ML043150023

to MWMECH-04-004, Monte Carlo Analysis of Dresden 2 & 3 and QC 1 & 2 MSSV Network Using Pooled Data and Design.

ML043150023
Person / Time
Site:	Dresden
Issue date:	10/28/2004
From:	Freeman J Exelon Generation Co, Exelon Nuclear
To:	Office of Nuclear Reactor Regulation
References
MWMECH-04-004, Rev 0
Download: ML043150023 (83)

Text

ATTACHMENT Calculation MWMECH-04-004, "Monte Carlo Analysis of Dr 2&3 and QC 1&2 MSSV Network Using Pooled Data and Design Methodology Approach," Revision 0

CC-AA-309-1001 Revision 2 l Page 1 of 1 ATTACHMENT I Design Analysis Cover Sheet Page 1 of 5 Design Analysis (Major Revision) I Last Page No. e12 L attdacktet X-1 Analysis No.: I MWMECH-04-004 Revision: 2 0

Title:

3 Monte Carlo Analysis of Dr 2&3 and QC 1&2 MSSV Network Using Pooled Data and Design Methodology Approach ECIECR No.: 4 3G2 1l Revision: 5 0 Station(s):' Dr /QC Component(s): 14 Unit No.: " 2&311&2 Discipline:' M Descrip. Code/Keyword: 10 SafetylQA Class: Safety related System Code: 12 Structure: I3 CONTROLLED DOCUMENT REFERENCES 1' Document No.: From/To Document No.: From/To Is this Design Analysis Safeguards Information?" Yes [3 No x If yes, see SY-AA-101-106 Does this Design Analysis contain Unverified Assumptions? 17 Yes 0 No x If yes, ATIIAR#:

This Design Analysis SUPERCEDES: '" N /A In Its entirety.

Description of Revision (list affected pages for partials):"I e5t1A 6 L- 155EI6 Preparer: 20 Kevin Ramsden b y 10/21/04 Print Name Name ISin Date Method of Review: 21 Dotalled Review E After -nate C laations (a )E Testing r Reviewer: 22 ip aA94Z-6h =04K t-S ~ 10/2?/0 PntName Nam at -

Review Notes: 2' Independent review i er review a Act. eatcc- wa SeA bvt Ae:- eoki ti-tes- CAY ,gwAcA

<,s;4 Wrave. kA.eUA.A a c5-rg vas bcev^ acet'qbee~a.l VI if ekc-AC <{tceA\er z¶4.py CevAStOi'-ot t~etU~t '5 tK (For External Analyses Only) i '4 M 24 /A 0 I External Approver: N/A PrntName Sign Name Date Exelon Reviewer: 25 by . N 1A N b+A Pri Ndme Sigri Name Date Is a Supplemental Review Required?26 Yes El No l If yes, complete Attachment 3 Exelon Approver: 21 Michael Strait _7_________ _ _/_ _/ _

Print Name Sign Name I Me

CC-AA-309 Revision 4 1 Page 15 of 16 ATTACHMENT 1 General Review Questions Page 1 of I Pqc e-2 DESIGNANALYSISNO. AWME C1-oA - c 4 REV: O Yes No N/A

1. Does the Design Analysis conform to design requirements?-ts? 4( T El

2. Does the Design Analysis conform to applicable codes, standards, and El regulatory requirements? goJCVwns ANkC OvesnT r4 El El

3. Have applicable design and safety limits been identified? El El

4. Is the analysis method appropriate? El

5. Are the methods used and recommendations given conservative relative to the design and safety limits? El El

6. Are assumptions/Engineering Judgments explained and appropriate?

7. Have appropriately verified Computer Program and versions been El identified, when applicable?

8. Does the Computer Program conform with the NRC SER or similar El 1:D document when applicable? El F1 El

9. Has the irput bean correctly incorporated into the Design Analysis?

10. Has the inp&Aeen'reviewed ya cogui7 t Vdesign authdrivesl El To 0

II. Are the analysis outputs and conclusions reasonable compared to the inputs and assumptionsCoUL-uS(ON iettfl 1kOND os El

12. Are the recommendations/results/conciusions reasonable based on previous experience? El El

13. Has a verification of the Design Analysis een performed by alternate methods? , Ai-tvC- Z-L. bj 6E g El Co

14. Has all inp a a been used correctly and is it traceable? El El

15. Has the effect on plant drawings, procedures, databases, and/or plant simulator been addressed? El

16. Has the effect on other systems been addressed? ' El

17. Have any changes in other controlled documents (e.g. UFSAR, Technical Specifications, COLR, etc.) been identified and tracked? El

18. When applicable, are the analysis results consistent with the proposed g license amendment? El El

19. Have other documents that have used the calculation as input been reviewed and revised as appropriate? El El

20. Have all affected design analyses been documented on the Affected E Documents List (ADL) for the associated Configuration Change? El

21. Do the sources of inputs and analysis methodology used meet current technical requirements and regulatory commitments? (If the input sources or analysis methodology are based on an out-of-date methodology or El El code, additional reconciliation may be required if the site has since committed to a more recent code)

22. Have supporting technical documents and references been reviewed when necessary? . , / El E CoC, ec~ E {t/g~

TITLE: EXELON MISSV NETWORK ANALYSIS REPORT 4Cr, CAie, A - 4 CD eVOo payc 02iq FINAL Originator: Date:

DRF Number: 0000-0013-2575 Y. Dayal 8/08/04 DRF Section: 0000-0030-0771 Report Number: 0000-0030-0771-2 Sheet I of 12 TABLE OF CONTENTS

1. Objective .............................. 3

2. Background .............................. 3

3. Validation of Results and Methodology ............................. 3; 3

4. Conclusions and Recommendations .............................. 5

5. References.......................................................................................................................5

TITLE: EXELON MSSV NETWORK ANALYSIS REPORT hT. COtc. AWCH4 -O- o4A ke'r. P)yA Z-%

FINAL Originator: Date:

DRF Number: 0000-0013-2575 Y. Dayal 8/08/04 DRF Section: 0000-0030-0771 Report Number: 0000-0030-0771-2 Sheet 2 of 12 List of Tables Table 1: Distribution Characteristics for Calculations ....................................................... 6 Table 2: Comparison of Calculated Network Valve Opening Pressures ........................... 7 Table 3: Comparison of Calculated Analytical Network Valve Opening Pressures ......... 8 Table 4: Comparison of Calculated Analytical Network Valve Opening Pressures ......... 9 List of Figures Figure 1: Network Valve Opening Pressure Distribution - Base Case ............................ 10 Figure 2: Network Valve Opening Pressure Distribution - Alternate Case ..................... 11 Figure 3: Safet Valve Flow vs. Pressure.......................................................................... 12

TITLE: EXELON MSSV NETWORK ANALYSIS REPORT Acr' c<u. fwK o -cO4 Ave o Poz C FINAL Originator: Date:

DRF Number: 0000-0013-2575 Y. Dayal 8/08/04 DRF Section: 0000-0030-0771 Report Number: 0000-0030-0771-2 Sheet 3 of 12

1. Objective This document provides an independent assessment and validation of the statistical methodology (Ref. I) for determining opening of main steam system valves (MSSV) on an over-pressure transient. The report specifically addresses the following items:

1. Validating the methodology developed and demonstrated in the calculation, for the inputs selected.

2. Recommendations for future application, particularly in regard to license amendment or ASME overpressure methodology submittal changes.

3. Concurrence that the calculation as written is reasonable for the application stated, that of safety significance and demonstration of operability.

2. Background

The current methodology uses the stated opening pressure of the valves, increases it by I%, and uses those opening pressures in the plant over-pressure analyses for MSIV closure events. However measurement of as-found valve test data suggests that the opening pressure for the valves is distributed, and the variability is more than the I%. This has led to some confusion on operability and safety issues, although it is known that the variability is such that valves open at both higher and lower pressure, and it is a very small probability that all valves open at the upper end of the measured variabilities.

A statistical method based on a structured approach is needed to assess the impact of the measured opening pressure distribution, and to determine if the impact matches the results from the standard I % method. In assessing the impact it is important for the statistical method to recognize that what needs to be analyzed is a network of valves which open to release steam and keep the dome and reactor pressure at acceptable levels.

The network has several valves, and each type of valve in the network has an opening pressure distribution function based on measurements.

Such a statistical method was used and results were presented in Reference 1. This report provides an independent assessment of the results.

3. Validation of Results and Methodology The approach used in Ref. I was statistically sound and the results were accurate. The methodology correctly recognizes that each valve (or each type of valve) has associated with it a probability distribution for lift pressure with respect to the setpoint, and that the distribution can be determined by evaluating measured as-found data. The results in Ref. I were obtained by the PLANETS plant network simulation program (Ref. 2) which correctly accounts for the fact that because of the uncertainties in individual valve performance, the order in which the valves open does not necessarily follow the setpoint values.

3.1 Valve Opening Pressures To validate the valve opening results from Ref. 1, two approaches were taken:

1) An alternate Monte Carlo calculation program, using Mathcad, was set up from first principles. The program chose 1000 random numbers from a normal distribution with the same average and standard deviation as used in Ref. I (called the Base Case), for each valve in the network. The network had I Target Rock SRV and 8 spring safeties. A list of the valves, setpoints and standard deviations are shown in Table 1. Two cases were run:

a. Base Case: For the Base Case the standard deviations were based on the measured results reported in Reference 3, without any multipliers due to number of data points in the measurement, and no adjustment for the observed bias.

TITLE: EXELON MSSV NETWORK ANALYSIS REPORT Aa c&A. c2-o-oo 4c Ec d FINAL Originator: Date:

DRF Number: 0000-0013-2575 Y. Dayal 8/08/04 DRF Section: 0000-0030-0771 Repor Number: 0000-0030-0771-2 Sheet 4 of 12

b. Alternate Case: For this case the standard deviations were increased by multiplying by the 2-sided K factor for 95% confidence corresponding to the number of data points in the measured data sample. This value, which is equivalent to 2-sigma for normal distribution was divided by 2 to obtain the 1-sigma value needed for the Monte Carlo calculations. The small observed negative bias in the data (Ref. 3) was also considered.

Results from these Monte Carlo calculations agreed well with the results from Ref. 1. A comparison is shown in Table 2. A plot of the valve opening pressures for the network from the Mathcad simulations are shown in Figure I for the Base Case and Figure 2 for the Alternate Case. As expected the Target Rock valve, with a low setpoint several standard deviations below the spring safeties, is clearly the first valve to open. For the spring safeties there is overlap, and is clearly noticeable.

2) An analytic closed form solution was obtained for the Ist, 2nd, 3rd and 9th valve opening, based on first principles. The solution was identical with the PLANETS solution for the I st valve, but since no analytic solution for other valve openings are given in PLANETS, those could not be compared.

Results from these analytic calculations agreed well with the results from the PLANETS and Mathcad Monte Carlo simulations. A comparison is shown in Table 3.

3.2 Pressure Relief To validate the flow versus pressure results from Ref. 1, an alternate Excel calculation spreadsheet was developed. The valves were modeled to achieve 50% flow when they reached their setpoint and increasing flow linearly to their rated value at an accumulation pressure of 3% above the opening setpoint. This is an accepted standard model used in safety analysis codes, and was the model used in Ref. 1. Use of this flow model requires an opening pressure value. For the statistical network analysis, the opening pressure corresponding to the 95 percentile value was used. This is considered appropriate for a network over-pressure analysis.

The flow versus pressure for several cases were calculated and plotted using the Excel program.:

1) 1%Drift Case: Individual valve opening pressures 1% above the nominal setpoint

2) Bounding 95,95 Case: Individual valve opening pressures corresponding to Bounding 95,95 values from Ref. 3

3) Base Case: Statistical network analysis with opening pressure corresponding to 95% percentile value from Base Case described in Section 3.1 item Ia.

4) Alternate Case: Statistical network analysis with opening pressure corresponding to 95%

percentile value from Alternate Case described in Section 3.1 item Ib.

The results from the Excel calculation are shown in Figure 3, and agree well with the results in Ref. 1. The area under the curves from pressure 1150 to 1350 psia show that the Base Case network analysis 95 percentile values yield 98.8% of the delivered flow from the standard I% drift individual valve case. Even for the Alternate Case network analysis the delivered flow is 97.2%. These percentages are significantly greater than the 77% for the individual valve case using bounding 95,95 values from Ref. 3. These results validate the Ref. I conclusion that the statistical network analysis provides almost the same total flow and pressure relief as that obtained using the standard 1% individual valve approach. The results also show that the Bounding 95,95 setpoint would not provide equivalent pressure relief.

An over-pressure evaluation for an MSIV closure transient was also performed for the statistical network Base Case analysis using the 95 percentile pressures as the setpoints, and this was compared to the standard I % individual valve case. The results showed that the dome pressure was only 0.8 psi higher for the Base Case and 1.5 higher for the Alternate Case, and the vessel pressure was only higher by 0.5 psi and 0.8 psi respectively. Results of this over-pressure analysis is shown in Table 4.

TITLE: EXELON MSSV NETWORK ANALYSIS REPORT Ac-.c~~c. ~M, cd-Q-04 ie~ 0 (cty4 2Se FINAL Originator: Date:

DRF Number: 0000-0013-2575 Y. Dayal 8/08/04 DRF Section: 0000-0030-0771 Report Number: 0000-0030-0771-2 Sheet S of 12

4. Conclusions and Recommendations The statistical network analysis methodology is technically defensible and appropriate for evaluating MSSV opening for over-pressure evaluations. The results are valid and demonstrate that although the measured as-left data appear to indicate a variability which is significantly higher than 1%, the statistical network solution using a 95 percentile value for the valve opening pressure gives results which are similar to those obtained by using the standard I % drift criterion. This provides a basis and justification for staying with the simpler 1% approach. Although the statistical approach is technically sound and provides an evaluation which is appropriate for both safety and operability issues, opting for this more complicated approach may require more effort to support in the long run.

The Base Case used the measured sample sigma value for the network evaluations. This may be challenged because it did not take into account the number of samples. Another evaluation similar to that described in Ref. 3, would need to be done with more data to justify the sigma value used in the Base Case.

If such data and evaluation is not feasible, the Alternate Case may be a suitable option. The Alternate Case includes a slight penalty for the number of samples, but justifiably includes the observed negative bias.

Peak pressure calculations for MSIV transient showed that there was only about 0.5 psi difference in results between the Alternate and Base case. For any license amendments or design calculations performed in the future, an uncertainty factor would need to be applied to the as-found data to bound the limited number of data points that are used in determining the sample standard deviation.

5. References I Exelon Calculation No. MWMEC-04-002, Rev 0. Also "Updated M/C Results" e-mail K. Ramsden to Y. Dayal, 8/3/04; and "Mirror Run of PLANETS" e-mail K. Ramsden to Y. Dayal, 8/4/04 2 "PLANETS: Plant Network Simulation Program", EPRI NP-7557-CCML, Oct 1991 3 "Dresden Main Steam Safety Valve Setpoint Tolerance Analysis" GE DRF No. 000-0013-2575, dated 6/21/04

TITLE: EXELON MSSV NETWORK ANALYSIS REPORT

&uT4.(A(c 4-vk Broa D k Qdeeye  %!

FINAL Originator: Date:

DRF Number: 0000-0013-2575 Y. Dayal 8/08/04 DRF Section: 0000-0030-0771 Report Number: 0000-0030-0771-2 Sheet 6 of 12 Table 1: Distribution Characteristics for Calculations Distribution Base Case Characteristics Spng Safeties Spring Safeties Spring Safeties Target Rock Number 2 2 4 1 Set point (Psia) 1255 1265 1275 1150 1 sigma (psia) 13.7 13.81 13.92 15.69 Mean (psia) 1255 1265 1275 1150 Distribution Alternate Case Characteristics Sprin Safeties Spring Safeties Spring Safeties I Target Rock Number 2 2 4 1 Set point (Psia) 1255 1265 1275 1150 1 sigma (psia) 17.35 17.49 17.63 29.38 Mean (psia) 1251.60 1261.58 1271.55 1146.33

TITLE: EXELON MSSV NE TWORK ANALYSIS REPORT Atzc*.- W ECAA-0470OF AP-If sulf P FINAL Originatorr: Date:

DRF Number: 0000-0013-2575 Y. Dayal 8/08/04 DRF Section: 0000-0030-0771 Report Number: 0000-0030-0771-2 Sheet 7 of 12 Table 2: Comparison of Calculated Network Valve Opening Pressures Valve Base Case Mathcad Monte Carlo Valve Opening Calc Results, N = 1000 mean median 5% 95% std dev

_ 1151 1151 1123 1177 16.26 2 1244 1245 1226 1259 9.56 3 1254 1254 1242 , 1265 7.24 4 1260 1261 1249 1270 6.56 5 1265 1265 1255 1275 6.19 6 1270 1270 1261 1279 6.21 7 1275 1275 1265 1287 6.53 8 1282 1282 1271 1295 7.32 9 1290 1290 1277 1306 8.92 Valve Base Case PLANETS Monte Carlo Valve Opening Calc Results (Ref. 1) mean median 5% 95% std dev 1 1150 1150 1124 1176 16.16 2 1243 1244 1227 1258 11.17 3 1253 1254 1240 1265 8.08 4 1260 1260 1248 1271 6.92 5 1265 1265 1254 1276 6.67 6 1270 1270 1260 1281 6.63 7 1276 1275 1265 1287 6.97 8 1282 1281 1270 1294 7.71 9 1291 1290 1276 1307 10.03 Valve Alternate Case Mathcad Monte Carlo Valve Opening Calc Results, N = 1000 mean median 5% 95% std dev 1 1147 1148 1098 1195 29.33 2 1244 1237 1228 1254 11.87 3 1247 1248 1231 1261 9.06 4 1255 1256 1242 1270 7.83 5 1261 1261 1249 1274 7.56 6 1268 1267 1255 1281 7.76 7 1274 1273 1261 1288 8.11 8 1281 1281 1267 1296 8.89 9 1292 1291 1274 1306 10.88 Valve Alternate Case PLANETS Monte Carlo Valve Opening Calc Results (Ref. 1) mean median 5% 95% std dev 1 1195 2 1253 3 1262 4 1268 5 1274 6 1280 7 1287 8 1296 9 1312

A-CA9r TITLE: EXELON MISSV NETWORK ANALYSIS REPORT M JMC-C14--00C -O r ,04

.ev, 0. PCqe a i FINAL - Originator: Fgate:

DRF Number: 0000-0013-2575 ( Y. Dayal 8/08/04 DRF Section: 0000-0030-0771 Report Number: 0000-0030-0771-2 Sheet 8 of 12 Table 3: Comparison of Calculated Analytical Network Valve Opening Pressures Valve Base Case Analytical Solution mean median 5% 95% std dev 1 1150 1150 1124 1176 15.7 2 1244 1244 1227 1258 9.4 3 1253 1253 1240 1265: 7.4 4

5 I 6 I 7

8 9 1291 1289 1276 1306 9.1 Valve Base Case PLANETS Analytical Results (Ret. 1) mean median 5% 95% std dev 1 1150 1150 1124 1176 15.9 2

3 4

5 6

7 8

9 Valve Alternate Case Analytical Solution mean median 5% 95% std dev 1 1146 1146 1098 1194 29.3 2 1236 1236 1215 1253 11.5 3 1247 1247 1231 1261 9.1 4

5 6

7 8

9 1292 1291 1274 1311 11.5

TITLE: EXELON MSSN' NETWORK ANALYSIS REPORT AG-r. 44(-Ca(-. 4-~eJ* P~q~e FINAL Originator: ' Date:

DRF Number: 0000-0013-2575 Y. Dayal 8/08/04 DRF Section: 0000-0030-0771 Re or Number: 0000-0030-0771-2 Sheet 9 of 12 Table 4: Comparison of Calculated Analytical Network Valve Opening Pressures TRANSIENT Name Case Peak Dome Peak Vessel I I Pressure I Pressure P(V)

(psig) (psig)

MSIVF 1% Tolerance 1338.9 1362.0 MSIVF Base Case 1339.7 1362.5 MSIVF Alternate Case 1340.4 1362.8

4-T Cr. C TITLE: EXELON MISSV NETWORK ANALYSIS REPORT

,MkW ac Li 0 A-- Qe,k iwPq e 7J FINAL Originator: -Date:

DRF Number: 0000-0013-2575 Y. Dayal 8/08/04 DRF Section: 0000-0030-0771 Report Number: 0000-0030-0771-2 Sheet 10 of 12 Figure 1: Network Valve Opening Pressure Distribution - Base Case Valve Network Opening Pressure Dist 350 Fl F2

- 250 F3 F4

- 200

• = FS V F6 4- 150 F7 FS

- 100 F9 50 0

1000 1050 1100 1150 1200 1250 1300 1350 1400 1000 HiH2,H3,H4, H-5,H6,H7, HS8,H9 1400 Line Pressure (psia)

A-c-r: CA&c-. TITLE: EXELON MSSV NETWORK ANALYSIS REPORT MWMGesc1 -Oar Dojr god&R. D I 21 FINAL Originator: te:

DRF Number: 0000-0013-2575 Y. Dayal 8/08/04 DRF Section: 0000-0030-0771 Report Number: 0000-0030-0771-2 Sheet 11 of 12 Figure 2: Network Valve Opening Pressure Distribution - Alternate Case Valve Network Opening Pressure Dist 350350 1 1 - 1 1 1 1 300 -

F1 F2

- 250-F3 F4

-200 F5 F6

- 150 F7 FS 100 F9 50 0K 0 1000 1050 1100 1150 1200 1250 1300 1350 1400 1000 H 1.H2.1-H3. H4. H5.1-H6. H7. HS,1-9 1400 Line Pressure (psia)

A-t chiC. TITLE: EXELON MSSV NETWORK ANALYSIS REPORT lM(Jg ~  !- + 04- ple V.CDg e 2, L FINAL Originator- M~te:

DRFNumber: 0000-0013-2575 Y. Dayal 8/08/04 DRF Section: 0000-0030-0771 Report Number: 0000-0030-0771-2 Sheet 12 of 12 Figure 3: Safety Valve Flow vs. Pressure Relief Flow vs Pressure 7-6

.:i~,<sR*X 5 ->*

-1% Drift

-Base Case -

Monte Carlo

-Bounding Value 2

11- -Alternate Case-Monte Carlo 0

1150 1200 1250 1300 1350 Pressure (psia)

EC EVAL 351882 PA #VtH OO- t)&4 /,e v.d O

&a' -

A review of the historical data for Dresden does not indicate any drift in the range of 3.6% low or 6.8% high. The individual instance of low drift has been identified as a result of spring wear into the spring cap. The investigation into the cause of this phenomenon is a tolerance accumulation of spring tilt. Target Rock has described the effect of spring wear into the spring cap as follows. As the spring wire wears into the bellows cap the spring remains in the helical groove worn into the cap. The spring is essentially fixed to the adjusting screw, however the bellows cap is free to move axially and rotate. If the spring wire is in contact with the upper portion of the helical groove there will be a net upward force and the set point will trend lower. Conversely, if the spring wire is in contact with the lower portion of the helical groove there will be a net downward force and the set point will trend higher. The data obtained from testing these valves during operation at the increased flow levels is inconsistent previous test data.

The cumulative reactor operating years for both units at Dresden equates to 14 years and the instance of occurrence of once. Analysis of this failure has determined that the excessive spring tilt tolerance accumulation on the mating parts and some vibration has resulted in a synergistic effect that has resulted in this anomalous performance. While this corrective action should preclude setpoint drift, it will not completely exclude this from occurring. With corrective actions in place for a modified spring cap, a spring selection criteria and a long-term redesign of the cap and spring assembly, should resolve this issue in the future. Based on previous performance and future enhancements, the data should be excluded from the pool in performance of a Monte Carlo analysis.

CALCULATION TABLE OF CONTENTS CALCULATION NO. MWMECH-04-004 REV. NO. PAGE NO.3 0

SECTION: PAGE PAGE REVISION NO.. NO.

TABLE OF CONTENTS 3 0 PURPOSE 4 0 INPUTS 4 0 ASSUMPTIONS 5 0 REFERENCES 5 0 IDENTIFICATION OF COMPUTER PROGRAMS 6 0 METHOD OF ANALYSIS AND ACCEPTANCE CRITERIA 6 0 RESULTS 8 0 CONCLUSION 12 [Last] 0 ATTACHMENT A - QC 1 &2 Valve Data Al to A3 0 ATTACHMENT B - Dr 2&3 Valve Data Bl-B3 0 ATTACHMENT C - MATHCAD QC T/R Statistics Worksheet C1-C4 0 ATTACHMENT D - MATHCAD QC MSSV Statistics D1-D4 0 Worksheet ATTACHMENT E - MATHCAD Data Combination Worksheet- El to E6 0 Target Rock S/RV Valves ATTACHMENT F - MATHCAD Data Combination Worksheet- F1-F6 0 Main Steam Safety Valves ATTACHMENT G - PLANETS Output Gl-G14 0 ATTACHMENT H - MATHCAD Monte Carlo PDF Worksheet Hi-H6 0 ATTACHMENT I - MATHCAD Valve Flow Worksheet 11-111 0 ATTACHMENT J - Validation of PLANETS Software Ji 0 a a

ICALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. 4 1.0 Purpose The purpose of this calculation is to perform a Monte Carlo statistical analysis of the Dresden Units 2 and 3 and Quad Cities Units 1 and 2 main steam safety valve networks. The intent is to demonstrate a statistically based technically valid alternative to traditional deterministically applied setpoint drift. The as-found data for the two plants is combined and utilized to develop a statistically based model of network performance applicable to both sites. A mathematical model of safety valve performance is generated to allow comparison and conclusions to be drawn.

Generally, safety valve drift is considered as a fixed percentage of the setpoint. Typically 1% or 3% of setpoint is used as a drift allowance. In application in safety analysis codes, this drift allowance is generally used additively and uniformly to a valve or group of valves with the same setpoint.. It is important to note that especially with groups of valves, assuming all of them drift to the highest possible setpoint is a very conservative approach, as will be demonstrated.

In contrast, employing a Monte Carlo analysis to a network will show that valve opening for a group of valves with the same setpoint will display a distribution, with some valves opening low and some opening high. The characterization of valve opening can be selected to include a desired percentage of the distribution; typically 95 percentile numbers would be selected for each valve to ensure that the result is conservative and bounds the majority of the data.

Employing a statistically based methodology to predict safety valve network performance requires careful consideration of the data to ensure appropriate conservatism exists in the final product. Specifically, the data distribution needs to be assessed, since this distribution is an assumption of the Monte Carlo. Data pooling requires evaluation in practical terms as well as statistical testing. Finally, the amount of data available requires assessment, and a method to expand the assumed distributions in the Monte Carlo input may be warranted. These considerations have all been included in this calculation, with the intent of producing a realistic, yet conservatively based characterization of the Dresden Units 2&3 and Quad Cities Units 1&2 safety valve networks.

2.0 Inputs

1. The Target Rock SRV setpoint is 1150 psia, (Ref. 1)

2. The Dresser MSSV configuration is 2 valves @1255, 2 valves @1265, and 4 valves @1275 psia, (Ref. 1)

3. The Target Rock nameplate capacity is 598000 lb/hr. (Ref. 1)

4. The Dresser nameplate capacity is 644500 lb/hr (Ref. 1)

5. Transmittal of Design Information "Dresden Main Steam Safety Valve as-Found Test Results," Doc ID CC2004-9997, dated 2/13/04 and included as Attachment B to this calculation.

'CALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. 5 3.0 Assumptions

1. The Target Rock and Dresser setpoint drifts are normally distributed. This has been tested and validated in this calculation.

2. The valve opening behavior will be assumed to be 50% open on reaching setpoint, linearly increasing to full flow at 103% of setpoint and linearly increasing with pressure. This is consistent with typical modeling practices.

3. The As-found data applied in this calculation includes the most recent data for the MSSVs for both Dresden and Quad Cities.

4. The As-found data for the Target Rock S/RVs does not include two data points, one from Dresden at -3.6% and one from QC at +6.8%. These test points are the subject of a detailed evaluation and have been excluded at the direction of Site Engineering.

[Reference 6]

4.0 References

1. OPL3, Dresden and QC PDLB for EPU/MELLA, Rev. 2

2. 'The Handbook for Statistical Analysis of Environmental Background Data", Naval Facilities Engineering Command, 1999.

3. "Applying Statistics", NUREG 1475,1994.

4. "Dresden Main Steam Safety Valve Setpoint Tolerance Analysis," GE DRF No. 0000-0013-2575, dated 6121/04.

5. "GENE review of Exelon Monte Carlo Calculations, " Report Number 0000-0030-0771-2, dated 8/08/04.

6. "Evaluation of T/R valves recent failures", Dresden EC EVAL 351882.

I CALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. 6 5.0 Identification of Computer Programs The Monte Carlo analysis was performed using the PLANETS computer code on the Exelon Unix Platform. This code is a Fortran-language statistical utility program developed by SLI for EPRI and provided to Exelon. This code was not supplied under EPRI quality assurance standards. It was specifically compiled for this application and tested to ensure appropriate results would be generated for the type of problem being addressed here. A validation comparison to supplied sample problems was performed and is included in Attachment J. In addition, the Reference 5 work performed an independent calculation that provides additional confirmation and validation of the PLANETS computer code.

This calculation was performed in part using Mathcad, version 11. Per procedure CC-AA-309-1001, Revision 0, step 4.3.6, use and documentation for this software is exempt from the Digital Technology Systems procedure IT-AA-1 01 because it is personal productivity software. Detailed printouts of the calculations or analyses were provided in the attachments so that specific recourse to the preparer is not required.

6.0 Method of Analysis and Acceptance Criteria' Statistical analysis of the Dresden and Quad Cities as found valve setpoint data was performed to characterize the data. The PLANETS statistical program was then used to perform a Monte Carlo analysis of the network. A MATHCAD model of the valve network was then applied to allow meaningful comparison between different treatments of setpoints.

6.1 As-found Valve Data Statistical Analysis The as-found valve data for Dresden is provided in the Reference 4 analysis. The Reference 4 analysis performed statistical evaluation of the Dresden data in accordance with Reference 3 guidelines, including calculation of the mean, standard deviation, W-test normality checks and development of single sided 95-95 bounding values.

The as-found valve data for Quad Cities is provided in EXCEL spreadsheet format in Attachment A. The data was treated in two groups, the mechanical spring safety valves and the Target/Rock S/RVs. The valve drift was calculated based on percent of setpoint. The means and standard deviations were then calculated. The standard deviations were based on sample vs population formulations(denominator includes n-1 vs n). Each data group was tested for normality. Since the spring safety valve group had a relatively large number of data points (70),

the D'Agostino normality test was applied, as recommended by reference 2. The Target Rock group consisted of 11 data points, and a W-test for normality was implemented in accordance with reference 3. Both data groups were shown to be normally distributed. In addition, the methodology contained in Reference 3 was applied to determine the 95-95 limits for the data based on single-sided tolerances.

The pooling of Dresden and Quad Cities as found data was considered reasonable, based on similarity of equipment and operating conditions. An F-test was performed for the Dresden and Quad Cities data to further establish acceptability of data pooling. Since the data all was normal, and the F-test showed poolability of data, the data was combined. Two groups of data resulted, one characterizing the Target Rock S/RVs, and the other describing the Dresser MSSV (spring safety).

I CALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. 7 The standard deviations for the combined data were calculated and two-sided k-factors for 95-95 bounding values determined. The k-factor determined in this fashion is divided by 2 and applied to the 1-sigma values, to conservatively broaden them and address the effects of limited number of as-found data points. The intent of this approach is to preserve the same level of confidence in the Monte Carlo input as would be captured by the 95-95 procedure.

6.2 PLANETS Monte Carlo Model The PLANETS code employs a relatively-simple set of input data to characterize the network.

Specifically, the nominal setpoint for each valve or group of valves is supplied. The valves were treated as having a normal distribution of drift. The standard deviation applied was taken directly from the characterization above, and was broadened to account for the limited number of as found points as noted above. The pressure range of 1100 to 1350 was swept using 250 steps or

'bins'. 100,000 histories were generated for this calculation. Since the desire is to focus on the latest opening valves, appropriate minus signs were added to the setpoints and pressure ranges, as suggested by the code manual.

The PLANETS code provides both an analytical solution to the network, capturing the statistics of the last opening valve, and an optional Monte Carlo simulation of the network, which provides statistical information for every valve in the network. This allows an independent check on the last opening valve data, and also yields the information necessary to develop 95h percentile setpoint data for the entire set of valves.

As an additional check of the PLANETS results, a MATHCAD worksheet was prepared to generate the probability density distributions for each valve and perform a 9 5 th percentile computation for comparison to the 95th percentile provided by PLANETS.

6.3 MATHCAD Integrated Safety Valve Model A model of the flow vs. pressure response of the valve network was developed to facilitate comparison between different setpoint application methods. The valves were modeled in groups for the standard drift methods. The valves were modeled individually to utilize the Monte Carlo analysis results. In all cases, the valves were assumed to achieve 50% flow on reaching their setpoint (including drift). After opening, the valve flow is modeled as linearly increasing to 100%

at an accumulation of 3% pressure rise above the opening point. Valve flow was modeled as linearly increasing with pressure. This approach is representative of the application in standard safety analysis codes.

This modeling was accomplished through the use of Mathcad programming features to define stepwise continuous functions. The Mathcad file used to model the valves pressure flow response is provided in Attachment F.

ICALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. 8 7.0 Results Current Analysis Basis The current analytical basis is to assume that all valves are at their maximum drift allowable values (1%). At this pressure the valve is assumed to open to 50% and then linearly increase area to 100% at 3% accumulation. Therefore the setpoints used in the analysis are:

Setpoint psia Setpt+1 % (psia)

TIR S/RV 1150 1161.35 Gr 1 1255 1267.4 Gr2 1265 1277.5 Gr3 1275 1287.6 Historical As-found Data Statistical Analysis I A series of data was collected and analyzed statistically as described in section 6.1. The data was tested and demonstrated to be normally distributed. A summary of the statistical data is provided in the tables below. The Mathcad worksheets for the Quad Cities statistical characterization are provided as Attachments C and D.

Quad Cities Unit 1 and 2 Data Summary Mean drift Standard Normality test/ Data 95-95 drift 0/o/setpoint deviation significance level Normal based on 1-0/o/setpoint sided tolerance

_°/o/setpoint Target 0.128 2.054 W-testl0.05 Yes 5.929 Rock Dresser 6.757E-4 0.952 D'Agostino/0.05 Yes 1.896 MSSVs Dresden Unit 2 and 3 Data Summary Mean drift Standard Normality test/ Data 95-95 drift 0/olsetpoint deviation significance level Normal based on 1-0/olsetpoint sided tolerance 0/o/setpoint Target -0.319 1.364 W-testl0.05 Yes 4.03 Rock Dresser -0.271 1.092 W-test/0.05 Yes 2.14 MSSVs

' CALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. 9 Data Pooling The data was examined for poolability based on the following considerations:

1. The valves are identical in design at both sites.

2. The operating conditions are very similar, in temperature, pressure, as well as main steamline flow rates.

3. Pooling of data is by type of valve, ie. Target Rock data together, and separately, the MSSV data together.

An F-test was performed for the Target Rock data in accordance with the guidance provided in Section 10-6 of NUREG 1475, with an alpha of 0.05. The result was that the data is poolable.

The same test was applied to the MSSV data with the same result. The worksheets detailing the F-test and pooled data statistical characterization are provided as attachments E and F. The statistical characterization of the combined is:

Dresden/Quad Cites Pooled Data Su mary Mean drift Standard One Two 95-95 drift based a times

%/I/setpoint deviation sided sided on 1-sided k2 J2 0O/lsetpoint 95-95 95-95 tolerance 0/o/setpoint k-factor k-factor 0/o/setpoint Target -0.06 1.766 2.425 2.794 4.222 2.467 Rock S/R V s _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Dresser -0.084 1.001 1.925 2.232 1.842 1.117 MSSVs Monte Carlo Analysis Based on the observed standard deviations of the as-found valve setpoints and the confirmed assumption that the data is normal, a calculation was performed for the valve network based on the following inputs:

1. la equal to 2.467% of setpoint for the Target Rock and 1.117% percent of setpoint for the MSSVs

2. Normal distribution applied, with tails to 5a (PLANETS default).

3. One T/R at 1150 psia setpoint

4. One group of 2 MSSVs at 1255 psia setpoint.

5. One group of 2 MSSVs at 1265 psia setpoint

6. One group of 4 MSSVs at 1275 psia setpoint

7. 100,000 histories were generated, based on code developer recommendations.

8. Bias (mean drift) not included in setpoint, since this results in a more conservative result.

The PLANETS output summary file for the run performed is provided in Attachment G. The following table summarizes the 9 5 th percentile data for each valve in the network and allows direct comparison to the 1% and 95-95 based drift case. An additional check of the last valve opening is provided by the PLANETS analytical solution, and very good agreement with Monte Carlo solution is obtained in this case. As a further check of the PLANETS Monte Carlo solution,

ICALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. 10 the base case was run with 500,000 histories. The summary of this run is located at the back of Attachment G and shows excellent convergence with the 100,000 history case. The Mathcad modeling that plots the individual valve probability density distributions and checks the 9 5th percentile values is provided as Attachment H.

Valve/nominal 1% Drift Analysis Monte Carlo 95 NUREG 1475 setpoint psia Setpoint (psia) percentile opening 95-95 Bounding point (psia) Values T/R /1150 1161.35 1196.2 1197.9 MSSV GR1 / 1255 1267.4 1258.1 1277.8 MSSV GRI /1255 1267.4 1265. 1277.8 MSSV GR2 / 1265 1277.5 1270.7 1288.

MSSV GR2 /1265 1277.5 1275.8 1288.

MSSV GR3 /1275 1287.6 1281.1 1298.2 MSSV GR3 /1275 1287.6 1286.9 1298.2 MSSV GR3 / 1275 1287.6 1294.4 1298.2 MSSV GR3 / 1275 1287.6 1307.2 1298.2 What is readily apparent is that there is a significant overlap between the Monte Carlo generated setpoints and the 1% drift setpoint case. It is also clear that the all valves drifted to the 95-95 setpoint bounds all but the last opening valve as predicted by the Monte Carlo method. The Target Rock Valve opening point predicted by Monte Carlo yields a comparable opening point to the 95-95 bounding approach. This is expected based on the fact that the Target Rock is a single valve with an opening point well below the MSSVs. The close agreement to the 95-95 bounding value provides confirmation of the one-sigma broadening approach applied to conservatively address limited numbers of data points.

Demonstrating the valve network performance in terms of flow vs. pressure allows a more meaningful comparison to be made. The Mathcad model of the valve network used to generate the flow vs. pressure for the various network setpoint arrangements is provided as Attachment I.

The results of this model are provided in Figure 1. This figure clearly demonstrates the flow response expected from the Monte Carlo is very close to that of the 1% setpoint drift analysis.

Integration of these curves for a fast pressure sweep from 1150 psia to 1350 psia shows that the Monte Carlo 95t percentile values yield 94.9% of the delivered flow from a 1% drift case. In contrast, the 95-95 basis setpoints yield 82.2% of the 1% drift case flow.

The valve model was also exercised to determine a traditional drift value that would provide equivalent flow to the Monte Carlo results. A value of 1.5% drift applied to all valves would yield comparable results. Additionally the flow model was exercised to determine the impact of the Target Rock valve drift on the overall results. If the Target Rock is excluded from the 1% base case and also from the Monte Carlo summation, the results show that equivalent flows occur. In other words, the actual MSSV valve performance when applied in a Monte Carlo calculation shows equivalence to a traditional 1% drift analysis.

I CALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. 11 Figure 1 Safety Valve Flow vs Pressure Comparison of Relief Flow vs Pressure

,6.4xl 0. 0o6 6.106 Qltot(p) 2 Q95tot(p) 4*1 0 6

=1 Qmctot(p) 6

> Q3tot(p) 3-10 a

2.106 l1.166 1150 p 1375

- 1% drift pressure psia

.. 95-95 drift

-- - 95 pc Monte Carlo 3% drift

ICALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. 12 8.0 Conclusion The Dresden and Quad Cities safety valve data have been examined statistically. The data has been shown to be normally distributed and poolable based on standard statistical practices. The combined data has been characterized statistically and a Monte Carlo model of the safety valve network has been prepared and exercised. The results were c6mpared with traditional drift allowance methods. The following observations can be readily made:

1) The use of Monte Carlo based valve network response developed from as tested data distributions suggests that the anticipated valve network performance, based on 9 5 th percentile criteria, is very close to the deterministic case with all valves drifted 1% high.

(approximately 5% variation in delivered flow)

2) Applying a larger uncertainty to the valve setpoints and treating them all as drifted high has the potential to create a very conservative treatment. Applying a 95-95 uncertainty to the Quad Cities valve network in this fashion leads to a decrease in predicted delivered flow of approximately 18%. The use of 3% drift leads to a decrease in predicted delivered flow of approximately 33%.

Based on these observations it can be concluded that the actual plant setpoint drift data, when addressed with conservative statistical methods does not explicitly support the current analysis basis of 1% drift on all valves. It does however demonstrate that the integrated response of the actual valve performance is substantially closer to the 1 percent basis than it is to a 95-95 based bounding valve performance criteria. The valve flow model suggests that a 1.5% drift allowance, applied traditionally will envelope the Monte Carlo based results.

The analyses performed have applied standard statistical practices and have included conservative broadening of the Monte Carlo model inputs to ensure appropriate levels of confidence are preserved. The analyses performed have employed a number of independent checks to ensure that the PLANETS code is providing appropriate data and to ensure the integrity and conservatism of the Monte Carlo solution results.

Final

[Last Page]

ICALCULAIN N.MWMECH-04-004 I CALCULATION NO. MWMECH-04-004 REVISION NO. 0 REVISIONNO.0 PAGE NO.

PAGE NO.

A-1 I A-il Attachment A - Valve As found Data SRV as-Found Test History Quad Cities 1&2 Dresser model 3700 Main Steam Safety Valves Outage or As-found Site Unit Valve ID Set Point Date lift  % Deviation Quad BK6251 1250 2/10/1993 1256 0.48 Quad BK6529 1240 2/13/1993 1244 0.32258065 Quad BK6295 1260 2/15/1993 1251 -0.7142857 Quad BK6531 1260 2/16/1993 1253 -0.5555556 Quad BK7156 1260 6/11/1994 1289 2.3015873 Quad BL2467 1250 6/11/1994 1257 0.56 Quad BK6306 1240 6/12/1994 1241 0.08064516 Quad BK7159 1250 6/12/1994 1260 0.8 Quad BK6294 1260 4/2/1996 1247 -1.031746 Quad BK7158 1250 4/2/1996 1265 1.2 Quad BK7164 1260 4/3/1996 1260 0 Quad BLl120 1240 4/3/1996 1232 -0.6451613 Quad BK6249 1250 1/9/1998 1242 -0.64 Quad BK7155 1260 1/13/1998 1260 0 Quad BK7163 1260 1/13/1998 1248 -0.952381 Quad BK7167 1240 1/13/1998 1249 0.72580645 Quad BK6251 1250 1/7/1999 1235 -1.2 Quad BK6295 1260 1/7/1999 1271 0.87301587 Quad BK6318 1260 1/7/1999 1254 -0.4761905 Quad BK6529 1240 1/7/1999 1245 0.40322581 Quad BK6531 1260 1/7/1999 1265 0.3968254 Quad BL1120 1240 1/7/1999 1234 -0.483871 Quad BL1132 1260 1/7/1999 1276 1.26984127 Quad BL2471 1250 1/7/1999 1258 0.64 Quad BK6266 1260 9/17/2001 1264 0.31746032 Quad BK7167 1240 9/17/2001 1252 0.96774194 Quad BK6264 1260 9/18/2001 1286 2.06349206 Quad BK7155 1260 9/18/2001 1268 0.63492063 Quad BK7163 1260 9/20/2001 1263 0.23809524 Quad BK7165 1240 9/20/2001 1248 0.64516129 Quad BK6249 1250 9/21/2001 1254 0.32 Quad BK6278 1250 9/21/2001 1265 1.2 Quad BK6252 1240 11/13/2002 1249 0.72580645 Quad BL2467 1250 11/13/2002 1235 -1.2 Quad BK7159 1260 11/14/2002 1268 0.63492063 Quad BK7164 1260 11/14/2002 1267 0.55555556 Quad BK6294 1260 9/8/1992 1257 -0.2380952 Quad BL1120 1240 9/8/1992 1235 -0.4032258

ICALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. A-2 Quad 2 BK7164 1260 9/10/1992 1253 -0.5555556 Quad 2 BK7158 1250 9/11/1992 1253 0.24 Quad 2 BK6249 1250 3/7/1994 1247 -0.24 Quad 2 BK7167 1240 317/1994 1238 -0.1612903 Quad 2 BK7155 1260 3/8/1994 1259 -0.0793651 Quad 2 BK7163 1260 3/8/1994 1265 0.3968254 Quad 2 BK7165 1240 5/10/1995 1220 -1.6129032 Quad 2 BK6318 1260 5/11/1995 1250 -0.7936508 Quad 2 BL1132 1260 5/11/1995 1272 0.95238095 Quad 2 BL2471 1250 5/11/1995 1243 -0.56 Quad 2 BK6529 1240 4/28/1997 1248 0.64516129 Quad 2 BK6251 1250 4/29/1997 1272 1.76 Quad 2 BK6295 1260 4/29/1997 1268 0.63492063 Quad 2 BK6531 1260 4/29/1997 1267 0.55555556 Quad 2 BK7156 1260 3/9/1999 1274 1.11111111 Quad 2 BK7164 1260 3/9/1999 1268 0.63492063 Quad 2 BK6294 1260 3/11/1999 1242 -1.4285714 Quad 2 BK6306 1240 3/11/1999 1224 -1.2903226 Quad 2 BK7159 1260 3/11/1999 1280 1.58730159 Quad 2 BL2467 1250 3/11/1999 1247 -0.24 Quad 2 BK6252 1240 3/12/1999 1213 -2.1774194 Quad 2 BK7158 1250 3/12/1999 1247 -0.24 Quad 2 BL1120 1240 1/31/2000 1229 -0.8870968 Quad 2 BL1132 1260 1/31/2000 1254 -0.4761905 Quad 2 BK6251 1250 2/1/2000 1226 -1.92 Quad 2 BK6318 1260 2/1/2000 1251 -0.7142857 Quad - BK6286 1260 5/12/1983 1266 0.47619048 Quad - BL2471 1250 5/24/1983 1252 0.16 Quad - BK7165 1240 6/3/1983 1225 -1.2096774 Quad - BK6318 1260 6/5/1983 1247 -1.031746 Quad - BK7165 1240 10/5/1987 1220 -1.6129032 Quad - BK6295 1260 2/18/2002 1225 -2.7777778 Quad - BL2471 1250 2/18/2002 1227 -1.84 Quad - BK6529 1240 2/19/2002 1221 -1.5322581 Quad - BK6531 1260 2/19/2002 1259 -0.0793651

I ICALCULATION' WO. MWMECH-04-004 CALCULATION WO. MWMECII-04-004

. REVISION NO. 0 REVISION NO. 0 PAGE NO.

PAGE NO.

A-3 I A-3 SRV as-Found Test History Target Rock 3 stage model 67F SRVs Outage or As-found %

Site Unit Valve ID Set Point Date lift Deviation Quad 1SN 120 1135 4/9/1999 1174 3.43612 Quad 1 SN 171 1135 10/11/2001 1110 -2.20264 Quad 1 SN 171 1135 6/20/2003 1131 -0.35242 Quad 1 SN 198 1135 9/10/1998 1137 0.17621 Quad 1 SN 225 1135 4/25/1997 1095 -3.52423 Quad 1 SN 225 1135 10/28/2003 1160 2.20264 Quad 2SN 120 1135 6/20/2002 1158 2.02643 Quad 2SN 171 1135 4/25/1997 1134 -0.08811 Quad 2 SN 172 1135 4/8/1999 1116 -1.67401 Quad 2SN 198 1135 1/9/2001 1138 0.26432 Quad 2SN 224 1135 4/24/1997 1148 1.14537

.sA

~ ~ Exel~rn Nuclear

[XjSafety-Related . Transmittal DOC ID

[ ]Non-Safety-Related Design Information C C1°0O61 9977

[ jAugmented Quality Dresden Station, Units: 2 & 3 Page 1 of 3 To: Pete Karaba Organization: Dresden Station Electrical Design Engineering Address/Location: Dresden Station

Subject:

Dresden Main Steam Safety Valve As-Found Test Results Status of Information:

• Verified a Unverified For Unverified DITs, Include the Method and Schedule of Verification In the "Description of Informnation.'

List Action Tracidng # assigned for verification of 'Unverified" Information:

_ _ -Descriptn-ofinfo atic-- -- ------- -'- - ---

The tables shown in Attachment A are the Dresden Main Steam Safety Valve (including the Target Rock valves) test results for the four most recent refuel outages for both units 2 and 3.

Purpose of Issuance: Support Operability Determination of Unit 3 as identified in CR 200174 Limitations: None References (Source of Information): Plant Records Prepared by: Robert Testin / 7 < _Date: 02/13/04 Prjn Name Signature Prepared by: -Daniel Oakley/ UI J F 9c  ! _ Date: 02/13/04 Printed Name / Signature Approved by: Doug Wise/ Date: 02/13/04 khted Nfme/tsignature Distribution: Doua Wise Dale Eaman This form has been reviewed against the requirements of CC-AAM310. Rev. 0 and Site Engineering Poricy Statement No. 6

a 1,

--- FTV~z7. U :VJ.

I -, 1- v 4 -A1 4 C~'L 4 6 Attachment A 414Av%~-4 I S5tv 3 Unit 2 Main Steam Safety Valve Test Results Serial Position Refuel Tag As-Found Within Date Number Removed Outage Pressure Lift 1% Tested From Remove . Pressure BK6290 2-0203-4E D2R18 1260 1270 Y 10/23/03 BK6260 2-0203-4F D2R18 1260 1263 Y 10/23/03 BK7161 2-0203-4G D2R18 1240 1248 Y. 10/23/03 BK6271 2-02034H D2R18 1250 1239 Y 10/23/03 BK6299 2-0203-4A D2R17 1240 1238 Y 10/27/01 BK6263 2-0203-4B D2R117 1260 1244 *N 10/27/01 BK6526 2-0203-4C D2R17 1250 1239 Y 10/27/01 BK6532 2-0203-4D D2R17 *1260 1250 Y 10/27/01 BK7162 2-0203-4E D2R16 1260 1286 N(2.06%) 10/09/99 BK6282 2-0203-4F D2R16 1260 1268 Y 10/09199 BK6527 2-0203-4G .D2R16 1240 1244 Y 10/09199 BK6304 2-0203-4H D2R16 1250 1252 Y 10/09199 BK7161 2-0203-4A D2RI5 1240 1212 N 03/27/98 BK6290 2-02034B D2R15 1260 1273 N(1.03%) 03/27/98 BK6271 2-02034C D2R15 1250 1240 Y 03/26/98 BK6260 2-0203-4D D2R15 1260 1266 Y 03/26/98 Unit 3 Main Steam Safety.Valve Test Results Serial Position Refuel Tag - As-Found Within Date Number Removed Outage Pressure Lift . 1% Tested From Remove Pressure BK6270 3-02034A D3R17 1240 1208 N 10/14/02 BK6265 3-0203-4B D3R17 1260 1227 N 10/14/02 BK6312 3-0203-4C D3R7 1250 1262 Y 110/14/02 BK6528 3-0203-4D D3R17 1260 1256 Y 10/14/02 BK6288 3-0203-4E D3R16 1240 1251 Y 09/26/00 BK7157 .3-02034F D3R16 1260 1259 Y 09/26/00 BK6530 3-02034G D3R16 1250 1266 N(1.28%) 09/26/00 B K7160 3-0203-4H D3R16 1260 1250 Y 09/26/00 BK6272 3-0203-4A D3Rl5 1240 1231 Y 02/04/99 BK6296 3-0203-4B D3RI5 1260 1250 Y 02104/99 BK6277 3-02034C D3R15 1250 1233 N 02/03/99 BK6525 3-0203-4D D3R15 1260 1259 Y 1.02/04/99 BK6299 3-02034E D3R14 1240 1237 Y 05/18/97

• BK6263 3-02034F D3R14 1260 1263 Y 05/17/97 BK6526 3-02034G I D3R14 1250 1234 N 05/18/97 I BK6532 _ 3-0203-4H I D3R14 1 1260 11254 I.Y 1 05/18/97 1 2 of 3

MVc-- cO' I GV-IOC-

'21 Attachment A 3 of 3

MWMECH-04-004 Rev. 0 Page C-1 Statistical Characterization and Normality Test for QC Target Rock Data This worksheet takes the valve data presented in the EXCEL worksheet in Attachment A and performs manipulations to get the mean, standard deviation, test for normality, and determination of 95-95 limits based on single sided tolerance.

QCTRraw:=

1, - ,,'.,1 11 0 1.17410Q3 I 11741 1.11*103

11 1110- -5 1.1 31-103 1.1 37-103 1.095*103 QCTRraw =

1.1 6103 QCTRpc QCTRraw - 1135.100 7- 1.1 58i103 1135 1.1 34-103 1.116i103 pQCTRpc := mean(QCTRpc) 1.1 38-103 1.148-103 pQCTRpc = 0.128 Var(QCTRpc) = 4.22 ca := Stdev(QCTRpc) Note Stdev is used rather than stdev to obtain sample statistics, ie. division by n-1, consistent with NUREG 1475 usage.

a = 2.054 the following commands sort the data in ascending and descending order QCTRpcI := sort(QCTRpc)

QCTRpc2:= reverse(QCTRpcl)

0: 3.436 -3.524

.1- 2.203 -2.203

2 2.026 -1.674 3 1.145 -0.352 4 0.264 '4 -0.088 QCTRpc2 = QCTRpcl =

5 0.176 0.176 6 -0.088 0.264 7 -0.352 1.145 8 -1.674 2.026

-2.203 2.203 10 -3.524 3.436

MWMECH-04-004 Rev. 0 Page C-2 we will apply the W-test for normality, as detailed in NUREG-1475, page7-10 n := length(QCTRpcI) n = II n is odd, therefore the following relationship is used to determine k 2

k=5 i := O..k- I the following operations create the table of ascending and descending values, take the difference, apply the multiplier from Table 6a, and generate the sum for use in the comparison test.

W, 0 := QCTRpcl1 W. 1 = QCTRpc2.

WI 2:= QCTRpcIj - QCTRpc21 0.5601 0.3315 Wcoef := 0.2260 coefficients from Table 6a of Reference 3 0.1429 0.0695

MWMECH-04-004 Rev. 0 Page C-3 W.3 j,3*:= Wcoef.1

(-3.524 3.436 -6.96 0.56 -3.898 4 :vI2 wi,3 -2.203 2.203 -4.405 0.332 -1.46 W = -1.674 2.026 -3.7 0.226 -0.836

-0.352 1.145 -1.498 0.143 -0.214

-0.088 0.264 -0.352 0.07 -0.024)

B W.

B =-6.434 Var:= var(QCTRpc)

B2 (n - 1).Var W= 1.079 taking the critical point from Table 6b of Reference 3 for a sample size of 11 and an alpha of 0.05 wO.05 = 0.85 W is larger than the critical point, therefore the data can be considered normal.

MWMECH-04-004 Rev. 0 Page C-4 Determination of 95-95 limits based on NUREG 1475 methods with number of points equal to 11, the one-sided tolerance limit factors for a normal distribution can be interpolated, Table T-1 I b, for 95 % confidence and 95% population k:= 2.911 - (2.911 - 2.736) 2 k = 2.824 therefore the 95-95 valve limit would be Set9595 := pQCTRpc + Oak Set9595 = 5.929

MWMECH-04-004 Rev. 0 Page D-1 Statistical Characterization and Normality Test for QC MSSV Data This worksheet takes the valve data presented in the EXCEL worksheet in Attachment A and performs manipulations to get the mean, standard deviation, test for normality, and determination of 95-95 limits based on single sided tolerance.

QC1240raw:=

°0 l 12441

1 l 12411 l QC125O0aw=

r0. 1256

1 1257 QC1260raw=

• i>-.;0'--> I.li 1K .

0 12511

,I 12531 calculate the drift for each valve group as a percentage of setpoint QCl240raw- 1240 QC1240pc:= *100 1240 QCl25Opc = QCl250raw - 1250.ioo 1250 QC260c *=QCI260raw - 1260 1260

MWMECH-04-004 Rev. 0 Page D-2 takes the drift percent data sets and combines them into one array QCpc:= stack(QC 1240pc, QC 1250pc, QC1 260pc) Iy 0 1-

-2.177 QCpcs:= sort(QCpc) -1.92

• 1.

2' -1.613

-a n := length(QCpcs)

-1.613

.4. -1.532 n = 70 5 -1.429 calculate the mean and standard deviation 6 -1.29 QCpcs = 7 -1.21 p := mean(QCpcs) 8 -1.2

-1.2 P = 6.757 x IO 4 i9 10 -1.032 11 -1.032 12 -0.952 a := Stdev(QCpcs) Note Stdev is used rather than stdev to obtain sample statistics, ie. division by 13 -0.887 a = 0.952 n-1, consistent with NUREG 1475 -0.794 usage. 15 -0.714 Var(QCpcs) = 0.907 the data has been tabulated and a mean and standard deviation calculated. The sort has been performed to arrange data from smallest to largest. With 70 data points the W-test is not practical and an alternate test (D'Agostino) is warranted. This methodology is documented in "The Handbook for Statistical Analysis of Environmental Background Data, Naval Facilities Engineering Command, 1999" on page 45.

MWMECH-04-004 Rev. 0 Page D-3 The following formulas employ the D'Agostino test for normality. A significance level of 0.05 will be employed 0:.. n - 1 E[ i + I - .5-(n + 1) ] QCpcsi

n cr D = 0.281 Y

D - 0.282094 0.02998798 0.5 Y = -0.42 n

from Table 8 of the reference, for n=70 a := .05 YO.025:= -2.652 YO.975:= 1.176 since Y falls between these limits, it cannot be concluded that the data is not normally distributed.

MWMECH-04-004 Rev. 0 Page D-4 Determination of 95-95 limits based on NUREG 1475 methods It is desirable to know what the 95-95 drift limits are for the actual plant data. The methodology documented in NUREG 1475 provides a means to accomplish this. Since drifting high is the primary concern, it is appropriate to apply a single sided tolerance approach. With the number of points equal to 70, the one-sided tolerance limit factors for a normal distribution can be interpolated, Table T-1 lb, for 95 % confidence and 95% population k:= 1.990 therefore the 95-95 valve limit would be Bounding9595 := St + a-k Bounding9595 = 1.896

MWMECH-04-004 Rev. 0 E-1 Poolability Testing for Target Rock data from Dresden and Quad Cities This test is based on NUREG 1475, page 10-6. The first check will be to determine the poolability of the Dresden and QC Target Rock Data. This worksheet excludes the data points from D and QC previously identified as outliers.

VarD:= 1.8606 nD := 8 dfD := 7 SD:= va SD = 1.364 VarQ:= 4.22 nQ:= 11 dfQ := 10 sQ:= Jar SQ = 2.054 a := 0.05 VarQ Fmax= =-

Fmax = 2.268 obtain the fcrit based on dfl=10 and df2=7 from Table T-4 fcrit := 4.76 since Fmax is less than fq, the null hypothesis cannot be rejected and the data is poolable

MWMECH-04-004 Rev. 0 E-2 the pooled variance then becomes VarD.(nD - 1) + VarQ.(nQ -1)

VpOol:= 2 nD+ nQ-VP00i = 3.248 Fpool := JP;0 spool = 1.802 The Dresden and QC data will also be combined directly for comparison DRTRraw:=

.ss x-.- o s it>;t2^ r1; -

~. . ...

0 1119

-1, 1122 QCTRraw:=

l 5 -; r ;_1o

. ' .a-

-1 . < I '-if;, ;

0 1174

1 11101 Poolraw

=stack(DRTRraw,QCTRraw)

MWMECH-04-004 Rev. 0 E-3 Poolraw - 1135 Poolpc: - 100 1135 puPoolpc:= mean(Poolpc) pPoolpc = -0.06 a := Stdev(Poolpc) c = 1.766 npooI:= length(Poolpc) npool= 19 Varpoo := Var(Poolpc)

Varpool = 3.12

MWMECH-04-004 Rev. 0 E-4 Determination of a 95-95 limit for the pooled data from Table 11a, the two sided 95/95 k value for 19 data points is 2.828 + 2.760 2

k2s = 2.794 c- k2s = 2.467 2

from Table 11 b, the one sided 95/95 k value for 19 data points is 2.453 + 2.396 2

kis = 2.425 the one sided 95/95 limit for the pooled data would then be Bounding 95 9 5 := pPoolpc + kIS a Bounding 95 9 5 = 4.222

MWMECH-04-004 Rev. 0 E-5 Input values for Monte Carlo will be based on setpoint expressed in psig, since all the statistical values were calculated in percent of setpoint. The Monte Carlo calculation is run in psia for convenience. The T/R 1 sigma values to be used will be:

T/R 1135psig/1150psiasetpoint k2s) onesigmatr:= 1135-- 100 .

onesigmatr = 28.006

MWMECH-04-004 Rev. 0 F-1 Poolability Testing for MSSV data from Dresden and Quad Cities This test is based on NUREG 1475, page 10-6. The first check will be to determine the poolability of the Dresden and QC MSSV Data. This worksheet excludes the data points from D and QC previously identified as outliers.

VarD:= 1.1925 nD:= 32 dfD := 31 SD := FVar SD = 1.092 SD 1.

VarQ:= 0.907 nQ := 70 dfQ := 69 sQ := - va-; sQ = 0.952 a := 0.05 VarD Fmax:= -

Fmax = 1.315 a double interpolation is needed to obtain the fq based on df1=31 and df2=69 fcrit= [1.82 (1.82- 1.67)] ((1.82 - 1!(1.82- 1.67)] [1.69 - 1L(1. 6 9 - 1.53)] r(6-L fcrit = 1.795 since Fmax is less than fcrit, the null hypothesis cannot be rejected and the data is poolable

MWMECH-04-004 Rev. 0 F-2 the pooled variance then becomes VarD.(nD - 1) + VarQ.(nQ - 1)

P°°l

• nD vpool.~ + nQ - 2 Vpooi= 0.996 0

pool FvA; ypooi = 0.998 The Dresden and QC data will also be combined directly for comparison QC1240raw :=,. ,.. ., . -

QC1250raw:=

, : '-"1:; °- -o' !.,. :;. -- -;,,1, , .:.! ,!

t 12561 I.1. 12571 QC1260raw :=

~l

.>o. < -~ -h 41 0! 12511 1 12531 calculate the drift for each valve group as a percentage of setpoint

MWMECH-04-004 Rev. 0 F-3 QC1240* = QC1240rawv- 1240 12400p:=.100 1240 (bC1250c= Q C250raw -1250 1250 QC1260c =QC1260raw -1260 p.- ~1260 *o takes the drift percent data sets and combines them into one array QCpc:= stack(QC 1240pc, QC1250pc, QC1260pc)

DR1240raw:=

1' ,-< 'O ' 3 ,8..

-- - I I

0: 1248 1-' 1238 DR1250raw:=

1 129, - ; I -,0 'z'

1 1391 DR1260raw:=

MWMECH-04-004 Rev. 0 F-4 DR124Oraw - 1240 DR1240pc:= .100 1240 DR1250- DR1250raw - 1250 1250 DR260c *=DR1260raw - 1260

p. 1260 takes the drift percent data sets and combines them into one array DRpc:= stack(DR1240pc, DR1250pc,DR1260pc) the following are a double check of the GE calculated values for Dresden ptDRpc:= mean(DRpc) tDRpc = -0.271 0

c DR:= Stdev(DRpc) a DR= 1.092 the following combines the data and performs the statistical characterization PoolDQ:= stack(DRpc,QCpc) gPoolDQ := mean(PoolDQ) pPoolDQ = -0.084 n := length(PoolDQ) n = 102 5

DQ:= Stdev(PoolDQ)

GTDQ = 1.001 Var(PoolDQ) = 1.002

MWMECH-04-004 Rev. 0 F-5 Determination of a 95-95 limit for the pooled data from Table 11a, the two sided 95/95 k value for 102 data points is k2s := 2.234 - (2.234 - 2.176). (10 - 100)

(150 - 100) k2s = 2.232 aDQ- = 1.117 sets the broadening for the Monte Carlo from Table 1lb, the one sided 95/95 k value for 102 data points is ki, := 1.927 - (1.927 - 1.870) ( 100)

(1501- 100) kIS = 1.925 the one sided 95/95 limit for the pooled data would then be Bounding9 59 5 := pPoolDQ + kIs aDQ Bounding9 5 9 5 = 1.842 Ignoring the mean value kIs.cDQ = 1.926

MWMECH-04-004 Rev. 0 F-6 Input values for Monte Carlo will be based on setpoint expressed in psig, since all the statistical values were calculated in percent of setpoint.. The Monte Carlo calculation is run in psia for convenience. The MSSV 1 sigma values to be used are:

Group 1 1240psig/1255 psia setpoint (DQ k2s) onesigma1 := 1240. 100 onesigma, = 13.848 Group 2 1250psig/1265 psia setpoint (DQ k2s) onesigma 2 := 1250-100 onesigma 2 = 13.96 Group 3 1260psig/1275 psia setpoint (DQ k2s) onesigma 3 := 1260. 0-0 100 onesigma 3 = 14.072

CALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. G-1 Attachment G - PLANETS Output File planets -- plant network simulation program version 1.0 -- august 20,1991 DrQC Pooled Main Steamline Safety Valves Pressure Case HlOpnPres input variable in units of psia lowest HIOpnPres considered= -1350.000 uniform HlOpnPres increment for tabular input distributions = 1.000 coarse HlOpnPres intervals for tabular input distributions

-.13490E+04 -.13480E+04 -.13470E+04 -.13460E+04 -.13450E+04 -.13440E+04

-.13430E+04 -.13420E+04 -.13410E+04 -.13400E+04 -.13390E+04 -.13380E+04

-.13370E+04 -.13360E+04 -.13350E+04 -.13340E+04 -.13330E+04 -.13320E+04

-.13310E+04 -.13300E+04 -.13290E+04 -.13280E+04 -.13270E+04 -.13260E+04

-.13250E+04 -.13240E+04 -.13230E+04 -.13220E+04 -.13210E+04 -.13200E+04

-.13190E+04 -.13180E+04 -.13170E+04 -. 13160E+04 -.13150E+04 -.13140E+04

-.13130E+04 -.13120E+04 -.13110E+04 -.13100E+04 -.13090E+04 -.13080E+04

-.13070E+04 -.13060E+04 -.13050E+04 -.13040E+04 -.13030E+04 -.13020E+04

-.13010E+04 -.13000E+04 -.12990E+04 -.12980E+04 -.12970E+04 -.12960E+04

-.12950E+04 -.12940E+04 -.12930E+04 -.12920E+04 -.12910E+04 -.12900E+04

-.12890E+04 -.12880E+04 -.12870E+04 -.12860E+04 -.12850E+04 -.12840E+04

-.12830E+04 -.12820E+04 -.12810E+04 -. 12800E+04 -.12790E+04 -.12780E+04

-.12770E+04 -.12760E+04 -.12750E+04 -.12740E+04 -.12730E+04 -.12720E+04

-.12710E+04 -.12700E+04 -.12690E+04 -.12680E+04 -.12670E+04 -.12660E+04

-.12650E+04 -.12640E+04 -.12630E+04 -.12620E+04 -.12610E+04 -.12600E+04

-.12590E+04 -.12580E+04 -.12570E+04 -.12560E+04 -.12550E+04 -.12540E+04

-.12530E+04 -.12520E+04 -.12510E+04 -.12500E+04 -.12490E+04 -.12480E+04

-.12470E+04 -.12460E+04 -.12450E+04 -.12440E+04 -.12430E+04 -.12420E+04

-.12410E+04 -.12400E+04 -.12390E+04 -.12380E+04 -.12370E+04 -.12360E+04

-.12350E+04 -.12340E+04 -.12330E+04 -.12320E+04 -.12310E+04 -.12300E+04

-.12290E+04 -.12280E+04 -.12270E+04 -.12260E+04 -.12250E+04 -.12240E+04

-.12230E+04 -.12220E+04 -.12210E+04 -.12200E+04 -.12190E+04 -.12180E+04

-.12170E+04 -.12160E+04 -.12150E+04 -.12140E+04 -.12130E+04 -.12120E+04

-.12110E+04 -.12100E+04 -.12090E+04 -.12080E+04 -.12070E+04 -.12060E+04

ICALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. G-2 l

-.12050E+04 -.12040E+04 -.12030E+04 -.12020E+04 -.12010E+04 -.12000E+04

-.11990E+04 -.11980E+04 -.11970E+04 -.11960E+04 -.11950E+04 -.11940E+04

-.11930E+04 -.11920E+04 -.11910E+04 -.11900E+04 -.11890E+04 -.11880E+04

-.11870E+04 -.11860E+04 -.11850E+04 -.11840E+04 -.11830E+04 -. 11820E+04

-.1181 OE+04 -.11800E+04 -.11790E+04 -.11780E+04 -.11770E+04 -.11760E+04

-.11750E+04 -.11740E+04 -.11730E+04 -.11720E+04 -.11710E+04 -.11700E+04

-.11690E+04 -.11680E+04 -.11670E+04 -.11660E+04 -.11650E+04 -.11640E+04

-.11630E+04 -.11620E+04 -.1 1610E+04 -.11600E+04 -.11590E+04 -.11580E+04

-.11570E+04 -.11560E+04 -.11550E+04 -.11540E+04 -.11530E+04 -.11520E+04

-.11510E+04 -.11500E+04 -.11490E+04 -.11480E+04 -.11470E+04 -.11460E+04

-.11450E+04 -.11440E+04 -.11430E+04 -.11420E+04 -.11410E+04 -.11400E+04

-.11390E+04 -.11380E+04 -.11370E+04 -.11360E+04 -.11350E+04 -.11340E+04

-.11330E+04 -.11320E+04 -.11310E+04 -.11300E+04 -.11290E+04 -.11280E+04

-.11270E+04 -.11260E+04 -.11250E+04 -.11240E+04 -.11230E+04 -.11220E+04

-.11210E+04 -.11200E+04 -.11190E+04 -.11180E+04 -.11170E+04 -.11160E+04

-.11150E+04 -.11140E+04 -.11130E+04 -.11120E+04 -.1111OE+04 -.11100E+04

-.11090E+04 -.11080E+04 -.11070E+04 -.11060E+04 -.11050E+04 -.11040E+04

-.11030E+04 -.11020E+04 -.1101 OE+04 -.11000E+04 path # 1 has 9 components divided into 4 group(s):

1 components in group # 1 2 components in group # 2 2 components in group # 3 4 components in group # 4 input distribution data for path #1 component group 1 input HlOpnPres distributed normally with mean value -1150.0000 and standard deviation 28.0060 component group 2 input HlOpnPres distributed normally with mean value -1255.0000 and standard deviation 13.8480 component group 3 input HlOpnPres distributed normally with mean value -1265.0000 and standard deviation 13.9600 component group 4 input HlOpnPres distributed normally with mean value -1275.0000 and standard deviation 14.0720 9 total components in network summary of group input distributions for path # 1 (reformulated on adequately detailed interval mesh)

ICALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. G-3 I HlOpnPres 1 cmp/gp 1 2 cmp/gp 2 2 cmp/gp 3 4 cmp/gp 4 1 -1349.000 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 2 -1348.000 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 3 -1347.000 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 4-1346.000 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 5-1345.000 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 .405693E-07 6-1344.000 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 .143848E-06 7-1343.000 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 .203784E-06 8 -1342.000 000000E+00 .OOOOOOE+00 .OOOOOOE+00 .287238E-06 9-1341.000 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 .402831 E-06 10-1340.000 .000000E+00 .000000E+00 .OOOOOOE+00 .562098E-06 11 -1339.000 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 .780383E-06 12 -1338.000 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 .107798E-05 13 -1337.000 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 .148158E-05 14 -1336.000 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 .202602E-05 15 -1335.000 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 .275658E-05 16-1334.000 .OOOOOOE+00 .OOOOOOE+00 .986013E-07 .373169E-05 17-1333.000 .OOOOOOE+00 .OOOOOOE+00 .169752E-06 .502630E-05 18-1332.000 .OOOOOOE+00 .OOOOOOE+00 .240596E-06 .673595E-05 19-1331.000 .OOOOOOE+00 .OOOOOOE+00 .339261 E-06 .898168E-05 20-1330.000 .OOOOOOE+00 .OOOOOOE+00 .475941 E-06 .119158E-04 21 -1329.000 .OOOOOOE+00 .OOOOOOE+00 .664269E-06 .157289E-04 22 -1328.000 .OOOOOOE+00 .OOOOOOE+00 .922374E-06 .206576E-04 23 -1327.000 .OOOOOOE+00 .OOOOOOE+00 .127422E-05 .269941 E-04 24-1326.000 .OOOOOOE+00 .OOOOOOE+00 .175126E-05 .350966E-04 25 -1325.000 .OOOOOOE+00 .OOOOOOE+00 .239460E-05 .454015E-04 26-1324.000 .OOOOOOE+00 .269143E-07 .325751 E-05 .584363E-04 27-1323.000 .OOOOOOE+00 .140757E-06 .440871 E-05 .748347E-04 28-1322.000 .OOOOOOE+00 .200633E-06 .593621 E-05 .953522E-04 29-1321.000 .OOOOOOE+OO .284493E-06 .795206E-05 .120883E-03 30 -1320.000 .OOOOOOE+00 .401307E-06 .105980E-04 .152479E-03 31 -1319.000 .OOOOOOE+00 .563143E-06 .140520E-04 .191364E-03 32-1318.000 .OOOOOOE+00 .786134E-06 .185364E-04 .238957E-03 33-1317.000 .OOOOOOE+00 .109172E-05 .243269E-04 .296884E-03 34 -1316.000 .OOOOOOE+00 .150821 E-05 .317628E-04 .366996E-03 35-1315.000 .OOOOOOE+00 .207275E-05 .412595E-04 .451382E-03 36-1314.000 .OOOOOOE+00 .283381E-05 .533214E-04 .552375E-03 37-1313.000 .OOOOOOE+00 .385416E-05 .685570E-04 .672561 E-03 38 -1312.000 .OOOOOOE+00 .521465E-05 .876949E-04 .814774E-03 39-1311.000 .OOOOOOE+00 .701870E-05 .111601 E-03 .982088E-03 40-1310.000 .OOOOOOE+00 .939777E-05 .141298E-03 .117780E-02 41 -1309.000 .OOOOOOE+00 .125178E-04 .177982E-03 .140540E-02 42-1308.000 .OOOOOOE+00 .165871 E-04 .223043E-03 .166854E-02 43 -1307.000 .OOOOOOE+00 .218649E-04 .278083E-03 .197097E-02 44-1306.000 .OOOOOOE+00 .286721E-04 .344930E-03 .231650E-02 45 -1305.000 .OOOOOOE+00 .374033E-04 .425658E-03 .270890E-02 46-1304.000 .OOOOOOE+00 .485395E-04 .522592E-03 .315181 E-02 47-1303.000 .OOOOOOE+00 .626639E-04 .638318E-03 .364868E-02 48 -1302.000 .OOOOOOE+00 .804777E-04 .775683E-03 .420260E-02 49-1301.000 .OOOOOOE+00 .102818E-03 .937786E-03 .481625E-02 50 -1300.000 .OOOOOOE+00 .130678E-03 .112796E-02 .549171E-02

ICALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. G-4 I 51 -1299.000 .OOOOOOE+00 .165222E-03 .134977E-02 .623037E-02 52 -1298.000 .OOOOOOE+00 .207813E-03 .160693E-02 .703279E-02 53 -1297.000 .OOOOOOE+00 .260023E-03 .190329E-02 .789859E-02 54-1296.000 .OOOOOOE+00 .323659E-03 .224278E-02 .882631 E-02 55 -1295.000 .OOOOOOE+00 .400774E-03 .262931 E-02 .981333E-02 56-1294.000 .OOOOOOE+00 .493683E-03 .306668E-02 .108558E-01 57-1293.000 .OOOOOOE+00 .604969E-03 .355850E-02 .119485E-01 58-1292.000 .OOOOOOE+00 .737487E-03 .410808E-02 .130850E-01 59-1291.000 .OOOOOOE+00 .894359E-03 .471827E-02 .142575E-01 60-1290.000 .106551 E-08 .107896E-02 .539137E-02 .154568E-01 61 -1289.000 .584175E-07 .129490E-02 .612897E-02 .166726E-01 62-1288.000 .697430E-07 .154597E-02 .693185E-02 .178935E-01 63 -1287.000 .831581 E-07 .183613E-02 .779979E-02 .191070E-01 64 -1286.000 .990273E-07 .216942E-02 .873150E-02 .203002E-01 65 -1285.000 .117775E-06 .254987E-02 .972450E-02 .214593E-01 66-1284.000 .139892E-06 .298147E-02 .107750E-01 .225703E-01 67 -1283.000 .165952E-06 .346799E-02 .118780E-01 .236193E-01 68 -1282.000 .196616E-06 .401293E-02 .130268E-01 .245927E-01 69-1281.000 .232649E-06 .461936E-02 .142137E-01 .254772E-01 70-1280.000 .274935E-06 .528979E-02 .154293E-01 .262606E-01 71 -1279.000 .324492E-06 .602603E-02 .166633E-01 .269319E-01 72-1278.000 .382494E-06 .682905E-02 .179038E-01 .274812E-01 73-1277.000 .450290E-06 .769885E-02 .191383E-01 .279005E-01 74-1276.000 .529427E-06 .863431 E-02 .203533E-01 .281836E-01 75-1275.000 .621678E-06 .963309E-02 .215347E-01 .283262E-01 76-1274.000 .729075E-06 .106915E-01 .226680E-01 .283262E-01 77-1273.000 .853935E-06 .118046E-01 .237390E-01 .281836E-01 78 -1272.000 .998904E-06 .129657E-01 .247333E-01 .279005E-01 79-1271.000 .116700E-05 .141671E-01 .256374E-01 .274812E-01 80-1270.000 .136164E-05 .153993E-01 .264387E-01 .269319E-01 81 -1269.000 .158672E-05 .166516E-01 .271255E-01 .262606E-01 82-1268.000 .184665E-05 .179122E-01 .276878E-01 .254772E-01 83 -1267.000 .214642E-05 .191680E-01 .281171E-01 .245927E-01 84-1266.000 .249168E-05 .204052E-01 .284070E-01 .236193E-01 85 -1265.000 .288879E-05 .216093E-01 .285531E-01 .225703E-01 86-1264.000 .334491E-05 .227656E-01 .285531E-01 .214593E-01 87-1263.000 .386813E-05 .238590E-01 .284070E-01 .203002E-01 88-1262.000 .446749E-05 .248749E-01 .281171 E-01 .191070E-01 89-1261.000 .515315E-05 .257993E-01 .276878E-01 .178935E-01 90-1260.000 .593646E-05 .266189E-01 .271255E-01 .166726E-01 91 -1259.000 .683014E-05 .273218E-01 .264387E-01 .154568E-01 92-1258.000 .784833E-05 .278974E-01 .256374E-01 .142575E-01 93-1257.000 .900683E-05 .283370E-01 .247333E-01 .130850E-01 94-1256.000 .103232E-04 .286340E-01 .237390E-01 .119485E-01 95 -1255.000 .118168E-04 .287836E-01 .226680E-01 .108558E-01 96-1254.000 .135093E-04 .287836E-01 .215347E-01 .981333E-02 97-1253.000 .154245E-04 .286340E-01 .203533E-01 .882631 E-02 98-1252.000 .175889E-04 .283371E-01 .191383E-01 .789859E-02 99-1251.000 .200314E-04 .278974E-01 .179038E-01 .703279E-02 100-1250.000 .227840E-04 .273218E-01 .166633E-01 .623037E-02 101 -1249.000 .258818E-04 .266189E-01 .154293E-01 .549171E-02

1 ICALCULATION CACLTO NO. MWMECH-04-004 O WEH0-0 REVISION NO. 0 EIINN.0PG PAGE NO. G-5 O -

I 102 -1248.000 .293634E-04 .257993E-01 .142137E-01 .481625E-02 103 -1247.000 .332709E-04 .248749E-01 .130268E-01 .420260E-02 104 -1246.000 .376503E-04 .238590E-01 .118780E-01 .364868E-02 105 -1245.000 .425519E-04 .227656E-01 .107750E-01 .315181 E-02 106 -1244.000 .480303E-04 .216093E-01 .972450E-02 .270890E-02 107 -1243.000 .541450E-04 .204052E-01 .873150E-02 .231650E-02 108 -1242.000 .609604E-04 .191680E-01 .779979E-02 .197097E-02 109 -1241.000 .685463E-04 .179121 E-01 .693185E-02 .166854E-02 110 -1240.000 .769779E-04 .166516E-Ol .612897E-02 .140540E-02 111 -1239.000 .863366E-04 .153993E-01 .539137E-02 .1 17j780E-02 112 -1238.000 .967096E-04 .141671 E-01 .471827E-02 .982088E-03 113 -1237.000 .108191 E-03 .129657E-01 .410808E-02 .814774E-03 114 -1236.000 .120881 E-03 .118046E-01 .355850E-02 .672561 E-03 115 -1235.000 .134888E-03 .106915E-01 .306668E-02 .552375E-03 116 -1234.000 .150326E-03 .963309E-02 .262931 E-02 .451382E-03 117 -1233.000 .167317E-03 .863431 E-02 .224278E-02 .366996E-03 118 -1232.000 .185991 E-03 .769885E-02 .190329E-02 .296884E-03 119 -1231.000 .206487E-03 .682905E-02 .160693E-02 .238957E-03 120 -1230.000 .228948E-03 .602603E-02 .134977E-02 .191364E-03 121 -1229.000 .253530E-03 .528979E-02 .112796E-02 .152479E-03 122 -1228.000 .280394E-03 .461936E-02 .937786E-03 .120883E-03 123 -1227.000 .309708E-03 .401293E-02 .775683E-03 .953522E-04 124 -1226.000 .341652E-03 .346799E-02 .638318E-03 .748346E-04 125 -1225.000 .37641 OE-03 .298147E-02 .522592E-03 .584363E-04 126 -1224.000 .414176E-03 .254987E-02 .425658E-03 .454015E-04 127 -1223.000 .455151 E-03 .216942E-02 .344930E-03 .350966E-04 128 -1222.000 .499542E-03 .183613E-02 .278083E-03 .269941 E-04 129 -1221.000 .547564E-03 .154597E-02 .223043E-03 .206575E-04

.130 -1220.000 .599438E-03 .129490E-02 .177982E-03 .157289E-04 131 -1219.000 .655390E-03 .107896E-02 .141298E-03 .119158E-04 132 -1218.000 .715652E-03 .894359E-03 .11 1601 E-03 .898168E-05 133 -1217.000 .780459E-03 .737487E-03 .876949E-04 .673596E-05 134 -1216.000 .850050E-03 .604969E-03 .685570E-04 .502630E-05 135 -1215.000 .924667E-03 .493683E-03 .533214E-04 .373169E-05 136 -1214.000 .100455E-02 .400774E-03 .412595E-04 .275658E-05 137 -1213.000 .108995E-02 .323659E-03 .317628E-04 .202602E-05 138 -1212.000 .1181 1OE-02 .260023E-03 .243269E-04 .148158E-05 139 -1211.000 .127824E-02 .207813E-03 .185364E-04 .107798E-05 140 -1210.000 .138161 E-02 .165222E-03 .140520E-04 .780383E-06 141 -1209.000 .149144E-02 .130678E-03 .105980E-04 .562098E-06 142 -1208.000 .160794E-02 .102818E-03 .795206E-05 .402831 E-06 143 -1207.000 .173134E-02 .804777E-04 .593621 E-05 .287238E-06 144 -1206.000 .186183E-02 .626639E-04 .440871 E-05 .203784E-06 145 -1205.000 .199961 E-02 .485395E-04 .325751 E-05 .143848E-06 146 -1204.000 .214484E-02 .374033E-04 .239460E-05 .405693E-07 147 -1203.000 .229769E-02 .286721 E-04 .175126E-05 .OOOOOOE+00 148 -1202.000 .245830E-02 .218649E-04 .127422E-05 .OOOOOOE+00 149 -1201.000 .262679E-02 .165871 E-04 .922374E-06 .OOOOOOE+00 150 -1200.000 .280325E-02 .125178E-04 .664269E-06 .OOOOOOE+00 151 -1199.000 .298775E-02 .939777E-05 .475941 E-06 .OOOOOOE+00 152 -1198.000 .318034E-02 .701870E-05 .339261 E-06 .OOOOOOE+00

ICALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. G-6 153 -1197.000 .338103E-02 .521465E-05 .240596E-06 .OOOOOOE+00 154 -1196.000 .358980E-02 .385416E-05 .169752E-06 ,OOOOOOE+00 155 -1195.000 .380661E-02 .283381 E-05 .986013E-07 .OOOOOOE+00 156 -1194.000 .403137E-02 .207275E-05 .OOOOOOE+00 .OOOOOOE+00 157 -1193.000 .426396E-02 .150821E-05 .OOOOOOE+00 .OOOOOOE+00 158 -1192.000 .450422E-02 .109172E-05 .OOOOOOE+00 .OOOOOOE+00 159 -1191.000 .475197E-02 .786133E-06 .OOOOOOE+00 .OOOOOOE+00 160 -1190.000 .500695E-02 .563143E-06 .OOOOOOE+00 .OOOOOOE+00 161 -1189.000 .526889E-02 .401307E-06 .OOOOOOE+00 .OOOOOOE+00 162 -1188.000 .553747E-02 .284493E-06 .OOOOOOE+00 .OOOOOOE+00 163 -1187.000 .581233E-02 .200633E-06 .OOOOOOE+00 .OOOOOOE+00 164 -1186.000 .609306E-02 .140757E-06 .OOOOOOE+00 .OOOOOOE+00 165 -1185.000 .637921 E-02 .269143E-07 .OOOOOOE+00 .OOOOOOE+00 166 -1184.000 .667029E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 167 -1183.000 .696576E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 168 -1182.000 .726506E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 169 -1181.000 .756756E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 170 -1180.000 .787262E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 171 -1179.000 -.81 7953E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 172 -1178.000 .848759E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 173 -1177.000 .879603E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 174 -1176.000 .910406E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 175 -1175.000 .941088E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 176 -1174.000 .971564E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 177 -1173.000 .100175E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 178 -1172.000 .103156E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 179 -1171.000 .106090E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 180 -1170.000 .108968E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 181 -1169.000 .111782E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 182 -1168.000 .114523E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 183-1167.000 .117181 E-01 .OOOOOOE+00 .0000002+00 .OOOOOOE+00 184 -1166.000 .119749E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 185 -1165.000 .122216E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 186-1164.000 .124576E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 187 -1163.000 .126819E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 188 -1162.000 .128938E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 189 -1161.000 .130926E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 190 -1160.000 .132775E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 191 -1159.000 .134478E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 192 -1158.000 .136030E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 193 -1157.000 .137425E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 194 -1156.000 .138656E-01 .000000E+00 .OOOOOOE+00 .OOOOOOE+00 195 -1155.000 .139721 E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 196 -1154.000 .140615E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 197-1153.000 .141333E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 198 -1152.000 .141875E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 199 -1151.000 .142237E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 200 -1150.000 .142419E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 201 -1149.000 .142419E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 202 -1148.000 .142237E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 203 -1147.000 .141875E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00

CALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. G-7 204 -1146.000 .141333E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 205 -1145.000 .140615E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 206-1144.000 .139721 E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 207 -1143.000 .138656E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 208 -1142.000 .137425E-01 .OOOOOOE+O0 .OOOOOOE+O0 .OOOOOOE+00 209 -1141.000 .136030E-01 .OOOOOOE+00 .OOOOOOE+O0 .OOOOOOE+00 210 -1140.000 .134478E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 211 -1139.000 .132775E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 212 -1138.000 .130926E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 213 -1137.000 .128938E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 214 -1136.000 .126819E-01 .OOOOOOE+00 OOOOOOE+00 .OOOOOOE+00 215 -1135.000 .124576E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 216-1134.000 .122216E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+O0 217 -1133.000 .119749E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 218 -1132.000 .117181E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 219 -1131.000 . 14523E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 220 -1130.000 .111 782E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 221 -1129.000 .108968E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 222 -1128.000 .106090E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 223 -1127.000 .103156E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 224 -1126.000 .100175E-01 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 225 -1125.000 .971564E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 226 -1124.000 .941088E-02 .OOOOOOE+00 .OOOOOOE+O0 .OOOOOOE+00 227 -1123.000 .910406E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 228 -1122.000 .879603E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 229 -1121.000 .848759E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 230 -1120.000 .817953E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 231 -1119.000 .787261 E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 232 -1118.000 .756756E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 233 -1117.000 .726506E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 234 -1116.000 .696576E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 235 -1115.000 .667029E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 236 -1114.000 .637921E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+O0 237 -1113.000 .609306E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 238 -1112.000 .581233E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 239 -1111.000 .553747E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 240 -1110.000 .526889E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 241 -1109.000 .500695E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 242 -1108.000 .475197E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 243 -1107.000 .450422E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 244 -1106.000 .426396E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 245 -1105.000 .403137E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 246 -1104.000 .380661 E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 247 -1103.000 .358980E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 248 -1102.000 .338103E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 249-1101.000 .318034E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 250 -1100.000 .298775E-02 .OOOOOOE+00 .OOOOOOE+00 .OOOOOOE+00 distribution for network with monte carlo check based on 100000 total histories

I CALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. G-8]

index HlOpnPres pdf-output cdf-output pdf-output-mc cdf-output-mc (analytical) (analytical) (monte carlo) (monte carlo) 1 -1349.0000 .OOOOOE+00 .OOOOOOE+00 .32500E-02 .325001 E-02 2 -1348.0000 .OOOOOE+00 .OOOOOOE+00 .OOOOOE+00 .325001 E-02 3 -1347.0000 .OOOOOE+00 .OOOOOOE+00 .OOOOOE+00 .325001 E-02 4 -1346.0000 .OOOOOE+00 .OOOOOOE+00 .OOOOOE+00 .325001 E-02 5 -1345.0000 .16235E-06 .162349E-06 .57000E-03 382001 E-02 6-1344.0000 .57565E-06 .737996E-06 .OOOOOE+00 .382001 E-02 7-1343.0000 .81549E-06 .155349E-05 .OOOOOE+00 .382001 E-02 8 -1342.0000 .11495E-05 .270295E-05 .OOOOOE+00 .382001 E-02 9-1341.0000 .16120E-05 .431498E-05 .OOOOOE+00 .382001 E-02 10-1340.0000 .22494E-05 .656436E-05 .OOOOOE+00 .382001 E-02 11 -1339.0000 .31229E-05 .968726E-05 .1OOOOE-04 .383001 E-02 12-1338.0000 .43138E-05 .140011 E-04 .OOOOOE+00 .383001 E-02 13-1337.0000 .59289E-05 .199299E-04 .OOOOOE+00 .383001 E-02 14 -1336.0000 .81075E-05 .280374E-04 .20000E-04 .385001 E-02 15 -1335.0000 .11031E-04 .390684E-04 .100OOE-04 .386001 E-02 16-1334.0000 .15130E-04 .541985E-04 .20000E-03 .406001 E-02 17-1333.0000 .20453E-04 .746513E-04 .30000E-04 .409001 E-02 18-1332.0000 .27435E-04 .102087E-03 .500OOE-04 .414001 E-02 19 -1331.0000 .36618E-04 .138705E-03 .20000E-04 .416001 E-02 20 -1330.0000 .48631 E-04 .187335E-03 .50000E-04 .421001 E-02 21 -1329.0000 .64262E-04 .251597E-03 .30000E-04 .424001 E-02 22 -1328.0000 .84494E-04 .336091 E-03 .500OOE-04 .429001 E-02 23 -1327.0000 .11054E-03 .446631 E-03 .13000E-03 .442001 E-02 24 -1326.0000 .14390E-03 .590527E-03 .14000E-03 .456001 E-02 25 -1325.0000 .18638E-03 .776908E-03 .19000E-03 .475001 E-02 26-1324.0000 .24026E-03 .101716E-02 .41 OOOE-03 .516001 E-02 27-1323.0000 .30830E-03 .132546E-02 .30000E-03 .546001 E-02 28-1322.0000 .39340E-03 .171886E-02 .36000E-03 .582001 E-02 29-1321.0000 .49948E-03 .221834E-02 .45000E-03 .627001 E-02 30-1320.0000 .63097E-03 .284931 E-02 .62000E-03 .689001 E-02 31 -1319.0000 .79306E-03 .364237E-02 .85000E-03 .774001 E-02 32-1318.0000 .99176E-03 .463413E-02 .10400E-02 .878001 E-02 33 -1317.0000 .12339E-02 .586806E-02 .12800E-02 .100600E-01 34-1316.0000 .15274E-02 .739543E-02 .14400E-02 .1150OOE-01 35 -1315.0000 .18809E-02 .927631 E-02 .18300E-02 .133300E-01 36-1314.0000 .23042E-02 .115805E-01 .23000E-02 .156300E-01 37-1313.0000 .28079E-02 .143883E-01 .27400E-02 .183700E-01 38 -1312.0000 .34035E-02 .177919E-01 .34700E-02 .218400E-01 39-1311.0000 .41033E-02 .218952E-01 .42200E-02 .260600E-01 40-1310.0000 .49199E-02 .268151 E-01 .54400E-02 .315001 E-01 41 -1309.0000 .58662E-02 .326813E-01 .59400E-02 .374401 E-01 42-1308.0000 .69546E-02 .396359E-01 .65500E-02 .439901 E-01 43-1307.0000 .81971 E-02 .478330E-01 .79900E-02 .519801 E-01 44-1306.0000 .96039E-02 .574369E-01 .95900E-02 .615701 E-01 45-1305.0000 .11183E-01 .686202E-01 .10790E-01 .723600E-01 46-1304.0000 .12940E-01 .815602E-01 .13070E-01 .854299E-01 47-1303.0000 .14875E-01 .964354E-01 .14480E-01 .999097E-01

ICALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. G-9 48 -1302.0000 .16984E-01 .113420E+00 .16550E-01 .116459E+00 49 -1301.0000 .19257E-01 .132677E+00 .19070E-01 .135529E+00 50 -1300.0000 .21675E-01 .154352E+00 .21750E-01 .157279E+00 51 -1299.0000 .24212E-01 .178563E+00 .24290E-01 .181570E+00 52 -1298.0000 .26832E-01 .205395E+00 .27360E-01 .208930E+00 53 -1297.0000 .29491 E-01 .234886E+00 .29360E-01 .238290E+00 54 -1296.0000 .32135E-01 .267021 E+00 .31781 E-01 .270071E+00 55 -1295.0000 .34700E-01 .301721 E+00 .34780E-01 .304851E+00 56 -1294.0000 .37117E-01 .338837E+00 .36720E-01 .341571E+0O 57 -1293.0000 .3931 OE-O1 .378147E+00 .38650E-01 .380221E+00 58 -1292.0000 .41203E-01 .419350E+00 .40769E-01 .420990E+00 59 -1291.0000 .42719E-01 .462069E+00 .43439E-01 .464429E+00 60 -1290.0000 .43788E-01 .505857E+00 .43869E-01 .508298E+00 61 -1289.0000 .44352E-01 .550209E+00 .44349E-01 .552647E+00 62 -1288.0000 .44364E-01 .594573E+00 .43789E-01 .596436E+00 63 -1287.0000 .43799E-01 .638373E+00 .43019E-01 .639455E+00 64 -1286.0000 .42654E-01 .681027E+00 .42049E-01 .681504E+00 65 -1285.0000 .40950E-01 .721977E+00 .40649E-01 1722153E+00 66 -1284.0000 .38731 E-01 .760708E+00 .38650E-01 .760803E+00 67 -1283.0000 .36067E-01 .796775E+00 .36930E-01 .797733E+00 68 -1282.0000 .33046E-01 .829821 E+00 .31940E-01 ..829673E+00 69 -1281.0000 .29772E-01 .859593E+00 .29931 E-01 .859604E+00 70 -1280.0000 .26355E-01 .885948E+00 .25860E-01 .885464E+00 71 -1279.0000 .2291 OE-01 .908859E+00 .22470E-01 .907934E+00 72 -1278.0000 .19543E-01 .928401 E+00 .19990E-01 .927924E+00 73 -1277.0000 .16347E-01 .944749E+00 .16840E-01 .944764E+00 74 -1276.0000 .13400E-01 .958149E+00 .13050E-01 .957814E+00 75 -1275.0000 .10758E-01 .968907E+00 .10930E-01 .968744E+00 76 -1274.0000 .84514E-02 .977358E+00 .85800E-02 .977324E+00 77 -1273.0000 .64937E-02 .983852E+00 .65200E-02 .983844E+00 78 -1272.0000 .48764E-02 .988728E+00 .50000E-02 .988844E+00 79 -1271.0000 .35767E-02 .992305E+00 .38900E-02 .992734E+00 80 -1270.0000 .25608E-02 .994866E+00 .271 OOE-02 .995444E+00 81 -1269.0000 .17884E-02 .996654E+00 .16100E-02 .997054E+00 82 -1268.0000 .12177E-02 .997872E+00 .10700E-02 .998124E+00 83 -1267.0000 .80780E-03 .998680E+00 .70000E-03 .998824E+00 84 -1266.0000 .52181 E-03 .999201 E+00 .43000E-03 .999254E+00 85 -1265.0000 .32804E-03 .999530E+00 .28000E-03 .999534E+00 86 -1264.0000 .20059E-03 .999730E+00 .23000E-03 .999764E+00 87 -1263.0000 .11923E-03 .999849E+00 .80000E-04 .999844E+00 88 -1262.0000 .68867E-04 .999918E+00 .9OOOOE-04 .999934E+00 89 -1261.0000 .38629E-04 .999957E+00 .OOOOOE+00 .999934E+00 90 -1260.0000 .21032E-04 .999978E+00 .50000E-04 .999984E+00 91 -1259.0000 .11111E-04 .999989E+00 .OOOOOE+00 .999984E+00 92 -1258.0000 .56923E-05 .999995E+00 .1OOOOE-04 .999994E+00 93 -1257.0000 .28271 E-05 .999997E+00 .OOOOOE+00 .999994E+00 94 -1256.0000 .13605E-05 .999999E+00 .OOOOOE+00 .999994E+00 95 -1255.0000 .63420E-06 .999999E+00 .OOOOOE+00 .999994E+00 96 -1254.0000 .28624E-06 .1OOOOOE+01 .OOOOOE+00 .999994E+00 97 -1253.0000 .12505E-06 .100000E+01 .OOOOOE+00 .999994E+00 98 -1252.0000 .52857E-07 .1OOOOOE+01 .OOOOOE+00 .999994E+00

ICALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. G-10 99-1251.0000 .2161OE-07 .1OOOOOE+01 .OOOOOE+00 .999994E+00 100 -1250.0000 .85434E-08 .1OOOOOE+01 .OOOOOE+00 .999994E+00 101 -1249.0000 .32649E-08 .100000E+01 .OOOOOE+00 .999994E+00 102 -1248.0000 .12058E-08 .100000E+01 .OOOOOE+00 .999994E+00 103 -1247.0000 .43022E-09 .100000E+01 .OOOOOE+00 .999994E+00 104 -1246.0000 .14826E-09 .100000E+01 .OOOOOE+00 .999994E+00 105 -1245.0000 .49339E-10 .100000E+01 .OOOOOE+00 .999994E+00 106 -1244.0000 .15851E-10 .1OOOOOE+01 .OOOOOE+00 .999994E+00O 107 -1243.0000 .49151 E-1 1 .100000E+01 .OOOOOE+00 .999994E+00 108 -1242.0000 .14707E-11 .100000E+01 .OOOOOE+00 .999994E+00 109 -1241.0000 .42458E-12 .100000E+01 .OOOOOE+00 .999994E+00 110 -1240.0000 .11823E-12 .100000E+01 .OOOOOE+00 .999994E+00 111 -1239.0000 .31753E-13 .100000E+01 .OOOOOE+00 .999994E+00 112 -1238.0000 .82225E-14 .100000E+01 .OOOOOE+00 .999994E+00 113 -1237.0000 .20529E-14 .100000E+01 .OOOOOE+00 .999994E+00 114 -1236.0000 .49400E-15 .100000E+01 .OOOOOE+00 .999994E+00 115 -1235.0000 .11458E-15 .100000E+01 .OOOOOE+00 .999994E+00 116 -1234.0000 .2561OE-16 .1OOOOOE+01 .OOOOOE+00 .999994E+00 117 -1233.0000 .45136E-17 .1OOOOOE+01 .OOOOOE+00 .999994E+00 118 -1232.0000 .93481E-18 .100000E+01 .OOOOOE+00 .999994E+00 119 -1231.0000 .18657E-18 .1OOOOOE+01 .OOOOOE+00 .999994E+00 120 -1230.0000 .25411 E-19 .1OOOOOE+01 .OOOOOE+00 .999994E+00 121 -1229.0000 .46983E-20 .100000E+01 .OOOOOE+00 .999994E+00 122 -1228.0000 .83680E-21 .100000E+01 .OOOOOE+00 .999994E+00 123 -1227.0000 .14353E-21 .100000E+01 .OOOOOE+00 .999994E+00 124 -1226.0000 .23703E-22 .100000E+01 .OOOOOE+00 .999994E+00 125 -1225.0000 .37701 E-23 .100000E+01 .OOOOOE+00 .999994E+00 126 -1224.0000 .57750E-24 .100000E+01 .OOOOOE+00 .999994E+00 127 -1223.0000 .85227E-25 .100000E+01 .OOOOOE+00 .999994E+00 128 -1222.0000 .12086E-25 .100000E+01 .OOOOOE+00 .999994E+00 129 -1221.0000 .16527E-26 .100000E+01 .OOOOOE+00 .999994E+00 130 -1220.0000 .21801 E-27 .100000E+01 .OOOOOE+00 .999994E+00 131 -1219.0000 .27687E-28 .100000E+01 .OOOOOE+00 .999994E+00 132 -1218.0000 .33992E-29 .100000E+01 .OOOOOE+00 .999994E+00 133 -1217.0000 .40200E-30 .100000E+01 .OOOOOE+00 .999994E+00 134 -1216.0000 .45813E-31 .100000E+01 .OOOOOE+00 .999994E+00 135 -1215.0000 .51008E-32 .100000E+01 .OOOOOE+00 .999994E+00 136 -1214.0000 .54274E-33 .100000E+01 .OOOOOE+00 .999994E+00 137 -1213.0000 .56826E-34 .1OOOOOE+01 .OOOOOE+00 .999994E+00 138 -1212.0000 .59023E-35 .1OOOOOE+01 .OOOOOE+00 .999994E+00 139 -1211.0000 .58095E-36 .100000E+01 .OOOOOE+00 .999994E+00 140 -1210.0000 .OOOOOE+00 .1OOOOOE+01 .OOOOOE+00 .999994E+00 141 -1209.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 142 -1208.0000 .OOOOOE+00 .1OOOOOE+01 .OOOOOE+00 .999994E+00 143 -1207.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 144 -1206.0000 .OOOOOE+00 .1OOOOOE+01 .OOOOOE+00 .999994E+00 145 -1205.0000 .OOOOOE+00 .1lOOOOOE+01 .OOOOOE+00 .999994E+00 146 -1204.0000 .OOOOOE+00 .1OOOOOE+01 .OOOOOE+00 .999994E+00 147 -1203.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 148 -1202.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 149 -1201.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00

i CALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. G-11 150 -1200.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 151 -1199.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 152 -1198.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 153 -1197.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 154 -1196.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 155 -1195.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 156 -1194.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 157 -1193.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 158 -1192.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 159 -1191.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 160 -1190.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 161 -1189.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 162-1188.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 163 -1187.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 164-1186.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 165 -1185.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 166 -1184.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 167 -1183.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 168 -1182.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 169 -1181.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 170 -1180.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 171 -1179.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 172 -1178.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 173 -1177.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 174 -1176.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 175 -1175.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 176 -1174.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 177 -1173.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 178 -1172.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 179 -1171.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 180 -1170.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 181 -1169.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 182 -1168.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 183 -1167.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 184-1166.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 185 -1165.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 186 -1164.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 187 -1163.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 188 -1162.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 189 -1161.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 190 -1160.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 191 -1159.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 192 -1158.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 193 -1157.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 194 -1156.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 195 -1155.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 196-1154.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 197 -1153.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 198 -1152.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 199 -1151.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 200 -1150.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00

ICALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. G-12 I N-201 -1149.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 202 -1148.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 203 -1147.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 204 -1146.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 205 -1145.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 206 -1144.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 207 -1143.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 208 -1142.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 209 -1141.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 210 -1140.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 211 -1139.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 212 -1138.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 213 -1137.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 214 -1136.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 215 -1135.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 216 -1134.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 217 -1133.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 218 -1132.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 219 -1131.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 220 -1130.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 221 -1129.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 222 -1128.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 223 -1127.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 224 -1126.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 225 -1125.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 226 -1124.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 227 -1123.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 228 -1122.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 229 -1121.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 230 -1120.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 231 -1119.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 232 -1118.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 233 -1117.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 234 -1116.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 235 -1115.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 236 -1114.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 237 -1113.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 238 -1112.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 239 -1111.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 240 -1110.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 241 -1109.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 242 -1108.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 243 -1107.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 244 -1106.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 245 -1105.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 246 -1104.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 247 -1103.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 248 -1102.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 249 -1101.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00 250 -1100.0000 .OOOOOE+00 .100000E+01 .OOOOOE+00 .999994E+00

lICALCULATION NO. MWMECH-04-004 I CALCULATION NO. MWMECH-04-004 REVISION NO. 0 REVISION NO. 0 PAGE NO. G-13 PAGE NO. G-13 I

summary statistics for analytic network solution mean value = -1290.708 median value = -1290.134 standard deviation = 9.199 1st percentile -1314.686 5th percentile -1306.774 10th percentile -1302.790 25th percentile -1296.530 50th percentile -1290.134 75th percentile -1284.276 90th percentile -1279.387 95th percentile -1276.608 99th percentile -1271.644 summary statistics for monte carlo network simulation (based on 100000 histories, seed = 732) sample mean = -1290.937 sample median = -1290.189 sample std. dev. = 9.906 sample 5th pct. = -1307.248 sample 95th pct. = -1276.599 monte carlo results for first through last performing component index mean median 5 pct 95 pct std dev 1* -1290.937 -1290.189 -1307.248 -1276.599 9.906 2 -1281.818 -1281.511 -1294.394 -1269.962 7.681 3 -1275.644 -1275.493 -1286.916 -1264.692 6.937 4 -1270.337 -1270.281 -1281.086 -1259.696 6.538 5 -1265.147 -1265.171 -1275.832 -1254.385 6.982 6 -1259.644 -1259.794 -1270.664 -1248.348 7.254 7 -1253.103 -1253.479 -1265.037 -1240.417 8.463 8 -1243.176 -1244.197 -1258.067 -1226.569 11.885 9 -1150.280 -1149.919 -1196.159 -1102.641 27.237

lICALCULAT1iON NO. MWMECH-04-004 I CACULTI~ NO.MWMCH-4-04 REVISION NO. 0 REISIN N. 0 PAGE NO. G-14 AGENO.G-I I

monte carlo history # 500000 summary statistics for analytic network solution mean value = -1290.708 median value = -1290.134 standard deviation = 9.199 1st percentile -1314.686 5th percentile -1306.774 10th percentile -1302.790 25th percentile -1296.530 50th percentile -1290.134 75th percentile -1284.276 90th percentile -1279.387 95th percentile -1276.608 99th percentile -1271.644 monte carlo results for first through last performing component index mean median 5 pct 95 pct std dev 1 -1290.924 -1290.165 -1307.236 -1276.533 9.931 2 -1281.828 -1281.516 -1294.426 -1270.014 7.754 3 -1275.664 -1275.506 -1287.000 -1264.709 7.018 4 -1270.346 -1270.275 -1281.092 -1259.714 6.633 5 -1265.159 -1265.204 -1275.839 -1254.441 6.955 6 -1259.652 -1259.813 -1270.655 -1248.354 7.500 7 -1253.065 -1253.433 -1265.029 -1240.317 8.696 8 -1243.180 -1244.202 -1258.095 -1226.528 11.864 9 -1150.237 -1149.846 -1196.135 -1102.658 27.265

MWMECH-04-004 RevO Attachment H- I Evaluation of Monte Carlo Results The PLANETS code provides the distribution information for the groups as shown here:

monte carlo results for first through last performing component" 0

" index mean median 5 pct 95 pct std dev"

" 1 -1290.937 -1290.189 -1307.248 -1276.599 9.906"

" 2 -1281.818 -1281.511 -1294.394 -1269.962 7.681"

" 3 -1275.644 -1275.493 -1286.916 -1264.692 6.937" 4 -1270.337 -1270.281 -1281.086 -1259.696 6.538" 5 -1265.147 -1265.171 -1275.832 -1254.385 6.982" 6 -1259.644 -1259.794 -1270.664 -1248.348 7.254"

" 7 -1253.103 -1253.479 -1265.037 -1240.417 8.463"

" 8 -1243.176 -1244.197 -1258.067 -1226.569 11.885" 9 -1150.280 -1149.919 -1196.159 -1102.641 27.237" this information can be input directly into Mathcad statistical functions to allow graphical representation and additional checks to be performed. Specifically, the distribution can be plotted and and the 95 percentile point recalculated for comparison to PLANETS data. This is done in the following pages.

MWMECH-04-004 RevO Attachment H- 2 Target Rock Valve x:= 1050.. 1250 range of interest m := 1150.28 mean value reported above a := 27.237 standard deviation reported above check 95 percentile a := qnorm(o.95,m,a) a = 1195.0809 compares with 1196.159 reported in Monte Carlo y:= 0,.001...025 Target Rock Probability Density 0.025

, 0.02 0.015 C0.005 1050 1100 1150 1200 1250 pressure psia

- T/R probability density

- 95 percentile

MWMECH-04-004 RevO Attachment H- 3 Group 1 Safety Valves xl := 1200..1300 x:= 1200..1300 range of interest ml := 1243.176 mean value reported above m2:= 1253.103 al := 11.885 standard deviation reported above a2 := 8.463 check 95 percentile a:= qnorm(O.95,ml,al) b:= qnorm(o.95,m2,a2) I a = 1262.7251 compares with 1258.067. and 1265.037 reported in Monte Carlo b = 1267.023 y:= 0,.001...05 Gr I Probability Density 0.05

• I e' 0.04

.9 C

- 0.03 Vl E!

X,,I /I 0:.0 1220~~~~~120 16I 20 10 0

C oo r- 0.01 200 1 pressure psia

-GR Ivlv I

- Grlvlv2

- 95 percentile vlv I 95 percentile vlv2

MWMECH-04-004 RevO Attachment H- 4 Group 2 Safety Valves xl := 1200..1300 x:= 1200..1300 range of interest ml := 1259.644 mean value reported above m2:= 1265.147 cl := 7.254 standard deviation reported above a2 := 6.982 check 95 percentile a:= qnorm(O.95,ml,cl) b:= qnorm(o.95,m2,a2, a = 1271.5758 1275.832 reported in Monte Carlo b = 1276.631 compares with 1270.664 and y:= 0,.001...0 6 Gr 2 Probability Density 0.06 r-s 0.04 Ca

.)

0.02 0.

I 0

1200 1220 1240 1260 1280 1300 pressure psia Gr 2 vlv I

-. Gr 2 vlv2 95 percentile

.-.---- vlv 1 95 percentile vlv2

MWMECH-04-004 RevO Attachment H- 5 Group 3 Safety Valves, first two valves in group xl := 1225..1325 x:= 1225..1325 range of interest ml := 1270.337 mean value reported above m2:= 1275.644 al := 6.538 standz ard deviation reported above <X2 := 6.937 check 95 percentile a:= qnorm(o.95,ml,al) b qnorm(o.95,m2,o2) a = 1281.0911 compares with 1281.086 and 1286.916 reported in Monte Carlo b = 1287.054 y:= 0,.001...06 Gr 3a Probability Density 0.08 _

e 0.06 -

c-;

Ca Z) e 0.02 -

0 1220 1240 1260 1280 1300 1320 1340 pressure psia Gr 3 vlv I

- Gr 3 vlv2

---

95 percentile vlv I

-- 95 percentile vlv2

MWMECH-04-004 RevO Attachment H- 6 Group 3 Safety Valves, last two valves in group xl := 1225..1325 x:= 1225..1325 range of interest ml := 1281.818 mean value reported above m2:= 1290.937 al := 7.681 standaard deviation reported above a2 := 9.906 check 95 percentile a := qnorm(O.95,ml ,ai) b := qnorm(o.95,m2,o2) a = 1294.4521 compares with 1294.394 and 1307.248 reported in Monte Carlo b = 1307.231 y:= 0,.001...06 Gr 3b Probability Density 0.06 _

C-W 2 0.04 U

U 2.D D 0.02 -

-0 E!

C.y 0

1220 1240 1260 1280 1300 1320 1340 pressure psia Gr 3 viv 3

- Gr 3 vlv4

---

95 percentile vlv I

- 95 percentile vIv2

MWMECH-04-004 Rev 0 Attachment I- 1 Prediction of Safety Valve Performance, D/QC Pooled Licensing Case This worksheet develops a mathematical relationship for valve flow vs pressure to allow direct comparsion of the effects of setpoint changes on predicted network flow performance.

p 1150,1150.5..1375 defines a pressure range variable Qmssv(P) := 644500- P main steam safety valve flow as a function of pressure and rated 1255 conditions, Ibm/hr QTR(P):= 598000. 1095 P Target Rock safety valve flow as a function of pressure and rated conditions, Ibm/hr the following define the valve opening setpoints for a 1%drift basis SPI := 1161.35 Target Rock valve SP2:= 1267.4 Gr 1 MSSVs SP3:= 1277.5 Gr 2 MSSVs SP4:= 1287.6 Gr 3 MSSVs the following relation defines a stepwise continuous function representing the valve. It allows 50%

flow at set pressure, and a linear ramp to full flow at 103% of set pressure.

Q I(p):=

0 if p<SPI QTR(P) +p - SPI t Mi QTR(P) IQT(2 +- . otherwise 2 ~.03-SPII the following plot demonstrates the flow vs pressure being defined for the TIR valve Ql(p)5.10' 1150 1200 1250 1300 1350 1400 p

MWMECH-04-004 Rev 0 Attachment I- 2 the following perform the same definitions for the 3 groups of MSSVs Gr1 MSSVs Q2(p) := 0 if p < SP2 r

mi{l Qmssv(P)

QmssQms 22

_.03.SP2 sv(P. - therise oSP2 Gr2 MSSVs Q3(p) := 0 if p < SP3 r Qmssv(P) Qmssv(P) ____p-hSP3 oenise mn ms() 2 + 2 t.03 SP3)1 Gr3 MSSVs Q4(p) := 0 if p < SP4 mi Q (P) Qmssv(P) Qmssv(P) p -SP4 otherwise m~Lms(~~ 2 + 2 r.03- SP4) sum the total flow vs pressure. Note that the number of valves in each group is used as a multiplier Qltot(p):= QI(p) + 2-Q2(p) + 2Q3(p) + 4Q4(p)

MWMECH-04-004 Rev 0 Attachment 1- 3 3%drift case the identical approach is applied for the 3% drift case SPI:= 1184.05 SP2:= 1292.2 SP3:= 1302.5 SP4:= 1312.8 Q13(p):= 0 if p <SPI QTR(P) QTR(P) (- PSI othenvise mir-r(P miQrQR(P)X 2 (P) 2 2 SPi

.03SP1)]

Q23(p):= 0 if p<SP2 miQ () Qmssv(P) 2 +

Qmssv(P) 2 rp - SP2f l.03-SP2)J otherwise Q33(p):= 0 if p<SP3 MifQ () Qmssv(P) Qmssv(P)p - SP3 otherwise m SSVP 2 2 V.03-SP3)1 Q43(p):= 0 if p <SP4 mi rQ () Qmssv(P) Qmssv(P) (p -_SP4] otherwise Q 2 + 2 l.03-SP4)J Q3tot(p):= Q3(p) + 2-Q23(p) + 2 Q33(p) + 4 Q43(p)

MWMECH-04-004 Rev 0 Attachment I- 4 95-95 case Perform a flow vs pressure calc for 95-95 setpoints. These are 4.222% for the T/R and 1.842% for the MSSVs SPI95:= 1197.9 SP295:= 1277.8 SP395:= 1288 SP495:= 1298.2 Q195(p):= 0 if p < SPI95 QTR(P) QTR(P) (p - SPI95 o mir QTR(P), ~~-2 other0Pise Q295(p) 0 if p < SP295

.1 Qm55V(P)

V2 (P + Qm55V(P) mzl QmSSV(P) Qmss(P ~ 52~~ {p - SP295) p-S25~

(.03.SP295 otherwise Q395(p):= 0 if p < SP395 f QmssV(P) Qmssv(P) (P - SP395)1 mSSV( 2 2 .03 SP395)]

Q495(p) 0 if p < SP495 QmsSV(P) QmssV(P) {p - SP495) ml Qmssv(P) ) 2 (p_-_SP495) otherwise 1LSv~ 2 + 2 I0.P9 Q95tot(p):= Q195(p) + 2.Q295(p) + 2.Q395(p) + 4.Q495(p)

MWMECH-04-004 Rev 0 Attachment I- 5 Monte Carlo 95th percentile results Perform a flow vs pressure calc for Monte Carlo based setpoints. Each valve is accounted for individually based on the 95th percentile setpoint calculated by PLANETS. The overall procedure is identical to that above.

SPlmc:= 1196.7 T/R SP2mc:= 1258.1 1st MSSV SP3mc:= 1265. 2nd MSSV SP4mc:= 1270.67 3rd MSSV SP5mc:= 1275.832 4th MSSV SP6mc:= 1281.09 5th MSSV SP7mc:= 1286.92 6th MSSV SP8mc:= 1294.4 7th MSSV SP9mc:= 1307.25 8th MSSV Qlmc(p):= 0 if p <SPlmc r QTR(P) QTR(P) pPlmc)o miLT()-2 + 2 l(.03-SPlmc)

Q2mc(p):= 0 if p <SP2mc r Qmssv(P) Qmssv(P) (p -_SP2mc vi miLQmssv(P) 2 + 2 .03iSP2mc Q3mc(p) := 0 if p < SP3mc Qmssv(P) Qmssv(P)( p - SP3mc]

mi Qmssv(P)' 2 + 2 o.03SP3mcse

MWMECH-04-004 Rev 0 Attachment 1- 6 Q4mc(p) := 0 if p < SP4mc Qmssv(P) Qmssv(P) (p - SP4mc o 2 2 t.03-SP4mc)

Q5mc(p):= 0 if p < SP5mc Qmssv(P) Qmssv(P) p - SP5mc) mi{nQmssv(P) 2 2 otherwise Q6mc(p):= 0 if p <SP6mc r Qmssv(P) Qmssv(P) ,p - SP6mc otw 2 2 t.03-SP6meC Q7mc(p):= 0 if p < SP7mc Qmssv(P) I Qmssv(P) (p - SP7mcj] otherwise 2 2 .03-SP7mc)

Q8mc(p) 0 if p < SP8mc r Qmssv(P) Qmssv(P) p - SP8mc oei 2 2 .03-SP8mc)

Q9mc(p) 0 if p < SP9mc mi Qmssv(P),

Qmssv(P) 2 2 (.03.SP9mc)

Qmssv(P) (p - SP9mc'1 otherwise Qmctot(p):= (Qlmc(p) + Q2mc(p) + Q3mc(p) + Q4mc(p) + Q5mc(p) + Q6mc(p)) ...

+ Q7mc(p) + Q8mc(p) + Q9mc(p)

MWMECH-04-004 Rev 0 Attachment 1- 7 Comparison of Relief Flow vs Pressure 6.10 6 -

i 440 0

ea 3-166_

1 .io6

.106 -

1150 1200 1250 1300 1350 pressure psia

- 1% drift

....... drift .95-95

--- ' 95 pc Monte Carlo

-' " 3% drift

MWMECH-04-004 Rev 0 Attachment I- 8 Integrating the flow pressure curves integrating the flow vs pressure functions and converting to lb/sec yields 1350 T 1150 Qltot(p) dp Ml := 360 3600 M = 1.252 x 105 1350 J Qmctot(p) dp 1150 Mmc = 1.188 x 105 Mmc :3600 j1350 J Q95tot(p) dp M9595:= 1150 M9 59 5 = 1.029 x 105 M9 5 9 5 .3600 T 1350 Q3tot(p) dp M := 150 3600 M3 = 8.36 x 1o4 the ratios between the base 1%case and the others is generated mmc = 0.949 Monte Carlo MI M9595

= 0.822 95-95 setpoint M3

= 0.668 3% drift ml

MWMECH-04-004 Rev 0 Attachment 1- 9 1.5% drift case the identical approach is applied for the 1.5% drift case SPI *= 1135-1.015+ 15 SPI = 1.167x 103 SP2:= 1240-1.015+ 15 SP2= 1.274x 103 SP3 := 1250-1.015 + 15 SP3 = 1.284x IO SP4:= 1260-1.015 + 15 SP4 = 1.294 x 103 Q115(p):= 0 if p < SPI rQ QR)+

QTR(P) 2 QTR(P).(P -SPI) 2 t.03-spi th1 ws Q215(p):= 0 if p < SP2

rQMssV(P) QMssV(P) (p -SP2)1 mi{Q ssXQmss mssv(P + . '- otherwise Q315(p) 0 if p < SP3 min[Q2ssv(P), QP + 2ms .03 -3)o Ep Q415(p)

= 0 if p < SP4 Qmssv(P) Qmssv(P) - SP4)]

mi{Qmssv(P) 2 2 - otherwise 2 2 .03.SP4)i QlStot(p) := Q115(p) + 2-Q215(p) + 2Q315(p) + 4Q415(p)

MWMECH-04-004 Rev 0 Attachment I- 10 J1350 1 Q15tot(p) dp 1150 3600 M 1 = 1.149 x 105

- =0.917 ml mc = 1.034 shows that Monte Carlo result and 1.5% are fairly equivalent M15 It is desirable to separate out the effects of the Target Rock on the above percentages Qlntr(p) := 2.Q2(p) + 2Q3(p) + 4Q4(p)

Qmcntr(p) := (Q2mc(p) + Q3mc(p) + Q4mc(p) + Q5mc(p) + Q6mc(p)) ...

+ Q7mc(p) + Q8mc(p) + Q9mc(p) 11350 f QlIntr(p) dp 1150 Mlntr = 30 3600 M 1 ntr = 9.081 x IO4 1l350 11350 Qmcntr(p) dp 1150 Mmcntr := 3600 Mmcntr = 9.089 x Io 4 these results suggest that the actual MSSV performance meets the 1% all drifted high case.

MWMECH-04-004 Rev 0 Attachment I- 11 Comparison of Relief Flow vs Pressure 710o6 -

6. io6 4 .106 0

2.106 -

I -le 1200 1250 1300 1350 pressure psia 1% drift 1.5% drift Monte Carlo 9595 drift

CALCULATION NO. MWMECH-04-004 REVISION NO. 0 PAGE NO. J-1 Attachment J Validation of PLANETS Installation The PLANETS code is part of a package of computer programs created to assist utility personnel apply statistical combination of uncertainties (SCU) methodology developed as part of the EPRI LWR setpoint analysis guidelines project. PLANETS was designed to interface with other codes in the setpoint analysis package, but also has substantial stand alone capabilities.

PLANETS is intended to enable users to statistically evaluate the performance characteristics of series/parallel networks of redundant components.

The PLANETS source code, along with the other codes of the SCU project, was provided as a utility code to Exelon in 1992. The codes were not under formal QA programs, but had undergone substantial validation and verification testing by the developer. The verification and validation test cases are documented in "PLANETS:Plant Network Simulation Program," EPRI NP-7557, October 1991. In addition, several sample problems, including a safety valve network problem similar to that being addressed in this calculation were included. The output files were provided as appendices to the report. In addition the manual described changes to the safety valve problem necessary to perform last-opening valve setpoint calculation and provided the answer for the user to match.

The following actions were taken to ensure appropriate installation and use of the PLANETS software on the Exelon UNIX platform:

1) Code manual was reviewed in detail, to understand the limits of applicability, limitations for use, and general intent of the software.

2) The fortran source coding was reviewed as well, to understand the overall structure and data paths, particularly the PLANETS and NETWORK routines.

3) The three sample problems, dice, MSIV closure, and MSSV network were run and output compared to the supplied output data. Good agreement was achieved in all cases. "Good agreement" in this case means exact matches for the analytical solutions and only minor variation in the fourth significant digit of the Monte Carlo calculation results.

4) The recommended input changes to the MSSV network example to calculate last valve opening characteristics were made and executed. Results agreed well with the provided answer.

5) Alternate verification of PLANETS calculations where possible. Appendix H documents checks made of 95th percentile calculations performed via MATHCAD.