ML20070R027
| ML20070R027 | |
| Person / Time | |
|---|---|
| Site: | Indian Point  |
| Issue date: | 01/24/1983 |
| From: | Kaplan S CONSOLIDATED EDISON CO. OF NEW YORK, INC., POWER AUTHORITY OF THE STATE OF NEW YORK (NEW YORK |
| To: | |
| Shared Package | |
| ML20070R032 | List: |
| References | |
| REF-GTECI-A-49, REF-GTECI-RV, RTR-NUREG-CR-2497 ISSUANCES-SP, NUDOCS 8301270242 | |
| Download: ML20070R027 (18) | |
Text
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00CMETED
'3 RC UNITED STATES OF AMERICA
'83 jpfl26 00 M9 NUCLEAR REGULATORY COMMISSION ATOMIC SAFETY AND LICENSING BOARD
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Before Administrative Judges:
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James P. Gleason,-Chairman Frederick J.
Shon Dr. Oscar H.
Paris
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In the Matter of
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CONSOLIDATED EDISON COMPANY OF
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Docket Nos.
N EW YORK, INC.
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50-247 SP (Indian Point, Unit No. 2)
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50-286 SP
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POWER AUTHORITY OF THE STATE OF
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January 24, 1983~
(Indian Point, Unit-No. 3)
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LICENSEES' TESTIMONY OF STANLEY'KAPLAN ON BOARD QUESTION 1.2 ATTORNEYS FILING THIS DOCUMENT:
Brent L.
Brandenburg Charles Morgan, Jr.
CONSOLIDATED EDISON COMPANY Paul'F. Colarulli OF NEW YORK, INC.
Joseph J.
Levin, Jr.
4 Irving Place MORGAN ASSOCIATES, CHARTERED New York, New York 10003 1899 L Street, N.W.
(212) 460-4600 Washington, D.C.
20036 (202) 466-7000 bo47 DR DOCK O T
PDR 3
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Introduction My name is Stanley Kaplan, Ph.D.
I am an associate consultant at Pickard, Lowe and Garrick, Inc.
My main area of work is in probability theory, risk and decision analy-ais, and particularly in probabilistic risk assessment methodology.
I was a principal investigator on the Indian Point Probabilistic Safety Study.
A statement of my l.'
professional qualifications is attached.
Board Question 1.2 asks:
What bearing, if any, do the results reported in NUREG/CR-2497, " Precursors to Potential Severe Core Damage Acci-dents:
1969-1979, A Status Report" (1982), have upon the reliability of the IPPSS (Indian Point Probabilistic Safety Study]?
For example, are there specific accident scenarios at Indian Point whose probability may have been inaccurately estimated in light of the real-life data reported and analyzed in NUREG/CR-2497?
II.
Response
NUREG/CR-2497, " Precursors to Potential Severe Core Damage Accidents:
1969-1979, A Status Report" (1982) attempts to calculate the frequency of severe core damage (SCD) accidents in domestic nuclear power plants as a whole without any effort to distinguish between different plants or types of plants.
It did this by sifting the Licensee Event Reports (LERs) for the period 1969-1979 and identify-ing incidents which it calls " precursors for potential
rE,
severe l core damage accidents."
It then put these precursors through an-event tree-type calculation procedure and derived an SCD frequency of 1.7 to 4.6 x 10-3 per year.
This range of values is significantly higher than that calculated in most other probabilistic risk assessments (PRAs).
For example,7the Reactor. Safety Study ~.(RSS) calculated a core melt frequency ~of 5 x 10-5, a factorlof almost 100 less.
,The question, therefore, arises as to whether-the NUREG invalidates the;RSS, the process of PRA in general, and the
'IPFSS:results-in particular.
To address this question' it is helpful to paraphrase the methodology and line of argument of this NUREG.
The essence of'it is as follows:
Up through 1979 we have had 432 years of reactor operation and one SCD accident, namely, TMI.
We have also had a' number of "near misses",
e.g., Browns Ferry and Rancho Seco.
We assign each of these near misses a " severity factor," which we get from the event trees.
Adding
.these.up, we consider.that the n6ar misses all together are the equivalent of about one more SCD accident.
So we consider that the statistical experi-ence, through 1979, is about two SCD events in 432 years which gives a frequency of 2/432 = 4.6 x 10-3 The way in which NUREG/CR-2497 evaluated those near misses.can be and has been subject to much criticism both from an engineering modeling basis (i.e., inaccuracies and oversimplifications in the event trea/ severity factor work)
-and on,the basis of statistical logic (e.g., that near i
1
i.
misses should not be counted at all).
For example, with respect to the near miss contribution to SCD frequency, the Institute of Nuclear Power Operation (INPO) review of the NUREG (Ref. 1) concludes that the NUREG calculation of this contribution is about 30 times too high for the_ plants as they.were at the time the events occurred.
Furthermore,
- his review points out that the NUREG did not recognize the many improvements that have been made in light of the lessons learned from the events.
Thus, INPO concludes that the NUREG frequencies are not appropriate either for past or future performance.
i While I agree with much of this criticism, for our purposes here the evaluation of the near misses is not the main issue.
For whether we consider that the experienced frequency of SCDs is one or two in 432 years makes little difference; both numbers are very different 9 rom the RSS results.-
With regard to the RSS result, it should be noted that first counting all free world nuclear power reactors, there are today aboot 1,500 plant years of experience.
Thus, our statistical evidence is now 1/1,500 rather than 1/432.
Secondly, the RSS result is for a different event, core melt rather than severe core damage, in a different type of plant, Surry rather than TMI.
With respect to the PRA process itself, we should note
^
~ that a PRA is, basically, a way of calculating the frequency.
of compound events from the frequencies of the "alemental"
[
events which together make up the compound event.
The way in which this is done is just pure logic.
The NUREG does not in any:way-impugn or invalidate the' basic process or methodology of PRA.
It.itself uses PRA. methodology in its calculation of severity factors.
Thus PRA, in general, in ou'r view, is not called into question by the NUREG.
How-ever,'in any particular application of PRA, there can, of
- course, be errors or omissions in logic or arithmetic.
{
Thus,-the Board's. question appropriately asks specifically if the frequency of.any IPPSS scenarios should be changed in
' light of the NUREG data.
The answer tc this is that the data reported in the 3
F i-lNUREG,'and the incidents analyzed there were known to the IPPSS analysts at the time of their study.
This knowledge was included in the scenario modeling and in the frequency.
calculations included in the IPPSS,'along with the data from their own review of the LERs and, most importantly, along E
'with the specific operating data from the Indian Point plants.. The publication of the NUREG, thus, provided nothing basically new.
It did, however, provide a useful focus of attention, particularly on the role of human errors I
of commission-in the accidents of the past.
It thus pro-t
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vided an opportunity to reexamine the IPPSS scenarios, particularly from the human error standpoint and from the standpoint of implementation of the lessons learned from past events.
After this reexamination, the IPPSS analysts confirmed that the probability curves for the IPPSS scenario frequencies accurately express our statt of knowledge of those frequencies, and that none of them require change in light of the NUREG.
This statement is particularly true for the scenarios included in the IPPSS study which represent incidents of the TMI-type.
Fur'.5er, it is worth noting that fundamental differ-ences in the design of the Indian Point and TMI plants make it vastly less likely that scenarios of the TMI-type could occur at Indian Point.
Among these design differences are the use at Indian Point of drum type steam generators with greater heat capacity (in the form of secondary coolant inventory), greater heat capacity of the primary coolant system (in the form of primary coolant inventory), and a reactor trip signal that would respond immediately to a loss of feedwater condition.
Hence, at Indian Point, there would be no immedie:e primary system pressure rise in response to a loss of feedwater.
Even if the auxiliary feedwater were delayed as much as 20 to 30 minutes, the primary system would not experience a pressure transient, and the relie.
L
valve would not lift; therefore, it could not stick and could not lead to a loss of coolant.
If auxiliary feed were delayed longer than this, and if the relief valve were to lift and stick open, there is, at Indian Point, direct monitoring of the position of this valve so_that the operators would be aware of its stuen condition.
They could then act to block the valve and/or inject coolant, thus bringing the plant to a stable condi-tion with no core damage.
The heat removal path required for this stability is provided by bleed and feed, forced circulation, and/or by natural circulation cooling which, at the Indian Point plants, is greatly enhanced by the elevated steam generator design.
One thing that has become clear through the post-RSS
?
PRAs is that the frequency of core melt or damage can be very different from plant to plant because of design differ-
-encec.
For example, various PRAs of different nuclear power plants hsve reported core melt frequencies ranging from abou*. 1.0 x 10-3 to 2.0 x 10-5 per reactor year (Ref. 2), a difference of about a factor of 50.
Even within the same plant, the core melt frequency can change when there is a design modification.
This was observed in the development of the IPPSS when such modificatiens were made to the Ir.dian Point plants.
y -
Finally,.it should be recalled from the IPPSS study a'.d the licensees' direct testimony on question 1 that a com-plete treatment of core melt frequency shou 3d be done with n
full. probability curves rather than single number " point" estimates and that core melt frequency itself is a poor indicator of pbblic health risks at Indian Point.
REFERENCES 1.
Institute of Nuclear Power Operations, " Review of NRC Report:
Precursors to Potential Severe Core Damage Accidents:
196901979, A Status Report," NUREG/CR-2497, 1982.
2.
Memorandum from William J. Dircks to NRC Commissioners (Jan. 5, 1983).
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cr n b.
NAME STANLEY KAPLAN EDUCATIO,N Senior Post-Doctoral Fellowship, University of Southern California, 1967-1969.
. Ph.D., Mechanical Engineering and Applied Mathematics, University of Pittsburgh..1960.
Pest-doctoral courses in mathematics at the University of P:ttsburgh and Carnegie: Institute of Technology, 1960-1965.
M.S., Mechanical Engineering, University of Pittsburgh,1958.
Graduate of the Oak Ridge School of Reactor Technology,1955.
B.S., Civil Engineering, City College of New York, 1954.
PROFESSIONAL EXPERIENCE General Summe g.
Mathematician and engineer well know for contributions to risk analysis and reliability theory, reaccor physics, kinetics, and computitional technique.
Specializes in probabilistic methodology; decision theory; risk analysis; and, particularly, applications of Bayes' theorem.
In this connection has worked specifically and recently on developing probabilistic and decision theoretic reatments of various phases of the energy business.
Included here are PRA anlayses of several existing nuclear plants, hazardous material transportation and storage, spent fuel pools, aircraft inpact, offshore oil drilling (enviro.. mental risk),
. underground oil storage, pipelines, and tarsands projects (business and ccrstruction risk).
Developer of the DPD method for probabilistic
- calculations, the two-stage Bayesian technique for data analysis, the
" set of triplets," " probability of frequency," "cause tab'e," and
" environmental table" concepts in risk analysis.
Originator of the Matrix Theory of Event Trees and DPD approach to seismic risk analysis.
~
Chronological Summary 1977-Present President, Kaplan & Associates, Inc., a consulting firm specializin),in risk an& lysis and applied decision th+ory.
Concurrently Adjunct Professor, Department of Chemical, Nuclear and Thermal Engineering, University of California, Los Angeles, and Associate Consultant, Pickard, Lowe and Garrick, Inc.
1975-1977 Private consultant specializing in risk analysis and d? cision theory.
1972-1975 Holmes & Narver, Inc., Anaheim, California.
Director, Advanced Technology Division; Director, Systems Sciences Division; Technical Director, Nuclear & S/ stems Sciences Group.
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m KAPLAN - 2 1971--1972-Director of Software Development, COMARC Design Systems, Inc., San Francisco, California.
1969-1971 Product Manager and Senior Staff Member, Computer Sciences Corporation, Los Angeles, California.
1967-1969 Special Research Fellow, U.S. Public Health Service at University of Southern California, Los Angeles.
1955-1967 Westinghouse Bettis Atomic Power Laboratory, West Mifflin, Pennsylvania.
Experimentali;t, Experimer.talist in Charge, Scientist, Senior Scientist, Fellow Scientist, Advisory Scientist.
1J54 Lecturer, Department of Civil Engineering, City College of New York..
1962-1967 Concurrently Adjunct Professor of Mechanical Engineering, University of Pittsburgh; Lecturer, Department of Mathematics, Carnegic Institute of Technology.
MEMBERSHIPS
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American Society of Civil Engineers.
American Nuclear Society. -
Society of Industrial and Applied Mathematics.
New York Academy of Sciences.
REPORTS AND PUBLICATIONS "Seabrock Probabilistic Safe y Assessment," Public Service Company of New Hampshire, to be pub:ished in 1983.
Kaplan, S., "A Matrix Theory Formalism for Event Tree Analysis--Application to Nuclear Risk Analysis," Risk Analysis, Vol. 2, No. 1, 1982.
Kaplan, S., "On Safety Goals and Related Questions," KAI-19, Reliability Engineering, Vol. 3, 1982 Kaplan, S., " Methodology for the Zion and Indian Point Probabilistic' Risk Assessments," proposed presentation at the Congres Annuel 1982, 57RP La Comparison des Risques Associes aux Grandes Activites Humanines, Avignon, France, Octcber 18-22, 1982.
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Heising, C. D., A. W. Barsell, K. N. Fleming, S. Kaplan, and B. J.
Garrick, "A comparison of Recent Nuclear Plant Risk Assessments,"
proposed presentation at the Congres Annuel 1982, SFRP, La Comparaison des Risques Associes aux Grandes-Activites.Humaines, Avignon, France, October 18-22, 1982.
Kapian, S., H. F. Perla, and D. C. B1ey, "A Methodology for Seismic Safety Analysis of Nuclear Power Plants," proposed presentation at the International Meeting on Themal Nuclear Reactor Safety, Chicago, Illinois, August 29-September 2,1982.
Bley, D. C., S. Kaplan, and B. J. Garrick, " Assembling and Decomposing PRA Results:
A Matrix rormalism," proposed presentation at the International Meeting on Themal Nuclear Reactor Safety,
. Chicago, Illinois, August 29-September 2,1982.
Kaplan, S., "On a 'Two-Stage' Bayesian Procedure for Detemining Failure Rates from Experiential Data," PLG-0191, preprint of a paper to appear in the IEEE Transactions on Power Apparatus and Systems, August 1982.
Garrick, B.
J., S. Kaplan, and D. C. Bley, "Recent Advances in Probabilistic Risk Assessment," prepared for the MIT Nuclear Power Reactor Safety Course, Cambridge, Massachusetts, July 19, 1982.
Fleming, K. N., S. Kaplan, and B. J. Garrick, "Seabrook Probabilistic Safety Assessment Management Plan,"PLG-0239, June 1982.
!Garrick,- B. J., S. Kaplan, D. C. Iden, E. B. Cleveland, H. F. Perla, D.
'C. Bley, D. W. Stillwell, H. V. Schneider, and G. Apostolakis, " Power Plant Availability Engineering:
Methods of Analysis, Program Planning, and Applications," EPRI NP-2168, PLG-0165, May 1982.
" Indian Point 2 and 3 Probabilistic Safety Study," Power Authority c,f the State of New York and Consolidated Edison Company of New York, Inc.,
March 1982.
Lin, J. C., and S. Kaplan, "SEIS3:
A Computer Program for Seismic and Wind Risk Assessment," PLG-0222, March 19C2.
Kaplan-S., "On the Method of Discrete Probability Distributions in Risk and Reliability Calculations--Application to Seismic Risk Assessment,"
Ri sk Analysi s, Vol.1, No. 3,1981.
Kaplan, S., B. J. Garrick, and P. P. Bienf arz, "On the Use of Bayes' Theorem in Assessing the Frequency of Anticipated Transients." Nuclear Engineering and Design 64, 1981.
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Ka' plan, S.,~ "On' The Method of Discrete Probability Distributions in Risk and Reliability Calculations--Application to Seismic Risk Assessment,"
' Ri sk Analysis, Vol.1, No. 3,1981..
"Zior, Prchabilistic Safety Study," Connonwealth Edison Company, September 1931.
Risk Analysis," PLG-0207 prepared as input to the NRC/ANS Probabilistic Risk Assessment Procedures Guide, September 1981.
Kaplan, S., "A Matrix Theory Formalism for Event Tree Analysis--Application to Nuclear Rick Analysis," preprint of a paper to appear in. Risk Analysis, Vol. 2, No.1,1983; PLG-0198, August 1981.
. Stillwell, D. W., B. J. Garrick, D. R. Buttemer, G. Apostolakis, J. C. Lin,: and S. Kaplan, " Analysis of the Pilgrim Nuclear Power Station Reactor Protaction System," PLG-0195, July 1981.
- Kaplan, S., " Matrix Format for PRA and Its Possible Usefulness in
- Licensing," presented to the ACRS Eubcommittee on Reliability and Probabilistic Risk Assessment, Los Angeles, California,. July 28, 1981.
. Kaplan, S., " Scarce Data Analysis Techniques," presented at -the ANS 1981 Annual Meeting, Miami Beach,. Florida, June 7-12, 1981.
Kaplan, S., G. Apostolakis, B, J. Garrick, D. C. Bley, and K. Woodard,
" Methodology for Probabilistic Risk Assessment of Nuclear Power Plants,"
draft version of a book in preparation, PLG-0209, Juna 1981.
Mulvihill, R. J., and B. J. Garrick, R. S. Hanson, S. Kaplan, Y. G. Mody, D. A. Reny, L. H. Riechers, and H. V. Schneider, " Comparative Evaluation i
lof Boiler Availability for Intermountain Power Project," PLG-0159, L
April 1981.
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Apostolakis, G., and S. Kaplan, " Pitfalls in Risk Calcu'.ations,"
Reliability Engineering, Vol. 2, No. 2, April 1981.
- Kaplan, S., and B. J. Garrick, "On the Quantitative Definition of Risk,"
PLG-0196, Risk Analysis, Vol.1, No.1, March 1981.
Garrick, B. J., S. Kaplan, and N. O. Siu, " Definition of Bounding Physical Tests Representative of Transport Accidents - Rail and Truck,"
PLG-0164, March 1981.
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KAPLAN - 5 Kaplan, S.,' B. J. Garrick, and G. L Apostolakis, " Advances in Quantitative Risk Assessment - The Maturing of a Discipline," IEEE Transactions on
_ Nuclear Science, NS-28, No.1, February 1981.
- Apostolakis,. G., S. Kaplan, B. J. Garrick, and R. J. Duphily, " Data
' Specialization for Plant Specific Risk Studies," Nuclear Engineering and-
' Design 56, 1980.
- Kaplan, S.,.L. H. Reichers, and B. J. Garrick, " Histogram Convolution Program (HICOP)," PLG-0157, December 1980..
Hanson. ' R. S., J. C. Lin, D. M. Wheeler, S. Kaplan, B. J. Garrick, c'
O. C., Iden, W. B. Holder, and L. G. H. Sarmanian, "An Assessment of the Reliebility of Turbine-Generators," PLG-0155, November i;80.
-Garrick, B. J.,. S. Kaplan, D. C. Iden, E. B. Cleveland, H. F. Perla, D.. C. Bley, and D. W. Stillwell, " Power Plant Availabi'ity Engineering, Methods of Analysis - Program Planning - Applications," 2 Vols.,
PLG-0148. 0ctober 1980.
Kennedy, R. P., 'A. C. Cor,ntil, R. D. Campbell, S. Kaplan, and H.
F. Perla, "Probabilistic Seismic Safety Study of an Existing Nuclear Power Plant," Nuclear Engineering and Design, Vol. 59, No. 2, August 1980.
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~ Kaplan, S., R.. S. Hanson,.B. J. Garrick, and J. W. Stetkar, "A Strategic Plan for a National Data System for Electric Power Plants," PLG-0144, July 1980.-
Garrick, B. J., S. Kaplan, G4 Apostolakis, D. C. Iden, K. Woodard, and T. E. Potter, " Seminar:
Probabilistic Risk Assessment of Nuclear Power Pl ants,". FmG-0141, July 1980.
Garrick,i. J., S. Kaplan, and D. C. Bl ey, " Seminar:
Power Plant B
'Probabilistic Risk Assessment and Reliability," PLG-0127, May 1980.
Garrick, B. J., and S. Kaplan, "A Conceptual Plan for a National Data System for Electric Power Plants," PLG-0131, April 1980.
Garr.ck, B. J., and S. Kaplan, "0yster Creek Probabilistic Safety Anal-ycis (OPSA)," presented at the ANS-ENS Topical Meeting on Thermal Reactor Safety, Knoxville, Tennessee, April 8-11, 1980.
'Kaplan, S., and B. J. Garrick, "A Strategic Plan for a National Reliability Data System," PLG-0125, March 1980.
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-Garrick, B. J., S. Kaplan, G. E. Apostolakis, D. C. Bley, and
-T.'E. Potter, " Seminar: Probabilistic Risk Assessment as Applied to Nuclear Power Plants," PLG-0124, March 1980.
Kaplan, S., and.B.,J. Garrick, "Try Probabilistic Thinking to Improve Power Plant Reliability," Pyer, March 1980.
. Apostolskis, G., S. Kaplan,.B. J. Gu rick, and W. Dickter, " Assessment of the Frequency of Failure To Scram in Light Water Reactors," Nuclear Safety, --Vol. 20, No. 6,' November-December 1979.
Kaplan, S., B. J.. Garrick; ~ and D. C. Bley, " Notes on Risk, hobability, and Decision," PLG-0113, November 1979.
U
'Garrick,-B. J., S. Kaplan, and S. Ahmed, "A Reliability Prealction
' Technique for Selected Thermomechanical Components of Gas Turbine Combined Cycle' Plants," PLG-0109, September 1979.
Garrick, B. J., S. Kaplan, P. P. Bicniarz, X. Woodard, D. C. Iden,
.H. F.- Perla, W. Dieter, C. L.- Cate, -T. E. Potter, R. J. Duphily, T. R. Robbins, D. C. Bley, and S. Ahmed, "0PSA, Oyster Creek Probabilistic Safety Analysis,C(Executive Summary, M2in' Report,
. Appendixes), PLG-0100 DRAFT, August 1979.
Kaplan, S., "A Numerical Method for Obtairdng Probabil.ity veras Frequency Distributions from EDAC's Data for Failuri of a Structur:1 Compenent Under Specified Accelerations," presented to the International
--Conference a Structural Mechanics in Reactor Technology, Berlin (West),
Germany, August 20-21, 1979.
Kaplan, S.,' and B. J.- Garrick, "On the Use of a Bayesian Reasoning in Safety and Reliability De';isions--Three Examples," Nuclear Technology, Vol.3 44,. July 1979.
Kaplan, S., and B. J. Garrick, " Notes on Prediction of Reliability,"
PLG-0.'.17. June 1979.
/nlan, S., and B. J. -Garrick, " Notes for a Workshop on Risk, Reliability, and Decision Under Uncertainty," presented at Batte%i Northwest Laboratory, June 1979.
Garrick, B. J., P. P. Bienfarz, and S. Kaplan, " Risk Analysis oi
-Transporting Oconee Spent Nuclear Fuel to the ficGuire Nuclear Station,"
PLG-0102, June 1979.
Garrick, B.- J., and S. Kapl Tn, " Training Engineers to be Reliability Practitionet.;," cresented to the Sixth Annual Reliability Engineering Conference for the Electric Power Industry," Miami Beach, Florida, April, 19-70, 1979.
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Kaplad, :S.,,h M. Vallance, anc C..L. Cate, J" Prediction of Frequency of
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Aircraft Crashes at the Three Mile Island Site," Nuclear Safety, 3:
October 1978.
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n Garrick,'B. J., S. Kaplan, and P. P. Bieniarz, " Input Material for Reliability'Section'of Westinghouse Turbine-Generator Proposal to Middle South Utilities," December ~1977.-
'Kaplan,.S., " Description of.0PTSWU-1, a Program for Computin? the Optimur Amounts of Separativa Work to. be Cantracted for," November 1976.
Kaplan, S,, " Notes on Pooling,' Meaning of, Types of, and Advantages of Also Notes on a Bookkeeping Concept for Equitable and Visible Management of. a Nuclear Pool," September 1976.
'Kaplan,.S., " Notes on the Concept of Inventory as it Relates to Uranium Procurement Planning," September 1976.
_ Garrick, B. J., and S. Kaplan,' "Reliabilit ' Technology and' Nuclear -
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Power," IEEE Transactions on Reliabilit[, Vol. R-25, No. 3, August 1976.
' Kaplard S.,."UPLAN, A~ Decision Theoretic-Tool for Uranium Procurement Planning," May 1975.
Kaplan, S., "On_ (Probabilistic Approach to Project Co,st Estimating,'
Consulting Engineer, February 1316.
Maplan, S., "On a Bayesian Type Methodology for Making Accept / Reject Decisions on Offshore Lease Bids," Journal of Petr'leum Technology,
. Ma rch '1976.
- Kaplan, S.,. and D. Trujillo, " Numerical-StJ Jies of the Partial Differential Equations Governing Nerve Impulse Conduction-I, the
. Significance of Lieberstein's Inductance Term," Journal of Mathematical Biosciences, Vol. 7, pp. 379-404, 1970.
Kaplan, S., and J. M. Vallance, " Notes on a Model for Evaluation and
- Optimization of Urtnium Procurement' Strategies for the CAPC0 Companies,"
(January 1976.
- Garrick, B. J., and S..Kaplan, "Reliabilit Technclogy and Nuclear Power," 1975.
F Garrick, B. 'J., S. Kaplan, "A Method for Evaluating Nuclear Plant Siting
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Concepts," presenteed before 'the Joint Committee on Atomic Development and Space, California Legislature, Sacramento, May 19, 1972.
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'KAPLAN - 8 Garrick, B. il., S. Kaplan, and 0. C. Baldonado, "On a Decison Theory
- Formalism for Nuclear Power Plant Siting," presented to the Conference on Unique -Siting Concepts for Nuclear Power Plants, Joint Committee on
' Atomic Development and Space, Sacramento, California,'May 9,1972.
Kaplan, S., " Variational Methods in Nuclear Engineering," Advances in
' Nuclear Science and Technology, Yol. V, P. R. - Greebler, editor, Acacemic
-Press, 19o9.
.Kaplan, S., "A New Derivation of Discrete Ordinate Approximations,"
Nuclear Science and Engineering, Vol. 34, No.1,1968.
Kaplan,:5., A. J. McNabb, and M. B. ' Wolf, " Input-Output Relations for a Counter. Current Dialyzer by the Method of Invariant Imbedding," Journal of Mathematical Biosciences, Vol. 3, No. 3,1968.
Kaplan, S., LA. J. McNabb, J. K. Siemsen, and D. Trujillo, "The Inverse Problem of Radiosotype Diagnosis - A Computational Model for Determining the Size and Location of Tumors," Journal of Mathematical Biosciences, Vol. 5, pp. 29-35,1969.
-Yasinsky, J.
B., and S. Kaplan, " Anomalies Arising from the Use of Adjoint Weighting in a Collapsed Group Space Synthesis Model," Nuclear Science and Engineering, Vol. 31, No. 2,1968.
Kaplan, S., " Canonical and Involutory Transformations 'of Variational Problems Involving Higher Derivatives," Journal of Mathematical Analysis
_and Applications, Vol. 22, No.1,1968.
Yasinsky, J.
B., and S. Kaplan, "On the Use of Dual Variational Principles for the Estimation ~of Error in Approximate Solutions of i
Diffusion of Problems,' Nuclear Science and Engineering, Vol. 31, pp. 80-90, 1968..
Kaplan, S., " Properties of the Relaxation Lengths in Pl-Double-P1 and Angle-Space Synthesis Type Approximations," Nuclear Science and Engineering, Vol. 28, pp. 450-463,1967.
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- Kaplan, S., J. A. Davis, and M. Nate? son, " Space-Angle Synthesis - An Approach to Transport Approximations," Nuclear Science and Engineering, Vol. 28, pp. 364-375, 1967.
Kaplan, S., and J. A. Davis, " Canonical and Invoittory Transformations of the Variational Principles of Transport Theory," Huclear Science and Engineering, iol. 28, No. 2, 1967.
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.Yasinsky,'J. B., and S. Kapian,'" Synthesis of Three-Dimensional Flux
-Shapes Using Discontinuous Sets ~ f Trail-Functions," Nuclear Science and Engineering, Vcl. 28,;pp. 426-437, 1967.
Gelbard, E. M.,-'and S. Kaplan. " Reality of Relaxation Lengths in Various Approximate Forms' of the' Slab Transport Equation," Nuclear Science and Engineering,-Vol. 26, No. 4, 1966..
Kaplan, S., and J. B. Yasi_nsky, " Natural Modes of the Xenon Problem with Flow Feedback - An Example," Nuclear Science and Engineering, Vol. 25, pp. 430-438,1966.
Kaplan, S., "An Analogy Betwen the Variational Principles of Reactor Theory and.Those of' Classical Mechanics," Nuclear Science and Engineering,.Vol. 23,-No. 3, 1965.
Henry, A. F., and S. Kaplan, "Some Applications of a Multimode Generalization of the Inhour Formula," Nuclear 3cience and Engineering, Vol. 22, No.'4, 1965.-
Kaplan, S., " Synthesis Methods in Reactor Theory," Advances in Nuclear
- Science, Vol.111, ' Academic Press, June 1966.
' Kaplan, S., E. M. Gelbard, " Invariant Imbedding and the Integra' ion Techniques of Reactor Theory," Journal of Mathematical Analysis and Acolications, Vol.11, No.1-3,190a.
Kaplan, S., A. F.. Henry, S. G. Margolis, and J. J. Taylor, " Space-Time Reactor Dynamics," Proceedings. Third United Nations International Conference on the Peaceful Uses of Atomic Energy, Geneva, Switzerland, 1964.
Kaplan, S., Editor and Contributor, Section 5.5, " Space-Time Kiretics,"
Naval Reactors Handbook, Vol.1.
Kapian, S~, "The Use of the Ray 1eight-Rit: Metnod in Non-Self Adjoint Prot' ems," IEEE Transactions, Vol. MIT-12, No. 2,1964.
'Kaplan, S., 0. J. Marlowe, and J. A. Bewick, " Application of Synthesis Techniques to Problems involving Time Depencence," Nuclear Science and Engineering, Vol.18, pp.163-176,1964.
1 Kaplan, S.,
"Some-New Methods of Flux Synthesis," Nuclear Science and Engineering,-Vol. 13, No. 1, 1962.
- Kaplan, S.,: and G. S'nnemann, "The Methods of Finite Integral Transforms in Heat Transfer Problems," Proceedings of the International Heat Transfer Conference, Boulder, Coloraco,19el.
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KAPLAN. - 10 Kaplan, S., "The: Property of Finality and the Analysis 'of Problems in
- Reactor Space-Time Kinetics by Yarious Model Expansions," Nuclear Science and Engineering,.Yol. 9, No. 3,1961.
Kaplan,' S., and S. G. Margolis, " Delayed Neutron Effects During Flux Til t
' Transients," Nuclear Science and Engineering, Vol. 7, No.' 3,1960.
Kaplan', S., and G.' Sonnemann, "A Ger,eralization of the Finite Integral Transform Technique-and Tables of Special cases," Proceedings.of.
Mid-Western Conference on Solid and Fluid Mechanics, Austin, Texas,195.0 i
Goldsmith, M.,- T. T. Jones, T. M. Ryan, S. ' Kaplan, and A. D. Vorhis,
" Theoretical Analysis of. Highly Enriched Light Water Moderated Critical Assemblies," Proceedings, Second United Nations International Conference on the Peaceful uses of Atomic energy, Pager P/2376,1958.
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