ML20062G855
| ML20062G855 | |
| Person / Time | |
|---|---|
| Site: | Oyster Creek |
| Issue date: | 06/13/1990 |
| From: | Johari Moore GENERAL PUBLIC UTILITIES CORP. |
| To: | |
| Shared Package | |
| ML20062G848 | List: |
| References | |
| C-1302-187-5300, C-1302-187-5300-01R1, C-1302-187-5300-1R1, NUDOCS 9012030055 | |
| Download: ML20062G855 (41) | |
Text
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STATISTICAI, ANALYSIS OF DRYWELL * "' ~
THICKNESS DATA THRU 4-24-90 C-1302-a87-[)00,011, _0a 1 of 454
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V-l!c2-16 005 1.0 PROBImf STATDENT The basic purpose of this calculation is to update the thickness measurement analyses documented in References 3.7, 3.8, and 3.11 by incorporating the measurements taken in March and April 1990.
Specific objectives of this calculation ares (1) Statistically analyze the thickness measurements in the sand bed region to determine the mean thickness and corrosion rate.
(2) Analyze the data taken since the 12R outage for Bays 11A, 11C, 17D, 19A, 19B, 19C, and the Frame Cutout between Bays 17 and 19 to determine if cathodic protection has reduced the corrosion rate.
(3) Statistically analyze the thickness measurements for Bay 5 at.
elevation 51' and Bays 9, 13 and 15 at elevation 87' to determine the mean th'.ckness and corrosion rate.
(4) To the extent possible, analyze the data for the new locations at elevation 51' and elevation 52'.
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1 Calc. No. C-1302-187-5300-011 Rev. No. O Page 2 of 454 i 2.0
SUMMARY
_OF_RESULTS Bay & Area Corrosion Rate ** Mean Thickness *** F-Ratio 2.1 Sand Bed Recion With Cathodic Protection - All Data 11A -15.6 12.9 mpy 870.4 1 5.7 mile 5.4 11C Top -35.2 16.8 mpy 977.0 112.5 mils 4.6 11C Bottom -22.4 14.3 mpy 865.0 1 7.8 mils 4.9 17D -25.0 12.0 mpy 829.5 1 4.0 mils 29.4 19A- -21.4 11.5 mpy 807.6 1 3.0 mils 39.5 19B -19.0 11.7 mpy 836.9 1 3.2 mils 21.3
-19C -24.3 11.3 mpy 825.1 1 2.3 mils 66.2 2.2 Sand Bed Recion With Cathodic Protection - Since October 1988 11A Not Significant* 878.0 1 5.9 mils 11C Top Not Significant* 996.6 1 8.3 mils i 11C Bottom Not Significant* 878.1 1 5.6 mils !
17D -23.7 14.6 mpy 830.1 1 3.8 mils 2.7 19A -20.6 13.9 mpy 808.2 1 3.2 mils 2.8 _,
'19B -11.8 13.9 mpy 841.2 1 3.3 mile 0.9 l 19C -21.5 13.5 mpy 826.3 1 2.9 mils 3.7 2.3 Eftnd Bed Recion Frame Cutout 17/19 Top Not Sigaificant* 986.0 1 4.7 mils 17/19 Bottom Not Significant* 1008.4 1 3.9 mils v
2.4 Sand Bed Recion Without Cathodic Protection 9D Not Significant* 1021.7 1 8.9_ mils 13A -39.1 1 3.4_ mpy "853.1 1 2.4 mils 16.9 13D Indeterminate 931.9 122.6 mils ISD Not Significant* 1056.5 1 2.3 mils 17A Top lot Significant* 1128.3 1 2.2 mile 17A Bottom Not Significant* 745.2 1 2.1 mils 1.3 i Not statistically significant compared to random variations in measurements
- Mean corrosion rate in mils per year i standard error of estimate
- Best estimate of current mean thickness in mile i standard error of the mean 001/0004.2
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s Calc. No. C-1302-187-5300-011 Rev. No. O Page 3 of 454 Bay & hIga Corrosion Rate ** Mean Thickness *** F-Ratio 2.5 Elevation 51' l-5/D-12 - 4.6 1 1.6 745.2 1 2.1 mils 1.3 5/5 Indeterminate 745.1 1 3.2 mils 13/31 -Indeterminate 750.8 111.5 mils 15/23 Indeterminate 751.2 1 3.8 mils 1
2.6 Elevation 52' 7/25 Indeterminate 715.5 1 2.9
~13/6 Indeterminate 724.9 1 2.9 13/32 Indeterminate 698.3 1 5.0 19/13 Indeterminate 712.5 1 3.1 2.7 Elevation 87' 9 Not Significant* 619.9 1 0.6 l
13 Not Significant* 636.5 1 0.8 l 15 Not Significant* 636.2 1 1.1 l
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l 2.5 Accarent Corrosion Rates These estimates of the corrosion rate are based on a least squares fit of the data. In those cases where the F-Ratio is less than 1.0 they should not be used to make future projections. For bays with cathodic protection, these apparent rates are for the period from October 1988 to April 1990. For the other bays, it is for all data.
l Apparent Apparent Corrosion Corrosion Ray Rate fmov) F-Ratio Ray Rate (movl F-Ratio 11A -16.2 1 8.6 0.2 9D -21.0 118.1 0.1 11C Top -25.0 110.6 0.6 13A -39.1 1 3.4 16.9 11C Bottom -16.7 1 7.1, 0.6 150 - 4.6 1 4.8 0.1 17D -23.7 1 4.6 2.7 17A Top - 6.8 1 3.7 0.3 19A -20.6 1 3.9 2.8 17A Bottom -17.7 1 7.6 0.01 19B -11.8 1 3.9 0.9 5 EL 51' - 4.6 1 1.6 1.3 19C -21.5 1 3.5 3 .~ 7 9 EL 87' - 0.2 1 0.9 zero 17/19 rop - 8.2 110.7 0.1 13 EL 87' zero 17/19 Bottom -13.1 111.6 0.1 15 EL 87' zero 001/0004.3
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Calc. No. C-1302-187-5300-Oll Rev. No. O Page 4 of 454 2.6 Evaluation of Individual Measurements Exceedina 99%/99% Tolerance Interval One data point in Bay 5 Elev. 51' fell outside the 99%/99% tolerance interval and thus is statistically different from the mean thickness.
Based on a linear regression analysis for this point, it to concluded that the corrosion rate in this pit is essentially the same as the overall grid, v
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Calc. No. C-1302-187-5300-011 Rev. No. O Page 5 of 454 3.0 JLETERENCES
'Drywell Steel Shell 31 GPUN Safety Evaluation SE-000243-002, Rev. O, Plate Thickness Reduction at the Base Sand Cushion Entrenchment Region" 3.2 CPUN TDR 854, Rev. O, "Drywell Corrosion Assessment" ll" 3.3 GPUN Ten 851, Rev. O, " Assessment of oyster Creek Drywell She 3, "Punctional 3.4 OPUN Installatior.. Specification IS-328227-004, Rev.
Requirements for Drywell Containment Vessel Thickness Examination" 2nd Edition, N.R. Draper & H. Smith, 3.5 Applied Regression Analysis, John Wiley & Sons, 1981 3.6 Statistical concepts and Methods, 0.K. Bhattacharyya & R.A.
Johnson, John Wiley & sons, 1977 Rev. O, " Statistical Analys is 3.7 GPUN Calculation C-1302-187-5300-005, of Drywell Thicirness Data Thru 12-31-88" 3.8 CPUN TDR 948, Rev. 1, " Statistical Analysis of Drywell Thickness Data" 3.9 Experimental Statistics, Mary Gibbons Natrella, John Wiley & Sons, 1966 Reprint. (National Bureau of Standards Handbook 91) 3.10 Fundamental Concepts in the Design of Experiments, 1982 Charles C.
Hicks, Saundpra College Publishing, Fort Worth, "Statisti t Analysio 1.11 GPUN Calculation C-1302-187-5300-008, Rev. O, of Drywell Thickness Data thru 2-8-90" s
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l calc. No. C-1302-187-5300-011 Rev. No. O Page 6 of 454 4.0 ASSUMPTIONS & R&fC DATA 4.1 BaekatRgad h is The design of the carbon steel drywell includes a sand bed whic located around the outside circumference between elevationsLeakage i i 8'-11-1/4" and 12'-3".1980, 1983 and 198F refueling outages ind cat ngdrywell drains during the that water had intruded into the annular region between the shall and the concrete shield wall. to The drywell shell was inspected in 1986 during the 10R outageThe inspecti.on metho determine if corrosion was occurring. 3.3.
term results and conclusions are documented in Ref. 3.1, 3.
bed monitoring program would be established. 110, 17D, repetitive 19A, Ultrasonic region at a nominal elevation of 11'-3" in bays 11A, 19B, and 19C.
f The continued presence of watre in theTherefore, sand bed UTraised concerns o potential corrosion at higher elevations.and the 51' 87' elevations in November measurements were taken at As a result of these inspections, 9, 13 1987 during the 11R outage.
repetitive measurements in Bay 5 at elevation 51' and in i
higher program to confirm that corrosion is not occurring at these elevations. f A cathodic protection system was installed in selected regions o f the the sand bed during the 12R outage to minimL*e corrosion o drywell._ The cathodic protection system was placed in service on The long term monitoring program was also January 31, 1989. in the sand expanded during the 12R outage to include measurements bed region of Bays ID, 3D, SD, 7D, 9A, 13A, 130, 13D, It 15A, 150 and 17 A which are not covered by the cathodic protection system. 17 also includes measurements in the sand bed region between but doesBays his and 19 which is covered by the cathodic protection syste region.
d region The high corrosion rate computed for Bay 13A in the sand beraised concern through February 1990 (Ref. 3.11) Therefore, the corrosion rate in the sand bed region of Bay 13D. the monitoring of this location using a 6"x6" grid was added toa 2-inch core sample In addition, long term monitoring program. the 6"x6" was removed in March 1990 from a location adjacent to monitored grid in Bay 13A.
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s, s Calc. No. C-1302-187-5300-011 Rev. No. O Page 7 of 454 Measurements taken in Bay 5 Area D-12 at elevation $1' through i March 1990 indicated that corrosion is occurring at his location.
Therefore, survey measurements were taken to determine the thinnest locations at elevation 51'. As a result, three now locations were added to the long term monitoring program (Bay 5 Area 5, Bay 13 Area 31, and Bay 15 Area 2/3). !
l The indication of ongoing corrosion at elevation 51' raised J concerns about potential corrosion of the plates immediately above :
which have a smaller nominal thickness. Therefore, survey I measurements were taken in April 1990 at the 52' elevation in all i bays to determine the thinnent locations. As a result of this l survey, four new locations were added to the long term monitoring plan at elevation 52' (Bay 7 area 25, Bay 13 Area 6, Bay 13 Area 32, and Bay 19 Area 13).
Some measurements in the long term monitoring program are to be taken at each outage of opportunity, while others are taken during each refueling outage. The functional requirements for these inspections are documented in Ref. 3.4. The purpose of the UT ineasurements is to determine the corrusion rate and monitor it over i time, and to monitor the effectiveness of the cathodic protection system.
4.2 Selection of Areas to be Monitored ,
A program was initiated during the 11R outage to characterize the l corrosion and to determine its extent. The details of this
[ inspection program are documented in Ref. 3.3. The greatest corrosion was found via UT measurements in the sand bed region at l
the lowest,acerisible locations. Where thinning was detected, additional measurements were made in a cross pattern at the thinnest section to determine the extent in the vertical and horizontal directions. Having found the thinnest locatione, i
- measurements were made over a 6"x6" grid.
l To determine the vertical profile of the thinning, a trench was excavated into the floor in Bay 17 and Bay 5. Bay 17 was selected since the extent of thinning at the floor level was greatest in that area. It was determined that the thinning below the top of the curb was no more severe than above the curb, and became less ,
severe at the lower portions of the sand cushion. Bay 5 was excavated to determine if the thinning line was lower than the floor level in areas where no thinning was detected above the floor. There were no significant indications of thinning in Bay 5.
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O. 6 i Calc. No. C-1302-187-5300-011 Rev. No. O Page 8 of 454 It was on the basis of these findings that the 6"x6" gride in Bays 11A, 11C, 17D, 19A, 198 and 19C were selected as representative locations for longer term monitoring. The initial measurements at these locations were taken in December 1986 without a template or markings to identify the location of each measurement.
Subsequently, the location of the 6"x6" grids were permanently marked on the drywell shell and a template is used in conjunction ,
with these markings to locate the UT probe for successive measurements.
Analyses have shown that including the non-template ,
data in the data base creates a significant variability in the Therefore, to minimite the effects of probe thickness data.
location, only those data sets taken with the template are included in the analyses.
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.The presence of water in the sand bed also raised Therefore, concern UT o potential corrosion at higher olevations. measurements were taken during the 11M outage. The measurements were taken in a band on 6-inch centers at all accessible regions at these elevations.
Where these measurements indicated potential corrosion, the If these measurements spacing was reduced to 1-inch on centers.
additional readings indicated potential corrosion, measurementsIt was on the basis .
were taken on a 6"x6" grid using the template.
of these inspections that the 6"x6" gride in Bay 5 at elevation 51' ;
and in bays 9, 13 and 15 at the 87' elevation were setected as representative locations for long term monitoring.
A cathodic protection system was installed and atinthe theframe sandbetveen bed region Bays of Bays 11A, lic, 17D, 19A, 198, 29C, The system was placed in 69rvice' 17 and 19 during the 12R outage.
on January 31, 1989.
The long term monitoring program was expanded as follows during the 12R outages Measurements on 6"x6" grids in the sand bed region of Bays 9D, (1) 13A, 15D and 17A.
The basis for selecting these locations is that they were originally considered for cathodic protection but are not included in the system being installed. '
Measurements on 1-inch centers along 3D, SD,a 6-inch horizontal
?D, 9A, 130, andstrip (2) in the sand bed region of Bays ID, 15A.-
These locations were selected on the basis that they are representative of regions which have experienced nominal ,
corrosion and are not within the scope of the cathodic protection system.
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+, e Calc. No. C-1302-187-5300-011 Rev. No. O Page 9 of 454 (3} A 6"x6" grid in the curb cutout between Bays 17 and 19. The purpose of these measurements is to monitor corrosion in this region which is covered by the cathodic protection system but does not have a reference electrode to monitor its performance.
The long term monitoring program was expanded in March 1990 as follows: _
(1) Measurements in the sand bed region of Bay 13D: This location was added due to the high indicated corrosion rate in the sand bed region of Bay 13A. The measurements taken in March 1990 were taken on a 1"x6" grid. All subsequent measurements are to be taken on a 6"x6" grid.
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(2) Measurements on 6"x6" grids at the following locations at elevation $1's Bay 5 Area 5, Bay 13 Area 31, and Bay 15 Area 2/3. These locations were added due to the indication of -
ongoing corrosion at elevation 51', Bay 5 Area D-1.
The long term monitoring program was expanded in April 1990 by _
adding the following locations at elevation 52's Bay 7 Area 25, Bay 13 Area 6, Bay 13 Area 32, and Bay 19 Area 13. All measurements are taken on 6"x6" gride. These locations were added due to the indication of ongoing corrosion at elevation 51' and the fact that the nominal plate thickness at elevation 52' is less than _
at elevation 51'.
4.3 UT Measurements The UT measurements within the scope of the long term monitoring program are performed in accordance with Ref. 3.4. This involves taking UT measurements using a template with 49 holes laid out on a 6"x6" grid with 1" between centers on both axes. The center row is _
used in those bays where only 7 measttrements are made along a 6-inch horizontal strip.
The first set of measurements were made in December 1986 without the use of a template. Ref. 3.4 specifies that for-all subsequent readings, QA shall verify that locations of UT measurements
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performed are within i 1/4" of the location of the 1986 UT measurements. It also spccifies that all subsequent measurements are to be within i 1/8" of the designated locations.
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- . 6 Ccic. No. C-1302-187-5300-011 Rev. No. O Page 10 of 454 4.4 Data at Plue Locations Seven core samples, each approximately two inches in dit. meter were removed from the drywell vessel shell. These samples were evalanted in Ref. 3.2. Five of these samples were removed within g _ ,,-
the 6"x6" gride for Bays 11A, 17D, 19A, 19C and Bay 5 at elevation 51'. These locations were repaired by welding a plug in each hole. Since these plugs are not representative of the drywell shell, UT measurements at these locations on the 6"x6" grid must be dropped from each data set.
The following specific grid points have been deleted:
Bay Area L21pu 11A 23, 24, 30, 31 17D 15, 16, 22, 23 19A 24, 25, 31, 32 19C 20, 26, 27, 33, 5 EL 51' 13, 20, 25, 26, 27, 28, 33, 34, 35 The core sample removed in the sand bed region of Bay 13A was not within the monitored 6"x6" grid.
4.5 Bases for Statistical Analysis of 6"x6" crid Data 4.5.1 h4sumotions The statistical evaluation of the UT measurement data to determine the corrosion rate at each location is based on the following assumptions:
(1) Characterization of the scattering of data over each 6"x6" grid is such that the thickness measurements are normally distributed.
(2) once the distribution of data for each 6"x6" grid is found to be normal, then the mean value of the thickness is the appropriate representation of the average condition.
(3) A decrease in the mean value of the thickness with time is representative of the corrosion occurring within the 6"x6" grid.
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Rev. No. O Page 11 of 454 If corrosion has ceased, the mean value of the (4) thickness will not vary with time except for random errors in the UT measurements.
(5)
If corrosion is continuing at a constant rate, the In mean thickness will decrease linearly with time.
this case, linear regression analysis can be used to fit the mean thickness values for a given Thezona to a corrosion straight line as a function of time.
rate is equal to the slope of the line.
The validity of these assumptions is assured by:
(a)
Using more than 30 data points per 6"x6" grid Testing the data for normality at each 6"x6" grid (b) location.
Testing the regression equation as an appropriate (c) model to describe the corrosion rate.
In These tests are discussed in the following section.
cases where one or more of these assumptions proves to be invalid, non-parametric analytical techniques can be used to evaluate the data.
4.5.2 statistical Acoroach The following steps are performed to test and evaluate the UT measurement data for those locations where 6"x6" grid data has been taken at least three times Edit each 49-point data set by setting all invalid (1) Invalid points are those which are points to zero. declared invalid by the UT operator or are at a plug location. (The computer programs used in the following steps ignore all zero thickness data points.)
Perform a Chi-squared goodness of fit test of each 49 (2) point data set to ensure th&L th- assumption of normality is valid at the 5% and 1% level of sLgnLfLcance.
(3) Calculate the mean thickness and variance of each 49 point data set.
F-test to Perform an Analysis of Variance (ANOVA)
(4) determine if there is a significant difference between the means of the data sets.
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- Calc. No. C-1302-187-5300-011 Rev. No. O Page 12 of 454 (5) Using the mean thickness values for each 6"x6" grid, perform linear regression analysis over time at each location.
(a) Perform T-test for significance of regression at the 5% level of significance. The result of this test indicates whether or not the regression model is more appropriate than the mean model. In other words, it tests to see if the variation of the regression model is statistically significant over that of a mea.)
model.
(b) Calculate the ratio of the observed F value to the critical F value at 5% level of significance. For data sets where the Residual Degress of Freedom in ANOVA is 4 to 9, this F-Ratio should be at least 8 for the regression to be considered "useful" as opposed to cimply "significant." (Ref. 3.5 pp. 92-93, 129-133)
(c) cagculatethecoefficientofdetermination (R ) to assess how well the regression model explains the percentage of total error and thus how useful the regression line will be as a predictor.
(d) Determine if the residual values for the regression equations are normally distributed.
, (e) If the regression model is found to be appropriate, calculate the y-intercept, the slope and their respective standard errors.
The y-intercept represents the fitted mean thickness at time zero, the slope represents the corrosion rate, and the standard errors represent the uncertainty or random error of these two parameters.
(6) Use a K factor from Table A-7 of Reference 3.9 and the standard deviation to establish a one-sided 99%/99% tolerance limit about the mean thickness values for each 6"x6" grid location to determine whether low thickness measurements or " outliers" are statistically significant. If the data points are greater than the 99%/99% lower tolerance limit, then the difference between the value and the mean is deemed to be due to expected random error. However, if the data point is less than the lower 99%/99%
tolerance limit, this implies that the difference is statistically significant and is probably not due to chance.
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- . s cale. No. C-1302-187-5300-011 Rev. No. O Page 13 of 454 4.6 Analysis of Two 6"x6" Grid Data Sets Regression analysis is inappropriate when data is available at only two points in time. However, the t-test can be used to determine if the means of the two data sets are statistically different.
4.6.1 Assumot12at This analysis is based upon the following assumptions:
(1)
The data in each data set is normally distributed.
(2) The variances of the two data sets are equal.
4.6.2 Statistical Acoroach The evaluation takes place in three steps:
(1) Perform a chi-squared test of each data set at 5% and 1% levels of significance to ensure that the assumption of normality is valid. .
(2) Perform an F-test at 5% and 1% level of slynificance of the two data sets being compared to ensure that the assumption of equal variances is valid.
(3) Perform a two-tailed t-test for two independent samples at the 5% and 1% levels of significance to ,
determine if the means of the two data sets are ystatistically different.
A conclusion that the means are n21 statistically different is interpreted to mean that significant corrosion did not occur over the time period represented by the data.
However, if equality of the means ir ejected, ignificantthis andimplies could that the dif ference is statistical' be due to corrosion.
4.7 _ Analysis of Sinale 6"x6" orld Data set In those cases where a 6"x6" data set is taken at a given location for the first time during the current outage, the only other data t taken-to which they can be compared are the UT curvey measuremen s at an earlier time. For the most part, these are single point I
measurements which were taken in the vicinity of the 49-point data set, but not at the exact location. Therefore, rigorous l
statistical analysis of these single data sets is impossible.
However, by making certain assumptions, they can be compared with the previous data points. If more extensive data is available at L
the location of the 49-point data set, the t-test can be ased to compare the means of the two data sets as described in paragraph 4.5.
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. in v p kNi cale. No. C-1302-187-5300-011 'I Rev. No. O Page 14 of 454 When additional measurements are made at these exact locations during future outages, more rigorous statistical analyses can be employed.
4.7.1 Assumotions The comparison of a single 49-point data sets with previous data from the same vicinity is based on the following assumptions:
(1) Characterization of the scattering of data over the 6"x6" grid is such that the thickness measurement n ll are normally distributed.
(2) once the distribution of data for the 6"x6" grid is found to be normal, then the mean value of the thickness is the appropriate represer.tation of the average condition.
(3) The prior data is representative of the condition at this location at the rerlier date.
4.7.2 statistical Aceroach The evaluation takes place in four steps (1) Perform a chi-squared test of each data set to ensure that the assumption of normality is valid at the 95%
and 99% confidence levels.
( 2,) calculate the mean and the standard error of the mean of the 49-point data set.
(3) Determine the two-tailed t value from a t distribution table at levels of significance of 0.05 and 0.01 for n-1 degrees of freedom.
(4) Use the t value and the standard error of the mean to calculate the 95% and 994 confidence intervals about the mean of the 49-point data set.
(5) compare the prior data point (s) with these confidence intervals about the mean of the 49-point data sets.
If the prior data falls within the 95% confidence intervals, it provides some assurance that significtnt
' corrosion has not occurred in this region in the period of time covered by the data. If it falle within the 99%
confidence limits but not within the 95% confidence limits, this implication is not as strong. In uither case, the corrosion rate will be interpreted to be "Not Significant".
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b if the prior data falls above the upper 99% confidence isnit, it could mean either of two thingst (1) significant corrosion has occurred over the timo period covered by the n deta, or (2) the prior data point was not representative of the condition of the location of the 49-point data set in 1986. There is no way to differentiate between the two.
In this case, the corrosion rate will be interpreted to be "Possible".
Y If the prior data falls below the lower 99% confidence limit, it means that it is not representative of the Et condition at this location at the earlier date. In this IE case, the corrosion rate will be interpreted to be l[
m
" Indeterminable".
M g 4.8 M yn d of Sinole 7-Point Data Set
& In Whoen cases where a '-~ i s data set is taken at a given
) during the current outage, the only locstion for the firr*
4h other dnta to whic' Jan be compared are the UT survey gj measurements take .a earlier time to identify the thinnest h regtens of the dr- 1 shall in the sand bed region. For the most ptet, these are 3 se point measurements which were taken in the vicinity of the 7 -eint data sets, but not at the exact locations.
Hovover, by makin; certain assumptions, they can be compared with the previous data points. If more extensive data is available at the Accation of the 7-point data set, the t-test can be used to compere the means of the two data sets as described in paragraph 4.5.
When additional measurements are made at these exact locations during futura outages, more rigorous statistical analyses can be employed.
4.8.1 &nsumotions The comparison of a single 7-point data sets with previous data from the same vicinity is based on the following aneumptions:
(1) The corrosion in the region of each 7-point data set is normally distributed.
(2) The prior data is representative of the condition at this location at the earlier date.
The validity of these assumptions cannot be verified.
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Calc. No. C-1302-187-5300-011 Rev. Nu 0 Page if of 454 4.8.2. Statistical Aeproac$
The evaluation takes place in four steps (1) Calculate the mean and the standard error of the mean of the 7-point data set.
(2)
Determine the two-tailed t value using the t distribution tables at levels of significance of 0.0$
and 0.01 for n-1 degrees of freedom.
(3) Use the t value and the standard error of the mean to calculate the 95% and 994 confidence intervals about the mean of the 7-point data set.
(4) compare the prior data point (s) with these confidence intervals about the mean of the 7-point data sets.
If the prior data f alls within the 95% confidence intervals, it provides some assurance that significant corrosion has not occurred in this region in the period of time covered by the data. If it falls within the 994 confidence limits but not within the 95% confidence In either limits, case, the this implication is not as strong.
corrosion rate will be interpreted to be "Not Significant".
If the prior data falls above the upper 994 confidence interval, it could mean either of two things: (1)
- significant corrosion has occurred over the time period covered by the data, or (2) the prior data point was not representative of the conditionThereofisthe no location of the way to differentiate 7-point data set in 1986.In this case, the corrosion rate will be between the two.
interpreted to be "Possible".
If the prior data falls below the lower 991 confidence limit, it means that it is not representative of the In this e condition at this location at the earlier date.
case, the corrosion rate will be interpreted to be
" Indeterminable",,
4.9 Evaluation _of Drywell Mean Thickness This section defines the methods used to evaluate the drywell thickness at each location within the scope'of the long term monitoring program.
001/0004.16 1
Cale. No. C-1302-187-5300-011 Rev. No. O Page 17 of 454 Evaluation of Mean Thickness Usino Rearession Analysis 4.9.1 The following procedure is used to evaluate the drywell mean thickness at those locations where regression analysis has been deemed to be more appropriate than the mean model.
(1) The best estimate of the mean thickness at these locations is the point on the regression line corresponding to the time when the most recent set of
.In the SAS Regression measurements was taken.
Analysis output (App. 6.2), this is the last value in the column labeled " PREDICT VALUE".
(2) The best estimate of the standard error of the mean thickness is the standard error of the predicted In the SAS Regression Analysis value used above.
output, this is the last value in the column labeled "STD ERR PREDICT".
(3) The two-sided 954 confidence interval about the mean thickness is equal to the mean thickness plus or minus t times the estimated standard error of the mean. This is the interval for which we have 954 confidence that the true mean thickness will fall within. The value of t is obtained from a t distribution table for 12M11 tails at n-2 degrees of freedom and 0.05 level of significance, where n is the number of sets of measurements used in theThe degre regression analysis. s (the y-intercept and t
mtheto n-2 because slope) two parame erare calculated in the regression analys with n mean thicknesses as_ input.
(4) The one-sided 95% lower limit of the mean thickness is equal to the estimated mean thickness minus t This times the estimated standard error of the mean.
is the mean . thickness for which we have 95%
confidence In thisthat thethe case, true mean value of t thickness is obtained does from not fall below. f a t distribution table for Ent 1All at n-2 degrees o freedom and 0.05 level of significance.
4.9.2 Evaluation of Mean Thickness Usina Mean Model The following procedure is used to evaluate the drywell mean thickness at those locations where the mean mod deemed to be more appropriate than the linear regression model. This method is consistent with that used to evaluate the mean thickness using the regression model.
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(1) Calculate the nean of each set of UT thickness measurements.
(2) Sum the means of the sets and divide by the number of sets to calculate the grand mean. This is the best estimate of the mean thickness. In the SAS Regression Analysis output, this is the value labelled "DEP MEAN".
(3) Using the means of the sets from (1) as input, calculate the standard arr.ct about thR mt&D. This is the best estimate of the standard error of the mean thickness.
(4) The two-sided 95% confidence interval about the mean thickness is equal to the mean thickness plus or minus t times the estimated standard error of the mean. This is the interval for which we have 95%
confidence that the true mean thickness will fall within. The value of t is obtained from a t distribution table for euual talla at n-1 degrees of freedom and 0.05 level of significance.
(5) The one-sided 95% lower limit of the mean thickness is equal to the estimated mean thickness minus t times the estimated standard error of the mean. This is the mean thickness for which we have 95%
confidence that the true mean thickness does not fall below. In this case, the value of t is obtained from a t dis *ribution table for EHR 1A11 at n-1 degrees of
,, freedom and 0.05 level of significance.
1
- '4.9.3 Evaluation of Mean Thickness Usino Sinole Data Set l
The following procedure is used to evaluate the drywell thickness at those locations where only one set of measurements is available.
(1) calculate the mean of the set of UT thicknees 5
measurements. This is the best estimate of the mean thickness.
l l (2) Calculate the siano cd *ror of the mean for the set of UT measurements. This is the best estimate of the standard error of the mean thicAness.
Confidence intervals about the mean thickness cannot be calculated with only one data set available.
001/0004.18
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Calc. No. C-1302-187-5300-011 Rev. No. O Page 19 of 454 4.10 gyglgation of Drywell corrosion Rate 4.10.1 Mean Model If the ratio of the observed F value to the critical F value is less than 1 for the F-test for the significance of regression, it indicates that the mean model is more appropriace than the regression model at the 5% level of significance. In other words, the variation in mean thickness with time can be explained solely by the random variations in the measurements. This means that the corrosion rate is not significant compared to the random variations.
In this case, an F-test is performed to compare the variability of the data set means between data sets with the variability of individual measurements within the data sets. If the observed F value is less than the critical F value, it confirms that the mean model is appropriate.
If the F-test indicates that the variability of the means is significant, the Least Significant Difference (LSD) is computed. This is the maximum difference between daca set mean thicknesses that can be attributed to random variation in the measurements. If the difference between the means of data sets exceeds LSD, it indicates that difference is significant. The difference between means is subtracted from LSD and the result is divided by the time between measurements to estimate the asignificant Corrosion Rate" !
in mile per year (mpy). If the difference between the mgans does not exceed LSD, then it is concluded that no significant corrosion occurred during that period of time.
4.10.2 Recreasion Model l 1
If the ratio of the observed F value to the critical F value is 1 or greater, it indicates that the regression model is more appropriate than the mean model at the 5%
level of significance. In other words, the variation in j mean thickness with timo cannot be explained solely _by the random variations in the measurements. This means that the corrosion rate is significant compared to the random variations.
Although a ratio of 1 or greater indicates that regression is significant, it does not mean that the slope of the regression line is an accurate prediction of the corrosion rate. The ratio should be at least 4 or 5 to consider the slope to be a useful predictor of the corrosion rate (Ref.
001/0004.19
l cale. No. C-1302-187-5300-011 Rev. No. O Page 20 of 454 3.J, pp. 93, 129-133). A ratio of 4 or 5 means that the variation from the mean due to regression is approximately titice the standard deviation of the residuals of the rogression.
72 have a high degree of confidence in the predicted c>rrosion rate, the ratio should be at least 8 or 9 (Ref.
3.5, pp. 129-133).
4.10.3 Best Estimate of Recent Corrosion Rate In most instances, four sets of measurements over a period of about one year do not provide a significant regression model which can be used to predict future thicknesses.
However, a least squares fit of the four data points does provide a reasonable estimate of the recent corrosion rate. This information is particularly valuable for assessing the effectiveness of cathodic protection and the draining of the sand bed region. Since a linear regression analysis performs a linear least squares fit of the data, the best estimate of the recent corrosion rate is the slope from the regression analysis for the period of interest.
These values are tabulated as the " Apparent Corrosion Rate" in paragraph 2.5.
v l
t i
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f Calc. No. c-1302-187-5300-011 Rev. No. O Page 21 of 454 5.0 CALetrLATIONS 5.1 6"x6" crids in Sand Bed Peaien With cathodie Protecti2D 5.1.1 Bay 11A 5.1.1.1 Bay 11A 5/1/87 to 2/8/90 Nino 49-point data sets were Since available for lies a plug this bay covering 4/24/90 period.
within this region, four of the points were voided in each data set. The data were analyzed as described in paragraphs 4.4, 4.5.1 and 4.6.1.
(1) The data are normally distributed.
(2) The regression model is appropriate.
(3) The regression model explains 78.3% of the variation about the mean.
(4) The residuals are normally distributed.
(5) The current mean thickness i standard error is 870.4 i 5.7 mils.
(6) The corrosion rate i standard error is
-15.6 1 2.9 mLis per year.
(?) F/F critical = 5.4. :
(B) The measurement below 800 mils was tested and determined not to be statistically different from the mean thickness.
5.1.1.2 Bay 11Ai 10/8/88 to 4/24/90 Five 49-point data sets were available for this bay covering this period.
(1) The data are normally distributed.
(2) The mean model is more appropriate than the regression model.
(3) The F-test for the significant of the difference between the means shows that the difference between the mean thickness are not significant.
e a
. I Calc. No. C-1302-187-5300-011 Rev. No. O Page 22.of 454 (4) The t-test of the last two data sets shows t' the difference between the mean
.kness is not significant.
(5) The current thickness based on the mean model is 878.9 1 5.9 mile.
(6) These analyses indicate that tne corrosion m rate with cathodic protection is not significant compared to random variations in the measurements.
I (7) The best estimate of the corrosion rate during the period based on a least squares fit-is -16.2 1 8.6 mile per year.
- 5.1.2 Bay 11C 5.1.2.1 Bay 11C: 5/1/87 to 4/24/90 Nine 49-point data sets were available for this bay covering this period. The initial analysis of this data indicated that the data are not normally distributed. The lack of normality was tentatively attributed to minimal corrosion in the upper half of the 6"x6" grid with more extensive corrosion in the lower half of the grid. To test this hypothesis, each data set ,
was divided into two subsets, with one containing the top three rows and the other
,, containing the bottom four rows.
Too 3 Rows (1) The data are normally distributed.
(2) The regression model is appropriate.
(3) The regression model explains 79% of the total variation about the mean.
(4) The residuals are normally distributed.
(5) The current mean thickness 1 standard error is 977.0 1 12.5 mils.
(6) The corrosion rate is -35.2 1 6.8 mile per
- year.
(7) F/F critical = 4.6.
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. t Calc. No. C-1302-187-5300-011 Rev. No. O Page 23 of 454 Bottom 4 Rows (1) seven of the nine data sets are normally distributed. The other two are skewed toward the thinner side of the mean. The Chi-square test shows that they are close to being normally distributed at the 1%
level of significance.
( 2') The regression model is appropriate.
(3) The regression model explains 80% of the total variation about the mean.
(4) The residuals are normally distributed.
(5) The current mean thickness 1 standard error is 865.0 1 7.8 mile.
(6) The corrosion rate i standard error is
-22.4 1 4.3 mils per year.
(7) F/F critical = 4.9 5.1.2.2 Bav 11c: 10/8/88 to 4/24/jQ r
Five 49-point data sets were available for this period. These data were divided into two subsets as described above.
,, Too 3 Rows (1) The data are normally distributed.
(2) The mean model in more appropriate than the regression model.
(3) The F-test for the significance of the difference between the means shows that the differences between the mean thicknesses are not significant.
(4) The t-test of the last two data sets shows that there is no statistical difference between their means.
(5) These analyses indicate that the current corrosion rate with cathodic protection is not sigt.ificant compared to random variations in the measurements.
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(6)
Based on the mean model, the current thickness 1 standard error is 996.6 1 8.3 mile. l The best estimate of corrosion rate during (7) this period based on a least squares fit I
is -25.0 1 10.6 mils per year.
Bottom 4 Rows (1)
Four of the five data sets are normally distributed. (See 5.1.2.1 above). .
The mean model is more appropriate than (2) the regression model.
(3)
The F-cost for the significance of the t difference between the means shows that the differences between the mean thicknesses are significant.
(4) The t-test of the last two data sets shows that there is no significant statistical difference between their means.
Based on the mean model, the current (5) thickness i standard error is 878.1 1 5.6 mile.
Based upon examination of the distribution
- (6) of the five data set mean values, it is concluded that the current corrosion rate l
is not significant compared to randomThe variations in the measurements. 897, measurements alternated as follows:
877, 891, 869, 863. Therefore the difference must be due to variations other than corrosion.
(7) The best estimate of the corrosion rate during this period based onmilsa least per year.
squares fit is -16.7 1 7.1 001/0004.24
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, . l Calc. N3. C-1302-187-5300-011 Rev. No. O Page 25 of 454 5.1.3 Bay 17D
)
5.1.3.1 Bay 17De 2/17/87 to 4/24/90 Ten 49-point data sets were available for this period. Since a plug lies within this region, four of the points were voided in each data ;
set. Point 24 in the 2/8/90 data was voided since it is characteristic of the plug thickness.
(1) The data are normally distributsd. J (2) The regression model is appropriate.
(3) The regression model explains 95% of the total variation about the mean.
(4) The residuals are normally distributed.
(5) The current mean thickness t standard error is 829.5 1 4.0 mile.
(6) The corrosion rate i standard e rror is '
-25.0 1 2.0 mLis per year.
(7) F/F critical = 29.4 (8) The measurements below 800 mile wet.
tested and determined not to be statistically different from the mean thickness.
l 5.1.3.2 Bay 17D 10/8/8B to 4/24/90 l
Five 49-point data sets were available for this
- period.
! (1) The data are normally distributed.
l (2) The regression model is more appropriate than the mean model.
(3) The regression model explains 90% of the variation about the mean.
(4) The residuals are normally distributed.
(5) The current mean thickness i standard error is 830.1 1 3.8 mile.
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- j Calc. No. C-1302-187-5300-012 Rev. No. O page 26 of 454 l J
l (6) The corrosion rate i standard error is
-23.7 1 4.6 mpy.
(7) F/F critical = 2.7 5.1.4 Bay 19A h 5.1.4.1 Bay 19As 2/17/87 to 4/24/90 Ten 49-point data sets were available for this period. Since a plug lies within this region, four of the points were voided in each data set.
(1) The data are normally distributed at the 1% level of significance.
(2) The regression model is appropriate (3) The regression model explains 96% of the total variation about the mean.
(4) The residuals are normally distributed.
(5) The current mean thickness i standard error is 807.6 1 3.0 mils.
(6) The corrosion rate i standard error is ,
-21.4 1 1.5 mpy.
(7) F/F critical = 39.5 (8) The data points that were below 800 mLis were tested and determined not to be statistically different from the mean thickness.
5.1.4.2 Bay 19As 10/8/88 to 4/24/90 i.
' Five 49-point data sets were available for this I period.
(1) The data are normally distributed.
l (2) The regression model'is more appropriate than the mean model, i
l 001/0004.26 l .
,O. e i Calc. No. C-1302-187-5300-011 Rev. No. O Page 27 of 454 (3)
The regression model explains 90% of the variation about the mean.
(4)
The residuals are normally distributed.
(5) The current mean thickness i standard error is 808.2 1 3.2 mils.
(6) The corrosion rate i standard error is
-20.6 1 3.9 mpy.
(7) F/F critical = 2.8 5.1.5 Bay 198 5.1.5.1 gav 198: 5/1/87 to 4/24/90 dine 49-point data sets were available for this period.
(1)
The data are normally distributed.
(2) The regression model is appropriate.
(3) The regression model explains 94% of the total variation about the mean.
(4)
The residuals are normally distributed.
(S) The current mean thickness i standard error is 836.9 1 3.2 mils.
(6) The corrosion rate i standard error is
-19.0 1 1.7 mpy.
(7) F/F critical = 21.3 (8) The measurements below 800 mils.were tested and determined not to be statistically different from the mean thickness.
5.1.5.2 Bav 19B 10/8!99_to 4/24/90 Five 49-point data sets were available for this period.
(1) The data are normally distributed.
(2)
The regression model is more appropriate than the mean model.
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1 (3) The regression model explains 75% of the l variation about the mean.
(4) The residuals are normally distributed.
(5) The current mean thickness i standard '
error is 841.2 1 3.3 mils.
(6) The corrosion rate i standard error is
-11.8 1 3.9 mpy.
(7) F/F critical = 0.9 5.1.6 Bay 19C 5.1.6.1 Bay 19c 5/1/87 to 4/24/90 Nine 49-point data sets were available for this period. Since a plug lies within this region, four of the points were voided in each data set.
(1) The data are normally distributed at the 1% level of significance, but appears to be developing two peaks.
(2) The regression model is appropriate.
(3) The regression model explains 98% of the total variation about the mean.
v (4) The residuals are normally distributad.
(5) The current mean thickness i standard error is 825.1 1 2.3 mile.
(6) The corrosion rate i standard error is
-24.3 1 1.3 mpy.
(7) F/F critical = 66.2 (8) The measurements below 800 mils were tested and determined not to be statistically different from the mean thickness.
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., s Calc. No. C-1302-187-5300-011 1 Rev. No. O i Isge 29 of 454 5.1.6.2 Bay 19ct 10/8/88 to 4/24/90 Five 49-point data sets were available for this period.
(1) The data are normally distributed at the is level of significance.
(2) The F-test for significance of regrassion indicates that the regression model is appropriate.
(3) The regression model explains 93% of the total variation about the mean.
(4) The residuals are normally distributed.
(5) The current mean thickness i standard error is 826.3 1 2.9 mile.
(6) The corrosion rate i standard error is
-21.5 1 3.5 mpy.
(6) F/F critical = 3.7.
5.1.7 Bave 17/19 Frame Cutout 12/30/88 to 4/24/90 Two sets of 6"x6" grid measurements were taken in December 1988. The upper one is located 25" below the top of the high curb and the other below the floor. There is no pqevious data. The upper location was added to the long term monitoring program.
Five 49-point data sets were available for this period.
These data were analyzed as described in 4.4, 4.5.2 and 4.6.1. The initial analysis of this data indicated that the first and last data sets are not normally distributed.
The lack of normality was tentatively attributed to more extensive corrosion in the upper half of the grid than the bottom half. To test this hypothesis, each data set was divided into two subsets, with one containing the top three rows and the other containing the bottom four rows.
001/0004.29
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Calc. No. C-1302-187-5300-011 j Rev. No. O i Page 30 of 454 Too 3 Rows (1) Four of the five subsets are normally distributed at the is level of significance but one is not. l l
(2) The mean model is appropriate. ]
(3) The F-test for the significance of the difference between the means shows that the differences between the mean thicknesses are not significant at is level of significance.
(4) These analyses indicate that the corrosion rate is not significant compared to the random variations in the measurements.
(5) Based on the mean model, the current thickness i standard error is 986.0 1 4.7 mils.
(6) The best estimate of the corrosion rato during this period based on a least squares fit is -8.2110.7 mils per year.
Bottom 4 Rows (1) Four of the five subsets are normally distributed at the 5% level of significance, and one at the is level of significance. ,
(2) The mean model is appropriate.
(3) The F-test for the significance of the difference between the means shows that the differences between the mean thicknesses are not significant at 1% level of significance.
(4) These analyses indicate that the corrosion rate la not significant' compared to the random variations i the measurements.
1
~ (5)
Based on the mean model, the current thickness i etandard error is 1005.7 1 5.6 mils.
(6) The best estimate of the corrosion rate during this period based on a least squares fit is -13.1 1 11.6 mils per year.
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l cathodie Protection l 5.2 6"x6" Crids in Sand Bed Recion Without 5.2.1 Bay 9D 12 /19/88 to 4 /24 /90 Five 49-point data sets were availabic for this period.
(1) The data are normally distributed.
(2) The mean model is more appropriate than the '
regression model.
(3) The current mean thickness is 1021.7 1 8.9 mile.
(4) The F-test for the significance of the difference between the mean thicknesses indicates that the The differences between the means are significant.
LSD analysis shows that this is due to the second measurement on 6/26/89 which is 33 to 52.3 mile higher than the other four.
(5) The t-test of the last two data sets shows that the difference between the mean thicknesses is not significant.
(6) The overall analysis indicates that there was no significant corrosion from December 19, 1988 to April 24, 1990.
(7)
The best estimate of the corrosion rate during this
, period based on a least squares fit is -21.0 1 18.1 mils per year.
5.2.2 Bav 13At 12/17/88 to 4/24/90 Seven 49-point data sets were available for this period.
(1) _The data are normally distributed.
(2) The regression model is appropriate.
(3) The regression model explains 97% of the total '
variation about the mean.
(4) The residuals are normally distributed.
(5) The current mean thickness 1 standard error is 853.1 1 2.4 mils.
001/0004A.2
cale. No. C 1302-187-5300-011 Rev. No O Page 32 of 454 (6) The indicated corrosion rate i standard error is
-39.1 1 3.4 mile per year.
(7) F/F critical = 16.9 (8) The measurements below 800 mils were tested and from the determined not to be statistically different mean thickness.
5.2.3 Bay 13D: 3/28/90 to 4/25/90 one 7-point data set and one 49-point data set are available for this bay covering this period.
(2) The 7-point data set is normally distributed at 5%
level of significance. The 49-point data set is normally distributed at 14 level of significance.
However, there is a diagonal line of demarcation separating a zone of minimal corrosion at the Thus, top corrosion from a corroded tone at the bottom.
has occurred at this location.
(2) The mean of the 7-point data set is not significantly dif ferent f rom the mean of the corresponding 7 points in the 49-poirt data set.
22.6 mile.
(3) The current means thickness is 931.9 1 It is concluded that corrosion has occurred at this location. However, with minimal data over a one-month period, it is impossible to determine the current corrosion rate.
5.2.4 gay I5D: 12/17/88 to 4/24/90 Five 49-point data sets were available for this period.
(1) The data are normally distributed.
(2)
The mean model is more appropriate than the regression model.
(3) The current mean thickness i standard error is 1056.5 1 2.3 mils.
(4)
The F-test for the significance of the difference between the mean thicknesses indicates that the differences between the means are not significant.
001/0004A.3
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- a calc. No. c-1302-187-5300-011 Rev. No. O Page 33 of 454 (5) The t-test of the last two data sets shows that the differenes between the mean thicknesses is not significant.
(6) There was no significant corroen. from December 17, 1988 to April 24, 1990.
(7) The best estimate of the corrosion rate during this period based on a least squares fit is -4.6 mils per year.
5.2.5 Bay 17At 12/17/88 to 4/24/90 Five 49-point data sets were available for this period The initial-analysis of this dt;a indicated that the data are not normally distributed. The lack of normality was tentatively attributed to minimal corrosion in the upper-half of the 6"x6" grid with more extensive corrosion in the
.7wer half of the grid. To test this hypothesis, each data
.at was divided into two subsets, with one containing the top threo rows and the other containing the bottom four rows.
i Too 3 Rows (1) The data are normally distributed.
(2) The mean model is more appropriate than the regression model.
(3) The current mean thickness 1 standard error is 1128.3 1 2.2 mils.
(4) The F-test for the significance of the difference.
between the mean thicknesses indicates the differences b3 tween the means are not significant.
=
(5) The t-test of the last two data sets indicates that the difference between the mean thicknesses is not significant.
(6) There was no significant corrosion during this period.
(7) The best estimate of the corrosion rate during this period based on a least squares-fit is -6.8 1 3.7 mils per year.
001/0004A.4
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- a l Calc. No. C-1302-187-5300-011 Rev No. O Page 34 of 454 Bottom 4 Rows (1) The data are normally distributed.
(2) The mean model is more appropriate than the regression model.
(3) The current mean thickness i standard error 950.83 1 5.3 mile.
(4) The F-test for the significance of the difference between the mean thicknesses indicates that the differences between the means are not significant.
(5) The t-test of the last two data sets indicates that the difference between the mean thicknesses is not significant.
(6) There was no significant corrosion during this period.
(7) The best estimate of the corrosion rate iuring this period based on a least squares fit is ,7.7 1 7.6 mils per year.
5.3 6"x6" celds at 51' Elevation 5.3.1 Bay 5 Area D-1 2 51' Elevation: 11/1/87 ts 4/24/90 Eight 49-point data sets were available for this period.
Th'N initial analysis of this data indicated that the data are not normally distributed. These data sets nam 9s' start with E. The following adjustments were made.to the data
, (1) Point 29 in the 9/13/89 data is much greater than the preceding or succeeding measurements. Therefore, this reading was dropped from the analysis.
(2) Point 9 is a significant' pit. Therefore, it was dropped from the overall analysis and is evaluated separately.
(3) Points 13 and 25 are extremely variable and are located adjacent to the plug which was removed from-this grid. They were also dropped from the analysis.
(4) Point 43 in the 11/01/87 data.is much less than any succeeding measurement. Therefore, this reading was dropped from the analysis.
001/0004A.5
-,-l,,-. - - - , , - - , , . , . . , , , , , . . . -
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Ca17. No. C-1302-187-5300-011 Rev. No. O Page 35 of 454 With these adjustments, the first and last data sets are normill, distributed at the 1% level of significance and the other five at 5%. These data set names start with F.
It was noted that the D-Meter calibration at 0.750" yielded readings which ranged from -1 mil for one set of measurements to + 4 mils for another. The data was adjusted to eliminate these biases. These data set names start with G. The final analyses are based on these adjusted data sets.
2 (1) The data are normally distributed.
, (2) The if,gression model is appropriate.
(3) The regression model explains 57% of the total variation about the mean.
(4) The residuals are normally distributed.
(5) The current mean thickness i standard error is 745.2 1 2.1 mils.
(6) The indicated corrosion rate i standard error is -4.6 1 1.6 mile per year.
(7) F/F critical = 1.3. Thus, the regression 's just barely significant.
(8) The F-test for significance of the difference between
, the mean thickness indicates that the differences are significant.
(9) The t-test of the last two data sets shows that the difference between the mean thickness is not significant.
(10) The measurements of the pit at point 9 were 706,.746, 696, 694, 700, 688, 699 and 689 mile. -The mean value of these measurements is 702.3 1 6.5 mile. A least squares fit shows that the best estimate of the
= corrosion rate during this period is -11.5 inils per year with R 2 =31%. The second measurement is much higher than the others. Dropping this point, the mean of the remaining measuranonts is 696.012.4 mile, and the best estimate of -the corrosion rate is
-4.9 mils per year with R2 = 49%. Recognizing that ,
the variability of single measurements will be about 6 times the variability of the mean of 40 measure-ments, it is concluded that the corrosion rate in the pit is essentially the same as the overall grid.
001/0004A.6
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Calc. No. C-1302-187-5300-Oll Rev. No. O Page 36 of 454 5.3.2 Bay 5 Area 51-5 at 51' Elevation 3/31/90 to 4/25/90 Two 49-point data sets are available for this time period.
(1) The data are not normally distributed. Th.ts is due to a large corroded patch near the center of the grid, and several small patches on the periphery.
When the data less than the grand mean were segregated, it was found that these subsets are normally distributed.
(2) The t-tests of the two complete data sets and the two subsets indicate that the difference between the mean thicknesses are not significant.
(3). The current mean thickness i standard error is 745.1 1 3.2 mile.
It is concluded that corrosion has occurred at this location. However, with minimal data over such a brief period, it is impossible to 3etermine the current corrosion rate.
- 5. 3. 3. Bay 13 Area 31 Elevation 51's 3/31/90 to 4/25/12 Two 49-point data sets are available for this time period.
-(1) The-data are to normally distributed. This is due to a.large corroded. patch at the left edge of the grid.
v When the data less than the grand mean were sagregated, it was found that these subsets are no.mally distributed.
.(2) The 5-test of the two complate data sets indicate that the difference between the means is statistAcally significant. However', the difference between the means of the two subsets is not statistically significant.
(3) The current mean thickness is i standard error is 750.8 1 11.5 mils.
It is concluded that corrosion has occurred at this location. However, with minimal data over such a brief period, it is impossible to determine the current corrosion rate.
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Calc. No. C-1302-18'-5300-011 Rev. No. O Page 37 of 454 3/31/90 to 4/25/90 5.3.4 Bay 15 Area 23 Elevation 51's Two 49-point data sats are available for this time period.
This is due (1) The data are not normally distributed.
to a large corroded patch.
When the data less than the grand mean were segregated, it was found that these two subsets are normally distributed.
The t-tests of the two complete data sets and the two (2) subsets indicate that the differences between the mean thicknesses are not significant.
(3) The current mean thickness i standard error is 751.2 1 3.8 mile.
It is concluded'that However, corrosion with has minimal occurred data over at a such this brief location.it is impossible to determine the current corrosion period, rate.
5.4 6" x 6" Grids at 52' Elevation 5.4.1 Bay 7 Area 25 Elevation 52's 4/26/90 0i.3 49-point data set is available. -.
(1) vThe data are not normally distr ibuted.
The subset of the data less'than the mean thickness is not normally distributed.
When four points below 700 mils were dropped from.the data set, the remaining data was found to be normally distributed. Therefore, the lack of normality of the complete data set is attributed to these thinner points. Three of these could sincebe considered to be they deviate from pits'(626, 657 and 676 mils) the mean by more than 3 sigma.
715.5 1 2.9 (2) The current mean thickness i standard is mils.
It is concluded that corrosion has occurred at this location.
001/0004h.8 l
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.~. * :- o calc. No. C-1302-187-5300-Oll Rev. No. O Page 38 of 454 5.4.2 Bay 13 Area 6 Elevation 52's 4/26/90 One 49-point data set is available.
(1) The data are not normally distributed.
The subset of the data less than the mean thickness is normally distributed. Thus, the lack of normality of the complete' data set is attributed to a large corroded patch at the left side of the grid.
(2) The current mean thickness i standard error is 724.9 1 2.9 mile.
(3) It is concluded that corrosion has occurred at this location.
5.4.3 Bay 13 Area 32 Elevation 52's 4/26/90 One 49-point data set is available.
(1) The data are not normally distributed.
The subset of the data less than the mean thickness is normally distributed. Thus, the lack of normality of the. complete-date. set is attributed to these corrosion patches.
(2) The current mean thickness i standard error is 698.3 1 5.0 mile, v
It is concluded that corrosion has' occurred at this location.
5.4.4 Bay 19 Area 13 Elevation 52's 4/26/90 one 49-point data set is available.
(1) The data are normally distributed. However, two adjacent points differ =from the mean by 3 sigma and 5 sigma. Thus, there is a pit.
(2) The current means thickness i standard error is 712.5-
_1 3.1 mile.
It is concluded that some corrosion has occurred at this location.
001/0004A.9 I
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Calc. No. C-1302-187-5300-011 Rev. No. O Page 39 of 454 5.5 6" x 6" Grids at 87' Elevation 5.5.1 Bay 9 87' Elevation 11/6(17_to 3/28/90 Five 49-point data sets were available for this period.
(1) The data are normally distributed.
(2) The mean model is more appropriate than the regression model.
(3) There was no significant corrosion during this period.
(4) The current mean thickness i standard error is 619.9 1 0.6 mile.
(5) The best estimate of the corrosion rate during this period based on a least squares fit is -0.2 0.9 mils per year.
5.5.2 Bay 13 87' Elevation: 11/10/97 to 3/28/90 Five 49-point data sets were available for this period.
(1) The data are normally distributed.
(2) The mean model is more appropriate-than the regression model.
(1) There was no significant corrosion during this period.
(4) The current mean thickness i standard: error is 636.5 1 0.8 mile.
(5) The best estimate of the corrosion rate during this period based on a least squares fit is zero mile = per year.
5.5.3 Bay 15 87' Elevation 11/10/87 to 3/28/90 Five 49-point data sets were available for this period.
(1) The data are normally distributed.
(2) The mean model is more appropriate than the regression model.
i 001/0004A.10
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calc. No. C-1302-187-5300-011 Rev. No. O Page 40 of 454 (3) There was no significant corrosion during this period.
(4) The current mean thickness i standard error is 636.2 1 1.1 milu.
(5) The best estimate of the corrosion rate during this period based on a least squares fit is zero mils per year.
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Calc. No. C-1302-187-5300-011 Rev. No. O Page 41 of 454 6.0 atEEt[plSEA 6.1 SPEAKEZ Programs 6.2 SAS Program 6.3 Computer Calculatiens i
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