ML20198K457

Summary of 971203 Meeting W/Nuclear Energy Institute in Rockville,Maryland Re Issues Related to SG Tube Database for voltage-based Alternate Tube Repair Criteria for Outside Diameter Stress Corrosion Cracking in Westinghouse Plants

ML20198K457
Person / Time
Issue date:	01/07/1998
From:	Stewart Magruder NRC (Affiliation Not Assigned)
To:	Essig T NRC (Affiliation Not Assigned)
References
PROJECT-689 NUDOCS 9801140424
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NUCLEAR RESULATORY COMMISSMHd wasumetow, e.c. asesse

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January 7, 1998

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MEMORANDUM TO: Thomas H. Essig, Acting Chief -

i Generic issues and Environmental Projects Branch i

Division of Rosator Program Management j

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Office of Nuclear Reactor Regulation l

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Stewart L. Magruder, Project Manager. Maw,4 Lh =h, Generic issues and Environmental Projects Branch Q

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Division of Reactor Program Management Offloe of Nuclear Reactor Regulation

SUMMARY

OF THE DECEMBER 3,1997, MEETING WITH NUCLEAR ENERGY INSTITUTE (NEI) REGARDING STEAM GENERATOR TUBE l

DATABASE FOR VOLTAGE-BASED ALTERNATE TUBE REPAIR

-i CRITERIA On December 3, igg 7, representatives of the nuclear power industry met with members of the Nuclear Regulatory Commission (NRC) staff in Rockville, Maryland. The purpose of the i

meeting was to discuss issues related to the steam generator tube database for voltage-based i

altomate tube repair criteria for outside diameter stress corrosion cracking in Westinghouse plants with drilled hole tube support plates. The main topics of discussion were statistical technioues for simulation and treatment of steam generator tube data obtained from French nucisar plants. Meeting attendees are identified in Attachment 1. T.* agenda and staffs viewgraphs are included as Attachment 2, The staff provided the following comments during the meeting:

4 With respect to statistical techniques for simulation, the staff commented that the currently adopted framework for performing conditional burst and leak calculations is Bayesian, which the staff and the industry both consider to be an appropriate model to address sampling uncertainty..

i Any industry proposed modifications to the current statistical analysis framework need to be

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justified in terms of the goals of the analysis and the adopted analysis framework. In addition, g7 the proposed modifications should be explicit with respect to the theoretical basis for the y

analysis framework; i.e., the formulation of the probabilistic problem and the model should be provided. This comment would also apply to the proposed attemative to the current probability i

of leak (POL) model or to the use of a Bootstrap approach Calculations should be based on a consistent mo ael and on applicable assumptions concoming data distrib"*lons and sampling

. mrtainty, i.e., the same analysis framework should be used for all the calculations, The I

s Jmptions made about the tail of the distributions should be conservative because the tail y

cad be justified by the data.

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January 7, 1998

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T c E ssig 2-i The staff ocmmented that the proposed single sided p. test for the leak rate vs. voltage data correlation is socoptable. The industry representatives indicated that this approach resuhs in a j

oorrelation and will be reflected in upcoming 90-day reports for plants with 7/8" tubing, j

i The staff commented that the industry proposed unbiased estimation for leak rate calculations se documented in section 6.3.2 of the EPRI report NP 7480 L is not scooptable for use in the current analysis framework because the approach has not demonstrated that the simulation will resuN in a conservative leak rate value at the 96% quantile.

t With respect to the industry's proposal to modify the current statistical POL rr:odel, the staff j

believes that the industry noods to apply Goodness of-Fit tests to the data to determine the j

applicability of the proposed model; and it needs to perform sensitivity studies to other statistical l

models to critically examine the proposed model.

i With respect to the industry proposed exclusion of French data from the steam generator database, the staff noted that it is advantageous to include the French data in the database because the French data contain high voltage data points sad have intergranular stress corrosion cracking (IGSCC) that has been in servios for an extended time which is valuable for the future application to domestic plants. The staff commented that: (1) statistical tests cannot be used by themselves as a decision tool for excluding the data, (2) the primary bases for including or excluding the French data should rest on the experimental protocol, (3) the industry 1

has not provided sufficient physical evidence to conclusively exclude the French data from the database (4) the industry needs to perform a quality assurance review of the French data, (5) the quality assurance review will need to be performed expeditiously in order to satisfy the schedule requirement in the protocol for updating the database, and (6) any rules or criteria for including or excluding the French data should be applied consistently across the database.

Wdh respect to the protocol for updating the steam generator database, NEl submitted the final version of the industry proposal in a letter dated October 28,1997. The staff finds the proposal acceptable and will forward a letter to NEl to bring this issue to a closure.

With respect to the proposed treatment of fractional tube indications in the tube integrity cWculations, the staff commented that it will review the proposed method when it is submitted formally.

Project No, 689 Attachments: 1 List of Attendees

2. Agenda and Vowgraphs cc w/att: See next page i

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T. Essig 2

January 7, 1998 The staff commented that the proposed single sided p-test for the leak rate vs. voltage data correlation in acceptable. The industry representatives indicated that this approach results in a correlation and will be reflected in upcoming 90-day reports for plants with 7/8 tubing.

The staff commented that the industry proposed unbiased estimation for leak rate calculations i

as documented in section 6.3.2 of the EPRI report NP.7480-L is not acceptable for use in the current analysis framework because the approach has not demonstrated that the simulation will result in a conservative leak rate value at the 95% quantile.

With respect to the industry's proposal to modify the current statistical POL model, the staff believes that the industry needs to apply Goodness-of Fit tests to the data to determine the applicability of the proposed model; and it needs to perform sensitivity studies to other statistical models to critically examine the proposed model.

With respect to the Industry proposed exclusion of French data from the steam generator database, the staff noted that it is advantageous to include the French data in the database because the French data contain high voltage data points and have intergranular stress corrosion cracking (IGSCC) that has been in service for an extended time which is valuable for the future application to domestic plants. The staff commented that: (1) statistical tests cannot be used by themselves as a decision tool for excluding the data, (2) the primary bases for including or excluding the French data should rest on the experimental protocol, (3) the Industry has not provided sufficient physical evidence to conclusively exclude the French data from the database, (4) the industry needs to perform a quality assurance review of the French data, (5) the quality assurance review will need to be performed expeditiously in order to satisfy the schedule requirement in the protocol for updating the database, and (6) any rules or criteria for including or excluding the French data should be applied consisten'Jy across ti,e database.

With respect to the protocol for updating the steam generator database, NEl submitted the final version of the industry proposalin a letter dated October 28,1997. The staff finds the proposal acceptable and will forward a letter to NEl to bring this issue to a closure.

With respect to the proposed treatment of fractional tube indications in the tube integrity calculations, the staff commented that it will review the proposJd method when it is submitted formally.

Project No. 689 Attachments: 1. List of Attendeet

2. Agenda and Viewgraphs cc w/att: See next page

. DISTRIBUTION: See attach page OFFICE PM:PGEB EMCB SC:PGE$ '

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I NRC INDUSTRY MEETING REGARDING STEAM GENERATOR DATABASE FOR VOLTAGE BASED ALTERNATE TUBE REPAIR CRITERIA DECEMBER 3,1997 LIST.OEATTENDEES NAME ORGANIZATION 1.

John Tsao NRC/NRR 2.

Rick Mullins Southern Company 3.

Steve Dembok NRC/NRR 4.

Stu Magruder NRC/NRR 5.

Brian Woodman APTECH Engineering 6.

Ron Gamble Sartrex 7.

Ted Sullivan NRC/NRR 8.

Jim Davis NRC/NRR 9.

Lee Abramson NRC/RES

10. Joe Muscara NRC/RES

11. Christopher Begley APTECH Engineering

12. Robert Keating Westinghouse

13. Patrick Hensler Pacific Northwest National Lab.

14. Stephanie Coffin NRC/NRR i

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AGENDA FOR NRC INDUSTRY MEETING REGARDING 1

STEAM GENERATOR DATABASE FOR VOLTAGE BASED ALTERNATE TUBE REPAIR CRITERIA DECEMBER 3,1997 8:00 AM 2:30 PM ONE WHITE FLINT NORTH ROOM O 10813

1. STATISTICAL TECHNIQUES FOR SIMULATION 8:00 am A. TREATMENT OF UNCERTAINTIES IN PARAMETERS-STAFF B. DISTRIBUTION FOR LEAK RATES-STAFF C. UNBIASED ES'ilMATION-STAFF D. PROBABILITY OF LEAK DATA-WESTINGHOUSE E. BOOTSTRAP APPROACH-WESTINGHOUSE

2. TREATMENT OF FRENCH DATA IN 7/8 TUBE DATABASE 10:00 am A. STATISTICAL ANALYSIS OF BURST DATA-STAFF B. IMPLICATION ON LEAK RATE DATA-STAFF C. PHYSICAL EVIDENCE-WESTINGHOUSE

3. CAUCUS 11:30 am

4. TREATMENT OF FACTIONAL INDICATIONS-WESTINGHOUSE 1:30 pm

5. CAUCUS /

SUMMARY

2:30 pm ATTACHMENT 2

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I S:13 : Dea:. Raue anc. 'ane Burso Probabi:.iuy :V:od.e:.s :for OJSCC Patrick G. Heasler PNNL Dec.1997 i

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Problem Formulation i

e Objective is to estimate the 95% quantile on Total Leak Rate for an inspected Steam Generator.

. Total leak rate is leak rate the steam generator would experience during a pressure transient.

. The Total Leak Rate Distribution depends upon the inspection results.

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,,,g Steun Gen Problem Formulation Simplified Leak Rate Model:

N T = { RuQu (1) k=1 e RuQu is leak rate of tube k.

e Qk is the conditionalleak rate, with lognormal distribution Fq(q #a,84).

• Ru is binary variable with Pr(Ru = 1) = logit(Q1 + $2 Vu).

e Want to Calculate Uss, where Pr(T < Ugs) =.95.

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Problem Formulation If unknown parameters S (alternatively Fq( ) and Pr(R

= 1) ) are known, then problem has been 3

solved:

e The distribution Fr( ) of T can be calculated numerically or by a Monte Carlo using the previous formulas.

. Result is Fr(t V,B) = Pr(T < t V,$)

e Fr( ) can be used to find Ugs.

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Parametric Uncertainty Problem: We don't know B, but have data than can be used to estimate S. These estimates will contain substantia.1 uncertainties. How can we modify the problem to account for this uncertainty?

Two solutions are available:

i e Bayesian solution: Treat $ as a random variable and describe uncertainty as a probability distribution.

i e Frequentist solution: Put confidence bounds on Ugs, which creates a tolerance bound or create a 95% prediction interval for T.

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1 Parametric Uncertainty Bayesian Solution:

. Use leak rate data X to calculate f($ X), the posterior distribution of $ given the data.

. Note: for this problem f($ X) can be expressed as f($ 8).

e Solution is 95% quantile of Fr(t V,X), which is:

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Parametric Uncertainty Bayesian Posterior:

f($ X) = f(X #)/(#)

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/(X) 4 Important Point: posterior f($ X) is completely determined by data distribution f(X.$) and prior f(S). If standard non-informative priors are chosen, then f($ X) is completely determined by f(X S).

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Advantage [of Bayesian Solution:

• Requires the least modification to present.

M.C. code to implement.

e Provides a coherent framework for dealing with all parametric uncertainty.

. Gives results that are asymptotically similar to frequentist results.

• Is a well-documented methodology.

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tm Steam Gen Unbiased Estimation Given the problem formulation, we are interested in the properties of an estimator of U, call it 93 Dos = h(X). The properties of other estimators (that are not even used to construct & )are not 93 relevant.

. Be.yesian Property: Fr(&

V,X) =.95.

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. Tolerance Bound Property:

93 < 6 ) =.95 Pr(U 93

. Prediction Bound Property:

Pr(T < 6

) =.95 93

. An estimate of the mean of Qu is not even used to construct the present 93

. Even if the mean of Qu were used to construct

&gs, its acceptability should be determined by one of the three properties above.

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Unbiased Estimation If we were interested in estimating q, the mean of Qu, EPRI's observations are corre.ct with the following qualifications, e There seems to be an error in " unbiased" estimation formula. If natural logs are used the formula is, SQ = eXP(MnQ)9( SfnQ)

(7) i so the formula for base-10 logs is, AQ = exp(In(10)MogQ)p(

In(10)2Sfoy )(8) i

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SQ = OXP(MnQ + 3[no)

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is asymptotically correct.

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Comments about log-normal

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• Fits existing data well (Fig. 6-8).

i o Has a very heavy right-hand tail.

Clearly is not bounded, as lea'k rate should be.

Important information about right hand tail b y 68st.

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Statistical Analysis of French Data e The GOF tests are performed correctly.

e The tests have.NOT been interpreted corre::tly.

• From the results presented, I would favor retaining the French data, and it would be to industry's advantage to do this.

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s-comparison 1

2 3

4 5

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null Hyp--

model 4 model 4 model 6 model 4 model 11 model 14 model 16 Alt Hyp model 1 model 5 model 7 model 8 model 12 model 15 model 17-N-H SSE-66.94 66.94 52.12 66.94 52.118 20.83 54.36 t

N-H 00F 91 91 72 91 72 47 61 A-H SSE 62.47 65.%

52.11 60.203 49.849 19.971 50.586 A-H DOF 89 89 7ti 87 70 45 59 F Stats 3.183 0.662 0.008 %

2.434 1.594 0.967 2.2 F stats DOF

2. 89

2. 89

2. 70

4. 87

2. 70

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2. 59 P value. I 4.6 51.83 99.2 5.32 21.1 38.8 12 comments reject Mi accept NH accept NH need more accept NH accept NH accept NH accept AH tests model 1 US and M data are from a different population than that of Edf data model 4 All (US. MB & Edf) data are from the same population.

model 5 All (US. M. & Edf) data that are less than 3 volts and data that are greater than 3 volts are from different populations.

model 6 US+MB data less than 3 volts and greater than 3 volts are from the same population.

model 7 US+MB data less than 3 volts and greater than 3 volts are from different populations.

model 8 US data. 2 data. and Edf data are from three separate populations.

model 11 US data and MB data are from the same population.

model 12 US data and MB data are from different populations.

model 14 MB data and EDF data are from the same population.

model 15 MB data and Edf data are from different populations.

model 16 Edf data and US data are frca the same population.

model 17 Edf data and US data are from different populations.

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Steam Gen Interpretation of Tests e A significant F-test implies (1) the model does not fit, or (2) something is " wrong" with the data.

4 e Original reason for conducting such tests was to evaluate (1), because validity of model is very important.

e These tests can be used to prove (1), but not (2).'

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external proof can be found that the data is 1

"in error."

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Stcam Gon Interpretation of Tests If Tests are significant:

1: MODEL DOES NOT FIT RELEVANT DATA: ITS VALIDITY IS IN DOUBT!!!!

2. Model can only be saved if we can PROVE that some of the data is not relevant.

3. Must show that the " type" of ODSCC that occurs in French generators can't occur in US generators.

9 4

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o-g Nuclear Energy Institute Project No. 689 cc:

Mr. Ralph Beedle Ms. Lynnette Hendricks, Director Senior Vice President Plant Support and Chief Nuclear Officer Nuclear Energy Institute Nuclear Energy Institute Suite 400 Suite 400 17761 Street, NW 1776 i Street, NW Washington, DC 20006-3708 Washington, DC 20006-3708 Mr. Alex Marion, Director Programs Nuclear Energy institute Suite 400 1776 l Street ~ ~W Washington, DC 20006-3708 Mr. David Modeen, Director Engineering Nuclear Energy Institute Suite 400 1776 l Street, NW Washington, DC 20006-3708 Mr. Anthony Pieirangelo, Director Licensing Nuclear Energy institute Suite 400 1776 i Street, NW Washington, DC 20006-3708 Mr. Nicholas J. Liparulo, Manager Nuclear Safety and Regulatory Activities Nuclear and Advanud Technology Division Westinghouse Electric Corporatior, P.O. Box 355 Pittsburgh, Pennsylvania 15230 Mr. Jim Davis, Director Operations Nuclear Energy institute Suite 400 1776 i Street, NW Washington, DC 2000S-3708

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NUCLEAR REGULATORY COMMISSION t

WASHINGTON, D.C. 30686 0001 January 7, 1998 MEMORANDUM TO: Thomas H. Essig, Acting Chief Generic lasues and Environmental Projects Branch Division of Reactor Program Management Office of Nuclear Reactor Regulation-FROM:

Stewart L. Magruder, Project Manager N tr Generic lasues and Environmental Projects Branch Division of Reactor Program Management Office of Nuclear Reactor Regelation

SUMMARY

OF THE DECEMBER 3,1997, MEETING WITH NUCLEAR ENERGY INSTITUTE (NEI) REGARDING STEAM GENERATOR TUBE DATABASE FOR VOLTAGE-BASED ALTERNATE TUBE REPAIR CRITERIA On December 3,1997, representatives of the nuclear power industry met with members of the Nuclear Regulatory Commission (NRC) staff in Rockville, Maryland. The purpose of the meeting was to discuss issues related to the steam generator tube database for voltage-based attemate tube repair criteria for outside diameter stress corrosion cracking in Westinghouse plants with drilled hole tube support plates. The main topics of discussion were statistical techniques for simulation and treatment of steam generator tube data obtained from French nuclear plants. Meeting attendees are identified in Attachment 1. The agenda and staffs viewgraphs are included as Attachment 2.

The staff provided the following comments during the meeting:

With respect to statistical techniques for simulation, the staff commented that the currently adopted framework for performing conditional burst and leak calculations is Bayesian, which the staff and the industry both consider to be an appropriate model to address sampling uncertainty.

Any industry proposed modifications to the current statistical analysis framework need to be justifwKiin terms of the goals of the analysis and the adopted analysis framework. In additi the proposed modifications should be explicit with respect to the theoretical basis for the analysis framework; i.e., the formulation of the probabilistic problem and the model should be provided. This comment would also apply to the proposed attemative to the current proba of Icak (POL) model or to the use of a Bootstrap approach. Calculations should be based on a consistent model and on applicable assumptions conceming data distributions and sampling uncertainty, i.e., the same analysis framework should be used for all the calculations. The assumptions made about the tail of the distributions should be conservative because the tail cannot be justifiM oy the data.

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""*N 7' T. Essig 2-The staff commented that the proposed single sided p-test for the leak rate vs. voltage data

- correlation is acceptable. The industry representatives indicated that this approach results in a i

correlation and will be reflected in upcoming 90-day reports for plants with 7/8" tubing.

The staff commented that the industry proposed unbiased estimation for leak rate calculations as documented in section 6.3.2 of the EPRI report NP 7480-L is not acceptable for use in the current analysis framework because the approach has not demonstrated that the simulation will result in a conservative leak rate valJe at the 95% quantile.

With respect to the industry's proposal to modify the current statistical POL model, the staff -

believes that the industry needs to apply Goodness-of-Fit tests to the data to determine the applicability of the proposed model; and it needs to perform sensitivity studies to other statistical

. models to critically exar, ins the proposed model.

With respect to the industry proposed exclusion of French data from the steam generator database, the staff noted that it is advantageous to include the French data in the database because the French data contain high voltage data points and have intergranular stress corrosion cracking (IGSCC) that has been in service for an extended time which is valuable for the future application to domestic plantsi The staff commented that: (1) statistical tests cannot be used by themselves as a decision tool for excluding the data, (2) the primary bases for including or excluding the French data should rest on the experimental protocol, (3) the industry has not providad sufficient physical evidence to conclusively exclude the French data from the database, (4) the industry needs to perform a quality assurance review of the French data, (5) the quality assurance review will need to be performed expeditiously in order to satisfy the 4

schedule requirement in the protocol for updating the database, and (6) may rules or criteria for including or excluding the French data shou!d be applied consistently act cs the database.

- With respect to the protocol for updating the steam generator database, NEl submitted the final version of the industry proposal in a letter dated October 28,1997. The staff finds the proposal acceptable and will forward a letter to NEl to bring this issue to a closure.

With respect to the proposed treatment of fractional tube indicatic s in the tube integrity calculations, the staff commented that it will review the proposed method when it is submitted formally.

Project No. 689 Attachments: 1. List of Attendees

2. Agenda and Viewgraphs

- cc w/att: See next page k.

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T. Essig Januan L 1998-Tha staff commented that the proposed single sided p-test for the leak rate vs. voltage data -

correlation is acceptable.- The industry representatives indicated that this approach results in a-correlation and will be reflected in upcoming 90-day reports for plants with 7/8" tubing.

The staff commented that the industry proposed unbiased estimation for Nak rate calculations

as documented in section 6.3.2 of the EPRI report NF-7480-L is not accsplable for use in the carrent analysis framework because the approach has not deraonstrated that the simulation will result in a conservative leak rate value at the 95% quantile.

With respect to the industry's proposal to modify the current statistical POL model, the staff a

believes that the industry needs to apply Goodness-of-Fit tests to the data to determine the applicability of the proposed model; and it needs to perform sensitivity studies to cther statistical

~ models to critically examine the proposed model.

c.

Wnh respect to the industry proposed exclusion of French data from the steam generator database, the staff noted that it is advantageous to include the French data in the database because the French data contain high voltage data points and have intergranular stress corrosion cracking (IGSCC) that has been in service for an extended.me which is valuable for the future application to domestic plants. The staff commented that: (1) statistical tests cannot be used by themselves as a decision tool for excluding the data, (2) the primary bases for including or excluding the French data shoud rest on the experimental protocol, (3) the industry has not provided sufficient physical evidence to anclusively exclude the French data from the database, (4) the industry needs to perform a quality assurance review of the French data, (5) the quality assurance review will need to be performed expeditiously in order to satisfy the schedule requirement in the protocol for updating the database, and (6) any rules or criteria for including or excluding the French data should be applied consistently across the database.

With respect to the protocol for updating the steam generator database, NEl submitted the final version of the industry proposal in a letter dated October 28,1997. The staff finds the proposal acceptable and will forward a letter to NEl to bring this issue to a closure.

With respect to the proposed treatment of fractional tube irdications in the tube integrity calculations, the staff commented that it will review the proposed method when it is submitted formally.

Project No. 68g Attachments: 1. List of Attendees

2. Agenda and Viewgraphs.

cc w/stt: See next page DISTRIBUTION: See attach page l

OFFICE PM:PGEB EMCB SC:PGEEL '

NAME SMagruder:sw6m JTsao/(f' FAkstu'lewicz DATE ilf/98 1/d/98 il 7 /98 I

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. Distribution: Mig; Summary w/ NEl Re SG Tube Database Dated ~Ja.nuary 7. 1998 Hard Copy ~

Docket Flie '

PUSUC PGEB R/F OGC ACRS SMagruder.

JTsao EMail -

SCollins/FMiraglia BSheron RZimmerman Glainas/JStrosnider JRoe

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NRC-lNDUSTRY MEETING REGARDING.

STEAM GENERATOR DATABASE FOR VOLTAGE-BASED ALTERNATE TUBE REPAIR CRITERIA DECEMBER 3,1997 LIST _OE.AITENDEES NAME ORGANIZATION 1.

John Tsao NRC/NRR 2.

Rick Mullins Southem Company 3.

Steve Dembek NRC/NRR 4.

Stu Magruder NRC/NRR 5.

Brian Woodman APTECH Engineering 6.

Ron Gamble Sartrex 7.

Ted Sallivan NRC/NRR 8.

Jim Davis NRC/NRR 9.

Lee Abramson NRC/RES

10. Joe Muscara NRC/RES

11. Christopher Begley APTECH Engineering

12. Robert Keating Westinghouse

13. Patrick Hessler Pacific Northwest National Lab.

14. Stephanie Coffin NRC/NRR i

l l

AGENDA.

FOR NRC-INDUSTRY MEETING REGARDING STEAM GENERATOR DATABASE FOR VOLTAGE BASED ALTERNATE TUBE REPAIR CRITERIA DECEMBER 3,1997 8:00 AM - 2:30 PM ONE WHITE FLINT NORTH ROOM O-10813

1. STATISTICAL TECHNIQUES FOR SIMULATION 8:00 am A. TREATMENT OF UNCERTAINTIES IN PARAMETERS-STAFF B. DISTRIBUTION FOR LEAK RATES-STAFF

- C. UNBIASED ESTIMATION-STAFF D. PROBABILITY OF LEAK DATA-WESTINGHOUSE E. BOOTSTRAP APPROACH-WESTINGHOUSE

2. TREATMENT OF FRENCH DATA IN 7/8 TUBE DATABASE 10:00 am A. STATISTICAL ANALYSi$ OF BURST DATA-STAFF B. IMPLICATION ON LEAK RATE DATA-STAFF C. PHYSICAL EVIDENCE-WESTINGHOUSE

3. CAUCUS 11:30 am

4. TREATMENT OF FACTIONAL INDICATIONS-WESTINGHOUSE 1:30 pm

5. CAUCUS /

SUMMARY

2:30 pm l

ATTACHMENT 2 1

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Problem Formulation e Objective is to estimate the 95% quantile on Total Leak Rate for an inspected Steam Generator.

. Total leak rate is leak rate the steam generator would experience during a pressure transient.

e The Total Leak Rate Distribution depends upon the inspection results.

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teos Steun Gen Problem Formulation Simplified Leak Rate Model:

N T = { RuQu (1) k=1.

e RuQu is leak rate of tube k.

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e Qu is the conditional leak rate, with lognormal distribution Fq(703: 44).

Ru is binary variable with Pr(Ru = 1) = logit(Q1 + f2Vu).

Want to Calculate Uss, where Pr(T < Uss) =.95.

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Problem Formulation If unknown parameters S (alternatively Fq( ) and Pr(Ru = 1) ) are known, then problem has been solved:

. The distribution Fr( ) of T can be calculated numerically'or by a Monte Carlo using the previous formulas.

. Result is Fr(t V,$) = Pr(T < tlV,$)

e Fr() can be used to find Uss.

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Parametric Uncertainty i

Problem: We don't know

, but have data than can be used to estimate $. These estimates will contain substantial uncertainties. How can we rnodify the problem to account for this uncertainty?

Two solutions are available:

e Bayesian solution: Treat B as a random variable and describe uncertainty as a probability distribution.

. Frequentist solution: Put confidence bounds on U9s, which creates a tolerance bound or create a 95% prediction interval for T.

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Parametric Uncertainty Bayesian Solution:

. Use leak rate data X to calculate f(B X), the posterior distribution of S given the data.

. Note: for this problem f($ X) can be expressed as f($ #).

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• Solution is 95% quantile of Fr(t V,X), which is:

Fr(t V, X) =

Fr(t V,B)f(S X)d (2) e &gs satisifies:

Fr($

V,X) =.95 (3) 95 W

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Parametric Uncertainty Bayesian Posterior:

($ X) = f(X s)f(s) f (4) i f(x)

~Important Point: posterior f($ X) is completely determined by data distribution f(X $) and prior f(S). If standard non-informative priors are chosen, then f($ X) is completely determined by f(X $).

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1 Parametric Uncertainty l

Advantagedof Bayesian Solution:

1 e Requires the least modification to present.

l M.C. code to implement.

I e Provides a coherent framework for dealing with all parametric uncertainty.

. Gives results that are asymptotically similar to frequentist results.

• Is a well-documented methodology.

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U 3814 2400 sTotss mL 2oss Steam Gen Unbiased Estimation Given the problem formulation, we are interested in the properties of an estimator of Ugs, call it Ogs = h(X). The properties of other estimators (that are not even used to construct &gs)are not relevant.

. Bayesian Property: F (O V,X) =.95.

T 95 e Tolerance Bound Property:

Pr(U95 < &gs) =.95

• Prediction Bound Property:

Pr(T < Og3) =.95

. An estimate of the mean of Qu is not even used to construct the present $gs.

. Even if the mean of Qu were used to construct

&gs, its acceptability should be determined by

(

one of the three properties above.

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Unbiased Estimation If we were interested in estimating q, the mean s

of Qk, EPRI's observations are correct with the following qualifications.

. There seems to be an error in " unbiased" estimation formula. If naturallogs are used the formula is, 1

f2Q = eXP(M g)9(3 nQ)

(7)

Sf in so the formula for base-10 logs is,

[2Q = exp(In(10)Mosq)p( In(10)2gpo9Q) g i

e Using the formula 1

fzq = exp(Mnq + 3 [ng)

(9) i S

h is asymptotically correct.

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Comments 'about log-normal

.i distribution e Fits existing data well (Fig. 6-8).

• Has a very heavy right-hand tail.

e Clearly is not bounded, as leak rate should 4

be.

Important information about right hand tail may exist.

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Comments about log-normal

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l Statistical Analysis of French Data l

• The GOF tests are performed correctly.

• The tests have NOT been interpreted l

correctly.

From the results presented, I would favor 4

retaining the French data, and it would be to industry's advantage to do this.

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comparison 1

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4 5

6 7

null Hyp model 4 model 4 model 6 model 4 model 11 model 14 model 16 Alt Hyp model 1 model 5 model 7 model a model 12 model 15 model 17 N-H SSE 66.94 66.94 52.12 66.94 52.118 20.83 54.36 N-H 00F 91 91 72 91 72 47 C1 A-H SSE 62.47 65.%

52.11 60.203 49.849 19.971 50.586 i

A-H DOF 89 89 70 87 70 45 59 F Stats 3.183 0.662 0.00806 2.434 1.594 0.967 2.2 F stats DOF

2. 89

2. 89

2. 70

4. 87

2. 70

2. 45

2. 59 P value. %

4.6 i 51.83 9.2 5.32 21.1 38.8 12 comments l reject NH accept NH accept NH need more accept E Laccept E accept E i accept AH tests l

imodel 1 US and 2 data are from a different population than that of Edf data model 4 ' All (US. MB & Edf) data are from the same populatfor model 5 All (US. 2. & Edf) data that are less than 3 wits and data tmt are greater than 3 volts are from if fferait populations.

model 6 US+MB dats less than 3 volts and greater than 3 volts are from the same population.

model 7 US+MB data less than 3 volts and greater than 3 vults are from different populations.

model 8 US data. MB data. and Edf data are from three separate populations.

model 11 US data and MB data are frun the same population.

model 12 US data and M data are from different populations.

model 14 MB data and EDF data are frau the same population.

model 15 MS data and Edf data are from different populations.

model 16 Edf data and US data are from the same population.

model 17 Edf data and US data are from different populations.

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i Interpretation of Tests e A significant F-test implies (1) the model does not fit, or (2) something is " wrong" with the data.

. Original reason for conducting such tests was to evaluate (1), because validity of model is very important.

. These tests can be used to prove (1), but not (2).-

I e (2) can only be concluded if compelling external proof can be found that the data is "in error."

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I Interpretation of Tests If Tests are significant:

1. MODEL DOES NOT FIT RELEVANT DATA: ITS VALIDITY IS IN DOUET!!!!

2. Model can only be saved if we can PROVE that some of the data is not relevant.

3. Must show that the " type" of ODSCC that occurs in French generators can't occur in US generators.

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Nuclear Energy institute Project No. 68g cc:

Mr. Ralph Boedle Ms. Lynnette Hendricks, Director Senior Vice President Plant Suppori and Chief Nuclear Omcer Nuclear Energy instituto Nuclear Energy Institute Suite 400 Suite 400 1776 i Street, NW 1776 i Street, NW Washington, DC 20006-3708 Washington, DC 20006-3708 Mr. Alex Marion, Director Programs Nuclear Energy institute Suite 400 1776 i Street, NW Washington, DC 20006 3708 Mr. David Modeon, Director Engineering Nuclear Energy Institute Suite 400 1776 i Street, NW Washington, DC 20006 3708 Mr, Anthony Pietrangelo, Director Licensing Nuclear Energy institute Suite 400 17761 Street, NW Washington, DC 20006 3708 Mr. Nicholas J. Liparuto, Manager Nuclear Safety and Regulatory Activities Nuclear and Advanced Technology Division Westinghouse Electric Corporation P.O. Box 355 Pittsburgh, Pennsylvania 15230 Mr. Jim Davis, Director Operations Nuclear Energy Institute Suite 400 1776 i Street, NW Washington, DC 20006-3708

.