ML12145A466
| ML12145A466 | |
| Person / Time | |
|---|---|
| Site: | South Texas  |
| Issue date: | 05/18/2012 |
| From: | Morton D, Popova E University of Texas at Austin |
| To: | Balwant Singal Plant Licensing Branch IV |
| Singal B | |
| Shared Package | |
| ML12145A232 | List: |
| References | |
| TAC ME7735, TAC ME7736 | |
| Download: ML12145A466 (22) | |
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Uncertainty modeling of LOCA frequencies and break size distributions for the STP GSI-191 resolution Elmira Popova, David Morton The University of Texas at Austin May 2012 1
Introduction In the initial quanti"cation (Crenshaw, 2012), Fleming et al. (2011) per-formed a substantial study designed to build upon the established EPRI risk-informed in-service inspection program (EPRI, 1999). The methodol-ogy of EPRI (1999) was used as the primary basis to develop the size and location-speci"c rupture frequencies for the initial quanti"cation. Although the overall methodology appears to be sound based on peer review (Mosleh, 2011) and reasonableness of the values obtained, NRC feedback in the Pilot Project reviews has resulted in further review of the approach. In this pa-per we propose a new approach to assign location-speci"c LOCA frequencies derived from the overall frequencies, as de"ned in Tregoning et al. (2008),
which we refer to as NUREG-1829.
The NUREG-1829 annual frequencies are neither plant speci"c nor plant-location speci"c. Yet they are used throughout the nuclear industry as an important input to PRA analyses, and therefore, they need to be preserved.
Conservation of the NUREG-1829 break frequencies is our guiding principle.
In this document we work with the six categories de"ned in Table 1, NUREG-1829 Volume 1, page xxi, as eective break size for the PWR 1
plants.
Table 1 shows the mapping between the NUREG-1829 notation and ours. In addition, we use the term distribution to mean a distribution functioneither cumulative distribution function (CDF), probability density function (PDF), or probability mass function (PMF)of a random variable used to model a speci"ed uncertainty.
Table 1: LOCA categories notation map Eective break size (inch) for PWR Notation 1
2 cat1 15 8
cat2 3
cat3 7
cat4 14 cat5 31 cat6 We should point out that South Texas Project PRA analysis uses only three LOCA categories, small, medium, and large. Our proposed methodol-ogy can be applied to any "nite number of break-size categories.
In this document we will use the term location to represent a speci"c weld case, using the terminology of Fleming et al. (2011). Overall there are two distinct approaches to derive location-or weld-case-speci"c LOCA frequen-cies: bottom-up and top-down. The "rst approach requires location speci"c failure data to estimate the corresponding probability of a weld failure. Sup-pose a break occurs and assume there are Mj dierent welds in the plant where breaks of size catj can occur, weld1,..., weldMj, then using the law of 2
total probability we can write:
P[catj] =
Mj X
i=1 P[catjlweldi]P[weldi], j = 1, 2,..., 6, where P[catj] is the probability of a catj LOCA given that a break occurs, P[catjlweldi] is the conditional probability of a catj LOCA given that the break occurs at weld i, and P[weldi] is the probability that the break occurs at weld i, where again, weld i represents weld case i, using the terminology of Fleming et al. (2011).
In the bottom-up approach we "rst must determine P[catjlweldi] (using estimation or expert elicitation).
Then, if we assume that each location is equally likely to have the break, we can multiply by 1/Mj and sum the resulting probabilities to obtain the total probability the break is a catj LOCA. If the bottom-up approach is followed the resulting total catj LOCA probability will not equal the number provided in NUREG-1829 (or at least it is very unlikely to yield that number). This approach, taken by Fleming et al.
(2011), is an inherently bottom-up approach. In an attempt to preserve the NUREG-1829 frequencies Fleming et al. (2011) developed an approximation scheme. In their review, the NRC technical team raised several questions about using this as a stand alone methodology, which has led us to take a dierent path.
The approach that we propose to take is rooted in the combining the top-down and bottom-up approaches: We start with the NUREG-1829 fre-quencies and develop a way to distribute them across dierent locations pro-portionally to the frequencies estimated using the bottom-up approach. In this way, we maintain the NUREG-1829 frequencies overall but also allow for location-dependent dierences. We should point out that we use the lo-3
cation speci"c tables as de"ned in Fleming et al. (2011). To our knowledge no other sources of location speci"c frequencies exist. If such information becomes available our proposed methodology can immediately incorporate that information.
For a top-down approach, we will use again the catj LOCA as an illus-trative example. The LOCA frequencies (NUREG-1829 Volume 1, page xxi, Table 1) are cumulative and so we compute the probability of a LOCA being in catj using the formula P[catj] = Frequency[LOCA catj] Frequency[LOCA catj+1]
Frequency[LOCA cat1]
for j = 1,..., 6 and where Frequency[LOCA cat7] 0. Again we assume there are Mj dierent locations in the plant where breaks of size catj can occur, weld1,..., weldMj. Assume, for the moment, given that we have a catj break, these Mj locations are equally likely to have the break, i.e.,
P[weldilcatj] = 1 Mj
, i = 1,..., Mj.
Then we have P[catj at weldi] = P[catj]P[weldilcatj] and so P[catj at weldi] =
P[catj]/Mj. Finally, applying the law of total probability, P[catj] =
Mj X
i=1 P[catj at weldi],
we see that the resulting probability of a catj LOCA matches exactly the NUREG-1829 probability. The approach we propose in this document, fol-lows the steps we have just outlined, except we propose replacing the simple assumption of a catj break being equally likely to occur across all locations with an approach that uses location-speci"c conditional probabilities that we infer from Fleming et al. (2011).
4
The above methodology distributes equally the LOCA frequencies as de-
"ned in NUREG-1829 Table 1 across all locations that can experience breaks from one or more of the six size categories. The six break size categories (from the NUREG-1829 Table 1) represent six bounded intervals. For a particular weld we need to be able to sample from the continuous interval of break size values. In addition, we would like to be able to sample from the distribution of the frequencies. The rows in Table 1 from NUREG-1829 represent the distribution of the frequencies by reporting the mean, median, 5th and 95th percentiles. We will use this information to "t six continuous distributions for each break size category.
2 Proposed Methodology 2.1 Fitting distribution to the LOCA frequencies We "rst describe how we "t a distribution to the frequencies for each break size category. In theory, there are an in"nite number of distributions that one can "t to the LOCA frequencies represented in NUREG-1829. For exam-ple, two split lognormal distributions are used in NUREG-1829 and gamma distributions are used in NUREG/CR 6928.
We choose to "t the bounded Johnson distribution, (Johnson, 1949) for the following reasons:
- The Johnson has four parameters, which will allow us to match closely the distributional characteristics provided by NUREG-1829. In order to obtain the parameters of the Johnson distribution we solve an opti-mization problem with constraints de"ned by the distributional char-acteristics.
5
- The Johnson distribution allows for a variety of shapes. In particular, skewed, symmetric, bimodal, or unimodal shapes can be obtained.
The cumulative distribution function (CDF) of the bounded Johnson is:
F[x] = { + f[(x )/]},
where [x] is the CDF of a standard Normal (0,1) random variable, and are shape parameters, is a location parameter, is a scale parameter, and f(z) = log[z/(1 z)]. We restricted our attention to bell-shaped PDF curves only. This was achieved by imposing a constraint 1 in our "tting algorithm. The "tted parameters of the Johnson distribution for each of the six categories are given in Table 2. The comparison between the NUREG-1829 distributional characteristics of the LOCA frequencies and the "tted ones are presented in Table 3. We note that the expert elicitation was for the 5%, 50% (median), and 95% quantiles, and did not involve eliciting the mean parameters. So we focus on matching the parameters elicited from the experts as indicated by the results in the "nal four columns of Table 3.
The six panels in Figures 1 and 2 show the "tted PDFs of the Johnson distribution for each category. Once the best "t is found, we sample the LOCA frequencies for each category to obtain Frequency[LOCA catj]a realization of the cumulative LOCA frequency to be in category j or larger.
2.2 Distribution of LOCA frequencies to dierent weld locations We "rst convert the sampled LOCA frequencies to probabilities using P[catj] = Frequency[LOCA catj] Frequency[LOCA catj+1]
Frequency[LOCA cat1]
(1) where 6
Table 2: Fitted Johnson parameters Johnson Parameters
Cat1 2.144623E+00 7.507774E-01 2.597254E-04 6.698783E-02 Cat2 1.365229E+00 4.195681E-01 4.822843E-06 3.646760E-03 Cat3 1.392766E+00 4.196874E-01 1.415507E-07 9.377713E-05 Cat4 1.701576E+00 4.554581E-01 5.609081E-09 1.302968E-05 Cat5 1.906196E+00 3.825140E-01 2.573251E-10 1.730668E-06 Cat6 2.525065E+00 3.816999E-01 1.853162E-11 8.868925E-07 Table 3: NUREG-1829 and "tted Johnson median, low and high quantiles values NUREG 1829 Values Fitted Johnson Relative Error 5th Median Mean 95th 5th Median Mean 95th 5th Median Mean 95th Cat1 6.90E-04 3.90E-03 7.30E-03 2.30E-02 6.89E-04 3.90E-03 6.68E-03 2.30E-02 0.20% 0.00%
8.56% 0.00%
Cat2 7.60E-06 1.40E-04 6.40E-04 2.40E-03 7.61E-06 1.39E-04 4.97E-04 2.41E-03 0.14% 0.38% 22.37% 0.62%
Cat3 2.10E-07 3.40E-06 1.60E-05 6.10E-05 2.09E-07 3.42E-06 1.24E-05 6.07E-05 0.52% 0.53% 22.69% 0.49%
Cat4 1.40E-08 3.10E-07 1.60E-06 6.10E-06 1.40E-08 3.09E-07 1.20E-06 6.12E-06 0.01% 0.28% 24.97% 0.25%
Cat5 4.10E-10 1.20E-08 2.00E-07 5.80E-07 4.18E-10 1.20E-08 9.91E-08 5.81E-07 1.99% 0.28% 50.47% 0.17%
Cat6 3.50E-11 1.20E-09 2.90E-08 8.10E-08 3.45E-11 1.21E-09 1.65E-08 8.04E-08 1.42% 0.43% 43.27% 0.75%
7
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0
50 100 150 200 x
PDF(x)
(a) Cat1 0.000 0.001 0.002 0.003 0
1000 2000 3000 4000 x
PDF(x)
(b) Cat2 0e+00 2e05 4e05 6e05 8e05 0
50000 100000 150000 x
PDF(x)
(c) Cat3 0.0e+00 2.0e06 4.0e06 6.0e06 8.0e06 1.0e05 1.2e05 0
200000 400000 600000 800000 1000000 1200000 x
PDF(x)
(d) Cat4 0.0e+00 5.0e07 1.0e06 1.5e06 0e+00 2e+06 4e+06 6e+06 8e+06 x
PDF(x)
(e) Cat5 0e+00 2e07 4e07 6e07 8e07 0.0e+00 5.0e+06 1.0e+07 1.5e+07 x
PDF(x)
(f) Cat6 Figure 1: Johnson PDF for each category 8
0.002 0.004 0.006 0.008 0
50 100 150 200 250 x
PDF(x)
(a) Cat1 6.0e06 8.0e06 1.0e05 1.2e05 0
5000 10000 15000 20000 x
PDF(x)
(b) Cat2 1.5e07 2.0e07 2.5e07 3.0e07 0e+00 2e+05 4e+05 6e+05 8e+05 x
PDF(x)
(c) Cat3 5.0e09 1.0e08 1.5e08 2.0e08 2.5e08 3.0e08 0e+00 1e+06 2e+06 3e+06 4e+06 5e+06 6e+06 x
PDF(x)
(d) Cat4 1.0e10 1.5e10 2.0e10 2.5e10 3.0e10 3.5e10 4.0e10 0e+00 1e+08 2e+08 3e+08 4e+08 x
PDF(x)
(e) Cat5 0.0e+00 5.0e12 1.0e11 1.5e11 0.0e+00 5.0e+08 1.0e+09 1.5e+09 2.0e+09 2.5e+09 3.0e+09 3.5e+09 x
PDF(x)
(f) Cat6 Figure 2: Johnson PDF for each category, zoomed to a narrower range of frequencies near the modes of the distributions 9
- J = {cat1, cat2, cat3,..., catB}: set of possible break types (categories),
- P[catj]: probability of observing a break that falls into category j given that a break was observed
- Frequency[LOCA catj]: frequency of break of type j or larger, j J
- Frequency[LOCA catB+1] 0.
As we describe above, there are a total of B = 6 categories in NUREG-1829. Given P[catj], the next step is to distribute that probability across all welds that can experience a break from that particular category. Not all types of welds can experience all types of breaks. We use Ij to denote the subset of locations that can have a break from category j.
We compute the probability that weld i will experience a break of type j using P[catj at weldi] = wi jP[catj], where wi j = P(weldilcatj) is the con-ditional probability of the break occurring at weld i given that we have a category j break. Restated, wi j is the fraction that weld i contributes to cat-egory js total break frequency from the bottom-up approach for i Ij.
Computation of wi j is straightforward.
The bottom-up approach gener-ates the frequency of category j breaks at location i, which we denote Freqbu[LOCA catj at weldi]. Given these frequencies, the wi j values can be computed using:
wi j = Freqbu[LOCA catj at weldi] Freqbu[LOCA catj+1 at weldi]
Freqbu[LOCA cat1 at weldi]
(2)
Given P[catj] from equation (1) and wi j from equation (2), we form P[catj at weldi] = wi jP[catj].
(3)
Since the sum of all wi j across i Ij is equal to one, with this approach we are guaranteed to match the NUREG-1829 speci"ed values for P[catj].
10
2.3 Sampling of the break size The "nal step is to sample the actual break size conditioned on the break category. Here we assume that the break size has a uniform distribution within a given category. Formally, we write breakSizei j U[minBreaki j, maxBreaki j], j J, i Ij, where
- minBreaki j = catminBreak j
- maxBreaki j = min{catmaxBreak j
, weldsize i
}
- catminBreak j
- minimum break size that would put it into category j
- catmaxBreak j
- maximum break size that would put it into category j
- weldsize i
- actual weld size (it cannot experience break size larger than its diameter).
2.4 Methodology summary Our approach requires two sampling loops in our simulator CASA GRANDE, Letellier (2011). We need one sampling loop for the break size within each category and an outer loop that samples LOCA frequencies.
Below is a step-by-step description of the procedure:
- 1. Input: N, the number of LOCA frequency samples, and S, the number of break size samples to generate.
- 2. Sample LOCA frequencies Frequency[LOCA catj], j = 1, 2,..., 6, from the "tted Johnson distributions for each break category; see Sec-tion 2.1.
11
- 3. Distribute uncertainty across plant-speci"c welds as described in Sec-tion 2.2.
- 4. Sample break size for each possible weld / break-category combination as described in Section 2.3.
- 5. Estimate, and store, performance measures using CASA GRANDE.
- 6. Go to step 4 and repeat until we obtain S break-size samples.
- 7. Compute, and store, performance measures.
- 8. Go to step 2 and repeat until we have obtained N LOCA frequency samples.
- 9. Form the summary of aggregated performance measures.
3 Illustrative Example We illustrate the approach we describe in the "rst four steps from Section 2.4 using the following example. Assume we have a total of six welds and these are the only locations where a break can occur. Three of them (welds 1, 2 and
- 3) are small and have sizes of 1.7, 2, and 2.5 inches and hence can experience only small breaks (category 1 and category 2). Two of those six (welds 4 and 5) are of medium size and have a diameter of 3.8 inches and thus can have small and medium breaks (category 1, category 2, and category 3 only; they cannot experience category 4, or larger, breaks). The last weld (weld
- 6) is large with a size of 35 inches and can have all types of breakssmall, medium, and large (category 1,..., category 6). A graphical representation of the system is shown in Figure 3.
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Figure 3: Example system depiction with six welds of various sizes that can each experience some subset of six types of breaks from category 1,...,category 6.
Adapting the notation developed in Section 2 to this example we have:
J = {cat1, cat2, cat3, cat4, cat5, cat6},
Icat1 = {weld1, weld2, weld3, weld4, weld5, weld6},
Icat2 = {weld1, weld2, weld3, weld4, weld5, weld6},
Icat3 = {weld4, weld5, weld6},
Icat4 = {weld6}, Icat5 = {weld6}, Icat6 = {weld6},
and 13
BreakSizeweld1 cat1 U[0.5, 1.625]
(4a)
BreakSizeweld2 cat1 U[0.5, 1.625]
(4b)
BreakSizeweld3 cat1 U[0.5, 1.625]
(4c)
BreakSizeweld4 cat1 U[0.5, 1.625]
(4d)
BreakSizeweld5 cat1 U[0.5, 1.625]
(4e)
BreakSizeweld6 cat1 U[0.5, 1.625]
(4f)
BreakSizeweld1 cat2 U[1.625, 1.7]
(4g)
BreakSizeweld2 cat2 U[1.625, 2]
(4h)
BreakSizeweld3 cat2 U[1.625, 2.5]
(4i)
BreakSizeweld4 cat2 U[1.625, 3]
(4j)
BreakSizeweld5 cat2 U[1.625, 3]
(4k)
BreakSizeweld6 cat2 U[1.625, 3]
(4l)
BreakSizeweld4 cat3 U[3, 3.8]
(4m)
BreakSizeweld5 cat3 U[3, 3.8]
(4n)
BreakSizeweld6 cat3 U[3, 7]
(4o)
BreakSizeweld6 cat4 U[7, 14]
(4p)
BreakSizeweld6 cat5 U[14, 31]
(4q)
BreakSizeweld6 cat6 U[31, 35].
(4r)
Below we enumerate the "rst four steps of the procedure from Section 2.4 for this example system.
- 1. Assume S = 1, N = 1.
14
- 2. Sampled LOCA frequencies (using the "tted Johnson distributions) are given in Table 4. The right-most column of Table 4 computes the probability mass for each category according to equation (1).
- 3. Break frequency tables for each weld obtained from the bottom-up ap-proach can be found in Tables 5-7. (For the full collection of location-speci"c frequency tables see Fleming et al. (2011).) Table 4 contains bins de"ning the break categories, as derived from Table 1. The asso-ciated categories for each break size are indicated in Tables 5-7.
Using Tables 5-7 we compute weights for each weld and report results in Tables 8-10. To describe the derivation of these weights we begin with Table 8. The weld 1 frequency value in that table is the dierence between the cumulative frequencies from the 0.5-inch row and the 1.7-inch row from Table 5. The weld 2 and weld 3 frequency values are the dierence between the frequencies from the 0.5-inch row and the 2-inch row from Table 5. The weld 4, weld 5, and weld 6 frequencies are simi-larly the dierence between the frequencies from the 0.5-inch rows and the 2-inch rows from Tables 6 and 7. Finally, we normalize the result-ing values using equation (2) to compute the weights wweld1 cat1,..., wweld6 cat1.
Tables 9 and 10 contain the results of the analogous calculations for category 2 and category 3. There is no need to form the corresponding frequency values for category 4,...,category 6 because these categories only occur for weld 6, and hence these weights are simply 100%.
Using equation (3) we now compute P[catj at weldi] for each category-weld combination. The results are given in Table 11. We see that the sum of the distributed probabilities match the target probabilities.
15
- 4. We simulate break sizes for each weld within each category using the uniform distributions with the parameters speci"ed in equation (4).
The sample is shown in Table 12.
Finally, we note that our assumptions lead to a piece-wise linear CDF governing the break size for a given weld. For example, consider weld 6. The CDF of the break size for that weld has six pieces with the slopes deter-mined by the P[catj at weld6] values and break points at the catmaxBreak j
bin boundaries of 1.625, 3, 7, 14, and 31 inches, see Figure 4.
Figure 4: CDF of break size distribution for weld 6 Conclusion In this document we present solutions to three problems:
16
- 1. How should we preserve the NUREG 1829 LOCA frequencies when distributing them across dierent locations (welds) in a nuclear power plant. The approach that we propose to take is rooted in combining the top-down and bottom-up approaches: We start with the NUREG-1829 frequencies and develop a way to distribute them to dierent locations proportionally to the frequencies estimated using the bottom-up approach. In this way, we maintain the NUREG-1829 frequencies overall but also allow for location-dependent dierences.
- 2. The six break size categories (from the NUREG-1829 Table 1) represent six intervals. For a particular weld we need to be able to sample from the continuous interval of break size values. We propose to use linear interpolation which is equivalent to assigning equally likely probabilities within each break size category.
- 3. How to model the distribution of the LOCA frequencies. We propose to "t the Johnson distribution to the NUREG-1829 quantiles of 5%,
50%, and 95%.
In this document we do not discuss the dierent sampling techniques needed. We will provide their description and examples in a separate docu-ment.
Acknowledgements We would like to thank Alexander Galenko for writing the optimization algo-rithm for the Johnson distribution and performing most of the computations we describe here.
17
Table 4: Sampled LOCA frequencies and corresponding probabilities Failure Type Category Break Size Bins (in.)
Frequency Probability small 1
[0.5,1.625) 3.9E-03 9.64E-01 small 2
[1.625,3) 1.4E-04 3.50E-02 medium 3
[3,7) 3.4E-06 7.92E-04 medium 4
[7,14) 3.1E-07 7.64E-05 large 5
[14,31) 1.2E-08 2.77E-06 large 6
[31,41) 1.2E-09 3.08E-07 Table 5: Frequency tables for small welds from bottom-up approach SMALL weld1 weld2 weld3 Small Bore SIR CVCS 1
1.5 2
1.414213562 2.121320344 2.828427125 B-J B-J B-J VF, SC, D&C D&C TF, VF, D&C 193 0
10 X, Break Size (in.) F(LOCA X) X, Break Size (in.) F(LOCA X) X, Break Size (in.) F(LOCA X) 0.5 (cat1) 1.22E-07 0.5 (cat1) 1.1402E-08 0.5 (cat1) 4.2814E-08 0.75 (cat1) 7.18E-08 0.75 (cat1) 6.843E-09 0.75 (cat1) 2.5696E-08 1 (cat1) 5.00E-08 1 (cat1) 4.8541E-09 1 (cat1) 1.8227E-08 1.5 (cat1) 4.30E-09 1.5 (cat1) 3.072E-09 1.5 (cat1) 1.1536E-08 1.7 (cat2) 2.30E-09 2 (cat2) 1.6483E-09 2 (cat2) 6.0274E-09 2.5 (cat2) 2.4179E-09 18
Table 6: Frequency tables for medium welds from bottom-up approach MEDIUM weld4 weld5 CVCS Pressurizer 4
3 5.656854249 4.242640687 BC B-J TF, D&C TF, D&C 4
14 X, Break Size (in.) F(LOCA X) X, Break Size (in.) F(LOCA X) 0.5 (cat1) 7.9803E-08 0.5 (cat1) 4.5883E-08 0.75 (cat1) 4.7896E-08 0.75 (cat1) 2.7565E-08 1 (cat1) 3.3975E-08 1 (cat1) 1.9569E-08 1.5 (cat1) 2.1502E-08 1.5 (cat1) 1.24E-08 2 (cat2) 1.1235E-08 2 (cat2) 6.6408E-09 3 (cat3) 4.5068E-09 3 (cat3) 2.7541E-09 3.8 (cat3) 2.3397E-09 3.8 (cat3) 1.3018E-09 Table 7: Frequency tables for large welds from bottom-up approach LARGE weld6 SG Inlet 29 41.01219331 B-F SC, D&C 4
X, Break Size (in.) F(LOCA X) 0.5 (cat1) 1.9783E-06 1.5 (cat1) 4.5932E-07 2 (cat2) 3.4469E-07 3 (cat3) 2.3061E-07 4 (cat3) 1.5971E-07 6 (cat3) 9.5224E-08 6.75 (cat3) 8.1186E-08 14 (cat5) 3.3453E-08 20 (cat5) 1.8122E-08 29 (cat5) 9.5661E-09 31.5 (cat6) 8.3016E-09 35 (cat6) 5.2422E-09 19
Table 8: Category 1 weld weights in total failure frequency using bottom-up approach Cat1 weld1 weld2 weld3 weld4 weld5 weld6 Total Frequency 1.20E-07 9.75E-09 3.68E-08 6.86E-08 3.92E-08 1.63E-06 1.91E-06 Weight 6.30%
0.51%
1.93%
3.59%
2.06%
85.61%
100.00%
Table 9: Category 2 weld weights in total failure frequency using bottom-up approach Cat2 weld1 weld2 weld3 weld4 weld5 weld6 Total Frequency 2.30E-09 1.65E-09 6.03E-09 6.73E-09 3.89E-09 1.14E-07 1.35E-07 Weight 1.70%
1.22%
4.48%
5.00%
2.89%
84.71%
100.00%
Table 10: Category 3 weld weights in total failure frequency using bottom-up approach Cat3 weld4 weld5 weld6 Total Frequency 4.51E-09 2.75E-09 1.97E-07 2.04E-07 Weight 2.20%
1.35%
96.45%
100.00%
Table 11: Distributed LOCA probabilities among all welds weld1 weld2 weld3 weld4 weld5 weld6 Total Target Cat1 6.07E-02 4.93E-03 1.86E-02 3.46E-02 1.98E-02 8.25E-01 9.64E-01 9.64E-01 Cat2 5.97E-04 4.29E-04 1.57E-03 1.75E-03 1.01E-03 2.97E-02 3.50E-02 3.50E-02 Cat3 X
X X
1.75E-05 1.07E-05 7.64E-04 7.92E-04 7.92E-04 Cat4 X
X X
X X
7.64E-05 7.64E-05 7.64E-05 Cat5 X
X X
X X
2.77E-06 2.77E-06 2.77E-06 Cat6 X
X X
X X
3.08E-07 3.08E-07 3.08E-07 20
Table 12: Sampled break sizes (inches) for all welds within each break cate-gory Weld 1
2 3
4 5
6 Cat1 1.1 0.6 0.87 1.34 0.79 1.23 Cat2 1.69 1.9 2.1 2.9 1.75 2.36 Cat3 X
X X
3.76 3.54 5.97 Cat4 X
X X
X X
9.67 Cat5 X
X X
X X
25.68 Cat6 X
X X
X X
32.67 References Crenshaw, J. W. (2012, January). South Texas Project Units 1 and 2 Docket Nos. STN 50-499, Summary of the South Texas Project Risk-Informed Approach to Resolve Generic Safety Issue (GSI-191). Letter from John W.
Crenshaw to USNRC.
EPRI (1999). Revised Risk-Informed In-Service Inspection Procedure. TR 112657 Revision B-A, Electric Power Research Institute, Palo Alto, CA.
Fleming, K. N., B. O. Lydell, and D. Chrun (2011, July).
Development of LOCA Initiating Event Frequencies for South Texas Project GSI-191.
Technical Report, KnF Consulting Services, LLC, Spokane, WA.
Johnson, N. (1949). Systems of Frequency Curves Generated by Methods of Translations. Biometrika 36, 149-176.
Letellier, B. (2011). Risk-Informed Resolution of GSI-191 at South Texas Project. Technical Report Revision 0, South Texas Project, Wadsworth, TX.
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Mosleh, A. (2011, October). Technical Review of STP LOCA Frequency Es-timation Methodology. Letter Report Revision 0, University of Maryland, College Park, MA.
Tregoning, R., P. Scott, and A. Csontos (2008, April). Estimating Loss-of-Coolant Accident (LOCA) Frequencies Through the Elicitation Process:
Main Report (NUREG-1829). NUREG 1829, NRC, Washington, DC.
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