kr0000503 kaeri/tr-1600/2000
TRANSCRIPT
KR0000503
KAERI/TR-1600/2000
Development of Material Balance Evaluation Technique(II)
2000. 6.
§ [
3 1 / 4
Please be aware that all of the Missing Pages in this document wereoriginally blank pages
2000td 6;
: 0|
ok
inspector
Balance Evaluation : MBE)1- operator
bias ^ ^ l - * !
(Stratification) •<>)
IAEAfe operator-inspector paired data# °
(random error)^}- Tfl-f-i^Hsystematic error)!-
7 } ^ stratification!-
(Difference) statistics, MUF-D(Inspector MUF)
l-^^i partial defects S ^ bias defects
lfe 4 item1!
stratum^£) i
1 -^ (MUF) ^7>, D
§•<>] $1^. I A E A ^ *%
M U F ^
, D
7]-
MUF
IMUF^l- D
IAEA7} ^7fl
. IAEAfe operator-inspector
-£ ^ ^ , 71
difference
- in -
2. Paired Data2| Quality Check 3
3. Identification of Outliers 4
4. Paired Data Comparison 5
~)\. Paired Difference 6
M\ Mean Difference 7
CK Paired Differences] S i @ A f 8
5-K Differenced 5 i 0 A [ 8
Or. S3*K>|0|| CHS- $fS|g SAf 10
1 1
Error) 11
M-. ^ISS^(Systematic Error) 19
6. Delta value 29
7. mm^x.mj\ 30
y\. ssgs 30
U-. Stratification 31
C-K 0|?Ht*Mi! (MUF) 31
36
UK Shipper/Receiver Difference 37
AK IMUFOnspector Estimate of MUF) 37
OK IMUF £ £ [ M+ 39
*K IMUF2| ^ £ | ^ a A f 3 9
xL not ^ o i _ AI
9K D m# n# 41
- iv -
1.
fe 4 stratum
a t 4^ -f*g-(Random).2.2>
IAEA7> #^Al^efl l-SH
(systematic) -2.*r
-fe Paired data comparison
*T§(Error Estimation)6
paired data^ outlier»
OutlieH
International
Target Value(ITV)»
Stratum^S SL
random error ^ systematic error7f ^ # 5 ] ^ , °l
# ^ ; r ^ ^ 7 K M a t e r i a l Balance Evaluation)^
^ x > ^ ^^1 operator-inspector^ ^ ^ $ 1 ^ data*
stratum ^ ^ H ! 4 ^ *>^4S. ^-^°> t!:4. °1 r ^°1 paired^ operator-
inspector data°11 tfleH quality ^ 4 # ^ 1 ^ ^ outlier^l s f l ^ s l ^ data-i-
^ # t t 4 . Paired data^l] tfl*><^ operator-inspector data* ^7113^3 . «1 L 5g
7r^>fe *)•$•§: ^^r°> ^ stratum^ -f^r^^Xrandom error) ^
(systematic error)l- ^i^t!:1^. ^I'fr^ random error^i- systematic^-
sample size
M.3L*\ <>fl >| fe operator-inspector data-2] pairing,
- 1 -
(error estimation) tfl$ is]
H i l 1/Utilization of Measurement Data
3) PainCom
i
id dataparison
r
CIR
Statement
\
1) Final Recordsafter QC Check
2) Identification of Outliers
Measurement PerformanceEvaluation (ERRKSI) /
4) MEASUREMENT ERRORDATABASE
Perf/Capab. Errors
r
6) Material Balance Evaluation
MUF-D MUF-G
DA&NDA
C I R Statement
Trend AFac/Mat
nalysis/Instr
Errors(TREND)
r
5) Delta Values
SampleCalculal
Rejectio
Sizetions
n Limits
2. Paired data^] Quality Check
"%• stratum^] ^Q *
£ stratum1! NDA
^ DA ^ ^ ^ 4 »
^ ^"(paired data)-^
Paired data^r
paired datafe ^-
^ v ^ data -fi-jL^
decay-correction
stratum1!
^r DA
MBA code, ^
batch H B ) J I PU«^
£. quality control^- ^
NDA
^ isotope
e ^IS-tf subsamplel-S. ^
subsample^: #
stratum^! heterogeneous
operator data^- *%•£-
2 . S o u r c e R e c o r d 2 | Q u a l i t y C o n t r o l
S o u r c e R e c o r d s
QUALITY CONTROLPairing of D ata
Unit Consistency CheckAveraging Over M ultiple M easurem ents
Decay Correction
Con v i rsior tuProgram Gmir jkd
R ( ( . u r d •>
;V Opeiato'r-Jnspi.ctor Paired Data
- 3 -
3. Identification of Outliers
Outlier^ .SL*r ^ 5 J A ] #
^ o ] ^ OutlieHl
relative difference ^t°l international target value(ITV)^l 5«11
s. outliers Zt
. z}-
4 . ITV^ operator-inspector difference datal- i :
performance value ^ , ^ ^ ^ l ^ ^ ^ l random ^ systematic error^0]
Outliers. ^ ^ ^ ^VS-lr^r ^-^}^>a(error estimation)
# ^ ^ ^ 1 ^7>A]oil^ outlieH
Paired data^l relative differencel-
x
i outlier «^^-#
Outlier 3 rf,<%) > 5 * ITV
- 4 -
4. Paired data Comparison
Operator(x)4 inspector(y) *]-5.-c- stratification
paired dataS] comparison^: £.€• stratum^ «
operator-inspector difference Jg7V*|)*||fe- n% 3 4 £
1 4 &•& paired data7f ^ 4 ^ 3 . ^ 3 4 : £ £
Paired data^l tfl^-^-fe- ^ S difference^ -
P a i r e d
, 3.
2, -f^r ^
3. 1. U-Concentration^l Paired data
Entry
NoItemNO Bottle X Y D Std(D) DREL Std(DREL) Sig.
JMP43
007
77221
77222
87.670
87.300
87.532
87.189
0899
1221
A123
77223
77224
77225
83.600
87.660
80.500
87.692
87.390
80.134
S. 2.
Variable
U-Conc (WT %)
U-235 (WT %)
Sample
size N
5
5
X 5 :(XBAR)85.346
Y ^ 5(YBAR)86.024
D ^ S(DBAR) (SDBAR)
t-TestDBAR/SDBAR
Sig.
3.
Variable
U-Conc(WT%)
U-235 (WT%)
DBAR SD % %RAND(O) %RAND(I) %SYS(O) %SYS(I) SDBAR%
— 5 ~
3. Operator-Inspector Paired data *
r
Stratum
n Items Sampled
T
Operator Data (x)
Paired Data for n Items
r
Calculation of- Individual Differences, d i and d i (%)- Mean Difference, d and d(%)- Std. Dev. of Differences, S a
Inspector Data (y)
IRandom and Systematic Error Propagation
- Std. Dev. of Meamn Difference, s^
r
Test for Significance of d
t=dl s-d
—PMeasurement Error
Data Base
7}. Paired Differences
A stratum % paired differenced
differenced
. Paired
U ^ U235
. d. y% rf.(%
- 6 -
i= Xi- yh rf,-(%) = 100t - yt)
x
D^- DREL*
= 87.67 - 87.532 = 0.138, dl{%) -6^? 8
7?-532) = 0.158°l
1-1
Entry
No
(D©(D
ItemNO
JMP43
007
0899
1221
A123
Bottle
77221
77222
77223
77224
77225
X
87.670
87.300
83.600
87.660
80.500
Y
87.532
87.189
87.692
87.390
80.134
D
0.138
0.111
-4.092
0.270
0.186
Std(D) DREL
0.158
0.127
-4.895
0.308
0.231
Std(DREL) Sig.
M-. Mean Differnece
• i - ^ s t ratum^ n i df ^^-^
n
Where x= n
- = Ijdj = Q.138 + 0.111 + ..+0.186 = _Q 6 7 7 6
= 100X-O776 = _ a 7 9 7 ] .ob.o4b
- 7 -
S. 2-1
Variable
U-Conc (WT %)U-235 (WT %)
Sample
size N55
X ^ S
(XBAR)85.346
Y J§5(YBAR)86.024
D ^ 3 "(DBAR)-0.6776
£^€*r(SDBAR)
t-TestDBAR/SDBAR
Sig.
3-1
Variable
U-Conc(WT%)
U-235 (WT%)
DBAR
-0.79
SD %
0.08
%RAND(O) %RAND(I) %SYS(O) %SYSQ) SDBAR%
Paired difference^
difference d
, outlier^
(n-1) =0.08
(SD of the mean differnece)
operator ^ inspector^]
» 2 I t. 2>" xr ' 0 yr J
n
differenced S
random/systematic error7} ^i .&.§]-£}-.
^ operator ^ inspector^
S. 3-1^] operator-inspector^) -T*^"
«.
- 8 -
SDBAR%(
3. 3-2^r operator-inspector
0.000982+ 0.0QQ972)5
= 0.0006758
Percentage*
= 100* 8(d) = 0.0006758 x 100 = 0.06758c»l
^= ~d{%)7\ sl-(propagated)^
3. 3-2
Variable
U-Conc(WT%)U-235 (WT%)
DBAR
~d{%)
-0.79
SD %
0.08
%RAND(0)
0.098
%RAND(I)
0.097
%SYS(O)
0.018
%SYS(I)
0.021
SDBAR%
S(dj%0.06758
S.
s(dj
(KfiO=85.346cdot {0.06758} over {100}= 0.0576M
- 9 -
5. 2-2
Variable
U-Conc (WT %)
U-235 (WT %)
Sample
size N
5
5
X
(XBAR)85.346
Y
(YBAR)86.024
D
(DBAR)-0.6776
aid)
SDBAR
0.05768
t-TestDBAR/SDBAR
Sig.
4.
7}
~d 7}
t-test
aid)
fe operator-inspector^:
•operator-inspector *H(d)7 r
operator-inspector ?>^ difference
. S.
3°]
0.003iH}
= I g_ i = i 0-6776aid) l ' 0.05768aid)
t valued
a 2-34
= 11.74
- ^ \t\ =11.74>3 1-
"Yes"6!^. °lfe sfl't stratum^
S\B.S. 3* a test
operator-inspector^:«=fl
2-3
Variable
U-Conc (WT %)
U-235 (WT %)
Sample
size N
5
5
X
(XBAR)85.346
Y
(YBAR)86.024
D
(DBAR)-0.6776
aid)
SDBAR
0.05768
t-Test
DBAR/SDBAR
11.74
Sig.
3 sigma
Y
- 10 -
4. ^^$SLX} (Measurement Error)
Hr 3.7)} -
true value
l # true valueS-^-E]
4 ^ paired operator-inspector data
. Paired operator-inspector datal:^:
outlier ^ ^ - 1 - 3 4 * M outlieri «H^s]^ data#^
4 . Paired data* °]-§-§H operator % inspector^
5>T, *„, Sysm 7fl-ar*H, °l^r #°1 ^ # ^ -2.2r!-ir rs<9 ^(performance
value)6! el- ^ 4 . ^ 1 ^ ^ i^Vl:^: paired-data^ *]& %>>}, ^ IK trend) ^ ^
rejection
^«>| 1 operator-inspectoral paired data-I- °l-§-^r°i random
systematic error!
7\. Random error estimation
a 4 ^ outlier7l- J\7\% operator/inspector^ paired dataoM, data7r
group # ,
groups
& 4^} Q^g- ^ t t operator ^ inspectoral paired data°ll Grubbs'
methods ^-§-*r°i operator-inspectoral random errorlt ^^§V^r ^^V-lr-i: Q
"£z\, Operator/inspector data^] A &•§: r^ ^^r(logarithm)S. ^
- 11 -
5. 4. Paired data
CD
©
Group
11223
Oper. $:
1497.13
4375.64
327.57
3300.97
924.15
Ins. Jt
1475.15
4412.20
326.58
3304.60908.40
x ,=Ln(Oper)
7.311305
8.383808
5.791702
8.1019726.828874
y ,=Ln(Ins.)
7.296515
8.392129
5.788675
8.103071
6.81185
group 1 operator^}- inspectoral
group
xs> = group H operator ^ inspector•£)
= Operator random error ^Q
= Inspectoral random error
= group
group
5. Data^
g(group)123
(gW Op.^S)7.8475576.9468376.828874
yg
(g1! Ins.^5)7.8443226.9458736.811685
m g
(groups # ^ ^)221
Grubbs' method^ operator ^ inspector variance
S H operator ^ inspectoral grQ-Br T2
operator°ll t}]^: variance-It- -i2-^-^
£.4, 5 ^ data
- 12 -
[ m2*i-(Z^«>2/»i,]/( mg-\)
„ 2
- 7=1 * » " " 2[ ~ (2-1)
[ (7.311305)2+ (8.383808)2—(7.311305 + 8.383808)= _______
= 0.575131
Tfl JEjEt], operator data^l tfl^r°i A group^S. _--_-
i = 2.668674,
[ = 0 ( F31°l zero7f
£ inspectoral tfl^r variancel-
Hi[
vVl2~
(2-1)
[ (7.296515)2+ (8.392129)2 (7.296515 + 8.392129)= _____
= 0.0.600185
-2.678214,
Operator£}- inspectoral ^^l : covariance#
2, Xgi ygi-( 2 «»• 2 ygi)l mg\k ntg-
i=\ t=i i=\ j /
- 13 -
= 0.587525
V212 = 2.67344
Group g i 31$ arX \
= V u - F112 = 0.575131-0.587525=-0.012394
= V I 2 - VU2 = 0.01266
- Vgl2
2 = V " 2 1 - V212 = - 0 . 0 0 4 7 6 6
= ^ 2 2 - 1 212 = 0.004774
Random error°ll tfl^ Grubbs'
_ . mg-l) - a rgj
<?%= g G ; i = 1,24
(2-l)(-0.012344) + (2-l)(-0.004766) _= -
2 —\= 0.008717
. Grubbs'
- 14 -
Grubbs' ^3*1 X l t f ^ ^-g-^ *r %A. ° 1 ^ £°1 Grubbs'
^^-°1]^ CELEX ^ ^ ^ 1 ^
^-S. operator-inspector random error*
fe Grubbs' methodic 3 1 ^ ff2^, F^ ^ F r i2 ^ 7 }
rl-V 6
=> S=-0.00858+0.008717=0,000137
0=1 , 2)
gl _ (2-1)(n.S7fil31) + (2-iK2.668674) + 0 — 1 6 o 1 0 0 o 5
=7% Li
(0.600185 + 2.638214) = L 6 3 9 1 9 9 5Li
mg-l) V g l 2
S12 =
n
0.587525+2.67344 _
- 15 -
(1.6391995-1.6304825) I " 1
(1.6219025-1.6304825) J
Q
Case 1 : -1 < Q < 2
„ 2 _ „ 2
Case 2 : Q < -1 a ^ Q > 2 ^ 3 - f
S2,= (3S S l2 ) / | S i - S f l
Sxy=S( 5 l2 + 2 s 2
2 ) / ( 5 l2 - 52
2), ( S l2>
= S(2 sy2+ s 22 ) / ( s 2
2 - S l2 ) , ( s2
2>
Q ^ 7 \ - 1 S . 4 cl 4 ^ r -62.6277^1 S.S. Case
Case 2 ^ 1 4 ^ S\%:
2 3 • (0.000137) • (1.6219025) nJ ~ 11.6391995-1.6219025 1 - 0 .
s 22 >
Sxy=S(2 5 j 2 + 5 22 ) / ( 5 2
2 - S l2 ) = 0.0386756
f(v)»
= [0.000137 y2 + 0.000274^+0.0385386] " 0 5
CELE ^ ^ ^ l - ^-^j-H-S. CELECConstrained Expected Likelihood
Estimator) -£*!- ^ ^ ^ - i - ^ -g- t l4 . CELE method*
- 16 -
^ 2 0 , ^ 30
n^r^l ^^fl^ife- Simpson's rule-i:
f °10= Kv)dv
J — oo
20 = §lAV)dv= 7130= f~Av)dv
j== J±jol\ A io ~r A 20 + -A 30) for ]=Z, 3
Aio4 Aso r ^ ^ - T 1 ^ : 0 ] AA ~, + ^ ^ 1 4 , Simpson's rule^:
l ^ 3000 interval^
^ 1000 intervals.
IO, ^
io = f Av)dv= f [0.000137 v2 + 0.000274w+0.0385386] ~ldv = 710.11*/ —oo J —oo
= f1AvVv= [\o.000137 v2 + 0.000274y+0.0385386] "Vy= / ^ 25.82585
[0.000137 v2 + 0.000274^+0.0385386] ~'rfv % 632.26415
Aw, A2o,
25.82585
( A10+ Aw+ ^30) ~ (710.11 + 25.82585 + 632.26415)
- 17 -
632.26415AM( A10+ Aw+ Ago) ~ (710.11 + 25.82585 + 632.26415)
CELEX
a\=vS [ where v = l Aj 7° + A 3 ) 1
CELEX ^ ^ ^ ] ^
= «/(o)fifo ^ 12.89°ls>/0
at= I (0.018J75TXJ2.89) + Q.462H38)X(0.000137) =0.0000646
o\=(l-v)S
a 1= 0.0000724
S operator ^ inspectoral random errorfe
V ^ i 2 = ^0.0000646 = 0.008073- 0.80% relative error
^ ^ = V <?22 = ^0.0000724 = 0.0085088-0;85% relative error
random error ^^-fe 5. 3- 1 operator-inspector^ Sxr(%) ^
A A A
- 18 -
4 . Systematic error estimation
Grubbs' method!-
systematic error!-
^ ^ t b operator
. Random error
inspector £]
Group
1
1
2
2
3
Oper. &
1497.13
4375.64
327.57
3300.97
924.15
Ins. &
1475.15
4412.20
326.58
3304.60
908.40
#,-=Ln(Oper)
7.311305
8.383808
5.791702
8.101972
6.828874
y , = Ln(Ins.)
7.296515
8.392129
5.788675
8.103071
6.81185
S(group)
1
2
3
xg
(group H
Op.^5)
7.847557
6.946837
6.828874
y*
(group l!
Ins.3! S )
7.844322
6.945873
6.811685
m g
(groups
#^ ^)
2
2
1
ic error)^1 ^ £ r operator^ inspector
Grubbs,
DODGRU ^ CELEX
fe Grubbs ^ A
r <%*} CELEX
si = Systematic error variance (between inspections) for operator
& = Systematic error variance for inspector
Operator(x) ^ inspector(y) •§•'&, operator-inspector co-variance#
- 19 -
(3-1)= 0.3104875
g)2lG\l(G-l)
J
(3-1) = 0.3152594
g= s= e=
=> K ^ , y) =0.3128348
7fl si systematic error ^^r^ l Grubbs'
I =
where c = m g1/G for operator
y) - ccr where c= 2 m g l/G for inspector
#=1
l " + "c —
C
23
si = V(x) - V(~x7y) - ca 2rl=0.3104875-0.3128348- | (0.0000646)=-0.0023904
<r%= V(yj- V(xy)- ca 2^=0.3152594-0.3128348-| (0.0000724)= 0.0023763
H-S. CELEX
CELEX a\
- 20 -
= ( a I + a |)=-0.0023904+0.0023763=-0.0000141
Case I : 5Q>0
Case E : 50>0
V(x)-V(x,~yj>0
vG)-vG,~yj>o
Case IE : S0<0
either V(xj-
or V(yj- VG,~yj<0 (1-
3 case^l^i ^ ^ ^- f S . random error ^3J*H ^r-g-^ CELE
tfl 1 s)iii+71- # ^ ^ 1 4 . 4 Case
Case I : > A
n by G
S2X by
S xy by V(x,y)
S by s0
a\Q o%$\ CELEXo
- 21 -
Case n : > ^ Av)°\)
n by G
S by Sx
si by F-
where F=[ S x + 2c( a \ + a \)}l[ S, + 2c{a2A+a %)]
S w by 2 %
Case m : > f-^r Av)^} ${x}s\^ €
n by G
S^by V(x)
Sxy by V(x,y)
S by 5 2, where
S2=V(xj+V(y)-2VCx,^)
ffd^ < 7 | ^ CELEX ^
o\= vS2+Ca2rl
Case n # 4^1
So = -0.0000141 < 0
(VG5-VG,~y))= 0.3104875-0.3128348 = -0.00235 < 0 7}
Case ffl<fl ^ ^ ^ 1 ^ 4 . Xy)°1] Case
- 22 -
Av)=[ S2 v2 + 2(V(x,y)- V(x)2)- V+ V(x)2)]'
S2= V(~x)+ vG)~2VCx, ~y) = 0.0000773
G = 3
• Av) = [0.0000773 v2 + 0.0046946y+ 0.31048752
/ o = f vAv)dv = 2.846429
^ i o = Av)dv = 703.2915J — oo
r 1
A2Q= Av)dv= Ix = 5.714649J o
-430= {~Av)dv = 241.939651
A2= , A , ^ a , A , = 0.006009
= 0.257413j
. Case m^l^ ^2 ^ ff|c] CELEX ^ ^ ^ 1 ^l-it^^ *kA A
2 ^ = (0.257413)(0.0000773)--| (0.0000646) = - 0.000023169
= (l-v) S2+ Ca\ = 0.000009135
a2& ^-i- ^-ai Case n #
Case n^] tfl^slfe- ^ ^ 1 ^ S71- S ^ S . rfl^SjPLfi Si - 1 :
- 23 -
si = F[ a l + c(o2A+ o2a)] &£ ^ H ^ «-4. ^ Si
S\=
- ^ ) + P ^ p where P=Prob( F^^Xc+0.0036) v2l vx)
vP &•& ^ ^
Uv) &•£
v i = V(d) = VG)+ VG)-2VG,~y) = 0.0000773
v2= G2r= Ori+ Oa = 0.0000646 + 0.0000724 = 0.000137
W i = G - l = 3 - 1 = 2
n2= 2J ( mg-\) = (2-1) + (2-1) + (1-1) = 2
£=max(l,6.19-0.42 «i) = max(l, 6.19-0.42 x 2) = max(l, 5.35) = 5.35
- 24 -
io = knx = 5.35 x 2 = 10.7
2o= n 2 if k=l
= ( 'n l o + l ) ( l - c ) / c if
^*V k &°1 liL4 an), c
-J- + 4- +i
= (10.7+1X1-f)/f =5.85
Ir-i: °l-g-SM
lHS. t; §H 0.0036-i-
-0.35 ln(t;-0.0025) + 33.2 In (18-v)
• L( v) = -0.35 Ln(y- 0.0025) + 33.2Ln(18-i>)
+ (1.925) Ln(w+ f) -8.275 Ln 1 +0.0008015 (t/+ | )
0.00082711
• L(0.0036) = 93.426431
= exp[L(t;)-L(0.0036)]
L(0.0036) = 93.426431
. 7 O t
- 25 -
o= vt(v)dv•J a
= f Kv)dvJ a
<>H, integral^ aJ*J3J: a ^ 0.0036°!^, ^tfl^t b ^ tfl^f^r 4 ^ . 4 3 .4 . IAEA
°flA:l^- ^ ^ ^ A S b &•%: 10-O.3- ^"-b4. Integral ^l^i^-cr random error
estimation's ^ 4 ^:ol Simpson's rule-8: AV-§-*}^, ^-& ^Q-%: ^ 1000
intervals. -sAl?!:4. °14 %=£: *Q^S>_£. IQ,
•0.0036
'10
.0.0036
'10
r 0.0036
• / 0 = vKv)dv= 0.0087179
•J 10
r 0.0036
/ i = Kv)dv= 0.05078
f vp= 0.1716798 1
vo( arl2+ a^2)%: -A]^\7) ^ \ ^ * ] ^ M v0
vo = 0.0036(1 -P) + P- vP where P=Prob( F^,Ml>(c+0.0036) v2l vx)
• P = P r o 6 ( F ^ . n l > ( c + 0 . 0 0 3 6 ) v2l vx)= Pro6( F 2 , 2> 1.187924) = 0.457
• • vo = 0.0036(1 -0.457) + (0.457X0.1716798) = 0.0804125
• • Sx= t;0( <J r i2+ <J^2)
= 0.0804125(0.0000646 + 0.0000724) = 0.000011017
Si &€ ^ 8 . * 5.3. Case E
- 26 -
si = F-
where F= [ S x + 2c( a \ + a 2^)]/[ S „ + 2c( <r * +
5 ^ by ^ ^
[ S
[0.000011017 + 2 • •§• (0.0000646 + 0.0000724)1= —L a J_ = ^ 1435537
[-0.0000141 + 2 • | (0.0000646 + 0.0000724)]
• • si =i =
= (1.1485537) • [-0.000023169 + 1 (0.0000646 + 0.0000724)]
= 0.000077446
= J- (0.0000646 + 0.0000724) = 0.00009133
Case n^ ]^ f- Xy)°ll ^^1^1^ ^^1-?! n, Sh s \
Av)
[0.000011017 v2 + 2(0.000091333-0.000077446)^+0.000077446] " L 5
= [0.000011017 w2 + 0.000027774v+0.000077446] ~L5
Case
- 27 -
/ o = I «Xw)fifc = 498103.2J 0
A10= f AtOafc; = 7429555j —00
r1
^ 2 0 = Av)dv= Ix = 1108331•/ 0
^ 3 0 = fC°Av)dv = 1525268^ 0
A 2 = , ,, , A™ , . , =0.110138
A ? n -x = 0.15157V -A 10+ -<^20+
=(0.20107)(0.000011017) = 0.000002215
• • e% = (l-v) Sx
= 0.000008802
^ # ^ ^ L S . operator^- inspectoral systematic error
si = V 0.000002215 = 0.0014883-0.149%
= ^ 0 . Q000088 02 = 0.0029668 0.297%
- 28 -
6. Delta Value (Relative Standard Deviation)
operator-inspector data
(historical data)l-i- °l-§-^: stratum1! -f
Operator^- inspectoral A stratum^
^^^-y]o|] rc|-5f yJ- z\ =^^^o\ ^ ^ ^ 4 . Stratum^ operator-inspector
#•§- °l-§-^H ^ ^ U - ^ ^ S . -S-tfla^^^(relative standard deviation)*
4 . Delta valued ^ ^ S . § ^ ^ r l - 4 ^ ^ ^ -8-°iS. IAEAfe delta value*Al^^fl^ ^ r^ ^^(sample size calculation)
(reject limits) -£^ -< 1 l-§-«V4.
historical datark ^-lLi|^l ^ ^ -y-^|s|-^ International Target Value*
^ delta value* # # ^ 4 . Delta value*
random = Jd^ + 5"1
systematic = y/S^ + Sys
total = ^(random )2 + (systematic )2
- 29 -
7. Balance Evaluation : MBE)
o\]
^ ^-g- 2:7]
. IAEA
^ #^*r^3§7]-(Material Balance Evaluation : MBE)
Stratification, , Difference ^ IMUF(MUF-D)
Unaccounted For : MUF)
Difference : SRDH
# ^ (Material
! (Shipper / Receiver
4.
D'iverslon o('M*
[ Dila F « ItlflcHlo n
tN o D a ta Fa Is if ic • t l o n
I D i v e r s i o n I n t o M U F
- 30 -
Stratification
Stratification^
, KMP,
31 Jl Hl r
, # ;§7l#3H(Material Description code),
^ U/Pu U= f-41 ^ N ^ £ £ 4 . Stratification ^ £
l S 7^]^ ^-g- |<H6> «r^f ICR
lS(Material Balance Table : MBT)1- ^ W . MBT
AS. PB, X, Y ^ PE £
313=!- (MUF)
= PB + X - Y - PE (PB :
(ICR),
MUF£] (random variable)7l-
^ ^ ^ S . MUF
, X : »}:<$, Y : #%, PE : ^ 31 uL) S.
MUF
MUF M U F *
MUF MUF
Strata^,
. MUF
stratum 1 ^ # ^ < ( batch ^r ^ item
- 31 -
random systematic 4 0^4. zj-
stratum^ error propagation
covariance^ tfl^F-jA£ Sl*]S
. MUF £#•§- ^ H r
^ S -71
where
4-8-4
X is the total element mass in the stratum
Sn is the random error for operator
Sa is the systematic error for operator
n is the number of operator's measurementsto estimate X
%• £*};•& A stratum ^ ^ > #
Vaf[MUF\= 2S — o
="I VariMUF]
^r°) true MUF
C= fa-tf) x
zero^l^l
H0:Prob(obs.MUF>C\true.MUF=0)=a2\-
^ %£.£. ^^^(cr i t ical
error*
MUF>3x
0.99874 §-^§1-4 -4
MUF*
Lower limit L = MUF -
^ - f ff = 0.0013 £^r (1-a) =
MUF ^ 7 > ^ MUF, MUF ^ ^ , true
'1 o )
Upper limit U = MUF + * ^ x GMUF,u - 2 ;
0 (zero)* ^ r ^ ^ 45}
- 32 -
Case
1
2
3
Ordering
0 L U
L U 0
L O U
Description
The true MUF is statistically significant
The true MUF is statistically significant.
(This is a negative MUF, could indicate human errors or
inadequate)
The true MUF is not statistically significant
case %q<>\ o.£. true MXJF7} zero^
l - ^ MUF *M
^-H, SRD(Shipper-Receiver Difference)^
MUF
trueMUF=0
MUF > 0
Odering
100
50
y
y
L-O-M-U
-100
50
y
n
L-M-0-U
100
33
n
y
0-L-M-U
-100
33
n
n
L-M-U-0
MUF
a. 64 stratum^ batch ^r, item *r, A
- 33 -
6.
Mat BaLComp.
PB
Increases
Decreases
PE
" " '
Stratum
PDUFSC
Total:UF-PL-Total:FFWSTotalFRPLSCTotal
Number
of batches150300800
1,250250100350
1,000150
1,1501,000
700550
2,250
Number
of items1,500
300800
2,600250
2,0002,2504,450
150
4,60012,00015,0001,500
28,500
^•x-avg -~~t
kg ofJJ-2352.0
50.01.0
50.00.5
5.00.5
0.10.50.7
MU =
\
ki; of I '-2353,000.0
15,000.0800.0
18,800.012,500.01,000.0
13,500.022,250.0
75.022,325.0
1,200.07,500.01,050.0o,-sn o
22 .11
Or.
0.00300.00250.0150
0.00250.0020
0.00200.0700
0.00200.00200.0150
0 "
0.00250.00200.0100
0.00200.0020
0.00200.0700
0.00200.00200.0100
Var(MUF)=
ka2 of U-235
Stratum*!
ndso
2)
Var{s)= X2 -n
» = 30002 • ( Q - 0 0 3
stratum0!]
150
powdeH
+ 0.0025 2) = 56.8
S. 6 . o]
nfl A stratum^!
VaAMUF\= S Var[Ks)] = 56.8 + 904.7 +...+110.7=341.8S
= 63.3OMUF=
- 34 -
6-1
Mat. BaL
Comp.PB
Increases
Decreases
PE
StratumPDUFSC
Total:UF-PL-Total:FFWSTotalFRPLSCTotal
Number
of batches150300800
1,250250100350
1,000150
1,1501,000
700550
2,250
Number
of items1,500
300800
2,600250
2,0002,2504,450
150
4,60012,00015,0001,500
28,500
1— _
5 xTavg .
kg of U-2352.0
50.01.0
50.00.5
5.00.5
0.10.50.7
;>• x • ' .
kg of U-2353,000.0
15,000.0800.0
18,800.012,500.01,000.0
13,500.022,250.0
75.022,325.0
1,200.07,500.01,050.09,750.0
M UF= 225:0
' 8r.
0.00300.00250.0150
0.00250.0020
0.00200.0700
0.00200.00200.0150
"> 8 s o •
0.00250.00200.0100
0.00200.0020
0.00200.0700
0.00200.00200.0100
Var[X] .
kg2 of U-23556.8
904.764.2
1,025.7628.9
4.0632.9
1,982.227.7
2,010.05.8
225.3110.7341.8
Var(MUF)= 4,010.4
-- \ — ^
MUF>3x aMUF
MUF = 225,
> MUF = 225 > 3 x 63.3 = 189.9 = aMm
7\ ^B.3, MUF °<J= r 7 l4 t l :4 . ° 1 ^ true MUF7>
MUF=225 kg^l operator^
9r, <m&\ MUF <$<>} 150 g
MUF = 150 kg < 3 x 63.3 = 189.9 kg = aMUF
°]E.3, true MUF^ z e r o i 4 3.x]
MUF
3LJL
M U F <$•&
- 35 -
oMUFo\) True MUF
Ca-trueMUFG MUF
20% ^ ^
kg-U235<H xfl, 1 ^ errorS
) w h e r e Ca= ta-a)- aMUF
-f (1 SQ=75kg^ U-235)olJi,
ff %
0.13
2.5
5.0
3
2
1.65
( 1 - /8) %
3.5
20.7
32.3
fe fa-,)!- 3A
• operator-inspector differenced
. 5Et!:, Safeguards criteria^
50 %S. fl-^^-ui # 4 . 50 %^
0MUF=25 kg-U2357|-
trueMUF
MUF 3g7r
23-
3.5 %
^ throughput JEfe
.3 <
$B= 67 kg-U235S
s)ES . operator
- 36 -
9X^-
y>. Shipper/Receiver Difference (SRD)
SRD^ ^7} £ ^ E]- AJ^^.W.E^ a><ysi ^ . g - ^Al-sV ^ shipper's data
4 ^-^lt 3-f #<d*Hr 3 H 4 . #, SRD7> «SM§1: 3-f SRD <# 3 1 ^
SRD(DI) = (shipper's value) - (receiver's value)
#e* l <fl>H SRD# iLjl«r^l ^-i- ^-f SRD7> ^ ^ J € °<M MUF
£ l operator^ €*1 SRD*
. IMUFdnspector Estimate of MUF)
^ # ^ ^ 1 partial defects Sfe bias defects* #*l*l-7l ^ ^ H IAEAfe
D ^f-^1*
MUF } ^
^^«rfe ^ ^ - S . D = MUF - MUFS ^ ^ ^ 4 . ^ ^ ^ stratum^^
^ ^ • ^ ^^>7} $inf^ o]^. bias^i ^ 4 ^ - i - ^ 7KV 27111- ^ Jl
D
stratum^ ^ ^ l f e - Scaling factor^
'*" o(vk)
Where o(s) : Operator declared stratum mass (stratum total)
o( v k)"". Operator declared mass of substratum verified by the inspector using
method k
^^^Hl(method) KS. # ^ ^ r x& °<J=-i: yj | H S *>^ method kS. $&&
- 37 -
stratum^ tfl^ inspector 4 ^ ^ i(s\ k)
i(s\ k)= rk;
inspector ^ ^ ^ ] # ^^§1-7] ^ t f l^ fe stratum
#wo>^ ^ S weighting factor^ ^-
Weighting factor* ^°\% ^- inspector7l- stratum1! ^ ^ ^ - i :
NDA« A]~g-s}$-g- ^-f, DA4 NDA* k={l,
weighting factor^ T 2 - ^ ^ "^l^r 4-§--
w\=- VariKs I 2)1{ VAR[I(s | 1)]} + { VaAKs I 2)]} '
Va7\Ks\ 1)1
Weighting factor* ^-^rfe ^ ^ ^ ^ ^ r -§ -^ variance T 1 ^
IMUF^l variance ^^}^ :8•^d\}*] weighting factor
. # , weighting factor ^}^ variance ^ ^ r ^-^^
yjlk)2- 82rk]
t^tt inspector
IMUF= ES o
- 38 -
°>. IMUF &<&
Inspector ^ 3 MUF7]- f-7ll3^-S zero^r
^ MUF £4r-i- ^l^^-^o> ^ 4 . ^ ^ A ^ C . ^ 3 stratification
4 error propagation ^ - i : 3-8-*rfe 4^°1 ^ ^ r 4 . Stratum # M
inspector ^ ^ £-# ^ , < r w l : ^ § r ^ ^ ^ ^ 4 ^ 4 ^"4.
S %j\k)2' d2rk]
J—
Where 8rk '• Inspector random error for verification method k
dsk '• Inspector systematic error for verification method k
i W inspector
Var[MUF]= 2
7l#t!: MUF^ t-test^
. MUF^] random variable^ ^ S zero# #fe
£r IMUF7>
$14^ ^ ^ 4 4 ^ 4 . # , ^T^l^^S. HO : IMUP=0
IAEA^ # ^ ^ 1 ^71-s-^^; ^-8-71^^ ^ 1 4 &^% I r^-^H 4^-^1-fe^ 5a
JLJEL3. {l-a)= 0.997^: ^d^§}<^ «^# ^ ^ ^ ^-§-§H, ^l^^-^rl : MUF±
MUF7} 3<riMUpa.4 ^ ^ : ^-f 7]-^^l HO : IMUF=0* ^ W H . 5 .
inspector MUF7> operator MUF l- x}°}7} § i 4 ^ ^€r^r tfll ^ 514.
- 39 -
MUF7)-
£• ^ 6 1 \+4 . IMUF7V 3
MUF £Efe bias defectl- f-«r
3.x] T?V MUF7> zero-S-4 2}-^
IMUF7]- zeroJi4
^ O ] J I MUF71- 3
^ operator Sfe inspectoral
Y e s
>
<L IMUF > 0 Z>
Yesf \
lnspc.i(.>r Ml 1{••« atci than / n o(IlMISHMl IllKIUUll
Mill cir bus (Mitts "
No
f
Op. / Inspmeas. problems
No
IMUF is zero
Inspector MUFislike
Operator MUFnot d iff. from zero
4.Inspector
4.
^ stratum^ tfl^ IMUF
Stratum^ -fr^^-^ ^^>§>fe
± 3 oKS)W 0(s) = (operator
inspector ^ ^ ^ | operator '^^
^ -S co = (Stratum^ tfl
^i^:)-i: a]H§>^ o(s)7V
4 -4^ ^ i :
Inspector estimateofstiutum total
tiiffci- fromoperator's cleclat ation
• Inspector estimateof stratum totalis the same than
operator's declaration
- 40 -
*}.
operator-inspector differencedd ^ }
= o(s)-i(s | Ar)
, stratum^ Slfe ^ i ^ l homogenous*}4^ ^7l difference -§-^^r
= rk- d(vk) [where, </( w*)= £ / x , - y;-1 k)]
Q £°] ^ ^ € ^r &£}. -n-§-tt £ ^ ^ ^ ^ ^ ^ 1«fl stratum totals
operator-inspector differenced
= 0(5) - I(s) where, O(s) =^X,-, and i(s) = S w * • Ks I A)
}. Bias ll 4€- MUF ^ ^ - i - 4<^}7l ^§}<^ D ^ ^ ^ 4 ^ -
D = I l A c - ZXS) where A=+l :
A c = - 1 :
D ^-^
-5d^i€ MUF<fl bias7> zero °AA ^ ^ - * ^ 4 ^ 7 1 ^§}<^ D
. D
= Var[ ^X{- ^wk-I(s\ k)]
Var[£Ks)]= j^x ) • S 2ro+( ^ x t)
2 • 82 • 82SO
- 41 -
D
Var[D]= 2 VariLKs)],
od=y/Var(D) A
D
D
defects *§•&
o]-g-*v
. D
D
4 ^ MUFi bias -fr^f-I
^- MUF ^ MUF 3*1- ^ ^ 4 ^r°l 3
M 3(7D ^t^-4 4 4 ^ MUF« 1 bias7]- Stfe
3<7C ^ S . 4 - ^ - f MUF7> bias£]^ bias
operator SE^ inspector ^ S M ^ I H
^ ^ . H , D
stratum
Y e s
MUF IS BIASED,diversion through. bias defects ?
Op. / Inspmeas. problems
IMUF is notbiased
- 42 -
1. IAEA, Statistical Concepts & Techniques for IAEA Safeguards, Fifth
Edition, IAEA, 1998.
2. E. Kuhn et al., Destructive Analysis and Evaluation Services for
Nuclear Material Accountability verifications, IAEA, 1996.
3. IAEA, International Target Values 2000 for Measurement Uncertainties
in Safeguarding Nuclear Materials, IAEA, 2000.
4. IAEA, ICAS Introductory Course on Agency Safeguards, Module 7,
ICAS/40-7.1.5/1, IAEA.(H3-*m)
5. IAEA, Statistical Analysis of Sample Data, IAEA, 1999.(S^r
6. KAERI/TR-1554/2000, " l - ^ ^ M W ^ ^ f l i t a ) " , 2000
- 43 -
s.
IMS
KAERI/TR-1600/2000
(II)
2000. 6
sfl 21 x 29 cm
IAEAfe #^ ;r^]3g7V(Material Balance Evaluation : MBE)* operator ^ inspector
l^Bflo] b i a s ^ ^ ^ . ^
IAEA7>
operator-inspector difference* <>l-§-SH
, Random error, Systematic error, n ] :D * i , MUF-D
BIBLIOGRAPHIC INFORMATION SHEET
Performing Org.Report No.
Sponsering Org.Report No. Standard Report No. IMS Subject
Code
KAERI/TR-1600/2000
Title / Subtitle Development of Material Balance Evaluation Technique(II)
Project Manager and Dept. Byung-Doo LEE
Researcher and Dept.
Pub.Place Taejon Pub. Org. KAERI Pub.Date 2000. 6.
Page Fig.and Tab. Yes(O), No( ) Size 21 x 29 cm
Note
Classified 0pen(O),0utside( ),_Class Report Type Technical Report
Sponsoring Org. Contract No.
Abstract (About 300 Words)
IAEA considers that the evaluation on Material Balance is one of the important
activities for detecting the diversion of nuclear materials as well as measurement
uncertainties and measurement bias. Nuclear material accounting reports, the results of
DA and NDA, the summarized lists of material stratified by inspector are necessary
for the material balance evaluation.
In this report, the concepts and evaluatuion methods of material balance evaluation
such as the estimation techiniques of random and systematic errors, MUF, D and
MUF-D are described. As a conclusion, it is possible for national inspection to
evaluate the material balance by appling the evaluation methods of the IAEA such as
error estimation using operator-inspector paired data, inspector MUF(IMUF) evaluation.
Subject Keywords (About 10 Words)
Material Balance Evaluation, Measurement errors, Random error, Systematic error,
MUF(Material Unaccounted For) evaluation, D(Difference) Statistics MUF-D