Date: 4/15/98 8:20pm
Subject:
P-scan and TestPro l
l- Update on Information obtained while calling about ASME Code work on Rewrite of Appendix Vill.
I talked with Larry Becker today, from the EPRI NDE Center. He is the head for I
' the administration of the PDI implementation of Appendix Vill at the conter. I asked about the P =can system regarding its qualification. It tums out that one company from Flonda (Larry could not remember the name just at that moment) brought in the P-scan system and successfully passed the test for piping. They only did it with one individual using a procedure that Joel Harrison had developed. Larry does not consider that the procedure or the equipment is qualified because their experience is that at least 3 people need to successfully pass in order for the equipment and procedure to be considered qualified.
I asked if the TestPro had gone through any testing. He said on company had orought through a system for only ferritic piping and that they had successfully passed. No other testing had been conducted using this system.
Just thought that you might be interested in this.
Steve Steven R. Doctor Pacific Northwest National Laboratory P. O.' Box 999, MSIN KS 26 Richland, WA 99352 Phone: 509-375-2495 Fax: 509-375-6497 Email: steven.doctorOpnl. gov i
l l ( q ;.
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From: ' Doctor, Steven R' < steven.doctoropnl. gov >
Subject:
P scan and TestPro To: AGH10 nrc. gov'" <AGH10 nrc. gov >, DAJ10 nrc. gov" <DAJ10 nrc. gov >,
"mta20inel. gov" <mta20inel. gov > "CKB10nrc. gov" <CKB10nte. gov >
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P scan and TestPro Creation Date: 4/15/98 8:20pm From: ' Doctor, Steven R' < steven.doctorOpnl. gov >
Created By: G ATED.nresmtp:' steven. doctor O pnl. gov" Recipients .
Post Office TWD2.TWP0 DAJ1 (Deborah Jackson)
Post Office WND1.WNP7 CKB1 (Charles (Ken) Battige)
AGH1 (Allen Howe)
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. From: 'Heasier, Patrick G' < patrick.heasierOpnl. gov >
To: "'AGH1 @ nrc. gov <AGH1 @ nrc. gov > d do w ,#m> >
Date: 4/13/98 4:09pm
Subject:
Evaluation of NDE capability for Storage Casks.
l To: Allen Howe l
l havt reviewed the material you put together, and as I said in the phone conversation, your strategy for evaluating sizing capability is sound. It simply needs to be extended a bit. The prediction interval that you have calculated (which is on measured size), can be used to produce an interval for true size.
The methodology for converting the predictied intervals on measured size to true size is quite simple, if you do it graphically.
This prediction interval can be used to determine if the sizing results are
" good enough." If the sizing error is too large or the calibration curve slope is too shallow, the prediction interval for true size will be infinite; this is a clear case when the sizing results are inadequate. Also, one would judge the sizing measurements to be inadequate if this prediction interval was so large that it covered most of the possible range of flaw sizes.
The prediction interval should also be used to introduce a ' safety factor" for sizing error when determining the size of a rejectable flaw. For example, suppose some sort of fracture mechanics analysis determined an 80% through wall flaw would be of safety concern. Suppose further that the regression analysis of a particular set of sizing results showed that the half-width of the prediction interval was about 20% in through-wall units. Then one would use a flaw rejection threshold of 80%20%=60% in actual inspection with this technique.
1.0 Formulas for a Prediction Interval The memo that Allen Howe put together on prediction formulas is correct, and all the formulas he presents are complete. I had remarked that the definitions for some of the terms he used in the formulas were missing, but I had not looked at the last page, and they are defined there.
These formulas should be easy to construct in Excell it is all simple algebra except the t-value, which is available as a statistical function in Excell.
Realize that the formulas presented in Howe's memo are for a new Y value. Since Y in this regression represents measured size, they don't directly produce a confidence bound on the corresponding X value (which is true size). However, one can accomplish this task by calculating upper and lower prediction bounds on Y for a large number of values of X, say 500. This will produce upper and lower bound curves, call them U(x) and L(x). If one obtains a new NDE measurement.
Y.new, then bounds on the true measurement are given by X. low and X. upper, which must satisfy U(X. low)=Y.new and L(X. upper)=Y.new.
This is easier to understand graphically. Plot the predicted regression line, and surround the line by the upper and lower prediction bounds, U(x), and L(x).
Plot the new measured value, Y.new, on the Y axis, and extend a horizontalline Q
e Wr6 Tot 6 W-
. gs
.l from this point until it intersects with U(x) and L(x). X. low will be at the f point this line intersects with U(x), while X. upper will be at the point that it intersects with L(x).
It should be remarked that the prediction interval presented in your memo is not the only prediction interval that could be calculated. One could also calculate a multiple prediction interval, which attempts to account for misclassification error when one calibration experiment is used repeatedly. One could also formulate this problem in terms of tolerance intervals, which attempts to account for calibration error in a different manner than measurement error.
I mention these other attematives, so that you know they exist. However, I wousd consider your formulation to be entirely adequate.
2.0 Use of Prediction Intervals for APC in Steam Generators.
You had asked if anyone else uses this methodology. This methodology is used all the time on instruments that use some sort of experimentally determined calibration curve. For example, almost any chemistry lab will make extensive use of these bounds A good analytic chemistry book would have a description of this procedure or some slight variant of it.
The example that closest to home that I can site is the work that industry has
, been doing for the inspection of ODSCC cracking in steam generators. To evaluate ODSCC, they record oddy current voltages on tubes and compare these voltage measurements to a plugging threshold.
1 How have they determined the plugging threshold? They have conducted two l calibration experiments that relate the measured voltages to tube burst pressure 1 and leak rates respectively. These calibration curves allow them to produce i regression curves that relate burst pressures and leak rates to voltage. They ;
i have specific burst pressure and leak rate thresholds that the tubes are supposed to meet, and use prediction bounds on these regression curves to translate these pressure and leak-rate thresholds into voltage thresholds.
)
There are several reports that describe this methodology, one that you might find most accessible is "PWR Steam Generator Tube Repair Limits- Technical
- Support Document for Outside Diameter Stress Corrosion Cracking at Tube Support Plates," TR-100407 by EPRI.
l CC: " Doctor, Steven R' < steven.doctorepnl. gov >
IL
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Subject:
Evaluation of NDE capability for Storage Casks.
l To: AGH1 O nrc. gov" <AGH1 O nrc. gov >
Cc: ' Doctor, Steven R' < steven.doctorOpnl. gov >
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Evaluation of NDE capability for Storage Casks.
Croation Date: 4/13/98 4:09pm From: 'Heasier, Patrick G' < patrick.heasierOpn!. gov >
Created By: G ATED.nrcamtp:' patrick.heasier O pnl. gov" Recipients Post Office WND1.WNP7 AGH1 (Allen Howe)
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i From: Allen Howef A/m JJ To: Intemet:pn!. gov: steven: doctor, intemet:Inel. gov:...
Date: 4/8/98 5:03pm
Subject:
Current inspection Schedule We are currently stated to inspect at Palisades during the week of 4/20/98. The scope will be to review one automated UT method -probably ' time of flight"- and the manual method for sizing. The week tentatively looks like this:
Susan Shankman, Acting SFPO Deputy Director may join us on part of this inspection.
Monday- Travel l
Tue - am - entrance meeting and technical discussion pm - procedure review and team meeting [ Steve D to arrive late]
Wed - am - UT automated demo pm - data review, VCC demo and team meeting Thur - am - manual demo and data review l pm - follow up and team meeting l
Fri - am - Exit meeting pm - travel CC: FCS, TJK1, EJL, TWD2.1WPO.DAJ1, SFS 2
i l 1 l I 1
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Current inspection Schedule Creation Date: 4/8/98 5:03pm From: Allen Howe Created By: WND1.WNP7:AGH1 Recipients Action Date & Time Post Office intemet mta2 Post Office Intemet doctor Post Office TWD2.TWP0 DAJ1 CC (Deborah Jackson)
Post Office WND1.WNP7 Delivered 05/29/98 02:53pm AGH1 (Allen Howe)
CKB1 (Charles (Ken) Battige)
EJL CC (Eric Leeds)
TJK1 CC (Timothy Kobetz) .
Domain. Post Office Delivered Route intemet Pending intemet:Inol. gov Intemet Pending intemet:pnl. gov: steven TWD2.TWP0 Pending TWD2.TWPO WND1.WNP7 05/29/98 02:53pm WND1.WNP7 Files Size Date & Time MESSAGE 693 04/08/98 05:03pm View 4109 04/08/98 01:03pm Options Auto Delete: No Expiration Date: None Notify Recipients: No Priority: Normal Reply Requested: No Return Notification:: None Concealed
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. From: Allen Howee ^h"JJ To: intemet:inel. gov:mta2, Intemet:pnl. gov: steven:do...
Date: 4/1/9812:31pm
Subject:
Here is the latest For your background, we have been trying determine what the weld examination process (system + data evaluation + acceptance criteria) should be capable of, to demonstrate a
' reasonable assurance
- that the welds in the MSB structural lid have sufficient integrity to meet the requirements.
The acceptance criteria will be based on a structural analysis using a method reviewed by the staff and including calculational margins as recommended by the ASME Code. While we have not seen the acceptance criteria, I feel that the results of the structural analysis should be modified to account for uncertainty in the measurement system (UT) and perhaps some addit;onal margin if that cannot be bounded with some confidence.
For the UT measurement (system + data evaluation), the demo effectively constitutes a
' calibration" exercise. That is, we have known inputs and we develop an output data set. A regression fit of the data yields a ' calibration curve" for evaluation. We can use the correlation coefficient and develop error estimates for that data to gain some confidence with the accuracy and precision of the UT measurement.
Attached is an excel file with the data from ANO's P-scan flaw depth measurements 0200 dog F and a O dog transducer. This was the data taken before the demo we witnessed. The data was taken from Ken's RMS spreadsheet. There are several points that share the same x, y coordinates thus they are not shown on the chart. Also I threw out the zero points from the flaws with no size data. Plotted along with the data are the 95% confidence standard error of the estimate limits, and an ideal curve. This presentation is a useful tool for evaluating the l' expected outputs for a given (known) input. It represents a good measure of the precision of the system. This is similar to the way that instrument calibration curves are presented.
Mike, the plots with the 95% confidence interval and the 95% prediction interval, you sent yesterday, represent different perspectives. (1) What are the formulas used to develop the curves? (2) Can you send me the data set from the demo you used? (3) Can you run curves '
l for the attached data set?
I will give you a day or so to digest this and then we can discuss it. How about 12:30 pm EST on 4/2/987
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Here is the latest
) Creation Date: 4/1/9812:31pm i From: Allen Howe Created By: WND1.WNP7:AGH1 Recipients Action Date & Time Post Office intemet ,
mta2 Post Office intemet doctor Post Office WND1.WNP7 AGH1 (Allen Howe)
CKB1 (Charles (Ken) Battige)
Domain. Post Office Dollvered Route intemet Pending intemet:Inol. gov Intemet Pending Intemet:pnl. gov: steven WND1.WNP7 Pending WND1.WNP7 Files Size Date & Time UT-TEST 2.XLS 22016 04/01/98 07:19am MESSAGE 2292 04/01/9812:31pm View 4109 04/01/98 07:31am Options Auto Delete: No Expiration Date: None Notify Recipients: No Priority: Normal Reply Requested: No Return Notification:: None Concealed
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From: Michael T Anderson <mta20inel. gov >
To: WND1.WNP7(AGH14 //ow f A/mJJ Date: 4/1/98 3:54pm
Subject:
j Data from P-Scan Demo Allen, Here is the Excel file with all data from the 0 and 45 degree exams performed during the Demo at 200 F. The plot you sent me is impressive, i
although l'm not sure I'm smart enough to understand the statistics in it.
11 you could a similar plot for this data, it might be useful. Thanks, i
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-, i 9-i omeim,.on (208)S26-8780 ii mta2Sinel, gov !
Idaho National Engineering Laboratory NDE Engineering Analysis and Applications I
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Received: from [134.20.200.80] by eloi.inel. gov (Post. Office MTA v3.1 release PO203a 10# 0-36734U600L100S0) with SMTP id AAA26893 for <agh10nrc. gov >; Wed,1 Apr 199813:50:37 -0700 Message ld: <3.0.2.32.10980401135400.007b8c000eloi.inet eve X-Sender: mta20 eloi.irul. gov (Unverified)
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Date Wed,01 Apr 199313:54:00-0700 To: agh10nrc. gov From: mta20inel. gov (Michael T Anderson)
Subject:
Data from P-Scan Demo Mime Version: 1.0 Content Type: multipart/ mixed; boundary =" =--
_891489240==_"
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_LO>__
+:lB_ _\pMike B_a=E a +=xx_:_"8X O l'++ 1 +_*GArial1 +_*$Arial1 +_*GArial1 +_*GArial*$'#,# #0_);\(*$'# ,# #0\)l'
$'# , # #0_);[R edN'$'# , # #0\)"$'#, # #0.00_);\('$'# ,# #0.00\)'"$'#, # # 0.00_);[ R edN'$'#,# #0.00\)7 *2
_(*$" #,##0_);_(*$" \(#,##0\);_(*$" " '_);_(O_).))_(* #,##0_);_(* \(#,##0\);_(*
- );_(O_)?,:_(*$" #,##0.00_);_('$" \(#,##0.00\);_('S-* " '??_);_(O_)6+1_(* #,##0.00_);_(*
\(#,##0.00\);_(* * *??_);_(O_) + _+ _+ _+ _+ _+ _+ _+
_+ _+ _+ _+ _+ _+ _+_+_+_+_)_+ *
- _ * + _ __* * + _ _ _ * +_
+ _ + 60_oQ_oQ_o0_o0_oQ_' Al Sheet 160 Sheet 2&oSheet31n:H Indication Act depth Weld ZoneTypeslaglOFerack Act Length 0 Dag. Call Depth 0 Deg. Call Length 45 Deg. Call depth 45 Deg. Call Length 3 and 4_
i) A) $EAD4BcE F n E- Feang N r/is, 4 I
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- Mall Envelope Info: (3522A802.B1D : 18 : 43805)
Subject:
Data from P-Scan Demo Creation Date: 4/1/98 3:54pm From: Michael T Anderson <mta20inel. gov >
Created By: GATED.ntcsmtp:'mta20inel. gov" Recipients Post Office WND1.WNP7 AGH1 (Allen dowe)
Domain. Post Office Route WND1.WNP7 WND1.WNP7 Files Size Date & Time MESSAGE 298 04/01/98 03:54pm p-scan demo.xis 16896 Part.002 132 Header 849 Options Expiration Date: None Priority: Normal Reply Requested: No Return Notification:: None Concealed
Subject:
No Security: Normal i
l From: Michael T Anderson <mta2 pinel. gov >
To: WND1.WNP7(AGH1)fl go m ,ofru.)
Date: 4/1/98 5:38pm l
Subject:
NRC Demo Data Men, Try this one, i
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'%)5% 9) M /Z/&f2,
Q Michael Anderson (208)526-8780 l mta2Olnel. gov l Idaho National Engineering Laboratory NDE Engineering Analysis and Applications {
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Received: From [148.184.176.31) igate.nrc. gov j
By smtp (GroupWise SMTP/ MIME daemon 4.11) i Wed,1 Apr 9817:32:35 EST I Received: from nrc. gov l by smtp-gateway ESMTPE id RAA20062 I for <agh1 Onrc. gov >; Wed,1 Apr 199817:33:37 -0500 (EST)
Received: from (134.20.200.80] by eloi.inel. gov (Post. Office MTA v3.1 I release PO203a 10# 0 36734U600L100S0) with SMTP id AAA29673 for <agh10nrc. gov >; Wed,1 Apr 199815:35:15 -0700 Message-Id: <3.0.2.32.19980401153836.007b82900 eloi.inel. gov >
X Sender: mta2 O eloi.inel. gov (Unverified)
X Maller: QUALCOMM Windows Eudora Light Version 3.0.2 (32)
Date: Wed,01 Apr 199815:38:36 -0700 To: agh1 @nrc. gov From: mta2 Olnel. gov (Michael T Anderson) l
Subject:
NRC Demo Data Mime-Version: 1.0 Content Type: multipart/ mixed; boundary ='========---= -- -
891495516== "
t j _. __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ -
Indication Weld ZoruType Act depth Act Length 0 Dog. Call Depth 0 Deg. Call Length 1 2 crack 0.05 0.5 2 2 crack 0.075 0.5 0.11 0.7 3 2 crack 0.1 0.75 0.15 0.7 4 2 crack 0.15 0.5 0.15 0.8 5 2 crack O.2 0.5 0.15 0.7 6 2 crack 0.25 1.5 0.3 1.6 7 2 crack O.1 0.5 0.3 0.8 8 1 crack O.05 0.5 9 1 crack 0.075 0.5 10 1 crack 0.1 0.75 0.19 0.7 11 1 crack 0.15 0.5 0.34 0.7 12 1 crack 0.2 0.5 0.26 0.8 13 1 crack 0.25 1.5 0.26 1.6 14 4 crack O.05 0.5 0.19 0.8 15 4 crack 0.075 0.5 0.19 0.7 16 4 crack O.1 0.75 0.2 0.8 17 4 crack O.15 0.5 0.15 0.8 18 4 crack 0.2 0.5 0.22 0.7 19 4 crack 0.25 1.5 0.25 1.7 20 3 crack 0.05 0.5 21 3 crack O.075 0.5 22 3 crack O.1 0.75 0.6 23 3 crack 0.15 0.5 0.6 24 3 crack O.2 0.5 0.6 (
25 3 alag 0.25 1.5 0.228 1.7 l 26 4 LOF 0.1 0.5 0.19 0.7 27 3 crack 0.1 0.5 . 0.3 0.6 28 3 and 4 crack 0.3 0.5 0.19 0.7 i 29 3 and 4 crack O.4 0.5 0.19 0.6 I 30 3 and 4 crack 0.5 0.5 0.4 0.7 i
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45 Dog. Call depth 45 Dog. Call Length -
0.1 0.6 l 0.1 0.8 l 0.17 1 !
0.12 0.8 0.17 0.8 0.27 1.7 0.2 0.9 '
O.23 0.9 0.2 1.1 02 1 0.27 0.9 0.3 2.1 0.24 0.6 0.21 ~ 0.6 0.35 0.6
)
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- - _ _ _ _ _ _ _ _ _ _ _ _ _ - . _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ o
s Mall Envelope info: (3522C086.CD6 : 9 : 44246) !
Subject:
NRC Demo Data Creation Date: 4/1/98 5:38pm From: Michael T Anderson <mta20inel. gov >
Created By: GATED.ntcsmtp:'mta20inel. gov' Recipients Post Office WND1.WNP7 AGH1 (Allen Howe)
Domain. Post Office Route WND1.WNP7 WND1.WNP7 Files Size Date & Time MESSAGE 24 04/01/98 05:38pm p-scan demo.xis 23552 Part.002 132 Header 841 Options Expiration Date: None Priority: Normal Reply Requested- No Returtt Notification:: None Concealed
Subject:
No Security: Normal l
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