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The effect of inspection and repair on the size distributions of the weld imperfections in nuclear power plant pipes
Nuclear Engineering and Design 60 (1980) 395-399 O North-Holland Publishing Company
THE EFFECT OF INSPECTION AND REPAIR ON THE SIZE DISTRIBUTIONS OF THE W E L D IMPERFECTIONS IN N U C L E A R P O W E R PLANT PIPES Jarmo R A U S S I * Institute of Radiation Protection, P.O. Box 268, $F-00101 Helsinki 10, Finland
Olli J.A. T I A I N E N Department of Energy Technology, Lappeenranta University of Technology, P.O. Box 20, SF-53851 Lappeenranta 85, Finland
Received 27 May 1980
The weld defects appearing in the pipes of the main steam system in a BWR power plant were studied. The effect of inspection rejection and repair on the imperfection size distribution was analysed. The size distributions before and after the inspection rejection as well as after the repair procedure were of the form a + b/x 2, where x is the imperfection size and a and b are coefficients. The portion of the rejected defects had the size dependence near to the form of the cumulative Gaussian function. The effect of repair on the initial size distribution had the form of the cumulative Poisson distribution. The butt welds of the pipes were welded with the T I G and the shielded metal arc welding methods. The root pass was welded with the T I G method using the wire of E70-$3 and with argon inert gas on the root side. The electrode for the surface beads was A S T M E7018. The X - r a y inspection was carried out according to the Finnish Standard SFS 3207 with class B using films of the classes II and III. The X - r a y radiographs were ranked along the I1W Collection of Reference Radiographic of Welds. According to the quality requirements the weld joints should have at least the number 4 (blue) in the scale of 1 • • • 5.
1. Introduction and inspection data The failure probabilities of nuclear power plant components can be estimated with a method which is based on the defect size distributions [1]. In this work the effect of inspection and repair after inspection on the imperfection size distributions of pipe welds is analysed. The data used was obtained from the X - r a y inspection of the weld joints in the main steam system of a B W R power plant. In order to avoid secondary factors affecting the study the inspection data was limited to the X - r a y picturds of 114.3 x 8.56 mm pipes. The seamless pipe material was SA-106 Grade B carbon steel for high-temperature service according to the A S M E Boiler and Pressure Vessel Code, Section II. The properties of the base material were adapted to meet the use purpose by limiting certain residual element concentration. The material chemical composition is given in table 1.
Table 1 The chemical requirements of the pipe material
* Present address: TVO Power Company, Kutojantie 8, SF02630 ESPOO 63, Finland. 395
Element
Composition w/o
C Mn P S Si AI, average/max.
<0.25 0.29-1.06 <0.048 <0.05 >0.10 0.015/0.020
396
J. Raussi, O.J.A. Tiainen / Effect of repair on the size distribution of weld imperfections
Table 2 The number of imperfections in all studied weld joints classified according to their size before and after inspection rejection and the subsequent repair Number of imperfections Imperfection size (mm)
Before inspection rejection, Yi
After the inspection rejection, gi
After the repair, h~
0-1 1-2 2-3 3--4 4-5 5-6
173 22 11 5 4 1
169 20 6 2 0 0
189 24 7 2 0 0
6-7
0
0
0
%-8 8-9 9-10 10-11
1 1 1 0
0 0 0 0
0 0 0 0
The imperfection types entered into the data of this study were pores, slag inclusions, lacks of fusion, lacks of penetration, cracks and tungsten inclusions. The weld defect sizes were measured in the film plane and all observations are presented in table 2.
2. Imperfection size distributions On the basis of the imperfection size classification in table 2 the best fitting functions were searched. The functions of imperfection size, x, which were fitted with linear regression against the inspection data were: a +bf(x) a exp(bf(x)) af(x )b N(x) =
a + b/f(x) 1
(1)
a +bf(x) x
a + bf(x) a + b ln/(x), where a and b are fitting coefficients. The function f ( x ) had the form
x
f(x)=
x~
(2)
(In x) 2. Table 3 shows the ten best fitting curves, y(x), for the imperfection size distribution before the inspection rejection. Table 3 shows also the square of the correlation coefficient, r 2, of the linearized fitting function and the square sum of the deviations between the fitting curve points and the observations. These quantities describe the goodness of the fitting. In table 3 the best fitting curve before rejection is y ( x ) = 1.359 + 42.977 mm2/x 2 when both r 2 and the square sum of deviations are taken into account. The curve is presented in fig. 1. Similar fitting was also done for the imperfection population from which for rejecting classified imperfections were taken away. Table 4 gives the fitting curves in this case. The best curve is g(x) = -0.772 + 42.488 mm2/x 2 which is shown in fig. 2. The imperfection size distribution was also determined when the rejected defects were repaired. Table 5 gives the ten best fitting curves in this case, the best being h ( x ) = -0.7835 + 47.537 mmZ/x 2. This curve is presented in fig. 3.
J. Raussi, O.J.A. Tiainen / Effect of repair on the size distribution of weld imperfections
397
Table 3 T h e t e n b e s t fitting c u r v e s f o r t h e i m p e r f e c t i o n size d i s t r i b u t i o n b e f o r e i n s p e c t i o n r e j e c t i o n n
F u n c t i o n y ( x ) (x, m m )
r2
~ (y(xi) - yi)2 i=I
1. y = 4 8 . 6 7 6 3 2. 3. 4. 5. 6. 7. 8. 9. 10.
y y y y y y y y y
= = = = = = = = =
x ( x 2 ) -0'927623
1.35887+42.9767/x 2 -17.4133 + 91.3568/x 8 7 . 8 5 4 4 - 4 9 . 7 2 7 5 x In x 7 5 . 3 8 5 4 - 10.5625 x x 53.6561 x e -°-51°49x 35.4029 - 2 3 . 9 1 1 7 x l n [ 0 n x ) 2] 6 1 . 2 2 1 4 - 1 5 . 1 3 8 5 x (In x ) 2 48.4986 - 0.749309 x x 2 3 5 . 7 1 3 9 x e o84549~1,x~
0.970031 0.999351 0.969097 0.70952 0.353478 0.810919 0.244995 0.24231 0.193188 0.742393
19.6246 22.055 791.60 7362 16370 17325 19093 19198 20655 22418
Table 4 T h e t e n b e s t fitting c u r v e s f o r t h e i m p e r f e c t i o n size d i s t r i b u t i o n a f t e r t h e i n s p e c t i o n r e j e c t i o n
Function
g(x ) (x, m m )
r2
~ (g(xi)- gi)2 i=1
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
g g g g g g g g g g
= = = = = = = = = =
-0.772198 + 42.4876/x 2 -21.1223 +91.4059/x 8 3 . 5 9 0 8 - 2 4 . 1 9 4 4 x In x 2 8 5 . 6 6 4 8 - 51.2783 × In x 7 6 . 6 3 7 7 - 11.13 × x 3 9 . 2 3 4 8 - 17.7056 x l n [ 0 n x ) 2] 44.1152 - 0.586172 × x 2 84.1545 e -2"3315(tnx)2 7 . 3 9 7 9 2 x (In x ) -2"3°33 1 / ( - 8 . 7 2 7 x 10 -2 + 0 . 3 5 0 9 3 4 x (In x ) 2)
0.999748 0.966895 0.683438 0.703949 0.3425 4 . 4 6 8 × 10 -2 0.155367 0.549008 0.336717 0.899786
6.42229 934.533 7570 7703 16468 20224 20874 21466 24611 27459
150
150
100
_o F--
100 y (x) = 1.359+42.977mm2/x 2
U_
O
g (x) = - 0.772 +z2.z~88 mm2/x2 LL
W
~: 5o
LU
~ 5o -
u_ O uJ en
i,i
Z
Z
IMPERFECTION SlZE, x(mm)
F i g . 1. T h e fitting c u r v e o f t h e i m p e r f e c t i o n size d i s t r i b u t i o n before inspection rejection, y(x).
1 2 3 4 5 IMPERFECTION SIZE,x (ram)
6
7
8
9
10
Fig. 2. T h e fitting c u r v e of t h e i m p e r f e c t i o n size d i s t r i b u t i o n a f t e r t h e i n s p e c t i o n r e j e c t i o n g(x).
J. Raussi, O.J.A. Tiainen / Effect of repair on the size distn'bution of weld imperfections
398
Table 5 T h e ten best fitting curves for the imperfection size distribution after the repair of the rejected defects n
Function h(x ) (x, m m )
r2
~ (h(xi ) - hi) 2 i=1
1. 2. 3. 4.
h h h h
= = = =
-0.783533 +47.5369/x 2 - 2 0 . 6 3 4 6 + 100.397/x 94.5181 - 2 7 . 0 4 8 4 In x 2 495.195 e -3~661 x
0.999427 0.967033 0.704376 0.759704
18.00 1035.9 9288 11168
5. 6. 7. 8. 9. 10.
h h h h h h
= = = = = =
80.0788 - 11.5758 x 6 4 . 4 8 3 2 - 16.6247 (In x ) 2 49.5182 - 0.821599 x 2 10.898 + 9.6386/(In x ) 2 7 0 . 8 4 9 4 e -6129°6(Inx~ 0 . 2 8 5 4 0 8 e-°3°2985 x2
0.351823 0.243838 0.188577 0.08855 0.779877 0.603467
20366 23760 25496 28639 34377 36243
the [1, 0] normal Gaussian distribution corresponding to the argument values of - 1 and +1 are 0.158 and 0.842. The rejection portions corresponding to 15.8 and 84.2 percent have x-values 1.76 mm and 6 mm respectively. Because the imperfection size mean value is 3.75 mm the standard deviation would be about 2.1 mm in the case that rejection portion is explained with the cumulative Gaussian distribution. The cumulative Gaussian function with the above standard deviation and mean value is drawn in fig. 4 together with P(x) of eq.
150
~100 Z
o I--
h (*) = - 0.7835 +47.537 mm2/x2
Lt. tw hi
~s0 t.L 0 oILl
(3).
CO
z
7
8
9 ' 10
IMPERFECTION SIZE,x (ram) Fig. 3. T h e fitting curve of the imperfection size distribution
after the repair of the rejected defects, h(x).
It can be concluded.that the defect size dependence of the rejection portion has the form which is quite near to the form of the cumulative Gaussian function. The D.P. Johnson's inspection uncertainty 8 and the inspec-
3. The effect of the rejection and the repair By dividing the imperfection distribution after the inspection rejection, g(x), by the initial distribution, y(x), the portion of accepted defects 1 - P ( x ) having the size less than x is obtained. Using the best fitting curves one gets 1 - P(x) = g(x) _ -0.772 + 42.488 mm2/x 2
y(x)- ~
4
~
"
lOO A
x 80
o_ z
CUMULATIVE GAUSSIAN / / / " / ~ FUNCTION - - /
z
_o
(3)
The rejection,portion, P(x), can be compared with the rejection probability by D.P. Johnson [2]. This has the form of the cumulative Gaussian function. The cumulative function values of
E 20 w
,
//
~ 60
,
P,x,.,
..jl
re"
1
2
3
/-.
INPERFECTION SIZE, x (ram)
5
6
7
8
Fig. 4. T h e portion of rejected defects and the fitted cumulative Gaussian distribution.
J. Raussi, O.J.A. Tiainen / Effect of repair on the size distribution of weld imperfections 1.0
//f
0,8 z
~
o.6
CUMULATIVE POISSON DISTRIBUTION ~
l.u
1
2
3
4
5
6
7
8
IMPERFECTION SIZE, xlmm)
Fig. 5. B(x) and the fitted cumulative Poisson distribution.
tion size S were 2.1 mm and 3.75 mm, respectively. Corresponding to 1 - P(x) = g(x)/y(x) also the ratio B(x) = h(x)/y(x) was studied. B(x) gives the effect of the repair procedure on the imperfection size distribution. Using the best fitting curves one gets
B ( x ) - h(x) - y(x)-
-0.7835 + 47.537 mm2/x z 1.359 + 42.977 mm2/x 2 '
(4)
This is sketched in fig. 5. The form of B(x) turned out to be near to the form of the cumulative Poisson distribution. The fitted cumulative Poisson function with mean value of 4.83 mm is also given in fig. 5.
4. Conclusions The size distributions of the studied weld
399
imperfections had the form of a + b/x 2, where x is the imperfection size and a and b are coefficients, before and after the inspections rejection and after the subsequent repair procedures. This differs from the more usual exponential distribution [1, 2] and the complementary error function distribution [3]. The reason is probably that the defects analysed in this study were all weld imperfections. The defect size dependence of the rejection portion was close to the form of the cumulative Gaussian distribution proposed in ref. [3]. The effect of repair on the initial distribution could be explained with the cumulative Poisson distribution. In order to analyse more thoroughly the inspection data a suitable subregion data collection is needed [4]. For doing this larger data material is needed.
References [1] An assesment of the integrity of PWR pressure vessels, Report by a Study Group under the chairmanship of Dr. W. Marshall, United Kingdom Atomic Energy Authority, 1976. [2] D.P. Johnson, Nucl. Engrg. Des. 43 (1977) 219-226. [3] D.O. Harris, Proc. Topical Meeting on the Probabilistic Analysis of Nuclear Reactor Safety, Amer. Nucl. Soc., Los Angeles, May 8-10, 1978, Vol. II. 7, pp. 1-10. [4] D.H. Shaffer, Proc. Symp. on the Reliability Problems of Reactor Pressure Components, IAEA Vienna, 10-13 December, 1977, Vol. II, pp. 331-339.
THE EFFECT OF INSPECTION AND REPAIR ON THE SIZE DISTRIBUTIONS OF THE W E L D IMPERFECTIONS IN N U C L E A R P O W E R PLANT PIPES Jarmo R A U S S I * Institute of Radiation Protection, P.O. Box 268, $F-00101 Helsinki 10, Finland
Olli J.A. T I A I N E N Department of Energy Technology, Lappeenranta University of Technology, P.O. Box 20, SF-53851 Lappeenranta 85, Finland
Received 27 May 1980
The weld defects appearing in the pipes of the main steam system in a BWR power plant were studied. The effect of inspection rejection and repair on the imperfection size distribution was analysed. The size distributions before and after the inspection rejection as well as after the repair procedure were of the form a + b/x 2, where x is the imperfection size and a and b are coefficients. The portion of the rejected defects had the size dependence near to the form of the cumulative Gaussian function. The effect of repair on the initial size distribution had the form of the cumulative Poisson distribution. The butt welds of the pipes were welded with the T I G and the shielded metal arc welding methods. The root pass was welded with the T I G method using the wire of E70-$3 and with argon inert gas on the root side. The electrode for the surface beads was A S T M E7018. The X - r a y inspection was carried out according to the Finnish Standard SFS 3207 with class B using films of the classes II and III. The X - r a y radiographs were ranked along the I1W Collection of Reference Radiographic of Welds. According to the quality requirements the weld joints should have at least the number 4 (blue) in the scale of 1 • • • 5.
1. Introduction and inspection data The failure probabilities of nuclear power plant components can be estimated with a method which is based on the defect size distributions [1]. In this work the effect of inspection and repair after inspection on the imperfection size distributions of pipe welds is analysed. The data used was obtained from the X - r a y inspection of the weld joints in the main steam system of a B W R power plant. In order to avoid secondary factors affecting the study the inspection data was limited to the X - r a y picturds of 114.3 x 8.56 mm pipes. The seamless pipe material was SA-106 Grade B carbon steel for high-temperature service according to the A S M E Boiler and Pressure Vessel Code, Section II. The properties of the base material were adapted to meet the use purpose by limiting certain residual element concentration. The material chemical composition is given in table 1.
Table 1 The chemical requirements of the pipe material
* Present address: TVO Power Company, Kutojantie 8, SF02630 ESPOO 63, Finland. 395
Element
Composition w/o
C Mn P S Si AI, average/max.
<0.25 0.29-1.06 <0.048 <0.05 >0.10 0.015/0.020
396
J. Raussi, O.J.A. Tiainen / Effect of repair on the size distribution of weld imperfections
Table 2 The number of imperfections in all studied weld joints classified according to their size before and after inspection rejection and the subsequent repair Number of imperfections Imperfection size (mm)
Before inspection rejection, Yi
After the inspection rejection, gi
After the repair, h~
0-1 1-2 2-3 3--4 4-5 5-6
173 22 11 5 4 1
169 20 6 2 0 0
189 24 7 2 0 0
6-7
0
0
0
%-8 8-9 9-10 10-11
1 1 1 0
0 0 0 0
0 0 0 0
The imperfection types entered into the data of this study were pores, slag inclusions, lacks of fusion, lacks of penetration, cracks and tungsten inclusions. The weld defect sizes were measured in the film plane and all observations are presented in table 2.
2. Imperfection size distributions On the basis of the imperfection size classification in table 2 the best fitting functions were searched. The functions of imperfection size, x, which were fitted with linear regression against the inspection data were: a +bf(x) a exp(bf(x)) af(x )b N(x) =
a + b/f(x) 1
(1)
a +bf(x) x
a + bf(x) a + b ln/(x), where a and b are fitting coefficients. The function f ( x ) had the form
x
f(x)=
x~
(2)
(In x) 2. Table 3 shows the ten best fitting curves, y(x), for the imperfection size distribution before the inspection rejection. Table 3 shows also the square of the correlation coefficient, r 2, of the linearized fitting function and the square sum of the deviations between the fitting curve points and the observations. These quantities describe the goodness of the fitting. In table 3 the best fitting curve before rejection is y ( x ) = 1.359 + 42.977 mm2/x 2 when both r 2 and the square sum of deviations are taken into account. The curve is presented in fig. 1. Similar fitting was also done for the imperfection population from which for rejecting classified imperfections were taken away. Table 4 gives the fitting curves in this case. The best curve is g(x) = -0.772 + 42.488 mm2/x 2 which is shown in fig. 2. The imperfection size distribution was also determined when the rejected defects were repaired. Table 5 gives the ten best fitting curves in this case, the best being h ( x ) = -0.7835 + 47.537 mmZ/x 2. This curve is presented in fig. 3.
J. Raussi, O.J.A. Tiainen / Effect of repair on the size distribution of weld imperfections
397
Table 3 T h e t e n b e s t fitting c u r v e s f o r t h e i m p e r f e c t i o n size d i s t r i b u t i o n b e f o r e i n s p e c t i o n r e j e c t i o n n
F u n c t i o n y ( x ) (x, m m )
r2
~ (y(xi) - yi)2 i=I
1. y = 4 8 . 6 7 6 3 2. 3. 4. 5. 6. 7. 8. 9. 10.
y y y y y y y y y
= = = = = = = = =
x ( x 2 ) -0'927623
1.35887+42.9767/x 2 -17.4133 + 91.3568/x 8 7 . 8 5 4 4 - 4 9 . 7 2 7 5 x In x 7 5 . 3 8 5 4 - 10.5625 x x 53.6561 x e -°-51°49x 35.4029 - 2 3 . 9 1 1 7 x l n [ 0 n x ) 2] 6 1 . 2 2 1 4 - 1 5 . 1 3 8 5 x (In x ) 2 48.4986 - 0.749309 x x 2 3 5 . 7 1 3 9 x e o84549~1,x~
0.970031 0.999351 0.969097 0.70952 0.353478 0.810919 0.244995 0.24231 0.193188 0.742393
19.6246 22.055 791.60 7362 16370 17325 19093 19198 20655 22418
Table 4 T h e t e n b e s t fitting c u r v e s f o r t h e i m p e r f e c t i o n size d i s t r i b u t i o n a f t e r t h e i n s p e c t i o n r e j e c t i o n
Function
g(x ) (x, m m )
r2
~ (g(xi)- gi)2 i=1
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
g g g g g g g g g g
= = = = = = = = = =
-0.772198 + 42.4876/x 2 -21.1223 +91.4059/x 8 3 . 5 9 0 8 - 2 4 . 1 9 4 4 x In x 2 8 5 . 6 6 4 8 - 51.2783 × In x 7 6 . 6 3 7 7 - 11.13 × x 3 9 . 2 3 4 8 - 17.7056 x l n [ 0 n x ) 2] 44.1152 - 0.586172 × x 2 84.1545 e -2"3315(tnx)2 7 . 3 9 7 9 2 x (In x ) -2"3°33 1 / ( - 8 . 7 2 7 x 10 -2 + 0 . 3 5 0 9 3 4 x (In x ) 2)
0.999748 0.966895 0.683438 0.703949 0.3425 4 . 4 6 8 × 10 -2 0.155367 0.549008 0.336717 0.899786
6.42229 934.533 7570 7703 16468 20224 20874 21466 24611 27459
150
150
100
_o F--
100 y (x) = 1.359+42.977mm2/x 2
U_
O
g (x) = - 0.772 +z2.z~88 mm2/x2 LL
W
~: 5o
LU
~ 5o -
u_ O uJ en
i,i
Z
Z
IMPERFECTION SlZE, x(mm)
F i g . 1. T h e fitting c u r v e o f t h e i m p e r f e c t i o n size d i s t r i b u t i o n before inspection rejection, y(x).
1 2 3 4 5 IMPERFECTION SIZE,x (ram)
6
7
8
9
10
Fig. 2. T h e fitting c u r v e of t h e i m p e r f e c t i o n size d i s t r i b u t i o n a f t e r t h e i n s p e c t i o n r e j e c t i o n g(x).
J. Raussi, O.J.A. Tiainen / Effect of repair on the size distn'bution of weld imperfections
398
Table 5 T h e ten best fitting curves for the imperfection size distribution after the repair of the rejected defects n
Function h(x ) (x, m m )
r2
~ (h(xi ) - hi) 2 i=1
1. 2. 3. 4.
h h h h
= = = =
-0.783533 +47.5369/x 2 - 2 0 . 6 3 4 6 + 100.397/x 94.5181 - 2 7 . 0 4 8 4 In x 2 495.195 e -3~661 x
0.999427 0.967033 0.704376 0.759704
18.00 1035.9 9288 11168
5. 6. 7. 8. 9. 10.
h h h h h h
= = = = = =
80.0788 - 11.5758 x 6 4 . 4 8 3 2 - 16.6247 (In x ) 2 49.5182 - 0.821599 x 2 10.898 + 9.6386/(In x ) 2 7 0 . 8 4 9 4 e -6129°6(Inx~ 0 . 2 8 5 4 0 8 e-°3°2985 x2
0.351823 0.243838 0.188577 0.08855 0.779877 0.603467
20366 23760 25496 28639 34377 36243
the [1, 0] normal Gaussian distribution corresponding to the argument values of - 1 and +1 are 0.158 and 0.842. The rejection portions corresponding to 15.8 and 84.2 percent have x-values 1.76 mm and 6 mm respectively. Because the imperfection size mean value is 3.75 mm the standard deviation would be about 2.1 mm in the case that rejection portion is explained with the cumulative Gaussian distribution. The cumulative Gaussian function with the above standard deviation and mean value is drawn in fig. 4 together with P(x) of eq.
150
~100 Z
o I--
h (*) = - 0.7835 +47.537 mm2/x2
Lt. tw hi
~s0 t.L 0 oILl
(3).
CO
z
7
8
9 ' 10
IMPERFECTION SIZE,x (ram) Fig. 3. T h e fitting curve of the imperfection size distribution
after the repair of the rejected defects, h(x).
It can be concluded.that the defect size dependence of the rejection portion has the form which is quite near to the form of the cumulative Gaussian function. The D.P. Johnson's inspection uncertainty 8 and the inspec-
3. The effect of the rejection and the repair By dividing the imperfection distribution after the inspection rejection, g(x), by the initial distribution, y(x), the portion of accepted defects 1 - P ( x ) having the size less than x is obtained. Using the best fitting curves one gets 1 - P(x) = g(x) _ -0.772 + 42.488 mm2/x 2
y(x)- ~
4
~
"
lOO A
x 80
o_ z
CUMULATIVE GAUSSIAN / / / " / ~ FUNCTION - - /
z
_o
(3)
The rejection,portion, P(x), can be compared with the rejection probability by D.P. Johnson [2]. This has the form of the cumulative Gaussian function. The cumulative function values of
E 20 w
,
//
~ 60
,
P,x,.,
..jl
re"
1
2
3
/-.
INPERFECTION SIZE, x (ram)
5
6
7
8
Fig. 4. T h e portion of rejected defects and the fitted cumulative Gaussian distribution.
J. Raussi, O.J.A. Tiainen / Effect of repair on the size distribution of weld imperfections 1.0
//f
0,8 z
~
o.6
CUMULATIVE POISSON DISTRIBUTION ~
l.u
1
2
3
4
5
6
7
8
IMPERFECTION SIZE, xlmm)
Fig. 5. B(x) and the fitted cumulative Poisson distribution.
tion size S were 2.1 mm and 3.75 mm, respectively. Corresponding to 1 - P(x) = g(x)/y(x) also the ratio B(x) = h(x)/y(x) was studied. B(x) gives the effect of the repair procedure on the imperfection size distribution. Using the best fitting curves one gets
B ( x ) - h(x) - y(x)-
-0.7835 + 47.537 mm2/x z 1.359 + 42.977 mm2/x 2 '
(4)
This is sketched in fig. 5. The form of B(x) turned out to be near to the form of the cumulative Poisson distribution. The fitted cumulative Poisson function with mean value of 4.83 mm is also given in fig. 5.
4. Conclusions The size distributions of the studied weld
399
imperfections had the form of a + b/x 2, where x is the imperfection size and a and b are coefficients, before and after the inspections rejection and after the subsequent repair procedures. This differs from the more usual exponential distribution [1, 2] and the complementary error function distribution [3]. The reason is probably that the defects analysed in this study were all weld imperfections. The defect size dependence of the rejection portion was close to the form of the cumulative Gaussian distribution proposed in ref. [3]. The effect of repair on the initial distribution could be explained with the cumulative Poisson distribution. In order to analyse more thoroughly the inspection data a suitable subregion data collection is needed [4]. For doing this larger data material is needed.
References [1] An assesment of the integrity of PWR pressure vessels, Report by a Study Group under the chairmanship of Dr. W. Marshall, United Kingdom Atomic Energy Authority, 1976. [2] D.P. Johnson, Nucl. Engrg. Des. 43 (1977) 219-226. [3] D.O. Harris, Proc. Topical Meeting on the Probabilistic Analysis of Nuclear Reactor Safety, Amer. Nucl. Soc., Los Angeles, May 8-10, 1978, Vol. II. 7, pp. 1-10. [4] D.H. Shaffer, Proc. Symp. on the Reliability Problems of Reactor Pressure Components, IAEA Vienna, 10-13 December, 1977, Vol. II, pp. 331-339.