Final Report, October 1979
RIING
RUEAP NGwER
MIT-NE-239
QUANTITATIVE METHODS FOR ASSESSING NUCLEAR FUEL CYCLE
DIVERSION RESISTANCE
Investigator
Carolyn D. Heising
Prepared by
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Cambridge, Massachusetts 02139
NUCLEAR EN I!NEERIN'
READING Ro M- M.I.T
QUANTITATIVE METHODS FOR
ASSESSING NUCLEAR FUEL CYCLE
DIVERSION RESISTANCE
Final Report, October 1979
MIT-NE-239
Prepared by
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Cambridge, Massachusetts 02139
Investigator
Carolyn D. Heising
Prepared for
Department of Energy
Nuclear Alternatives System Assessment Program
Washington, D.C.
MIT Principal Investigator.
M. Miller
Energy Laboratory
ABSTRACT
This paper reviews available methods for quantifying nuclear fuel
cycle diversion resistance.
The SAI ranking approach,
and diversion path analysis (HEDL),
Charm method
along with the works of Selvaduray
(Stanford), Silvennoinen et al (Finland), Papazoglu et al (MIT),
Heising (Stanford) and Fleming et al (General Atomic) were reviewed
and compared.
This review revealed a surprising degree of similarity
and consistency between both attribute definition and quantification
approaches employed, most modelers basing their work on standard
utility theory.
Differences are due more to the level of sophisti-
cation each analyst strived for in defining their model than to any
inherent inconsistency internal to risk analysis procedures,
Appli-
cation of the methods to a sample problem involving a comparison of
both commercial and non-commercial routes to weapons usable material
show close agreement of results for those methods most firmly based
on utility theory.
Heuristically conceived methods render conflict-
ing results that are probably not reliable.
Table of Contents
ABSTRACT
I.
Introduction: Methods for Quantifying
Proliferation Resistance................................
A.
B.
C.
II.
Methods for Quantifying Proliferation Resistance........
A.
B.
C.
D.
E.
F.
G.
H.
III.
Proliferation and the Nuclear Power Industry.........
Risk Assessment and Quantification Methods:
Previous Applications to Other Risks in
the Nuclear Industry and the Logic for
Extension to the Proliferation Problem............
A Comment on Quantitative vs Intuitive
Decision-Making: Is a Quantitative
Approach to Proliferation Worthwhile?.............
1
1
3
4
6
6
Ranking vs Gaming Approaches........................
Previous Work: SAI's 1977 Review of Methods
8
(CHARM and Diversion Path Approaches).............
10
..
(ERDA).............
Development
Method
SAI's Ranking
G. Selvaduray's "Heuristic" Rating/Ranking
12
Approach..........................................
..
15
Index.......
Silvennoinen's and Vira's Vulnerability
Bayesian Decision Analysis: I. Papazoglu et al's
22
Multi-Attribute Decision Theory Model.............
Bayesian Decision Analysis: C. Heising et al's
Cost-Benefit Approach to Quantifying
Proliferation Risk in the Nuclear Fuel Cycle...... .. 28
Societal Risk Approach: K. Fleming et al's
36
Markov Model......................................
Comparison of Methods/Conclusions.......................
45
REFERENCES
APPENDIX A:
APPENDIX B:
Examining Selvaduray's Method for Assessing
the Safeguardability of Various Reprocessing
Technologies.....................................
A-1
Support Calculations for Table IX............... .
B-1
B.
1
Methods for Quantifying Proliferation Resistance
I.
Introduction:
A.
Proliferation and the Nuclear Power Industry
The past several years have seen the rise of concern over the
connection between the worldwide spread of nuclear power and nuclear
weapons proliferation. 12
This concern was expressed by President
Carter in his April 1977 decision to defer commercial reprocessing and
the breeder reactor.3
Also formed at that time were the International
Fuel Cycle Evaluation (INFCE)
ment.
and the NASAP program of the U.S.
govern-
At the outset, so many fuel cycle alternatives were suggested4
that the only methods available for analysis seemed to be those of a
quantitative ilk.
However, as it became clear that the real choices
for the United States involved only a few of the suggested alternatives,
the need for quantitative comparisons became less urgent,
Some persons
questioned the desirability of using quantitative methods
citing the
lack of expert concensus on even such seemingly non-controversial subjects as uranium supply as invalidating
quantitative approaches.
Others argued that proliferation is simply too large and unwieldy a
topic to be handled in any quantitative, quasi-scientific framework.
This paper attempts to address some of the misgivings that have
arisen concerning quantitative analysis,
reviewing attempts that have
been made (to this date) to place the risk of proliferation from commercial nuclear power into an analytic framework.
The viewpoint ex-
pressed in this paper is that of one who has personally wrestled with
the proliferation problem from a quantitative perspective.
The view-
point expressed is therefore admittedly biased in the favor of quantitative methods.
2
Figure 1
Comparison of Average LWR Accident Risks
with Fuel Cycle Facility Risks (Consequences
in 50-yr. Person-REM Radiation Exposure)
Probability of Accident With Consequences Greater
Than or Equal to x
10-
4
V
Average LWR (Wash-1400)
10 -5
10-6
Riprocessor
(a ll accidents)
10-8
Reprocessor
(no final filters failure)
MOX Plant
Cladding Waste
Repository
10-10
High-Level Waste
Permanent Repository
10-11
10-12
10-13
10~1
I
I
100
10
|
102503
I
I
es4
I
5
I
I
106
107
108
x: 50-yr Person-REM
The study results shown are those of WASH-14005 and SAI. 1
The MOX fabrication plant services the annual requirements
of sixteen 1 GWe LWRs; the reprocessor, fifty LWRs per year.
The HLW repository houses the waste generated by 280' LWRs
per year. For spent fuel permanent disposal, the results
for the HLW repository represent a close approximation.
3
B.
Risk Assessment and Quantification Methods:
to Quantifying Nuclear Power Risks
Previous Applications
Probably the most well-known example of a risk analysis study is
that of MIT's Norman Rasmussen et al.
(WASH-1400).5
Fault tree-
reliability assessment techniques were applied to quantify LWR accident
risks.
The results were then expressed as a probability-consequence
curve.
The pioneering role of WASH-1400 in
establishing increased
and public-government acceptance for the entire discipline
credibility
of risk analysis cannot be underestimated, for until that time, no risk
analysis had been used for so important a task - previous applications
had proved far too academic.
In the fiel_- of nuclear engineering, use
of quantitative risk analysis has been on the increase, particularly in
nuclear safety applications.6-9
Use of risk techniques has spread into
the broader area of fuel cycle accident risk assessment 10'1
where
comparisons between reactor and fuel cycle risks have been made
(see Fig. 1).
Branching out still further in application are those studies that
quantify nuclear waste repository risks of release to the biosphere 12,13
and those that address the even trickier problem of nuclear theft andsabotage. 1 4 ,15
In the area of safeguard systems reliability analysis,
quantitative methods are being applied to help for example, plant
designers to more comprehensively deal with subnational diversion risks
directly in the plant design process. 1 6 ,1 7
Regulatory agencies are also
keenly interested in risk assessments to help set standards in the nuclear
industry.
For example, the NRC is applying these methods to over fourteen
specific areas related to nuclear safety;l8 these include such topics as
impact of turbine missiles, an assessment of alternate ECCS configurations,
development of requirements for offsite emergency response plans, etc.
4
With all the risk assessment activity in the many areas that
constitute the nuclear enterprise, it is not surprising that these
techniques have also been applied to analyze the nuclear proliferation
problem.
The logic that underlies such application is very simple
based upon one possible answer to the question:
"What other approach
for analysis can be better?"
C.
A Comment on Quantitative vs. Intuitive Decision-Making:
Quantitative Approach to Proliferation Worthwhile?
Is a
Underlying the application of quantitative risk assessment to
the proliferation problem is the tacit assumption that no other
analytic approach can be as useful or so well scientifically validated.
Reliance on intuitive analyses is thought to mislead more frequently
than quantitative analyses; the reliability of a scientific, quantitative approach is considered to be greater than for other methods of
approach.
The single most useful aspect of a quantitative approach
is that the problem must be carefully dissected into its parts; much
that is only peripheral to the question is therefore done away with
leaving the most important aspects fully exposed.
It must be emphasized, however, that quantitative analyses cannot
substitute for the political process wherein decisions are made by
reaching
political concensus on controversial issues.
The role
quantitative analyses can play is in helping to reach that final concensus.
To ignore the potential
of quantitative analyses for
analyzing important policy issues and to rely solely on intuitive judgment is to ignore a tool that can be of great service in resolving differences of opinion.
The proper role for quantitative analysis
5
therefore, is as a tool useful in helping to reach political concensus;
it is not an end in itself.
As is the case with any tool, the end product of its application
depends not so much on the tool's integrity as on the abilities of the
person(s) using the tool; the analysis can only be as good as the
ability of the analyst permits.
Thus, when critics point to the
(admittedly) many "bad" applications of the past, they should not
conclude, as they often mistakenly do, 19,2
is inherently at fault.
that it is the tool that
Rather, it should be understood that analysts'
abilities vary; some are more experienced, better trained and more
insightful than others.
Just as some artists are more talented in
the use of the tools of the artistic trade, some analysts are more
adept in the use of analytic tools.
Quantitative analysis, like any
other discipline, is neither a completely robotic task devoid of human
*
aspects nor a strictly unscientific, subjective pastime.
Also, while
some analyses (just like some paintings, books, and journal articles)
may be very carefully done, others are not so well attended to.
All of
these considerations should be kept in mind as we now proceed to compare the various quantitative methods available for analyzing proliferation risk.
Interestingly, many persons view quantitative policy analysis as a
2
while others, mainly
robotic, impersonal misapplication of science
within the scientific-technical community, view the practice as too
unscientific, subjective and untheoretical to be considered worthwhile. 2 2
6
II.
Methods for Quantifying Proliferation Resistance
A.
Ranking vs. Gaming Approaches
Two major approaches to analyzing the relative proliferation
resistance of commercial/non-commercial nuclear technologies have been
identified.
These are the ranking of attributes/societal risk and war
By far the most prevalent in use is the ranking
gaming approaches.
method wherein a set of characteristics or attributes of a nuclear
system are singled out that most influence its inherent resistance or
proneness to national diversion of nuclear materials (proliferation
risk).
Then, the attributes are assessed and compared for nuclear
technologies of interest (e.g., PUREX reprocessing vs. CIVEX reprocessing).
Several methods for assessing each attribute and then comparing
them have been developed and are discussed in this paper.
These
methods include those of SAI, Charm, diversion path analysis (HEDL),
Selvaduray (Stanford), Silvennoinen .at al (Finland) and Heising
(Stanford).
Most of these methods, as will be shown, are based on ap-
plications of standard utility theory and therefore share many similarities.
The work of Fleming et al (General Atomic) uses a societal risk
approach based on a Markov model of states and activities associated
*
with proliferation.
An interesting approach that has yet to be directly applied to
specifically analyze the proliferation problem involves a war gaming
**
approach.
*
**
In this approach, two adversaries, possibly a non-weapons
It attempts a fault-event tree analysis where probabilities of events
are estimated as known distributions. A Monte Carlo simulation is then
used to estimate frequencies. However, input data is given in terms of
a series of attributes that correspond well with the other methods.
This approach has been outlined by Benedict and Miller in a talk given
at Harvard by Dr. Miller, MIT-EL78-001, February 1978.
7
state (NWS) on the verge of acquiring a nuclear explosiv-;e capability
and the United States, for example, would be simulated in terms of likely
action response sequences that might evolve out of the NWS's attempt to
deploy its nuclear capability.
The war gaming approach has mostly been
applied by military analysts to simulate military operations between
two or more opposing forces using rules, data, and procedures designed
to depict an actual or assumed real-life situation.
It is primarily a
technique used to study problems of military planning, tactics and
*
strategy
but could be applied to investigate diplomatic, international
and economic-militaristic sanctions applied against an erring NWS,
There are three types of war games in common use today; the
training game is the least complex and is designed to provide the participants with decision making opportunities similar to those that may
be experienced in combat.
The operational game deals in the current
organizations, equipment and tactics.
It is more complex than the
training game and is used to test operational plans.
The research game
is still more complex and is designed to study tactical or strategic
problems in a future time frame.
War games can be manual, computer-
assisted or be totally computerized.
As can be seen, it may be quite
possible to employ such techniques to determine the efficacy of various
competing nonproliferation policies, in particular, those that involve
limitations on nuclear power facility exports or special arrangements
for their operation.
However, application of this approach will require
careful examination of the possible policies available.
See Shubik, M. and Brewer, G., Models, Simulations, and Games
R-1060-ARPA/RC, Rand Corporation, May 1972, pp, 80-81.
-
A Survey,
8
B.
Previous Work: SAI's 1977 Review of Methods (CHARM, VISA, Diversion
Risk and Societal Risk Approaches)
In a work sponsored by the Electric Power Research Institute
(EPRI), Albert and Straker reviewed several proliferation resistance
assessment methods 23 all falling within the ranking-of-attributes
category.
Conclusions of that work indicated that methods for the
evaluation of proliferation resistance of alternative systems were
"ivery preliminary".
The study made three recommendations:
(1) that design criteria for proliferation resistance be developed so
as to determine an "acceptable" level of proliferation risk for a
nuclear technology,
(2) that questions in the format of the classic debate be generated
with cases both pro and con represented, i.e., "can the LWR fuel cycle
with plutonium recycle be designed to be acceptable from a proliferation standpoint?", and
(3) that continued use of ranking approaches be followed to identify
weak points in alternative systems and to indicate where engineered
proliferation resistance might prove worthwhile.
Three methods were singled out and applied in the SAI work; the
basis for the selection was that no others had been developed which
were useful at that time.
These three included:
method, (2) Diversion Path analysis and (3)
the "Chati"
SAI's own approach de-
veloped for ERDA, a multiple criteria approach.
is discussed in part C below.
(1)
The ERDA-SAI method
The Charm and Diversion Path analyses
are now discussed.
The Charm method was outlined in 1976 24 and views proliferation
risk as the attractiveness of the fuel cycle as a target for adversary
9
actions leading to the fabrication of a nuclear explosive device.
This "attractiveness" is determined by a collection of characteristics
which are reduced to a single number called "Charm".
This factor is
defined in the form of an equation:
N
Ti
X = E
i=l A iPiS iD
where
X
= charm factor,
N
= number of diversion points,
Ti
= duration of appearance,
S
= self protection factor of material, such as radioactivity level, etc.,
A
= minimum number of locations from which material
is diverted,
P i=
D
effort to process and produce a device from
stolen material, and
= risk of detection and the risks due to the nature
of the material.
The diversion path method
problems
based on subnational safeguards
was developed by HEDL to quantify the proliferation risk of
fuel cycles.25
The approach taken is quite similar to Charm.
liferation risk of a fuel cycle is derived from the equation:
TPWF = MAF x DPF x RMF
The pro-
TPWF = total proliferation weight factor,
where
MAF
= material attractiveness factor,
DPF
= distribution parameter, and
RMF
= removal mode factor.
The MAF term is heuristically defined as:
MAF = MTF x MDF x RHF
MTF = material type factor,
where
MDF = material description factor, and
RHF = radiation hazard factor.
Also, DPF =
rQ/Ms where Q = mass of material and M5
5
required for one explosive.
=
material mass
The removal mode factor (RMF) is intended
as a means of assigning a value to the method used to divert the
special nuclear material.
C.
Three paths were considered:
RMF
Path
1
Simple Theft
0.75
Substitution of inert material
0.1
Substitution of isotopic material
SAI's Ranking Method Development (ERDA)
SAI developed a preliminary method under ERDA auspices for evalu-
ating the proliferation resistance of alternative systems as part of
NASAP.
An initial attempt in this program was the development of the
Charm method described earlier.
Further work evolved a multiple
11
attribute method26 (defined as the ERDA methodology in Albert and
Straker's report
23
).
*
This method defined several attributes to be
assessed to determine a multiple criteria factor
single factor
through six indices:
as opposed to a
time, resource requirements,
weapons production, inherent difficulty, detectability and interruptibility.
the
maker
The last three are combined into a single factor called
failure
index.
A weight factor, to be determined by a
is then assigned to each index to rank the fuel cycles.
decision
Albert
and Straker further elaborated on these six indices in their report
by defining nine indices:
time from decision to first weapon (yrs),
time from material acquisition to first weapon (yrs), cost to produce
first weapon (dollars), professional personnel to produce first weapon
(number of personnel), material unattractiveness, material safeguardability, difficulty, detectability and interruptability (the last five
indices being dimensionless).
dices, quantitative
"Medium",
For each of the five dimensionless in-
figures-of-merit
and "High" values shown in
were assigned to determine "Low",
the final results table.
The
figures of merit appear to vary from 0 to 25, but no explanation is
given in the work to explain the method used to assign these figures.
Also, in Albert and Straker's application of the methods, quantitative
weighting factors were not determined although a short discussion was
made (p. 55) concerning the impact of equal weights placed on quantitative factors and the possibility that such weights would not
The ERDA methodology described here was later extended and placed
into a multiattribute decision theory approach by Papazoglu et al,
at MIT. Their work is described in part F of this report.
12
influence the analysis applied to their particular sample problem.
However, such weighting factors might need be determined for appli*
cations to problems other than the one addressed by SAI.
(The work
by Papazoglu et al. attempts to determine weighting factors for these
attributes; see part F below.)
D.
G. Selvaduray's "Heuristic" Rating/Ranking Approach
Dr. G. Selvaduray of Stanford University has developed a method
for evaluating the inherent safeguardability of various reprocessing
methods as one part of his doctoral thesis.
27
In that work, Selvaduray
devised a method by which some fourteen reprocessing methods for thermal
**
reactors
could be compared with respect to eleven parameters, one of
**
which included safeguardability of strategic nuclear materials aspects.
In assessing the safeguards parameter,
Selvaduray defined five sub-
parameters (or attributes) the combination of which could be rated according to a heuristic method he developed independently.
These five
The sample problem examined by Albert and Straker concerned a comparison between four reactor/fuel cycles: (1) the LWR once-through, (2)
thorium prebreeder, (3) LWR with Pu Recycle and (4) IMFBR.
**
The fourteen were selected froma larger sampling space of over thirty
known methods. The fourteen were selected as being most representative
of processes with the best possibilities for commercialization and included processes for thorium fuel although most
analyzed were designed for LWR fuel.
Other parameters included: (1) technical complexity, (3) magnitude of
waste problems, (4) sensitivity to changing safety regulations, (5)
sensitivity to change in fuel type, (6) maintenance problems, (7) stage
of development, (8) reliability, (9) risk to population, (10) economic
advantage and (11) decontamination factor (attribute (2) is safeguards).
13
sub-attributes included:
(1) ability to extract pure Pu from process
stream without additional processing necessary after diversion occurs,
(2) location of reprocessor (defined as either "on" or "off"-site from
one or more reactors) which impacts on transportation considerations
and the size of the reprocessor that therefore affects the material
flow through the process streams, (3) decontamination factor, a measure
of the radiation level inherent to the process stream from which material
might be diverted, (4) labor intensity, defined as the number of persons able to gain access to process streams (measured either as "high"
or "low"), and (5) the number of process streams (measured either as
"several" or "few").
Using these five attributes, Selvaduray created tables that
rated
the 48 possible combinations of the five attributes (see Fig. 2).
The rating (r) assigned to each combination was allowed to vary between
1.00 to 10.00 where each of the 48 possible combinations assumed a
separate rating value (e.g., 1.00, 1.17, 1.35, 1.52, etc.).
ratings (r) were then multiplied by a ranking (R)
These
placed on safeguard-
ability as one of the eleven main parameters used in Selvaduray's
analysis.
The formula used to arrive at a final numerical "performance
factor", E, as set up by Selvaduray is:
11
r iRi
10
1R
i=l
i = 1, 11 attributes
j = 1, 14 processes
a
Figure _2
Possible Combinations of Selvaduray's Safeguard Parameter
Attribute 1
Attribute 2
Attribute 3
Pure Pu
Extractable
Location
Decontamination Factor
I
Attribute 4
Labor
Intensity
j
Sub-Attributes
Attribute 5
Effluent
Streams
High
Yes
H
High
On-Site
Several
I
No
I
I
Of f-Site
Low
15
where the denominator represents a normalization factor as derived
*
by Selvaduray.
E.
Silvennoinen's and Vira's Vulnerability Index
The work of Silvennoinen and Vira in Finland 2829 used a multi-
attribute approach to assess
proliferation risk for several fuel
cycle facilities (spent fuel storage, enrichment plants and an independent pathway followed by the non-weapons state clandestinely).
The authors defined six criteria to which they assigned a quantitative
value.
These six criteria had been identified in a Booz, Allen and
Hamilton report of 197730 and are defined as follows:
(1) the minimum
cost of the weapons construction once the fissile material is available, (2) the minimum time required to produce a weapon, (3) the
marginal cost incurred when a commercial civil power program is amended
to contribute to
material for
weapons production, (4) quality of the separated
weapons production, (5) detectability of the conceiv-
able clandestine weapons production and (6) accessibility and accountability of source material or weapons-grade material.
criteria
was assigned a value from 1 to 9
using
a
Each of these
scaling
*
The method heuristically derived by Selvaduray can be shown to be a
variation of multi-attribute decision theory where the value functions
and weighting factors used by Selvaduray are linearly defined (see
part III of this report).
Selvaduray, trained as a chemical engineer,
was not exposed to formal methods of operations research yet was able
to derive what he believed to be a "heuristic" ranking method that
is surprisingly well-related to decision theory methods. This adds
credence to the ideas of those who claim that decision theory models
well the logical thought process of the human mind.
16
method for priorities in hierarchical structures as outlined by
Saaty.31
The diversion resistance of the paths was then judged in
view of each criterion following the approach used by Heising. 3 2
The first step in the quantitative evaluation comprises the
relative weighting of the six criteria.
The criteria are then applied
to each proliferation pathway in terms of the type of material that
could be diverted (seven in all):
(1) enriched uranium fuel in a
system with no enrichment facility of its own, (2) fresh MOX fuel, (3)
recently discharged spent fuel, (4) long-stored (15 yr old) spent fuel,
(5) spent fuel in a final repository (>15 yr old), (6) spent fuel in a
sealed final repository not intentionally retrievable, and (7) separated
reprocessed plutonium (PUREX based reprocessor - no alternatives to
PUREX were considered).
Pathways 1, 3, and 4 were further split into
two routes - military and civil facilities to obtain weapons-usable
material.
Each pathway was evaluated separately for each of the six
criterion x
as a function of the amount y
of the source material.
The relative values x1 -k3 were derived from data used and collected by
Heising.32
The values for ,x4 -x 6 were deduced by judgmental techniques
'31
based on Saaty's method.
The overall vulnerability index for each of
the seven materials examined was computed by summing up the ratings for each
attribute x.,
j
= 1-6 and simultaneously weighting each attribute as
follows:
n
u(y )
=-
[r
j=.
1+X w.u
Ji
(y
)
i
-
1].
J
17
where
= vulnerability index of material flow level y
for material type j, j = 1-7
u(yi)
= weighting factor on jth attribute,
w
j
=
1 to 6
A = free parameter to normalize w.
This relation was derived explicitly from Keeny's work on utility
33
theory
such that
n
ui(yi)
=
1 for all j;
For the case where Z w
[
= 1, A
=
(+
l
) - 1] = 1.
0 and the equation above simplifies
j
to the familiar form:
n
u(y)
=
Z W
j=l
u
Silvennoinen et al. observed the condition
y)
n
Z
w
=
1 for their sub-
j=li
jectively assigned weighting factors w .
In their work, the authors
consider the military-civilian/commercial options as a choice a NWS
could make when deciding between the seven material types
available to them.
In their work, they assume equal preference for
military vs civil in computing their final results.
In a slightly different approach to calculating the
indices
vulnerability
(or total value functions) for each of the seven material
types, the authors suggest the use of "fuzzy integration" as reported
in Sugeno's work.34
Instead of a weighted average, the index is taken
as a fuzzy integral uF(Yi) over all the criteria x,
j = 1-6:
Table I
Comparison of Vulnerability Indices (Total Value Functions) on Seven Material
Types for Utility vs Fuzzy Integration Theory
Vulnerability Index (u(yi))
Material
Flow
Fuel Type
1. Enriched U
(MTSWU)
2. MOX Fuel
(MTHM)
Utility Theory
*
Fuzzy Integration
140
.30
.23
4600
.54
.60
30
.51
.48
1000
.54
.48
oo
3. Short Cooled
Spent Fuel
30
.12
.19
(MTHM)
1000
.36
.24
4. 15 yr Old
Spent Fuel
30
1000
.17
.36
.23
.28
5. Spent Fuel
in Open
Repository
30
1000
.14
.24
.20
.22
30
1000
.08
.12
.16
.16
6. Spent Fuel
in Closed
Repository
6
E
j=1l
w
=
1.
19
f
uF(Yi)
a(YiX) g()
X
X = {x }, a(yi,X)
where
=
ui(yi) and g(-) is a measure of
integration.
One interpretation of the fuzzy integral above is tantamount to maxmin
algebra:34
n
F
V a(Yi'xj) A g(F1 )
J=1
V and A denote maximum and minimum operations, respectively.
where
The set F
sets.
i
and the structure of g(-) are taken from the theory of fuzzy
The measure g(F) is defined by a parameter A as follows:
g (F)
X
Setting F
=
(1 + X w )-1
r
= -1[
eF
X and determining X exactly as was done in utility theory
defines g(F) uniquely.
The results of using this method were compared
with the more familiar utility theory by the authors
(Table I; 0 is
most resistant; 1 is
least resistant).
Once having determined the vulnerability indices for each of the
fuel types, an overall
proliferation risk index
(PRI) was determined
for given fuel cycles that might include the seven different material
types:
20
T
T (1+r)
max {u(yi(t)} dt + DRI
0
PRI =
T
(1 + r) -t
where
dt
DRI = risk of irretrievable phase
fT
(1 + rD) t uy
6 (Tl))
dt
where (1 + rD)-t is a time preference factor, rD is a discount rate
and y 6 (T1 ) is the total amount of spent fuel disposed; T is a given
time horizon, u(Y ) is the vulnerability index
calculated earlier,
and r is a discount rate not necessarily equal to rD.
This formulation
was applied to assess the difference between three LWR fuel cycle
options with results shown in Table II.
Table II.
Overall Proliferation Risk Index (PRI)
for Three LWR Fuel Cycle Options Measured*
as Function of Time and Discount Rate (r)
r = .04
r = .02
1.
Once-Thru
.41
.6
2.
U-Recycle
.28
.28
3.
U- and Pu-Recycle
.45
.45
*
0 signifies most resistant, 1 least resistant.
The time horizon looked at is 20 years (T
=
20); timing considerations
must be taken into account because of the dependence of u(y ) on the
21
material flows which fluctuate in time.
In spent fuel disposal, the
discount rate (r) influences the risk index (PRI).
Compared to
complete recycle the once-thru alternative entails a higher proliferation risk for r = 0.02 whereas the risk is the same order of magnitude for r = 0.04.
The uranium recycle case is lowest because it is
assumed reprocessing is done outside the NWS so that Pu is never made
available
either in the stored spent fuel or in fresh MOX fuel .
It
is also assumed that the spent fuel is sent to the reprocessor in a
short period of time while for once-thru, the spent fuel is allowed to
be stored within the NWS.
The authors point out that the most difficult aspect of applying
either utility or fuzzy integration methods
as outlined in their work
is the subjective assignment of the weights (w.).
They suggest a
workshop approach where a number of experts would be consulted to obtain weights.
They conclude that reprocessing and plutonium utiliza-
tion should be retained in a more resistant system or country and that
no MOX fuel be sent to a NWS.
They also advocate sending spent fuel
back to repositories in weapons states.
In
Silvennoinen's work,~ it
is
found that when economics are also- con-
sidered along with proliferation risk in a multigoal optimization approach, an option called "M' becomes optimum:
"M" is a strategy wherein
most of the NWS spent fuel would be reprocessed at a reprocessor located in a weapons state, all uranium would be recycled and some MOX
fuel sent back for use in the NWS.
a result in the NWS.
Some spent fuel would be stored as
The MOX fuel used would reside in the core over
22
a longer time interval and would be shipped at irregular time periods.
They show that consideration of multiple objectives can pronouncedly
*
impact on the optimum fuel cycle option.
F.
Bayesian Decision Analysis:
Decision Theory Model
I. Papazoglu et al.'s Multi-Attribute
On the prompting of the DOE and through funding from the NASAP
program, I. Papazoglu at MIT, with the advice and aid of M. Miller,
N. Rasmussen, H. Raiffa and E. Gyftopoulos,35 developed a formal
method for assessing the relative diversion resistance between nuclear
fuel cycles.
Borrowing from and extending upon the earlier work done
at SAI (see Section C of this report), Papazoglu defined five attributes
pertaining to diversion resistance
into three sub-attributes
of which the third was sub-divided
resulting in seven total attributes.
attributes were defined as follows:
(1) the development time
These
or the
time it takes from start to finish to develop a nuclear explosive using
diverted nuclear material, (2) the warning period
defined as the per-
centage of the development task left to complete at the time of detection
by outside agents, (3) the inherent difficulty of utilizing the technology as a source of nuclear fissile material
defined further by a
breakdown into three sub-attributes - the radioactivity level of the
diverted material in the process, the status of scientific and technical
information known about the process by the potential proliferator, and
the level of criticality problem associated with the process, (4) the
*
Their applications have been restricted to analyses of LWR options
only.
23
weapons material quality
defined as the type of nuclear material di-
verted (i.e., either weapons or reactor-grade plutonium, or enriched
uranium (U-233 or U-235)), and lastly, (5) the development cost of the
explosive construction attempt.
The above attributes were developed on the basis of determining
a set that would be:
(1) complete, covering all aspects of concern to
the problem at hand, (2) operational, be meaningful to the decision
maker so that he can understand the implications of the alternatives,
(3) non-redundant, avoid double counting of characteristics, and (4)
minimum in number, the number of attributes should be kept as small as
possible.
Papazoglu et al. concluded that the major objective of the
proliferator is to find a pathway out of all available that
least resistance
with the
allows him to achieve a nuclear weapons capability.
Since the desired level of capability might vary between proliferators,
the method defines "aspiration levels" a given proliferator might have
that might influence his choice of a suitable pathway.
The major ob-
jective was then defined as being equal to satisfying two sub-objectives:
(1) increase
tiveness
the likelihood of success
of the pathway.
and (2) increase the
attrac-
Attractiveness was further divided into de-
creasing the weapons development time and the monetary cost involved
while the likelihood of success was divided into likelihoods of internal
failure and external detection.
The likelihood of internal failure was
further divided into inherent difficulty of fissile material procurement
and weapon design/fabrication (Fig. 2).
To derive a quantitative indicator of the relative diversion resistance of a given fuel cycle, a value function
V(x)
was defined so
Figure 2
Decomposition of Major Objective into Sub-Objectives3 5
Decrease Pathway
Proliferation Resistance
I
Increase
Increase
Success
Likelihood
Attractiveness
of Pathway
.9
Decrease
Development
Time
__T_
.W
Decrease
Financial
Cost
I
Decrease
Internal Failure
Likelihood
Decrease
Inherent
Difficulty in
Material
Procurement
Weapon
Development
Time
(x1)
Monetary
Cost
(x5)
I -
Index of
Inherent Difficulty
(x3)
Decrease
External Detection
Likelihood
- I
4:-
Decrease
Inherent
Difficulty in
Weapon Design
& Fabrication
Weapons
Material
Quality
(x4)
Warning
Period
(x2)
25
that a dimensionless numerical indicator
be calculated.
varying from -1 to 0
could
The numerical indicators for each attribute are then
multiplied by weighting factors (X ) and summed over the total number
of attributes to arrive at
single numerical indicator for each
a
fuel cycle.
Basically, the purpose of the value function is to provide a
numerical measure of the relative attractiveness of the various proliferation pathways available to the would-be proliferator.
Assuming
preferential independence between attributes (i.e., the proliferator's
value placed on each attribute is independent of the value placed on
any other attribute), the value function is
from utility theory
:
5
V(x -x
i V i(x)
.E
5
i=l
Because the third attribute (inherent difficulty) is divided into three
sub-attributes, the above expression becomes:
X1 V1 x 1) + X2 V2 (x2)
V(x1-x5
3
+
E
X3j
3j(x3j
+ X4 V4 (x4 )
j=1
+ X5 V 5 (x5 )
where the value functions for each of the five attributes are:
26
development time (x1 in years):
V (x
=
- 1, 8
e~
=
.49 non-crisis, .83 crisis
warning period (in %):
V2 (x2) = eYX 2 - 1,
y = 6.93
radioactivity level (in R/hr at 1 m
1!
21
101
V31 (x31 ) 10 1-.02 _-.16
x3 1
from source):
3
4
-. 5 -. 84
1
5
1 6
-. 96
-1
status of information (x3 2 referring to levels denoted as A, B, C...I):
criticality problems (x 3 3 either "High",
V33 ("Low")
= 0,
V3 3
"Medium",
or "Low"):
'Med") = -. 5, V3 3 ("High") = -l
weapons material quality (x 4 refers to type of material):
V4 (r.g.Pu) = -1,
V4 (w.g.Pu) = -.5,
V4 (H.E. U-233) = -.25 and V4 (H.E. U-235) = 0
27
and finally, for monetary development cost (106 1975
V
=
-
5
ax5 ; a = 2.6 x 10~4,
= 1.27 non-crisis
5-5
a = 10-5,
=1.9 crisis
Weighting functions (Xi) derived from interviews with selected
experts utilizing a standard Delphi technique were assessed for two
hypothesized divertor decision environments - non-crisis and crisis
(Table II).
Table II.
Pareto Weights on Diversion
Resistance Attributes
Weighting
Function
Attribute
Non-Crisis
Environment
Crisis
Environment
Development Time
A
.13
.31
Warning Period
X2
.15
.07
Status of Information
X3 1
.38
.37
Radiation Level
X32
.16
.16
Criticality Problems
X33
.04
.04
.03
.01
Weapons Material Quality
Development Cost
5.11
.04
This was done because it was assumed that a proliferator's choice of
pathway would be influenced by the environment in which the decision
takes place.
In a crisis situation
development cost, for example, be-
comes less important to the hypothetical decision-maker while development time assumes a more important stature.
In the business-as-usual
28
or non-crisis environment, the weights assume a different set of
values.
By allowing for possible large differences in the decision-
making environment, Papazoglu et al.'s approach can account for a
larger number of possible diversion scenarios.
Combining the weights with the value functions allows one to
calculate dimensionless numerical indicators that vary between -1 to 0
(where -1 is most resistant, 0 least resistant) for each examined fuel
cycle.
The importance of these final numerical indicators are as rela-
tive values rather than absolute values of proliferation resistance.
In summary, Papazoglu et al. have followed closely the theory of multiattribute decision theory in their methodological development.
They
have also gone the extra step to determine through Delphic interviews
the relative weighting factors (X ) and value functions
selected experts place on each attribute (xi).
V(xi)
This final step
complished through careful construction of questionnaires
that
ac-
represents
a definite advance over other methods discussed in this report (the
importance of this distinction is described more fully in part III of
this report).
G.
Bayesian Decision Analysis: C. Heising et al.'s Cost-Benefit
Approach to Quantifying Proliferation Risk in the Nuclear Fuel Cycle
C. Heising et al.'s
EPRI-sponsored work at Stanford University
involved as cost-risk-benefit approach to assessing proliferation risk
from a given fuel cycle.32
Our work basically followed a Bayesian
decision analysis approach where uncertainties on both economic
29
parameters and national security were explicitly defined in terms of
probability distributions.
With regard to proliferation, the overall
risk represented by the commercial nuclear fuel cycle
inclusive of
the impact that plutonium recycle and breeder introduction in the
United States might have on non-weapons states (NWSs)
was compared
with the risk already existing from non-commercial routes to nuclear
material attainment.
As is shown in Fig. 3, the analysis of diversion
resistance was limited to an examination of the relationship between
the number of commercial reprocessors built and operating in a NWS and
the likelihood
of a NWS
successfully constructing a weapon.
The analysis does not include an examination of success of internationally applied sanctions or timing considerations that impact on
sanctions
success.
As in the other methods discussed in this report,
the emphasis lay in establishing quantitative rankings representing the
relative attractiveness of available routes.
This was accomplished by
defining 10 attributes considered to influence the NWS in making its
decision (Fig. 4).
(1)
These attributes included:
Domestic Availability of Technology (compares the present global
distribution of various technical routes; e.g., research reactors are
owned and operated by over 50 countries while no commercial reprocessors
are operating anywhere in the developing world);
(2)
Import Availability (compares the relative importability of one
option over another; e.g., research reactors are far easier to import
than are, say, enrichment plants);
(3)
Capital, Operating, and Maintenance Costs;
(4)
Suitability for Clandestine Operation;
Figure 3
Influence Diagram Indicating Relationship Between U.S. Reprocessing
Decision and NWS Technical Success in WeaponConstruction.
0
Note that the ranking method is trying to determine the relationship between the
number of commercial reprocessors in a NWS and the potential for technical success
of the NWS in weapon construction. The other relationships have not been included
in ranking methods, mainly because analysts are technical people by training and
are most expertly concerned with effects on technical NWS success likelihoods.
31
(5)
Difficulty of Technical Implementation,
(6)
Number of Weapons Attainable from the Material Flow,
(7)
Quality of Weapons Material,
(8)
Number of Technical Personnel Required,
(9)
Level of Support Technology and Industry Required, and
(10) Time Required to Construct a Facility.
The procedure followed was to make numerical assignments on eacn
key attribute.
The first two attributes (domestic and import avail-
ability) were treated separately because of dependence on the time
period examined.
The other seven attributes were compared simultan-
eously to determine an overall ranking for each route deemed the
A
32
"technical attractiveness" factor (Rj - see Table 7.5, p. 7-1432
Data on each attribute was extracted from the literature but was
qualitative in nature (e.g., information was often expressed in terms
of "high", "medium" or "low").
Therefore, if the data revealed a
"high" cost for a particular route in comparison to the other alternatives, a rating of .3 = (1-.7) on a scale of 0 to 1 was assigned to
indicate the relative economic attractiveness of that particular route.
Thus, even qualitative statements made regarding, for example, the
degree of organization or detectability of the operation were placed
into quantitative terms through this assessment procedure (Table III).
Table III.
Qualitative Rating
Numerical Assignments Associated with
Qualitative Rating
Numerical Assignment
Very High
High
.9
.7
Medium
Low
Very Low
.5
.3
.1
Figure 4.
NWS DECISION TO ACQUIRE WEAPONS MATERIAL
DECISION TO
ACQUIRE NUCLEAR
WEAPONS MATERIAL
TYPE AND NUMBER
OF WEAPONS
DESIRED
RELATIVE A TTRACTI VENESS
OF ROUTES TO WEAPONS
MATERIAL A TTA INMENT
DOMESTIC
A VAILABILITY
OF TECHNOLOGY
IMPORT
AVAILABILITY
1 Research Reactor + MPRP
Small (A)
Yes
Yes
The decision faced by the Nth Country after it has decided to pursue the development
of'a nuclear weapons capability is to determine which route (or routes) available
are to be used to attain weapons-usable material as a function of the scale of
capability it desires.
Yes
33
Then, for each technological route to weapons usable material,
the numerical assignments for each attribute were summed to arrive at
an overall numerical assignment for the particular technology.
This
procedure corresponded to the following equation:
V'
N Tj.X
m
Z
n
iZ
i
V (x )).
i
i
j
V .
j=1
where
V
= total numerical value calculated for route
V
= sum of total numerical values for each route i,
J;
m
Z
j=l
NTi
j = 1 to m;
= normalized total numerical value for route j,
m
E
N
=
1;
j=1
The
xi
= weight placed on attribute i; in this case
xi = 1/n (equal weights assumed for each attribute);
V (xi)
= numerical assignment made on attribute i
assuming value x (high, med, low, etc.).
value functions
Vi(xi) used were based on a linear hypothesis; it
was assumed that the value placed on a "high" outcome for an attribute
was equal to 1 minus the value placed on a "low" outcome - symmetry of
values was assumed.
Also, equal weights (Xi) were assumed for each
*
The effect of using non-linear value functions, as was done by
Papazoglu et al. is discussed in part III.
Table V
COMPARISON OF MULTI-ATTRIBUTES OF AVAILABLE ROUTES
TO WEAPONS MATERIAL
ROUTE
ATTRIBUTE
1
3 Capital/O&M
costs (106 $)
4 Suitability
for clandestine
operation
5 Difficulty of
technical
8 Number of
technical
5
6
7
8
9
High
-
100
Med.
High
Med.
-
149
-
Low
Low
-
V. High
500-1000
V. High
1300+
V. High
650-1500
V. High
1300+
-
-
200-500
3000
51
Med.
96
High
High
V. High
V. High
-
Med.
Low
Low--Med.
Med.- High
Low
Low
Low
-
Low
Low- Med.
Med.
-
V. Low
-
Low
Low
Low
Low
V. High
High
V. High
High
V. High
High
V. V. High
Med.
V. V. High
High
High
High
High
High
-
-
V. High
V. High
High
Low
-
Low
-
-
...
-
Low
>1
1-4
-
10-20
-
10-20
-
-
30
-
-
2-20
-
-
2-20
-
-
-
2-20
-
Sev. kgs.
-
1
-
-
3
25
-
<<1
-
V. High
V. High
-
-
-
Low
Low
Med.
Med.
(Med.)
V. Low
Med.
-
High
V. High
Low
Low
V. High
V. High
-
V. High
-
15
V. Low
-
High
Med.
High
Med.
High
Med.
-
Med.
High
High
-
-
Med.
High
400
Med.
personnel
-
-
-
50
100-200
2000-10,000 2000-10,000 200-500
200-500
-
--
Low
Low
Med.
Med.
Med.-High
High
V. V. High
Med.
-
-
Med.
V. V. High
Med. -Med.
-
-
-
-
Low
Low
High
V. High
High
High
High
Low
-
1-3
2-3
1-3
3-4
2-3
5-8
4-6
3-5--
3
facility
+2
+2
6-8
-
-
--
(years)
<1
5
7-11
7
16
10 Time required
to construct
-
-
2-20
required
9 Level of support
technology and
industry
required
Low
-
able per year
from material flow <1
material
4
10
60-120
50+
23
Low
7 Quality of
weapons
3
56
15-40
50+
10
implementaion
6 Number of
weapons attain-
2
(Data from four references:
-6-8
7-11
lamarsh Starr-Zehroski SAI and Westinnho:u;I
-
-
-
High-Med.
Med.-Med.
Med.
23
-
-
600*M-
AN--
35
attribute; each attribute was
equally as important as
assumed
any other - no single attribute was considered more significant than
the others.
This was based on the assumption that, for a particular
Nth country, all attributes would be considered equally as important
in influencing their final decision regardless of the decision-making
Results of a sample analysis
environment they might find themselves in.
using this method are given in Table IV based on data shown in Table V.
Table IV
Results of Evaluation of Alternative Near-Term Routes to SNM
**
Route
Attribute*
1
2
3
4
3
.9
.9
.1
4
.7
.9
5
.7
6
5
6
.1
.. 1
.5
.5
.1
.3
.7
.1
.1
.3
.7
.7
7
.7
.9
8
.9
9
7
8
9
.3
.5
.3
.5
.3
.1
.3
.1
.5
.1
.1
.3
.9
.3
.5
.5
.3
.5
.3
.3
.5
.5
.5
.5
.5
.5
.1
.1
.5
.5
.5
.5
.5
.9
.5
.3
.1
.1
.5
.5
.5
.5
10
.9
.7
.3
.3
.3
.1
.5
.1
.5
Total
6.0
Normalized
.192
5.8
.186
2.4
.077
2.0
.064
2.2
.071
3.6
.115
3.2
.102
2.6
.083
3.4
.110
Attributes by Number are: (3) Capital, Operating and Maintenance Costs, (4) Suitability for Clandestine
operation, (5) Difficulty of technical implementation, (6) Number of Weapons Attainable per year,
(7) Quality of Weapons Material, (8) Number of Technical Personnel Required, (9) Level of Support
Technology and Industry Required, and (10) Time Required to Construct Weapon.
**
Routes available are: (1) Res. Reac. + MPRP, (2) Prod. Reac. + MPRP, (3) Power Reac. + MPRP,
(4) Power Reac. + Com. Rep., (5) Diff. Cascade, (6) Centrifuge, (7) Aerodynamic Jet, (8) Electromagnetic Sep., and (9) Accelerator.
36
H.
Societal Risk Approach:
K. Fleming et. al.'s Markov Model3 6
K. Fleming et. al's ACDA - sponsored work at General Atomic used a
societal risk approach to assessing the relative proliferation risk of
nuclear systems.
The assessment approach followed
a logic similar to
that applied to quantify the ldvel of safety in nuclear power plants with
respect to accidental releases of radioactivity.
Fleming et. al.'s pre-
vious work on quantifying HTGR-related accident risk using reliability/fault
tree methods provided the background for their treatment of proliferation
risk assessment.
The GA team defined proliferation risk as a mathemetical
expression based on the following relation for risk:
where R
c
H
risk, the expected value of the consequences per unit time,
=
consequence of undesirable event i,
=
=
by carrying out scenario
frequency of attempt to produce c
j, and
p
=
by attempting to carry
probability of successfully producing c,
out scenario
j.
With regard to nuclear weapons proliferation,
measure the undesirable consequences (c ) in
the GA team decided to
terms of the number of- weapons
obtained in a successful proliferation attempt.
They considered
several
scenarios' since many pathways exist involving the nuclear fuel cycle that
can lead to such a successful proliferation attempt.
Thus, for scenarios
involving the nuclear fuel cycle, a simplified definition of risk based on
the general formulation above was developed:
37
R =
where
H
iHp
=
c
frequency of attempt to acquire nuclear
weapons by carrying out s.cenario i,
probability of successful completion of
P=
scenario i, and
c
=
number of weapons obtained by successfully
carrying out scenario i.
These parameters were further disaggregated as follows:
q,
c, =m f
where
n
frequency of attempt to carry out any proliferation scenario,
q=
m
probability that scenario i
=
is
selected,
amount of material at the specific point
in the fuel cycle
selected for diversion
(kg), and
f
=
number of weapons obtained per unit of material
located at the diversion point (weapons/kg).
These definitions lead to the final expression for proliferation risk used
by the GA team:
R = 11
q p
miff
The GA team went on to apply this expression in quantifying the level of
relative risk inherent to various fuel cycles.
They did not attempt to
quantify the factor H (frequency of attmept to proliferate) as this is a
Figure 5
Methodology for Assessment of Proliferation Resistance
COMPARE RISK
QUANTIFY
SCENARIO
PROBABILITY
a
WITH ALTERNATIVE
FUEL CYCLES
00
39
factor independent of the fuel cycle.
Therefore, their final results are
expressed as conditional probabilities dependent on this factor.
Further
simplification of the method included the assumption that q.=1 for i = k
where k is that pathway found for each individual fuel cycle that is most
likely to lead to a successful completion of one or more weapons.
plement this simplification, the GA team
To im-
quantified the entire spectrum
of scenarios possible for each fuel cycle.
Also, before the above equation
can be applied, all diversion points needed to be identified.
This was
the first step in the analysis and was carried out by assuming that diversion points consist of each facility in L . fuel cycle and each transportation link where nuclear material might be found.
The second step was
to identify proliferation scenarios whose probabilities were then assessed
in step 3 while the number of weapons obtainable from each scenario
calculated separately in step 4.
was
This done, the relation above was then
applied to calculate the relative risks (R)
of each fuel cycle (Figure 5).
Basically, the GA approach uses a three factor formulation of proliferation fisk (pi,fi,m.) where each of the three factors are calculated
on the basis of separate models and/or assumptions.
The GA team spent
considerable time and effort developing an approach to assess p i, the
probability of successful completion of scenario i, while basing the
values for f
and mi on assumptions related to a given size of the nuclear
system assumed to be operating inside a NWS.
a Markov transition state model where p
The model for p
involved
can be calculated using Monte Carlo
type methods based on five time factors (TpTw' dl'
d 2, and
ponds to six possible states of the system. (Figure 6).
T
s)
corres-
The time-dependent
probability of occupying each of the six states, where state 3 is the state
40
Figure 6
STATE
Markov Model of States and Activities Associated with Proliferation
1
STATE 3
STATE 2
TW
PRLIf LHiATION
STATk
7
AVERAGETIMETO
COMP.ETE INDICATED
ACTIVITY
ACl1VITIES
ASSUCIArED WITI
TRANSI'ER FROM
STATE 1U STATE
T,
41
at which nuclear weapons capability is obtained, was calculated using a
procedure originally developed for nuclear safety calculatior
based on
These methods are applicable here to the
fault trees and
logic models.
assessment of p
bacause there are limited or no statistical
For the GA study,
to estimate these probabilities.
was based on the Markov model shown in Figure 6.
data in which
the logic model used
Thus,
to assess pi, the
user of the method need only specify the average values of the completion
times for each state (Table VI) which are then input
to a code that cal-
culates each transition state probability.
To calculate f
x mi = c,
on a series of assumptions,
approach used.
the GA team chose to base their estimate
none of which are inherent to the mathematical
However, two of these assumptions substantially affect the
results produced by the GA team; these assumptions are that: (1)
of technology in
the NWS is
the level
sufficiently high so that any difficulties in
material conversion associated with radiation/criticality level or number
of technical personnel required can be ignored,
technology of the NNWS is
cycle facilities
the level of nuclear
adequate for operating and maintaining all fuel
assumed located in
are conducted on a first
(i.e.;
its
boundaries),
and (2)
calculations
year of operation basis for a system assumed to
consist of lOGW(e) of electrical generating capacity (i.e., time efforts
are neglected).
These assumptions are different from those used in
the
other assessment methodologies which approach the problem from the point of
view of a country not yet assumed
to have embarked on a nuclear power path.
Therefore, it is assumed that radiation level, criticality and handling
problems, etc. do affect a NWS decision between technological routes to
Table VI
SPECIFIC ACTIVITIES ASSOCIATED WITH NATIONAL PROLIFERATION
Symbol for Average
Completion Time
Impact on Risk
of Proliferation(a)
Preparation
T
Unfavorable
Design weapon
Construct reprocessing facility
Test non-nuclear components of nuclear weapon
Weapons
T
Unfavorable
Recover plutonium or HEU from fuel
Fabricate nuclear components of weapon
Assemble weapon
Intelligence
gathering
Tdl
Favorable
Monitor purchases of high explosives
Study international relations
Conduct reconnaissance activities
Safeguards
Td
Favorable
Inspect fuel cycle facilities
Monitor material flows and inventories
Identify loss of electrical generation
Proliferation
T
Favorable
Carry out diplomatic negotiations
Type of
Activity
p
production
termination
2
Example of Activity
Apply economic sanctions
(a)Unfavorable - increases
risk; favorable - decreases risk
43
weapons.
Secondly, disregarding time efforts seriously alters results pro-
duced on the relative risk of the once-through fuel cycle where spent fuel
mounts up over a period of years to large quantities while radiation levels
are continually decreasing.
Based on these considerations, the preliminary
results of the GA team are not discussed here.
However, it
should be point-
ed out that the method outlined by GA could be applied successfully given
a different set of assumptions were used for calculating their three factor
formula.
44
Table VII
Attribute Comparison Between Methods
II
III
CHARM
X = "Charm" factor
Diverson Path
TPWF = Total Proliferation
Weight Factor
SAI's (ERDA) Method
no single factor produced
1.
1. Material Attractiveness
l.A. Material Type
l.B. Material Description
l.C. Radiation Hazard
2. Distribution Parameter:
Mass of Material Required
for Explosive
3. Removal Mode Factor
(single theft, substitution of inert material,
substitution of isotopic
material)
I
No. of Diversion
Points
2. Self-Protection
Factor (radioactivity level,
etc.)
3. Minimum No. of
Locations from
which Material is
Diverted
4. Effort to Process
and Produce a
Device from Stolen
Material
5. Risk of Detection
and the Risks Due to
the Nature of the
Material
1. Time Factors
A. Time from Decision to
First Weapon
B. Time from Material
Acquisition to First
Weapon
2. Cost (to produce first
weapon)
3. Professional Personnel
Required
4. Material Unattractiveness
A. Difficulty
B. Detectability
C. Interruptability
D. Safeguardability
IV
V
VI
Selvaduray's
Heuristic Method
Safeguardability Index-
Silvennoinen and Vira's
Vulnerability Index
Papazoglu et al.'s
Multiattribute Approach
1. Mirimum Cost of Weapons Construction Once Material Available
2. Minimum Time to Weapon
3. Marginal Cost Incurred when
Commercial Civil Program Amended
to Weapons Purposes
4. Quality of Material for
Weapons Purposes
5. Detectability of Weapons
Production Attempt
6. Accessability and Accountability
of Source Material
1. Weapon Development Time
2. Warning Period
3.A. Radioactivity Level
) Inherent
B. Status of Information ) Difficulty
C. Criticality Problems )
4. Weapons Material Quality
5. Monetary Cost
1. Ability to Extract
Pure Pu from Process
2. Location of Facility
(on/off reactor site)
3. Decontamination Factor
(radiation level)
4. Labor Intensity (No. of
Personnel Required)
5. No. of ?rocess Streams
VII
Heising's Cost-Benefit
Approach (Bayesian
Decision Analysis)
1.
2.
3.
4.
5.
6.
Domestic Availability of Technology
Import Availability
Capital, O&M Costs
Suitability for Clandestine Operation
Difficulty of Technical Implementation
No. of Weapons Attainable from
Material Flow
7. Quality of Weapons Material
8. No. of Technical Personnel Required
9. Level of Support Technology and
Industry Required
10. Time Required to Construct Facility
Fleming et al's Societal Risk Approach
1.
Diversion Point
2.
Mass (kg)
3.
Characteristics of SNM at Time of Diversion
a.
b.
c.
d.
Chemical Form
Physical Form (solid, gas, etc.)
Isotopic Composition
Radiation Dose Level (low, medium or high)
4.
Method of Conversion to Weapons Usable Material
5.
Weapons Conversion Factor
6.
Timely Warning Characteristics
45
III.
Comparison of Methods/Conclusions
It should be clear from this examination that all of the methods
reviewed have used a common approach in developing quantitative methods
by which to analyze nuclear fuel cycle diversion resistance.
All
methods have followed a process of attribute enumeration and definition,
and have displayed a remarkable degree of agreement in this process.
The attributes as defined by each of the methods are compared in
Table VII.
However, the degree of mathematical completeness evidenced in
each method varies and is mostly dependent upon the analyst's knowledge
of multi-attribute decision theory.
For example, the work of Heising
et al., Papazoglu et al. and Silvennoinen et al. all expressly use formal
decision theory in
setting up the mathematical relationships between
attributes and final numerical
indicators.
Silvennoinen goes a step
further into the realm of new mathematical techniques by inclusion of
fuzzy integration.
While Heising's method
relies on a number of simplifying
assumptions (i.e., linearity of utility functions and equivalence of Pareto
weights), Papazoglu et al. follow through by use of Delphic techniques
in establishing non-linear utility functions and non-equivalent weighting
factors.
These functions and factors are therefore based on expert opinion
other than the analysts themselves and represent a concensus of those
interviewed and questioned.
*
The work of SAI was not carried out to the point
where a final
quantitative ranking could be reached but helped in the process of
*At least in the SAI unclassified work.
Table VIII
Correspondence Between Method Attributes
VII
Heising's **
Attributes
3
4
I
CHARM
3
2
la-c/lb
--
--
III
SAI
3
2
4B
1C
2
1A
--
--
5
6
7
8
9
10
II
Diversion
Path (HEDL)
--
1B
--
4
--
IV
Selvaduray
Stanford
*
V
VI
Silvennoinen Papazoglu et al.
Finland
MIT
1,2
2
4
5
2
4A
3
5
3B/C
4D
4C
3
5
1
4
--
--
--
1A/B
--
--
VIII
Fleming et al.
GA
--
6
---
3
4
3A
3A
1
--
1
3
2,5
3
--
4
6
*
The correspondence shown is approximate as determined from the attribute definitions given in the
papers (See Table VI).
**
Heising's attributes are defined as follows (see Table VI): (3) Capital, O&M Costs, (4) Suitability
for Clandestine Operation, (5) Difficulty of Technical Implementation, (6) No. of Weapons Attainable from Material Flow, (7) Quality of Weapons Material, (8) No. of Technical Personnel Required,
(9) Level of Support Technology and Industry Required, and (10) Time Required to Construct Facility.
-r_
47
attribute definition (Papazoglu et al. derived many of their definitions
Selvaduray's work, though not as well
from the earlier SAI work).
theoretically based in the methods of Operations Research, demonstrates
the principle held by many decision theorists that decision theory is
an accurate description of the logical human thought process.
Selvaduray
approaches the problem of choosing between alternatives by defining the
relation:
11
r
E
j
=
R
11
10 E R
i=l
which can be placed into the notation of decision theory as follows:
E =ErR
10-ER
where
i
V(x ) x
i
i
EX
V
Tl
1
V
T
E = Selvaduray's performance factor;
r = Selvaduray's rating factor;
R = Selvaduray's ranking factor;
V(x ) = decision theoretic value function placed on attribute
value x ;
X
= decision theoretic weighting factor placed on
attribute i; and
V
= total value function summed over all attributes i
for a particular technological route j.
Thus, Selvaduray has managed to independently derive the same formulation for determining final evaluation indices as is done in formal
decision theory.
This result is of particular significance because it
Table IX
Final Results:
Rankings Placed on Pathways to Weapons Usable Material (in %)
Method
Route to*
Material
1
2
3
4
5
6
7
8
9
*
VII
Heising's
Method
I
CHARM
22.5
21.7
6.6
4.5
6.6
10.6
9.0
7.0
11.0
7.1-21
10.4-43.5
0
0
2.6-6.3
27-42
5.4-6.9
9.3-34-9
0
II
Diversion
Path (HEDL)
6.1
25.3
1.6
3.6
15.7
15.7
15.7
15.7
.1
III
SAI
0
IV
Selvaduray
Stanford
V
Silvennoinen
Finland
VI
Papazoglu
MIT
18.6
18.9
.4
.4
10.9
16.0
11.6
11.6
11.6
23.6
23.2
5.3
2.6
6.6
11.8
9.0
9.0
9.0
20.1-24.7
19.4-23.0
.8-3.0
.05-1.0
5.5-8.0
15.2-20.8
12.0-15.8
14.5-18.9
8.9-11.7
The routes to material are: (1) Research Reactor + Minimum Plutonium Recovery Plant (MPRP), (2) Production
Reactor + MPRP, (3) Power Reactor + NPRP, (4) Power Reactor + Commercial Reprocessor, (5) Diffusion
Cascade, (6) Centrifuge, (7) Aerodynamic Jet, (8) Electromagnetic Separation and (9) Accelerator.
-A00
49
was work independently formulated apart from any specific knowledge of
utility theory.
However, Selvaduray's work fails to apply standard
methods for arriving at value functions (see Appendix A) although he
does use a questionnaire addressed to over 100 experts to determine
the relative weighting factors X
defined in his work.
used to rank the eleven attributes
The importance of Selvaduray's work is therefore
less related to the efficacy of the heuristic method he applied than
to the fact that his own careful study of the problem led to his
"discovery" of utility theory, a sign that the theory does indeed
model the logical human thought process.
A Sample Problem Comparing Methods
To gain further insight into how the various diversion resistance
methods compare, it is useful to examine a sample problem.
The problem
examined is taken from the author's thesis in which nine currently
available routes to weapons material were analyzed and compared with
respect to their diversion resistance to obtain indicators of the
relative probability that a non-weapons state would choose one route
over another.
Using the data of Table V, it is possible to place all
methods on an equal footing to compare results.
The approach taken is to determine the correspondence between
the eight attributes defined in the author's work and the attributes
defined in the other methods (TableVIII). Then, the other methods can
be applied consistently to the available data. * Final results showing
The method developed at GA by Fleming et al. was not found to be easily
applicable to this problem without substantial use of computer codes
unavailable to the author. Therefore, it was not included in the
comparison conducted here.
50
relative rankings in % of the nine pathways to weapons usable material
are given in Table IX.
These results show a close agreement between
the methods of Heising, Silvennoinen and Papazoglu et al.
The Charm
and diversion path results are significantly different but are probably
not reliable because they are based on heuristic methods.
Selvaduray's
method is more firmly based in mathematical theory than are either
Charm or diversion path methods, but again is not as firmly based as
are those of Heising, Silvennoinen or Papazoglu.
Note, however, that
Selvaduray's results are not much out of agreement.
To conclude, it appears that those methods based on utility
theory render similar results.
Method IV is probably less reliable
than V, VI or VII since, although it bears a close resemblance to
utility theory, it is not a formal application of the theory.
In the
author's estimation, methods I and II must be viewed very cautiously
*
because they are not based on any confirmed theoretical process.
With regard to the work by Fleming et al. at General Atomic, a
re-examination of the'definition used for consequences is suggested.
The problem with defining proliferation risk to be proportional to
number of weapons producible is that it does not reflect the concensus
*
An interesting result forthcoming from this exercise is that, given
the validity of the data base, the commercial power reactor-commercial
reprocessor route (#4) consistently is ranked as being very unattractive to a would-be proliferator, and is more diversion resistant than
many of the independent pathways. However, although the relative risk
appears small, it is not to be disregarded as insignificant. The
proper conclusion to draw, as in the case of reactor accident scenarios,
is that the risk does exist such that all reasonable technical precautions should be taken to minimize this risk.
51
that proliferation risk arises from the development of a first weapon
independent from subsequent number produced.
Further, since number of
weapons produced is proportional to fuel cycle flow rate, an inherent
bias is built-in against those fuel cycles which exhibit the highest
nuclear material flow rates.
Thus, more proliferation prone tech-
nologies with smaller flow rates may be overlooked (e.g.,
reactor/MPRP route).
the research
This problem can be rectified if the method is
recast to assess the risk as a function of the likelihood of a given
fuel cycle contributing to the successful development of a first
weapon capability.
Finally, some comments are in order with respect to the proper
interpretation of quantitative method results.
results --
and methods --
peer review.
It is important that
be carefully scrutinized and subjected to
As is the case with reactor safety analyses, this re-
view process can reveal points of disagreement among experts, needed
improvements in data/probability estimation in addition to other
modifications.
The proper role of analysis is to aid policy-makers
in reaching reasoned conclusions; it is not a substitute for the
policy-making process.
As quantitative methods continue to develop,
become more widespread and acceptable, the possibility for analysts
to misuse analysis to support positions of advocacy will decrease as
will the use of unstructured qualitative, intuitive approaches.
The
need for logically structured, technically based analyses is becoming
greater as problems become ever more technical and complex.
To dis-
regard a scientific approach to difficult policy matters is a risk
that implies far greater negative consequences than the risk that such
methods will be applied incorrectly and/or without objectivity.
52
References
1.
Nuclear Power: Issues and Choices, 1st ed., Ballinger, FordMitre Study, 1977.
2.
Greenwood, T. et al., Nuclear Proliferation: Motivations,
Capabilities and Strategy for Control, McGraw-Hill, New York, 1977.
3.
President Carter,
"Statement by the President on Nuclear Power",
April 7, 1977.
4.
Strauch, S., "Alternatives to Separation of Plutonium to Reduce
Nuclear Proliferation Risk", Fuel Cycle Conference 1977, AIF,
April 24-27, 1977, Kansas City.
5.
Rasmussen, N.C. et al., Reactor Safety Study, WASH-1400, 1975.
6.
Vaurio, J.K., "Response Surface Techniques Developed for Probabilistic Analysis of Accident Consequences", ANL, 1978.
7.
Beck, W. and Schmidt, F.A., "Probabilistic Analysis of Codes and
Calculations Results in Nuclear Reactor Safety", IFK-Stuttgart,
FRG, 1978.
8.
Webster, F.A. and Benjamin, J.R., "Probabilistic Analysis of
Fire Risks for the Design of Fire Protection Systems in Nuclear
Power Facilities", EDAC, USA, 1978.
9.
Aldrich, D., Rasmussen, N.C. et al., "Examination of Off-Site
Emergency Protective Measures for Core Melt Accidents", Sandia
and MIT, 1978.
10.
Candolfo, G. et al., "Some Aspects of the Risks Associated with a
Mixed-Oxide Fuel Production Plant", AGIP-Nucleare and JRCIspra, Italy.
11.
Fullwood, R.L., Ritzman, R. and Mendoza, Z., "Working Paper for a
Probability/Consequence Analysis of a Nuclear Fuels Recovery and
Recycling Center", SAI-054-77-PA, June- 1977.
12.
Campbell, J.E. et al., "Development of Risk Assessment Methodology
Applicable to Radioactive Waste Isolation", Sandia/USNRC, 1978.
13.
Heckman, R.A., "Determination of Performance Criteria for HighLevel Solidified Nuclear Waste from the Commercial Nuclear Fuel
Cycle: A Probabilistic Safety Analysis", Lawrence Livermore
Laboratory, 1978.
14.
Owen, P., "Analysis of the Risk from Sabotage of Nuclear Power
Plants", Stanford University, EES Dept., Nov. 1975.
53
15.
Topp, S.V., "Detailed Sabotage Analysis of a Commercial Reprocessing Plant", DPST-76-233, May 19, 1976 (classified).
16.
Heinrich, L.A., "Safeguards Planning in a Plant Design Process",
DP-MS-77-55, ANS San Francisco Meeting, Nov. 1977.
17.
Heinrich, L.A., "Safeguards Requirements for a 10 MTU/day LWR
Fuel Reprocessing Plant", DP STD-LWR-76-4, Nov. 16, 1976.
18.
Levine, S., "Probabilistic Methods in the Nuclear Regulatory
Process", USNRC, 1978.
19.
Lovins, A., "Cost-Risk-Benefit Assessments in Energy Policy",
George Washington Law Review, Vol. 45, August 1977, pp. 917-943.
20.
Hoos, I., "The Assessment of Methodologies for Nuclear Waste
Management", Transcript, U.C.Berkeley, 1976.
21.
Taylor, V., "Subjectivity and Science:
Belief", MIT Technology Review, 1979.
22.
Personal communication with several engineers who shall remain
anonymous here.
23.
Albert, T.E. and Straker, E.A., "Analysis of the Proliferation
Resistance of Alternative Fuel Cycles", Final Report to EPRI,
A Correspondence about
RP620-23, SAI-77-872-LJIF, Dec. 6, 1977.
24.
D'Zmura, A.P., An Approach to Comparative Evaluation of Nuclear
Fuel Cycle Proliferation Risk, Nov. 29, 1976.
25.
Maltese, M.D.K., K.E. Goodwin, J.C. Schleter, Diversion Path
Analysis Handbook, Vol. 1 - Methodology, Vol. 2 - Example,
US ERDA, Division of Safeguards and Security, October 1976.
26.
Kendrick, H. et al., A Preliminary Methodology for Evaluating
The Proliferation Resistance of Alternative Nuclear Power Systems,
SAI Report No. SAI-78-596-WA, June 15, 1977.
27.
Selvaduray, G.S., "Comparative Evaluation of Nuclear Fuel Reprocessing Techniques for Advanced Fuel Cycle Concepts", Ph.D.
Dissertation, Dept. of Applied Earth Sciences, Stanford University, Stanford, March 1978.
28.
Silvennoinen, P. and Vira, J., "Quantitative Assessment of
Relative Proliferation Risks from Nuclear Fuel Cycles", Technical Research Centre of Finland, Nuclear Engineering Laboratory,
P. 0. Box 169, SF-00181, Helsinki 18, Finland.
29.
Silvennoinen, P., Vieno, T., and Vira, J., "Fuel Cycle Optimization with Non-Proliferation Objectives", Transactions of the
American Nuclear Society, Vol. 31, European Nuclear Conference,
Hamburg, Germany, May 6-11, 1979, pp. 304-306.
54
30.
"Viewpoints on Key Issues and Evaluations Criteria for Assessing
the Potential of Alternative Nuclear Energy Systems for Improving
Proliferation Resistance", TID-28078, Booz, Allen and Hamilton,
Inc. (1977).
31.
Saaty, T.L., "A Scaling Method for Priorities in Hierarchical
Structures", J. Math. Psychol. Vol. 15, No. 234, 1977.
32.
Heising, C.D., "The Reprocessing Decision: A Study in Policy
Making Under Uncertainty", Dissertation, Dept. of Mechanical
Engineering, Stanford University, 1978 (EPRI NP-931).
33.
Keeney, R.L., Operations Research, Vol. 22, No. 1, 1974.
34.
Sugeno, M., in Fuzzy Automata and Decision Processes, M.M. Gupta,
Editor, North Holland Publishers, New York, 1977.
35.
Papazoglu, I. et al., "A Methodology for the Assessment of the
Proliferation Resistance of Nuclear Power Systems", MIT-EL-78-021,
September 1978.
36.
Fleming, K.N., Tully, G.R., and Deremer, R.K., "A Risk Assessment
Methodology for Evaluating the Proliferation Resistance of Nuclear
Energy Systems", GA-A15290, General Atomic Project 3769, Arms Control
and Disarmament Agnecy Sponsorship, April 1979.
A-1
Appendix A
Examining Selvaduray's Method for Assessing the
Safeguardability of Various Reprocessing
Technologies
Selvaduray defines five sub-attributes that influence the
guardability
of a given reprocessing method.
safe-
The way in which he
assigns quantitative ratings (r) on the 48 possible combinations that
could be assumed by interchanging possible attribute
is
Assigning ratings of between
probably not mathematically justifiable.
0 to 1 based on equi-intervals of (.17)
states
units each, he constructs
tables beginning with the Pu extractability of the process (yes/no),
its location (on-site/off-site), decontamination factor (high, medium
or low), labor intensity (high/low) and number of effluent streams
(several/few).
Through the rating assignment process, Selvaduray has
implicitly assigned weighting factors (X) on the five sub-attributes
as follows:
X = .63
1.
Pu separation
A = 5
+
2.
Location
A = 2
+X 2 = .25
3.
Decontamination factor
A = .5
+
3 = .06
4.
Labor Intensity
A = .25
+
4 = .03
5.
Effluent streams
A = .17
5 = - .02
(A = mean difference in resulting ratings), ZA
= 7.92
Had he placed the attributes in a different order, he would generate
different A's for each attribute.
Since he has not consciously as-
signed the values noted, they probably do not adequately reflect his
expert opinion (or anyone else's).
Clearly, the implicit X's Selvaduray
is using are not reflective of his own beliefs about the relative importance of each sub-attribute.
Support Calculations for Table
Appendix B
IX
I. CHARM Method
X la
Pathways
1
Z
3
4
5
6
7
8
9
Mass flow
of Material
(MT/yr)
M
MF
N
E
H F
PD
si i D±
lb
Fraction Divertible w/
or w/o sfgds
F
1-4
10-20
10-20
30
2-20
2-25
2-20
4-20
1 or less
lc
Simple
Device
Mass(MT)
M
2
3
Self ProCost to
tection
Fabricate
Factor (R/hr)Weapon(10 6 $)
S
P
100
100
105
105
1
1
1
1
105
10
10
1000
1000
1000
100
500
100
500
4
Time Required to
Produce
Device (yrs.)
D
1-3
1-5
2-11
5-11
4-7
3-16
3-16
3-23
3-16
Charm
X
-4
3.3-40x10
2-20x10-3
9-18x10-9
2.7-6 xlO- 8
2.9-50x10-4
1.25-83x10-3
2.5-133x10-4
4.3-670x10-4
1.25-7x10-9
7.1-21
10.4-43.5
'.0
1%-0
2.6-6.3
27-43
5.4-6.9
9.3-34.9
Notes:
Attribute (la) corresponds to the "Q" factor in the HEDL diversion path method, (lc) to the "M" factor and attribute (2)
to the "RHF" (see part 11 of this appendix). Attribute (2) is rated the same way as for the diversion path method on a
scale from 0.to 1 where 1 represents a very high level of self protection (radiation level v. high). Cost to fabricate
weapon (factor P, attribute 3 here) is also rated on a scale from 0 to 1 where a very low cost corresponds to a very high
Also, the time required to produce a weapon is rated on a 0 to I scale as was done in Silvennoinen's and
attractiveness.
Heising's work.
MxF - Q in HEDL method.
I-h
B-2
HEDL Diversion Path Method
II.
(1)
TPWF = MAF x DPF x RMF
(2)
MAF = MT? x MDF x RHF
(3)
DPF =
/QIN~
Q - mass of material in fuel cycle, Ms - mass required for single
device
R.G. Pu 30 kg HE U-235 35 kg
W.G. Pu 10 kg
(4)
WMF
Path
1.0
0.75
0.1
Simple Theft
Substitution of Inert Material
Substitution of Isotopic Material
Material
Path
Type
MTF
MDF
RHF
1
2
3
4
5
6
7
8
9
R.G.Pu
W.G.Pu
R.G.Pu
R.G.Pu
H.E.U-235
H.E.U-235
H.E.U-235
H.E.U-235
R.G.Pu
1.0
1.0
1.0
1.0
.8
.8
.8
.8
1.0
.8
.8
.8
.8
.8
.8
.8
.8
.8
.7
.7
.1
.1
1.0
1.0
1.0
1.0
.1
(MT/yr) (MIr)
Q
M
DPF
RMF
.03
.1
.1
.3
.105
.105
.105
.105
.005
.03
.01
.03
.03
.035
.035
.035
.035
.01
1
3.2
1.83
3.2
1.73
1.73
1.73
1.73
.71
0.75
1.0
0.75
1.0
1.0
1.0
1.0
1.0
1.0
MAF
.56
.56
.08
.08
.64
.64
.64
.64
.08
TPWF
%
.43
1.79
.11
.256
1.11
1.11
1.11
1.11
.06
6.1
25.3
1.6
3.6
15.7
15.7
15.7
15.7
.1
E - 7.086
RMF (Removal Mode Factor): Simple theft of material is possible
(5)
only in case of commercial reprocessor where Pu is obtainable. Military
routes require no diversion and therefore are not prone to be detected.
Therefore, we modify the HEDL method here to include a category of
material with the same rating as the simple theft path; that is, the
path wherein material is derived from clandestine military operations
outside of IAEA safeguards.
MDF (Material Description Factor): In routes (1)-(4) and (9) Pu
(6)
nitrate solutions will need be handled in the PUREX NPRP and commercial
reprocessor. In routes (5)-(8), binary compqunds, gases, etc., will
need be handled in the enrichment processes.
(7)
1(1:
It is assumed uranium is enriched to 80% for enrichment routes.
Q is defined as the mass of material that can be diverted without
(8)
detection during one year.
III.
SAI's Method
SAI's method did not describe a way to convert qualitative/
quantitative data on attributes to quantitative single factors.
Therefore, the SAI method is not applicable to the sample problem.
B-3
IV. Selvaduray's Method
Attributes
L.Indep. U235JZEF 2 Location
Pu Streams?
(Weapons
Material
Covert
Pathways ,ahwv
Quality)
Oaiv
Yes
1
Research (High Quality)
Reactor +
, uitability
Clandestine
Operation)
High
3 Decont.
Factor
(Opposite
of
Radiation
Level
High
I
I
Rating
4 Labor
Intensity
(same as Stat,
Of Information)
V. Low
5 Effluent
Streams
(No.
of_Weapons)
Fev/
(10-r
%
(8.83)
1.17
18.6
(9.00)
1.00
18.9
AP
2
Production
Reactor +
MPRP
Yes
(Very High
Quality)
V. High
High
Med
Several
- 17)
Power
Reactor+- No
Low Quality)
MPRP
Low
V. Low
High
Several
Low
V.
V. High
Several
9.83
.4
( .17)
9.83
.4
4
Commercial
Reactor
No
(Low Quality)
Low
+
Comm. Reprocessor
_.
......
5
Yes
(Med. Quality)
Low
V. High
High
Several
(5.17)
4.83 10.9
Centrifuge
Yes
(Med. Quality)
High
V. High
Med
Several
(7.61)
2.39 16.0
Aerodynamic
Jet
Yes
(Med.
Med
Several
Diffusion
Cascade
6
Quality)
Low
Y.High
4.48
11.6
8
Electromagnetic
Separation
Yes
(Med. Quality)
Low
V. Low
Med
Several
(5.52) 11.6
4.48
9
Accelerator
Yes
(Med.
Low
V. Low
Med
Several
(5.52)
4.48 11.6
Quality)
Z(1-r)-47.51
B-4
V. Silvennoinen
Pathways
et.al's
K1
*
1 (C)
Method (Finland)
1)
2
V(x 2 )
3
V(X 3 )
V(X4 )
V(X 5)
V(X 6 )
-
V.Low
1.00
Low
.75
High
.75
High
.75
.74
23.6
V.Low
1.00
Low
.75
V.Low
1.00
High
.75
V.High
1.00
.728
23.2
V.Low Cost
1.00
2 (M)
-
6
5
4
ZXV(Xi)
3 (C)
V.High Cost
0.00
-
High
.25
Med.
.5
V.Low
0.00
Low
.25
.165
5.3
4 (C)
V.High
0.00
-
High
.25
V.High
0.00
V.Low
0.00
Low
.25
.08
2.6
V.High
0.00
High
.25
High
.25
Low
.25
Med.
.5
.2075
6.6
-
Med.
.5
V.High
0.00
Med.
.5
Med.
.5
Med.
.5
.37
-
High
.25
Med.
.5
High
.25
Low
.25
Med.
.5
.2825
9.0
-
Med.
.5
V.High
0-00
V.High
0.00
Low
.25
Med.
.5
.2825
9.0
High
.25
Low
.25
Med.
.5
.2825
9.0
5 (M)
6 (M)
7 (M)
8 (M)
9 (M)
-
-
Med.
.5
High
.25
*Silvennoinen et al's
method characterizes a process by the source material available and the
material flow rate achievable. Therefore, pathways here are described by source material type
and expected flow rate to be consistent with the method here applied:
(1)
Res Reac + MPRP: Material Flow: R.G. Pu trom spent fuel,
flow rate:<< 3OMTEM/yr, short cooling time.
(2) Prod Reac + MPRP: Material -Flow: W.G. Pu from production fuel,
flow rate: up to 30 MTHM/yr, short cooling time
(3) Pow Reac + MPRP: Material Flow: R.G. Pu from spent
flow rate: up to 30 MTHM/yr (probably less),
cooling time to reduce radiation hazard (spent fuel assumed diverted
from spent fuel ponds located in NWS that may be as old as 10 yrs.)
(4) Pow Reac + Com Rep: Material Flow: R.G. Pu from com. PUREX plant
process stream assumed located inside NWS, flow rate: up to
30 MTHM/yr (assumed standard size commercial reprocessor), radiation
level low because of high decontamination factor C,10 6 for PUREX).
(5)
-(8) Enriehment Plants:
clandestine plant.
(9)
Accelerator:
Iaterial Flow:
Material Flow:
W.G.
High Enriched U-235 passed through
Pu; flowrate:
up to 30kg Puf produced per year.
The authors define two sets of weights, one for civilian(C) routes and
X1 is assessed for M but not for C; X is assessed
other for military(M).
2
for C but not for M:
Unsep. R.G. Pu.
X4
X3
X2
X
Pu
.30
.11
.17
.15
C
.35
.20
.10
M
The ratings are based on a 0 to 1 scale where 0 means the value to the
non-weapons state if a path is least attractive and 1 most attractive:
0
.25
.5
.75
1
V. Low Attractiveness
Low
Med
High
V.High
11.8
IM.
rapazoglu at. al.'s
Method
3
Covert Pathways
Research Reactor
Development
Time (Yrs.)
Inherent Difficulity
Warning Period
Status of
(%)
Information
Radiation
Level (R/Hr )
1-3
< 10
1-5
< 5
E(2,2)
10
2-11
V15
F(2,3)
10
* A(1,1)
10
2
Weapons
Development
Material
Quality
6
(10 $)
High
R.G.Pu
10
Low
V. High
W.G.Pu
10
High
Low
R.G.Pu
1000
Criticality
Low
OeR?
2
Production
Reactor + HPRP
3
Power Reactor
+
5
U'
4
Power Reactor
+
Commercial Rep.
5
Diffusion*
Cascade
6
Centrifuge
5-11
> 50
1(3,3)
105
High
a%0
4-7
3-16
>30
> 15
H(2,3)
0
E(2,2)
0
High
Med
Low
R.G.Pu
1000
Med
HEU-235
1000
Med
HEU-2 65
7
Aerodynamic
Jet
8
Electro Magnetic
25-50
3
> 30
> 50
E(2,2)
0
E(2,2)
0
High
High
Med
HEI-235
$I'-235
100
500
100
Separation
*
9
Accelerator
25-50
__________________I
C- Crisis Environment
NC- Non- Crisis Environment
> 30
E(2,2)
I___________
105
Med
__________
Med
HEU-235
500
VI.
Papazoglu et.al.'s
Attribute 1:
(1)
C '17NC -05-
Method
1
-.
28
-1
Results of Papazoglu's Method:
2
-. 03
-. 07
Normalized Results In Right-Hand Column
10(1+E)
Normalized
3c
4
5
-. 026
-. 026
0
0
0
0
0
0
-. 226-'336
-.146- -196
.774-.664
.854-.804
6.64-7.74
8.04-8.54
.19-20.8
.247-20.1
0
0
-.276- -406
-.176- -246
.724-.594
.824-.754
5.94-7.24
7.54-8.24
.t3-. #95
.23-.194
3a
3b
0
0
-. 02
-. 04
-. 06
-. 06
-. 026
-. 026
0
0
0
0
-. 04- .07
-.09- 715
-. 35
-.36
-. 154
-.154
-. 04
-.04
-. 01
-. 03
-. 04
-. 11
-. 884--.97
-. 864- -974
.116-.03
.136-.026
.3-1.16
.26-1.36
.009-.03
.008-.03
(4) C r31
NC -.12- -.13
-.07
-. 15
-.38
-. 38
-. 154
-. 154
-.04
-. 04
-.01
-. 03
-.04
-. 11
-1
-. 984--~994
0
.016-.006
0
.16-.06
0 - 0
.005-.001
(5) C .31
NC -11- -13
-.06- -07
-.13- -15
-.32
-.32
0
0
-.04
-.04
-.005
-.015
-.04
-.11
-.775- 7785
-. 725--.765
.225-.215
.275-.235
2.25-2.15
2.75-2.35
.07-.06
.08-.055
(6) C -28- -31
NC -.
1 - -13
-.095
-.098
-.06
-.06
0
0
-.02
-.02
-.005
-.015
0
-.02
.46-:49
-.323-~353
.54-.51
.677-.647
5.4-5.1
6.77-6.47
.157-.137
.208-.152
(7) C-31
NC--.13
-.06
-.13
-.06
-.06
0
0
-.04
-.04
-.005
-. 015
-.04
-.11
-.515
-.485
.485
.5 5
4.85
5.15
.14-.13
.158-.12
(8) C -28
NC i1
-.07
-.15
-.06
-.06
0
0
-.04
-.04
-. 005
-.015
0
-.02
-. 455
-.385
.545
-.
615
5.45
6.15
.159-.147
.189-.145
(9) C 731
13
NC -.
-.06
-.13
-.06
-.06
-.02
-. 02
-.005
-. 015
-.04
-. 11
-.649
-. 619
3.51
3.81
.102-.094.117-.089
(2) C -17- ;3
NC-.05- -12
(3)
C -. 25- -31
NC-.08- -.13
C-Crisis Environment
NC-Non-Crisis Environment
-.154
-.154
-
.351
.381
0en
VII. Heising's Method Applied to Problem Expressed with Papazoglu et. al.'s Attribute Definitions
1
Covert
Development
Pathways
Time
3
Inherent Difficulty
2
Warning Period
Research
V. Low
Low
Reactor +
.9
.7
Status of
Information
Radiation
Level
V. High
4
Quality
Development
Cost
V. Low
Weapons
Materia:
Critical'ft
5
Low
Low
High
.9
.7
.7
.7
Med.
Low
Low
.9
.x
1. yg
44l
Normal
-ized
5.5
.225
5.3
.217
1.6
.066
1.1
.045
MPRP
2
Production
Reactor +
MPRP
3
Power Reac-
tor +
HPRP
Low
.7
High
.3
V. Low
.5
.9
Med
V.Low-Low
.5
.2
.7
V. High
.1
V. High
V. Low
.7
.9
.9
High
Low
.1
.3
.3
High
Low
V. High
.1
.3
.1
High
.1
Med.
.5
V. High
.1
1.6
.066
Med.
.5
Med.
.5
Med.
.5
2.6
.106
High
Med.
High
.1
.5
.3
2.2
.09
1.8
.07
2.7
.11
V.
4
Power Reac-
tor
+
High
.3
V. High
V. Low
.1
.1
V. High
.1
Commercial
toepo wer
5
Pathway
Diffusion
Cascade
6
Centifuge
Pro
Time.C
Wann
High
.3
High
.3
Low
.3
V. High
.1
Med.
.5
Med.
.5
-na-
Med.
-na-
7
Aerodynamic
MAd
Jet
.5
8
Electro
Magnetic
High
.3
.5
V. High
.1
V. High
.1
Med.
.5
-na-
High
.1
Med.
.5
Med.
.5
Med.
.5
High
.3
Med.
.5
V. High
Med.
.5
Med. .5
High
.3
Separation
9
Accelerator
.1
td