ML20062G860

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Rev 1 to Design of Ultrasonic Test Insp Plan for Drywell Containment Using Statistical Inference Methods
ML20062G860
Person / Time
Site: Oyster Creek
Issue date: 11/01/1990
From: Leshnoff S
GENERAL PUBLIC UTILITIES CORP.
To:
Shared Package
ML20062G848 List:
References
TDR-1027, TDR-1027-R01, TDR-1027-R1, NUDOCS 9012030056
Download: ML20062G860 (40)
v • d • e


Text

. _ _ _ -

3 7 h gf TDR No. 1027 Rtvicion No. 1 Budget Technical Data Report Activity No. 402950 Page 1 of _l&_

Project: Department /Section ENGINEERING & DESIGN OYSTER CREEK DRYWELL CORROSION Release Date Revision Date Document

Title:

DESIGN OF A UT INSPECTION PLAN FOR THE DRYWELL CONTAINMENT USING STATISTICAL INFERENCE METHODS Originator Signature Date Approval (s) Signature Date S. D. LESHNOFF -

N///fd

'1 a. M L. tolu /90 vu Acoroval for External Distribution Date Does this TDR include recommendation (s)? Yes X No If yes, TFWR/TR#

  • Distribution Abstracts A. R. Baig BACKCROUND:

F. P. Barbieri As a result of drywell corrosion at Oyster Creek, B. D. Elam, Jr. Ultrasonic Test (Ut) thickness measurements are J. C. Flynn periodically being taken. In the past these measure-J. P. Moore, Jr. ments have been utilized to identify locations whose M. A. Orski thickness is reduced. By repeated measurements in D. G. Slear these areas at the same location, statistically derived P. Tamburro corrosion rates have been determined. A new UT inspection plan whose purpose was to provide a basis for statistical inference that the drywell thickness satisfies minimum required was developed. The drywell is statistically characterized using a limited number of plate thickness measurements. The purpose of this TDR is to document the basis for this inspection plan._

s (For Additional Space Use Side 2)

This is a report of work conducted by an individual (s) for use by GPU Nuclear Corporation. Neither GPU Nuclear Corporation nor the authors of the report warrant that the report is complete or accurate. Nothing contained in the report establishes company policy or constitutes a commitment by GPU Nuclear Corporation.

  • Abstract Only I - ,

l 9012030056 901126 i PDR ADOCK 05000219 p PNU l

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  • Abstract Continuation TDR No. 1027 Revision No. 1 SOLUTION:

Using 6" x 6" grids for UT measurements, randomly choose 60 loctaions but do not include sand bed gride. Finding no unsatisfactory areas in remaining observations is the basis to conclude, with a 5% risk of error, that 95% of the drywell is free of such areas. A different sample is used each time that the assessment is made. Finding no repairable areas within grido provides a level of assurance of better than 99% that the drywell is free of such areas. Apply statistical inference methods as far as possible and where there are limitations use a judgement approach in order to determine whether corrosion is or is not occurring.

i la

y . . . - .. -

I DOCUMENT NO.

'l W; UC 68r TDR 1027 DESIGN OF A UT INSPECTION PLAN FOR THE DRYWELL CONTAINKENT USING STATISTICAL INFERENCE HETHODS REV

SUMMARY

OF CHANGE APPROVAL DATE 1 1. Add to both Background and Solution sections that there are limits to statistical inference which are overcome by judgement methods,

2. Change derived to estimated.
3. Change reference in text.
4. Add section for References.
5. Clarify Table 1.
6. Explain simulation notation and practice and number of units sampled.
7. .Use Figure Ib for section distribution equal to 0.05.
8. Define stratification.
9. Use sand bed plates instead of sand bed when describing stratification.
10. Use estimate instead of failure and clarify multiple trials.
11. Add a statement showing that simulations demonstrate both accuracy and sensitivity of inspection plan.
12. Introduce insignificant change when using acutal number of plates per strata.
13. Add section addressing finding one or more unacceptable observations, including Figure 3.
14. Add statements to clarify approach to local low areas.
15. Correct equations for variance.
16. Add section on disposition of results.

N0036 (03 90)

) o i- ,

TOR 1027 Rev. 1 Page 2 of 38 TABLE OF CONTENTS t

SECTIONS gjf[3 Background 3 Solution 3 Technical Appr)ach 4

' simulation of Stratified-Sampling 7 L ,.

Accuracy of Random Sampling by Sim>dations 7 l

More complicated Simulatione and Recommended Sampling Plan 9 l

Finding One or More Unacceptabir, Observations 13 Use of cells Within Gride 13

' Scope of Application 19 Acceptance criteria 19 Sampling Scheme contingency Plan 20 Disposition of Results 20 References. 21 .

' Attachment lAs Simulation of Five Part Stratified Sampling Plan 25 Attachment 18: Additional Simulation of'Five Part Stratified 31 Sampling Plan Attachment 2: Sand Bed Zone Excluded 34 Attachment 3:- Non-Stratified Sampling 37' w-(

012/079.4

e e TDR 1027 Rev. 1 Page 3 of 38 BACKCROUND:

As a result of urywell corrosion at oyster creek, Ultrasonic Test (UT) thickness measurements are periodically being taken. In the past these measurements have been utilized to identify locations whose thickness is ,

reduced. By repeated measurements in these areas at the same location, statistically estimabed corrosion rates have been determined. A new UT (j[)

inspection plan whose purpose was to provide a basis for'statiatical inference .

l that the drywell thickness satisfies minimum required was developed. The drywell is statistically characterized using a limited number of plate thickness measurements. The purpose of this TDR is to document the basis for b) '

l this inspection plan.

l 1

SOLUTIONt' Using 5" X 6" grids for UT measurements, randomly choose 60 locations of a possible 60,000 but do not include sand bed grids. Finding no unsatisfactory areas in remaining observations is the basis to conclude', with a 5% risk of error, that 95% of the drywell is free of such areas. Therefore, this sampling plan will develop 954 confidence that 95% of the drywell is free of such areas. A dif ferent sample is used each time that the assessment is made. Finding no repairable areas within grids providos a level of assurance )

of.better.than 99% that the drywell is free of such areas. Apply statistical inference methods as far as possible and where there are limitations use a judgement approach in order to determine whether corrosion is or is not occurring.

012/079.5

  • e TDR 1087 Rev. 1 Pr.ge 4 of 38 TECHNICAL APPROACH:

A non-parametric statistical approach using attribute sampling that assumes no prior knowledge of the distribution of corrosion above the sand bed region is the basis for the augmented inspection plan. The acceptance criteria is that the mean and local thicknesses of the shell equals or exceeds a required min. mum thickness plus a corrosion allowance necessary in order to reach the nex: inspection.

S;atistically, a predicted value, A u, f the maximum number of defects in the population, N, reflecting a selected level of risk can be used so that for this value "a" defects in sample "n" are expected at a low probability,CK u.

The lower the probability, the larger the sample size. If "a" or less are found, then the selected risk is not exceeded. If ">a" are found, the selected risk is exceeded.. Sample size "n" can be computed given Au ""d C< . For 5% of the surface as unacceptably degraded for A u, then "n" is found to be 59 atCX u = 0.05 and a = 0. That in, no observations which do not satisfy the acceptance criteria (i.e., grids) can be found in a sample of 59 with a 5% risk that the actual number of grids which would not satisfy the acceptance criteria exceeds Au without rejecting the hypothesis. Using 60 grids, there is only a 5% chance of finding nc gri.de whose thickness is belew the acceptance criteria given 5% of the population below this thickness.

Finding none in a sample of 60 is remote so that if none are found below this thickness, then the assumption about the defective proportion L- t ow the acceptance criteria thickness is probably an overestimate. S i. . /

012/079.6 1

- o e h TDR 1087 y Rev. 1 Page 5 of 38 observations is a good basis for a sampling plan. There is also the possibility that the actual number of defective grids is less than Au and f the hypothesis is rejected due to chance alone. This is evaluated in the

)

discuneion of finding one or more unacceptable observations (see below). The f determination of the appropriate sample size is expressed formally by:

_[ )% _,

Pr (1, n-1) l(A,u N-Au) "

i=0 E

w

$ IAu a) ((N-A # (u (Ref. 1) /

u ) (n-a)) / Nn C L

L Where N Cn is the number of combinations of n units chosen

_ from N,

=

N Cn = NI ni (N-n)!

Results as shown in Table 1

=

~

For a sample size n = 59 observations, it la evident from Table 1, that the probability'for finding zero unsatisfactory observations is 0.0482, which is R

less than the assumed value of 0.05. Therefore, finding no occurrences in 59

- observations satisfies the selected level of risk with only a .05 probability cf error.

=

It is also evident from Table 1 that for a sample size n = 124 that the cumulative probability of finding up to two occurrences of failures, which is

^

the sum of all three row entries, also satisfies .05. If, for this larger sample only one occurrence is observed, then this is the basis to conclu('e that the actual number of occurrences in the population is less than the assumed value. Furthermore, finding no occurrences is even more evidence of this.

e

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U' TDR 1087 Rev. 1 Page 6 of 38 TABLE 1 i

PROBABILITY OF OCCURRENCES N = 60,000 NUMBER OF OCCURRENCES SAMPLE SIZE -0 1 2 2- --- --- ---

58 0.0508 0.156 .234 59 0,0482 0.15 .230

.123 0 0.0116 0.0374 124 0 0.0111 0.0361 1012/079.8 -

_ = _ _ _ ___ _ _ _-___ - __ _____- _ __ - _ _ ___ - - _ _ - - _ - _ __ _ - _ _ - - - - - _ - - -

_= _ _ _ _ . . . _ . _ _ _ _ . . . . . _ _ . . . .

o 6 TDR 1027 Rev. 1 Page 7 of 38 Using this same method, it can be shown that for 10% of the total surface area as the selected risk, the sample size is reduced to 29 at a 5% risk. At n = 60, the risk is only 2%.

The results in Table 1, the work of Mr. J. P. Moore of GPUN, have been independently verified by Dr. D. G. Harlow, Associate Professor of Mechanics, Department of Mechanical Engineering and Mechanics, Lehigh University.

Simulation of Stratified Samolinot The most severe corrosion has occurred in the sand bed reglon. This region may not always contain the most service limiting location, howeve , because of as-supplied local thickness. The previous measurement locations in this region will not be abandoned as part of this program since these are necessary in order to determine corrosion rate. It is appropriate to deliberately proportion the new observation locations in order to limit the total number of random grids that can fall in any one region. For purposes of assessing the performance of a random sampling, simulations will be performed.

&peuracy of Random Samolino Evaluated by Simulationes A stratified sampling plan has been simulated by Professor Harlow. In rigure la, a total of 100 panels is used to represent the total number of plates used to. fabricate the drywell. Consider the drywell divided into two strata without bias as to proportion of occurrences when the acceptance criteria is not met, the sand bed region and everywhere else. Ten plates, which are not necessarily contiguous, represent the lower strata, including portions of 019/079.9

e e TDR 1027 l Rev. 1 Page 8 of 38

(-

those plates which may be under the drywell floor and 90 comprise the upper strata. It is assumed that as much as five percent of the entire population q does not meet the acceptance criteria. Assuming an equal probability of these observations in each strata (0.05), the actual proportion, P1, arrived at by I simply counting the randomly simulated defective units in both strata is, P1 = $

l 0.04833. The sample of the simulation is accomplished by randomly observing I 1

1 15 units in the first stratum and 45 from the second stratum of a total of 60 f) l 1

observations, representing a one percent sample of available units. The measured characteristics are recorded as 1 if the unit does not meet the y thickness criterion and as 0 otherwise. The estimated proportion pl, for sampling without replacement, le 0.047, a slight underestimate, t

The simulation shows that the sampling plan is very promising. Figure Ib uses I the same assumptions and proportion as for the first section distribution

((}

(0.05). The only difference is that a different random selection of 60 l l

observations wan made. The bottom line, however, changed. The overall i estimated strata proportion, pl, has declined to 0.02. The simulation of the 1

sampling plan no longer accurately reflects the reference proportions. A sampling plan is judged on satisfying this criteria. Repeated sampling using different grids each time will resolve this problem. The simulation studies show that the estimated proportione are more or less accurate depending on l

random selection of observations only. Based on the simulations it would be ,

d incorrect to conclude, using a single sample, that the overall risk assumption i

i is not violated or that it is violated because of random selection. A number of selections of different samples will consistently provide a good estimate 012/079.10

e s TDR 1027 Rev. 1 Page 9 of 38 of the actual number of defects i.a the population on average. A good, experimental design uses a different sample each time an estimate is made. It

_ is proposed for this program that a different sample, each of the same size, be used each time an estimate of the defective proportion needs to be made so that the conclusion is not based on chance alone.

=

- Finding no unacceptable occurrences after a number of repetitions of the sampling plan, using different samples, is evidence that the assumed risk is not exceeded. A single finding of no unacceptable occurrences is consistent with the assumed risk.

Simulations of larger populations with the sample assumed risk at the same probability for error show the same good overall performance, but with like sensitivity to random variation.

MORE COMPLICATED SIMULATIONS AND RECOKMENDED SAMPLING PLAN:

g- A five part stratified random sampling plan is proposed in order to make the most of 60 grids. The five strata represent five zones of the drywell (Figure 2). Stratification divides a heterogeneous population into subpopulation, each of which is internally homogeneous. Each strata is sampled at the same portion, considering plates, as for the total population of plates. Better precision should be obtained than by ignoring the

(( differences in the population. Plates in each zone will be randomly selected with one' grid selected randomly per plate. The simulation of this scheme is 012/079.11 e-

0- 4 TDR 1037 Rev. 1 Page 10 of 38 included in Attachment 1, Part A. The stratification is based on relative proportions using existing qualitative knowledge of both material lost due to corrosion and rate of material lost. The sampling plan is summarized as E follows:

NUMBER OF PLATES SAMPLED e 1 GRID PER PLATE FROM TOTAL NUMBER OF 198X DESCRIPTION PLATES PER STRATA (ESTIKATED)

Intersection of 3 I

sand bed plates and l{f) drip zones b

II Drip zone 12 III Sand bed plates 9 l()

IV All else 32 V Cylinder 4 The sampling plan simulation shows satisfactory accuracy over 25 trials. No single estimate exceeding 5% is reason to reject the assumed level of risk. A

/ff) single sample may be unrepresented due to chance alone. A different random sample 11s used each time this assessment is made.

Attachment 1, Part B, is an additional simulation of the same five part stratified sampling plan where 100' repeated random' samplings of size 60 are b

considered. .In this simulation the performance of sampling process is characterized by forming c distribution of the estimation results. At the 90%

confidence limit, the estimate of defect proportion falls between 0.096 and

-- 0.0037. This shows the risk, due to chance, that the structure is concluded to be unsatisfactory where, in fact, it is.

012/079.12

_g ___.

0- 4 TDR 1027 Rev. 1 Page 11 of 38 Using a one-sided t-score, an appropriate measure of the distribution of the estimates about the true mean, at = 0.05, the performance of the sampling process does not exceed 0.05, 95% of the time. This verifies the utility of the stratified sampling plan.

The confidence interval can be narrowed by increasing the proportion of the surface area that is scanned by UT. Using the grid location as a center, use of the A-scan on a best effort basis, will provide this process improvement.

The A-scan device need only be set to the local minimum thickness as a threshold.

The sand bed condition with respect to material lost due to corrosion has

=already been characterized. Abe:t 67% of the sand bed zone perimeter has been surveyed by UT. By this means, the most severely co;*;oded zones have been iden-tified throughout the sand bed, including that portion below the drywell floor.

Attachment 2 is an additional simulation of the same five part stratified sampling plan, except that sand bed zone grids are excluded, if they are randomly selected. The saving of inspection time and exposure, the amount deper.dir.g on chance for each sample, is justified by comparing mean estimates and stand.ard deviations for 100 trials. Assuming 5% defective, the simulation including the r,and bed zone grids as they are selected, shows a mean estimate of 0.046 with a standard deviation of 0.024 while the simulation excluding the sand bed zone grids as they are selected shows a mean estimate of 0.044 and standard deviation equal to 0.026 (using proportion P1 for comparison).

012/079.13

e s- r TDR 8037 Rev. 1 Page 12 of 38 Also, using the t-score, as described above, this sampling process does not exceed 0.048, 95% of the time. By comparison, this is slightly less accurate.

6 Simulation of non-stratified sampling is shown in Attachment 3. This sampling plan does not use the accumulated corrosion information. This simulation I shows that by ignoring what is already known about the degree of corrosion, l-the sampling process accuracy is reduced because of the increased standard l'

y deviation. The mean estimate is 0.047, but the standard deviation has I

increased to 0.030.

1 l

A1 , using the t-score as above, the upper 95% confidence limit, U95' 18 0.052. This is slightly inaccurate, but in a nonconservative direction.

l.

Table 2 summarizes the results of the simulations.

Simulation also shows that the random sampling plans are not only acceptably accurate but acceptably sensitive, as well. Simulation shows that finding no

]

(I) unacceptable observations occurs less than 5% of the time, as intended.

Changing the simulation in Attachment lb to reflect the actual number of plates per strata results in U95 = 0.055. The change is insignificant so (

l that the estimates used'in the above simulations are representative of the performance of the random sampling process.

012/079.14 l

e a TDR 1027 Rev. 1 Page 13 of 38 Findino One or More Unacesotable Observations:

In the simulations, finding one or more of the 60 observations to be less than the minimum thickness predominated. Finding one or more using this sample i

doesn't prove anything unique and conclusive about the level of structural assurance. For example, one or more unacceptable observations can occur at a 5% probability with 99.9% of the drywell free of unacceptable observations. A 1

conclusion about drywell, structural adequacy with one such observation is not l$

appropriate because a better condition can result in an unacceptable observation. Finding none does confirm the original hypothesis.

The probabilities of finding none ( e4 ) or finding one or more unaccei.s nale observations using a sample of 60 observations for a number of populations containing different portions of unacceptable observations are shown in l Figure 3. The probability of finding one or more, 4, is 4 = (1 -c>L ) .

I Use of celle Within Grids:

Minimum required mean plate thickness and minimum required local plate s thickness each must' satisfy design. basis stress' criteria. In addition,

(

minimum required mean plate thickness must satisfy ASKE design basis stability criteria to prevent buckling. Minimum required mean plate thickness pertains to a shell course and minimum required local plate thickness pertains to a single local area or the sum of local areas within reference distances, if there are more than one local area.

012/079.15

. - - .. - . _ . - . = _ . -.

. e- -e i

TDR 1027 Rev. 1 Page 14 of 38 q-TABLE 2 RESULTS OF SIMULATIONS 5% DEFECTIVE P1 P2 MEAN STANDARD MEAN STANDARD ESTIMATE DEVIATION 0 95 ESTIMATE DEVIATION Five part stratification 0.046 0.024 0.050 0.052 0.022 including sand bed Five part stratification 0.044 0.026 'O.048 0.043 0.026 not including sand bed No stratification, not 0.047 0.030 0.052 --- ---

including sand bed f

. NOTE: By simulation it can be shown that the mean estimate is less accurate for an: assured 10% defective population using a sample size of = 30.

012/079.16

10^ a-.-e  : .  :  :  : .  : c.

e

  • zero bad

't a a at least one bad e

0.8 A T'- a e a N h 9 A D ~ 0.6 -9I 9/

.5

_O #&

U Ao N = 60,000

-8 04 -f* n = 60 ci-

- i*

-f a %e 0.2 -f A

'I t  ::

e < :o 4 **

0.0 ..

r e  ; e e g e c  ; g  ; g g 0.10 0.12 0.14 0.16 0.18 0.20 U 0.00 0.02 0.04 0.0S ' O.08 2, f/6.3 Fraction of BAD Grids

o o l TDR 1027 Rev. 1 Page 16 of 38 A grid of individual measurements will be the basis for estimating the mean i plate thickness. There is no code requirement for either the minimum or maximum grid size necessary to determine mean plate thickness. However, the grid size should be large enough to capture the local, minimum thickness in a 2.5" diameter or smaller circle and no larger than 2.5VRt, which is the distance that uniform shell thickness must extend around an unreinforced opening. Local minimum thickness must satisfy both local membrane stress criteria and code rules for unreinforced openings.

The grid size should be large enough to contain enough single observations to minimize the impact of a pit on the mean thickness while minimizing radiation exposure of personnel taking the measurements. A 6" X 6" grid of 49 data points on two inch centers fulfills these criteria. It conservatively captures i

a-2" diameter ci cle and is more conservative than a 2.5VRt radius circle since l there is less berefit from averaging. The 6" X 6" grids will also be used to establish that not more than 0.1% of the surface area satisfying the required mean thickness criteria contains locally low areas. That is, no more than one i l

I l locally low area per reference circle. Therefore, equate the requirement that I I

99% of the area is free of holes to a 99% probability of finding no locally low h))

l area.

l Analysis of variance of 2" X 2" cells contained within a single 6" X 6" grid will show whether the difference between the required mean and local thickness is significantly more than the lower 99.9% tolerance limit one-sided, times the standard deviation for the 2" X 2" cells. The one percent probability is consistent with the one percent loca'. reduction permitted by the code.

i 012/079.18

.---;-.;-,i.,,,,-'-l;"'.,..,,...

0

  • TDR 1037 Rev. 1 Page 17 of 38 Statistical inference regarding the Pariance of the observed grid means about the true grid mean of the population is not important. The concern here is variance of reference 2" X 2" cell measurements about an assumed mean equal to the acceptance thickness for a particular plate.

As developed by Mosers. J. P. Moore and M. A. Orski of CPUN, with review and concurrence by Dr. J. Orsini, Profascor of Management and System Design, Fordham University, the pooled variance of 49 cell measurements per grid, the average of four points per 2" X 2" cell, taken over 60 grids, totalling 540 observations, is the basis to establish the lower, single-sided tolerance limit for a single cell thickness.

The definition of X 2, the parameter characterizing a normal distribution, relates sample variance, S 2, and population variance, 7 2, X2,32 (n -1) EQUATION 1 g2 Where n = sample size = 540 and 2

(nt - l' S 2, =1 , for j = 540 and nt = 4 for all 1 (nt - 1) ,

i=1 Where (xt - x)2-2 =1 S i, , where j = 4 (j - 1) 012/079.19

. _ - _- . _ - - . - _ . - . . - . ~ _ - . . . - . _ - . . - _ _ - _ _ - .

O

  • TDR 8027 Rev. 1 Page 18 of 38 Since n is large, C2 can v. cciputed accurately using X2 at a signit.cance equal to 0.1.

Here the mean plate it.ickness is assumed and a tolerance limit is necessary to predict an individual observation. For a normal distribution of a larga number of individual observations, the difference between the population mean, ,A

, and an individual observation, x, is given by the 2 parameter, ta l EQUATION 2 E = Ig C 7 is obtained from Equation 1, above. Thedifferencel,flisthe difference, 1 , between the assumed population mean and a local thickness of sof *O]%

l l

/n i ,

i .

m .

0' bk.f --*

44 n,. . + Lif .

=

> Q { --

Fits.7 DIFF8788'W 8 # N8" A*de L OC A L mucueus$ ausS M **e"WD mnm v4Lw an individual cell. It is highly unlikely for a local cell thickness to be less thant lx-fl=E 99,9 ' E EQUATION 3 l

l The distribution of results should show that the probability of an unacceptable local low area is very str.all.

1 012/079.20

e s a e l TDR 3037 l Rev. 1 Page 19 of 38 Using pooled variance, an individual cell thickness is estimated at the lower 99.9% confidence limit. Based on the 1U4, ton of local thicknesses, there is a high cenfidence ^5at no ropait.ble u :' areas will b6 found, i.e., that the critical differences are more than that shown by the measurements,

($Lcrit.<[L 99,9) as shown in Figure 4.

SCOPE OF APPLICATION:

Since no portion of the drywell is purposely excluded on theoretical grounds, the inspection plan applies to the entire structure except welds, those areas oven which a 6" X 6" simply won't fit, and penetrations.

Crido drawn at random falling in the sand bed region of the sphere will be disregarded because this tone is characterized in an ongoing manner by numerous gride and strip measurements. Previous measurements below the drywell floor in excavated trenches, showed that material loss due to corrosion was no worse than above the floor. This results in ALARA savings without sacrifice in sampling accuracy.

ACCEPTANCE CRITERIA A repairable grid is one that does not satisfy the local low spot minimum thickness. The 6" X 6" grid is a conservative gauge that could have been larger. Its utility is for corrosion rate assessment. Larr9r grids tend to drive the mean thickness upward. The use of pooled variance of grids with the 012/079.21

o e TDR 1027 Rev. 1 Page 20 of 38 reference mean thickness ensures that the local minimum thickness is obtained conservatively. Finding no repairable areas within grids provides a level of assurance of better than 994 that the drywell is free of such areas.

The corrosion allowance can be based on the estimated corrosion rate because nothing can be inferred about rate by this assessment. It is not appropriate to use a 954 confidence interval rate estimate based on other, routinely revisited grids.

Samolina Scheme continoenev Plant should a randomly selected grid turn out to be inaccessible, consistent rules will be provided, in the inspection specification, to locate an alternate without introducing eny biases.

Dianesition of Results:

Finding an unacceptable mean thickness is reason to better characterise the area in order to show that th3 region is, in general, in much better l condition. If a mean thickness, established using a 6" x 6" grid, does not f} }

meet minimum requirements, enlarge the inspection grid to an area one and a half feet on a side and obtain additional readings. Use the enlarged grid to compute a new me.n chickness. This will improve accuracy, as well.

012/079.22

.. . . . ~ . _. . _ _ _ _ _ _ . _ . _ __ . _- - , _ _ .. ____ -

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o oc  !

1 TDR 1027 i

)

Rev. 1 Page 21 of 33  ;

e I

REFERENCES 1

,1. Personat- communication entitled " sampling Flane for the oyster creek '

Drywell," D. G. Harlow to 8. D. Leshnotf, 5/22/90. .

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012/079.23

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  • TDR 1027 Rev. 1 Page 22 of 38 iTIAi2SIM twt nsater ms 0F 5tCTl0hl i.e. stratt. !i 2.

ENT!! -! nunter 0F FANEL5 !N strat,,n 3

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INT!? ? ! . cer :T 7460.': IN strntum 2 i) 7-I +:*.a; ~ter :T !;'!;! s .::
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!.-I :ta. *. ter :7 .S: Ti e ic:0

!-t o, cer *1 .s:Ti : N

!!:::0N! 1 T3 213 400 ;400

INTti i e :rfcas se;t> .al:9 :.ticFli!! 79[ t 4;[;I p;p:,;c;;;,,

SECT!!N !!!!Il!LTION 3. :: 0.}! 0.;!

it0T!CN D:iTPl!JTl:S a;. 2 0.1538461538 0.03946153946 itCT::'I *!iit!!UTION no. 3 0.25 0.02?77777778 l PROPORT!0N Pi = 0.04833333333 PROP 0RTION P2 = 0.049 PROPORTION P3 = 0.05133333333 ..

INTtt THE NUMt!I n10F SAMPLIS DIS!IED POR stratus 1 0

15 INT!I THE NUMt!R n2 0F SAMPLES DISittD TOR stratum 2 0

45 INTil THE total number OT UNITS T0 f t SAMPLID.

Os .

60, sampling without replacement

!$T!MAftD STRATA PROPORTIONS pi = 0.06666666667 0.04444444444 ISTINATfD STIATA P90F0tTIONS P2 = 0.06666666667 0.04444444444 ISTIMAftD STRATA PROP 0RTIONS p3 = 0.1331333333 0.02222222222

!$TIMATED Pt0P0tfl0N Pi = 0.64466666667 d-ISTIMATID PROP 0tfl0N P2 = 0.04666666667 IST! MATED PROPORTION P3 = 0.03363333333 ISTIMATID VARIANCE OP ti = 7.987264405t*4 ISTIMAftD vat!ANCE OP P2 = 7.987264465t*6 ISTIM4ftD VAtl ANCE OP P3 = 4.631601949t*4 f(6, l A. Stkut A Tl0N OF RANO%

LA M,DL/MG'U$l% W C 012/679.24

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)

TDR 1027 Rev. 1 g7gg;gggp Page 23 of 38

?WI Pueber es OF IICI:;NT. :.4. s*rtte. Il 2.

INT!? tw! -eter OT 1;S!* l :1 str at.m :

28 10 IN!!7 7 ! ,*ter :T ? E!*.! :'. strat.m ;

, i'.

7 ! t: W. v cer 'T ! at'.i e 1::

all."!: 7:!;' +." !!7 :1 .'9:75 li : sert::n1 T-:P IA: ! at'..

I'!!! !. ! a iter % ;T JN: 73 ?!? P at'.. ,

t i)
Twt i:tal v ter $T .N: 73 e i::0 THE *Weer I .N!!! !1 i t' 7 :Si 1 73 i *i iO: 54M INT!! t a frnas vtu ,=!n 'ti:7:3!3 !HE INT!!! 7:P'.LAT!!N.

0:

.01 l SIC 7::S D:1!!!$UT!CN no. 1 ). 5 0.': 5 itCT!0N D: lit!)UT!ON no. 28 0.4567307692 4.607692300t *3 SECT!!N ? lit!30 TION no. 310.4583333333 4.62962763t*3 PROP 0ff!;N ?! = 0.01033333333 PROPCIT!CN P2 = 0.04016666667 790F037!0N P3 = 0.04833333333 Itttti THE NUMBRI nt 0F SAMPLlt DISitID FOR stratus 1 0

15 INTil THE NUFRII n2 0F SAMPLIS Dtl!IED F,03 stratus 2 28 45 INTIR Ut total number 0F UNITS TO 88 SAMPLID.

On 60 samptins without replacement IST!PAft) STRATA PROPORTIONS pt = 0 0.02222222222 ISTI N Til ITIAft PROP 0RTIONS p2 = 0.6666666667 0 Elf!MTtD STRATA P90F0tfl0N$ P3 = 0.4646666667 0 tlf!MTID FICPORTION pt = 0.02 -

l R$fiMYD P90F0t?!0N p2 = 0.04666666667 IST!MTID PROPORTION P3 = 0.04666666667 l

!$7tMfD Vet!4Et CF pt a 3.0792368HI*4 ISTi m itt Wal4E t Of p2 = 1.620470575t*4 IST!MTtt WB14EI 0F P3 e 1.630470575t*4 FIC.Ib StMVL AYt0AJ OF AAkt 20h L 012/019.2s SAMPLt% vst% M0 $rRATA.

TDR 1027 3 Rev. I 1

Page 24 of 38 l j ORYWELL I
i l

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$Ulst?'1 e tr4p zone and sandbed: WClit )

IW!it! 1 trip rene ontw *!!f IAD . TDR 1027 i

i !!!! 3 a sand bedi lap Rev. 1 h!!!! 4

  • rest af the sphere 1000 Pace 25 of 38 i.li!! ! = :siinser8 IIST ATTA?HM.ENT b.

J.!

-! w .tter
n. *:1veer P aris
T PsNtil lN Sulitt$ a 1001.2.3.4.5 lI ! 2: 1! !: 1 04W ecu cF I, P*9'T 2 aliw!: 7:74:, NU'!!P T i's IAF7it ;;N!?S !! : tents:ti Tcptau pag;,3 p gg g p g,96 i:t,W.

' 7-! '<."!!7 lT .':75 ?!? ? a t. av = 6:0.

7-t t:tt; aster :T '.N: Ti = (0.000. - -

l 7-! e.eter :T M:!i IN iglitti 1.2 3.4.5 l3 li:00 12000 7000 11200 4300 t'e!!! t * ?r a nt sa: U I 4 SAleC7tP!:A7:0N 0T THE INT!Pt P!PV1A?!0N.

28 0.05 i; tit? ::i!!!!w!!0N %.

it 0.2124437529 0.1262243765 0.06311218823

5. ;4 9)?!0!!! *3 !.04 3)?50!lt *4 l';iitt bliittlVT10N B0. 21 0.3924646712 0.0?$49293564 0.03924646712 0.01167358713 7.641293564I*3 )

l 770F017:0N Pi = 0.05125

PROPCli!0N P2 s 0.0501 THE NUMitt Of PANILS 70 II SAMPLID POR subsets 1 - 5
  • 3.12.9.32.4.

l sampling without replacement ISTINAft) STIATA P9070tT!0NS p1

  • 0 0.1666666667 0.11111111110 0 '

Il?!NAft) STRATA PROPORTION $ P2 a 0 0 0.1111111111 0 0 IS?!NATID PROPORTION Pi . 0.05 '

tit!FAftD PROPORTION P2

  • 0.01666666667 l

IST!MAttD vat!ANCE OF pi = 7.09232622t *4 I i

ISTINAftD VAtl ANCE OP P2

  • 2.466M0771t*4 '

4 l S t Nuritti 0F PANELS 70 II SAMPLID POR subsets 1 - 5 = 3.12.9.32.4.

sa:Pling without replacement I tii!NAttD STRATA PROP 08710NS pi 0 0.00333333333 0 0.03125 0 IS?!NATED STRATA P90P0ffl0#8 p2 = 0 0.00333333333 0 0 0 tit!NAftD Pt0 Pott!0N 76 e 0.03291466667 IST!MTI)Pt0P0tfl0Npt's901666666667 ISTINAi!D Vet!ANCE Of pi e 5.0995256778 4 ISTIMATED vat! ANCE OP P2 = 2.543Mit973 4 i

i

\

THE NUNitt 0F PANttl 70 38 5AMPLID P05 subsets 1 - 5 = 3.12.,9.32.+.

sampling without replacement t j

tST1M4ft9 8ft4TA PIOP0tT!0NS p1 = 0.3333333333 0.01333333333 0.11111111110 0

)

, 137tMAttD STRATA Pt0P08T10N$ p2 a 0.6666666667 0 0.1111111111 0.03125 0 L R$TLM Tit, PROPORTION pi e 0,03 1,13t!Mattp FRGP0FTION r2

  • 0.06625 012/07'9.'27

O ~

oo s a mm a se was 4 =ase v? pd o 6. t771 d13338 '4 tor 1027 Rev. 1 THE NVFitt 0F PANtt$ T0 II SAMPLI) POR subsets 1 - 5 = 3.12.9.32.4. 47 i s, sa: pitas without replacement

!!T! MAT!D 13f;*Aitt 177ATA 37tATA P70P0tT!;NS PROPOITIONS P2 a 0 0 0 0 071 a 0.3333333333 ).1666666667 0 0.03125 0 i

o !!!:*a7ID 770F077!0N P1

  • 0.06625

.., tit!*47t* PPCP077:0N P2

  • 0 117 " T!! " 7! AN0t CP P1
  • 7.031!66001t *4

!!!:*at!D Vet!AN0! Of p2 = 0 THE NsMitt CP PANtti 70 It iAMPLtD POR subsets 1 - 5 = 3.12.9.32.4.

sacpling without repla:ement Ett!PAftb STRATA Pt0P08T10NS P1 s 0 0.25 0.1111111111 0 0 IST! MAT!D STRATA Pt0F0tT!0Ns p3 0.3333333333 0 0 0.03125 0 ISTIMAftD PROPORTION p1 s 0.06666666667 ISTIMAftD PROP 0RTION P2 8 0.03291666667 '

ISTINATI) Vetl ANCE OF P1 = 0.711211127t*4 tlTIMAft) vat! ANCE OF P2 e 4.406100552t*4 THE NUMitt 0F PANtti 70 It SAMPLI) FOR subsets 1 - 5 = 3.12.9.32.4.

sampling without replacement ISTIMAftD STRATA PROP 0RTIONS p1 = 0.3333333333 0.1666666667 0.3333333333 0 0 llTIMAft) STRATA PROP 0RTIONS p2 = 0.3333333333 0 0 0.03125 0 ,

t.

j. IST!MAft) PROPORTION pi e 0.1 -

l IST!MAftD PROPORTION p2 = 0.03291666667 ISTIMATED VAll4NCE C? ,e1 e 1.208661904t*3 ISTIMAftl VetlANCE Of p2 e 4.4041005588*4 TMt NUM9tt 0F PANILS

. - M 88 SAMLID POS subsets 1 - 5 = 3.12.9.38.4.

sampling without replassesett ISTIMAftl lftATA P90P W ffent #1 = 0 0.1666666667 0 0 0 ISTINAffl ITIATA P90P0ft10NS p3 = 0.6666666667 0.08333333333 0.1111111111 0.03185 0 InflMAft) P90P0lfl0N p1 e 0.03333333333 BlTIMatt) 780P0ttl0N p3 e 0.04291666667 R$71MAftl Vall4NCE OF p1 e 4.621345449t*4 e tlTIMAfti Vell4**t OF p2 e 9.417003338 4 THE NVMtt! 0F FANILS 70 It SAMPLES FOR subsets 1 a 3.62.i 34.4.

- - - ~ .- . . . . - - - _ - - - _ . - _.- -_~._-___ _- -. -.- -

o** ' ' ' '

, K' TDR 1027 lit.~h;D lio?0ift:$ p1 s 0.03333311n) a y. 1 i

I tit!."4!!D P10P087'SN pi s 0,'3291600007 Page 27 of 38 I

)

13;:-J '7' *ial: ANCE CT P1 s 4.394!?tisit *4 t i '. . M AP:ANCE :T p2 = 1.12i? 199t*!

ATT Is

, 7-! %"!!7 :T P ANEL3 !) It larPLID TCP sutsets 1 - ! s 3,12,9,32,4.

16t7.;*3 sithC9t replacement ti!:";!!D $7PA7A PPCP077:CNS p1 s 0 0.164fissi67 0.2222222222 0 0 ti!!*aT!) liiATA PPOPolf!0NS P2 = 0.6060666667 0.1606666667 0 0 0.25 tit:N T!? 770F0t!!0N P1 s 0.06666666667

!$T:~at!D PF0PCIT!QN p2 s 0.096666664(7 Est:Fatt) val! ANCf 0F P1 = 0.942531799t*4 Ist! N TED VallANCE OF P2 = 7.47412693i*4 THE NUMlti 0F PANILS 70 II SAMPLID FOR subsets 1 - 5 = 3.12.9.32.4.

sampling without replacement 1871MATID STRATA PROP 0RTIONS p1 = 0 0.1666666667 0 0 0 ISTINAtt) 67347A PROPORTIONS p2 = 0.3333333333 0 0 0 0 ISTINATID PROPORTION p1 = 0.03333333333

.!$71N47tD PROPORTION p2 = 0.01666666667 ISTINAftD vat! ANCE of p1 = 4.625385449t*4 ~

IST!MAft) VallANCE OF p2 e 1.0504160728*4 THE NUNIII 0F PANttl 70 II SAMPLI) FOR subsets 1 - 5 = 3.12. 9. 32. 4.

sampling without replacement ISTINATED STRATA PROP 0RTIONS M = 0 0.08333333333 0 0 0

.ISTINAftD STRATA PROP 0tTIONS y) = 0.6666666667 0.1666666667 0 0 0 ISTIMAft0 PROPORTION pi e 0.01666666667 IST!MAftD PROP 0RTION 30 s 0.06666666667 ISTIMAftp vat! ANCE OF'pii 2. 5439619tT!*4 Ilf!NAftD VAtlANCE OF 38 e 6.47600232it*4 THE NUMitt 0F PANILS 70 It SAPfLIS FOR subsets 1 - 5 = 3.12. 9. 32.4.

stapling without replacement I$TiMATID 8ftATA PB0F08T!ONS pi e 0.3333333333 0.1666666667 0.2222222222 0 0 ISTIMAft) STRATA PROP 0RTIONS p2 s 0.6666666667 0.00333333333 0 0.03125 0 ISTIMAftp Pt0P0tT!0N p1 = 0.08333333333 '

.tSt!MAftp PROPORTION p2 = 0.06625 ttTlMeTfD VetIANCI of 71 = 1.0793148671*3

O[sE *.*: 3 Uhout ter4 asseint TDR 1027 IST!MAftD ST1ATA PROPORTIONS p1 a 0 0 0.11111111110 0 Rev. 1

!$7! MAT!! !TintA PICPORT!0NS p2 0.6666666667 0 0 0.03125 0 Page 28 of 38 ISTIMa!!D PPOPOPT!0N P1

  • 0.01666666667 R$f1 MATED P90 Pott!0N p2
  • 0.04950333333 IST!
  • 2.464940771t *4 U l' ISTIMATID vat! ANCf Of p2 s 4.406100!$2[*4 THE NUMt!I 0F PANtt$ 70 ft lAMPLID FOR subsets 1 - 5 = 3.12.9.32.4.

santling without replacement flTIMAftD STRATA PROP 0RTIONI p1 = 0.4666666667 0.1666666667 0 0 0 ISTIMAftD STRATA PROPotTIONS p2 0.6666666667 0.08333333333 0.1111111111 0.09375 0 IST! MATED PROP 0tt!ON pi e 0.06466666667 ISTIMAftD PROPORTION p2 e 0.1154166667 ISTIMAftD VAllANCE OF P1

  • 6.476002321t*4 BlT! MATED VARIANCE OP p2 a 1.403358545t*3 THE NUMitt OF PANttl 70 It SAMPLID POR subsets 1 - 5 a 3.12.9.32.4. '

sampling without replacement IST!NATED STRATA PROP 0RT!0NS p1 = 0.3333333333 0.00333333333 0.2222222222 0 0 IST!MettD STRATA PROP 0RTIONS p2 s 0 0.08333333333 0.11111111110.03125 0 BRTIMAftD P80108T10.1 p1

  • 0.06666666667 l IST!MATID Pt0P0tfl0N P2 = 0.04950333333 ISTIMAftD Vet!ANCE Of p1
  • 8.711725219t*4 IlflMAT!D VAI! ANCE OF P2
  • 7.566466440t*4 THE NUNitt)0F PANILS TO 88 $AMPLID FOR 1 - subsets 5 = 3.12.9.32.4.

sa:Pling without replacement i

ISTIMTED STRATA PROPQRTIONS p1 = 0.3333333333 0.03333333333 0 0 0

!$71 HATED STRATA P90PetT10t$ p2 = 0 0.1666666667 0.1111111111 0 0 IsilMATED 780P0t!!0N h 0.03333333333 ISTIMAftb P90F0tt10N 'pa[$0.08 IST!MAttD VARI ANCE OF p1 a 4.39457886?t*4

ISTIMATED VAtl ANCE OF P2 = 7.09232622t *4 THE NUMitt OF PANELS 70 It $AMPLED F;t subsets 1 - 5

  • 3.12.9.32.4. '

sa:pline without replacement

!!TIMATED STIATA PROPOPTIONS pi e 0.33333'333330.16(iiiii670.111111111100 tiTIMattb STRATA P90P0tT!0MS p2 = 0.3333333333 0.1666666667 0 0 0 bTtMattbprotoptfon.*.^accescreeca

se n se. 6e vas s =%s we pa o ** **e ma.'vos e 0 85fifw.dJ Wst.im g VF pd

  • 6.4760023dit 4 TDR 1027

. Rev. 1 T'. t NPl!? 0! ?6tLS 7011 iAFP'!D 10! satset 1-  : .:;.),::.4. Page 29 of 38

ner ; 9 .:'.h . :a711:1nont 137 ";7!: 17?;7; ??:!;17:C:il #1 = ; 0.:46666664? : ;!:;1133;) : :

!!!:*-7I: !!7-74 77:7:17:3hi 72 = ; :.;333333333! ? ;..;;;g ) g

,!!!:* !! ??:!:;7::. p: a ). i333333333 Ii *: 4!! 77:! ?! :'. pi s ).0?;.51sisii?

!!!:*;7!: af: W:t GP pi a 017i0021it*3 117:~ *!; -;;h;I 7 p2 = !.07912!6??t *4

!st %*!!! OT !btL3 ** !! iAMPLID TOR subsets 1 - 5 = 12.9.12.4.

sampitna wtht replatement

!$T!MA!!D iTIATA PFCPoli!0NS P1 = 0 0.08333333333 0 0 0 137: MAT!D STPATA P70F0ti:0NS p2 = 0 0.25 0 0 0

!$T!NATED 790F0tt:0N p1 = 0.01666666667 IST!MAftD PROPORT!0N p2 = 0.05 EST!MAftD VAllANCE Of p1 = 2.5439619978 4 ISTMATID VAll ANCE Of p2 = 6.2442703568 4 THE NUMitt CF PANtts 70 It SAMPLID FOR subsets 1 - 5 = 3.12.9.38.4.

sampling without replacement ISTINAft0 STRATA P90F0tt!0N8 p1 = 0 0.09333333333 0 0 0

!$t!MAftD STRATA PROP 0RTIONS p2 = 10 0 0 0 I$flMAftD F30P08T!0N p1 = 0.01666666667

!$7! MATED PROPORT!0N p2 = 0.05 ISTIMAftD VAllANCE Of pi = 3.5439619978 4 ISTIMATID VAll ANCE 0F p2 a 0 THE NUMitt OF PANELS g SAWJs) POR subsets 1 - 5 = 3.12.9.38.4.

g.-.. . .

sampitne wl9eut repleaspekt * *** '

IST!MAft) STRATA P90F0t?!ONS pt e 0 0.08333333333 0 0 0 IST! M TID STRATA P90P08T10NS tt = 0 0.25 0 0.03125 0 ..

ESTIMAftD PROP 0RTION pi = 0.01666666667 ISTIMAft) PROP 0RTION pt = 0.06685 IST!Miti vat! ANCE Of p1 = 3.5439619971*4 ISTIMAftD V4814NCE OF p2 = 0.799034036t*4 THE NUMtti 0F PANILS 70 It $4MPLg8 FCI subsets 1 - 5

  • 3.12.7.32.4.

saapitr,s witt.out replacement

9 TDR 1027 Rev. 1 Page 30 of 38 1271 M it; 720?OITION 31 a 0.01666666667 IST! MAT!!' Pf0F0ffl0N p2 = 0.0666666f 667 A TT. Is.

Ett! mfd WI! ANCE Of p1 e 2.466940??it*4 R$?!MTID WRI ANCE Of p2 e 2.543961997t*4 l

THE MUMitt 0F PANILS TO 88 SAMLED FOR subsets 1 - 5 a 3.12.9.32.4.

sa:pling without replacement IST!MTED STRATA PROPORTIONS p1 = 0 0.25 0.2222222222 0 0 i 'ISTIMTED STRATA PROPotTIONI p2 = 0.6666666667 0.03333333333 0 0.0625 0 l ISTIMTED P90F0tT!0N p1 0.08333333333 l IST! M TID PROPORTION p2 a 0.0025 l )

I ISTI M TED vat!ANCE Of p1 1.056141671t*3 l Elf!MTID vat! ANCE OF P2 = 9.H00311538*4 l l

l THE NUMbit OF PANELS 70 St SAMPLID FOR subsets 1 - 5 = 3.12.9.32.4.

1 sampling without replacement '

ISTIMTED STRATA PROP 0RTIONS p1 = 0.6666666667 0.25 0 0 0 -

R$7! M TED STRATA PROP 0RTIONS p2 a 0.6666666667 0 0.1111111111 0 0 ISTIMTED PROP 0RTION p; . 0.00333333333 ISTIMTED PROPORTION p2 = 0.05 ISTIMTED wt! ANCE OF P4 = 0.0M807220t*4 IST!MTED WRI ANCE Of p2 a 4.3175576438*4 THE NUM382 0F PANELS to It SAMPLID FOR subsets 1 - 5 = 2.12.9.32.4.

sampling without replacement ISTIMTID STRATA PROPORTIONS p1 0.3333333333 0.08333333333 0.11111111110 0 881127t STRATA PROP 0RTIONS p2 = 0.3333333333 0.1666666667 0 0 0 IST! M Tit PROPORTION pi

  • 0.05 ..

!$7!MTID PROPORTION p2

  • 0.05 tlTIMTID Wtl ANCE Of p1 a 6.06151964t*4 IS?!MTED VARI ANCE OF P2
  • 6.476002321t*4 1

j

\

012/079.32 i_

  • r

. , $UBS!?25!Il THE NUnitR OF SU35t;S ns a 5. i SUB$tt i o drtP sens and sanfted! WOIST TDR 1027 ,

SUBSIT 2 w drip tone onlW3 VIIY BAD Rev. 1 '

SUBSIT 3

  • sand bed: IAD Page 31 of 38 SUBSIT 4
  • rest of the spheret GOOD SUBSIT 5 = cWlinjer: BEST THE number OT PANELS IN Su stTS 1.2.3.4,5 !$ 5 20 15 52 8 ,

THE total nutter 0F PANEL 3 = 100 /. TT4 C HMEN ,l lb I ASSUPE: TOTAL NU"itR OT 6x6 SAMPLE UNITS IS identical TCR EA0H PANIL.

THE NUM!tp OT VN!TS PIP PANEL nu = 600.

MvLATICN Cf s MPJ THE total numter 0F UNITS = 6>.000. MA" / F/G r.) JA M Puu6 PLA 4 THE number OT 'JN!TS !!i SUS $til 1.2.3.4.5 !$ E012000 9000 31200 4900 INTIR 1

  • Pr(bad unit >t 4 OHAFACTERIZATION OF Tat ENT!!! POPULATION.

Of 0.05

$U!$1T D!$7' BUT!]N no is 0.L24437529 0.1262243765 0.0631121892 0.0050499751 0.0005043975

$UISti DISTP!BUTION no. 21 0.3924646792 0.07949253!6 0.0392464678 0.0i!69S5971 0.0078492936 PP0 PORTION Pi = 0.04735 FPOPORTION P2 = 0.0$15 sampling without replac' ent THE NUMBER OF PANELS TO BE SAMPLID TOR subsets 1 - 5 = 3.12,9,32,4.

1 MAXIMUM OF *HE EST!MATISI 0.1166666667 0.03726821082 1 1 0.1325 0.03469665474 11 MINIMUM OT THE ESTIMATts: 00000000 AVtfAGE OF THE !$TIMAttSt 0.045925 0.0228240 M 69 0.91 0.99 0.05165 0.02247775917 0.88 0.98 STD DIV 0F THE EST! MATES 0.02409039543 7.305016591t*3 0.2876234913 0.1 0.02850819482 9.331828116t*3 0.3265986324 0.1407052941

-UPPIP TU0-SIDED NOFMAL v.90 AND 0.95 CONT!DENCE LIN!T = 0.09628466044 0.1051476805 LOWil TV0-SIDED NOPMAL 0.90 AND 0.95 CONFIDENCE LIMIT = 3 715339564t*3

  • 5.147680519t*3 P!( h at) . s1 0 at) -TEST 90 TEST 95 P2(hat) s2(hat). TEST 90 TEST 95 0.0333333 0.0209633 1 1 0.0829167 0.0300526 1 1 .. ,

0.0500000.0.0261937- 1 1 0.0162500 'O.0159861 1 1

0.0658333 0.0305628 1 i' O.0333333 0.0209633 1 1 0.0333333 0.0215067 i 1 0.0333333 0.0209633 1 1 0,0500000 0.0261945 1 1 0.0829167 0.0306873 1 1 0.0000000 0.0000000 0 i v.0662500 0.0300526 1 1 0.0333333 0.0209633 1' i 0.0500000 0.0207737 1 1 C.0829167_0.0339088 1. 1 0.1162500' O.0296645 0 0 0.0495833~ 0.0263631 1 1 0.0829167 0.0306873 1 1 0.1000000 0.0324390' 0' 1 0.0333333 0.0209633 i .1 0.0666667 0.0284515 1 1 0.1000000 0.0266314 0 1 0.0333333 0.0223S50 i 1 0.0662500 0.0300526 i 1 0.0166667 0.0i!9498 1 1 0.0333333 0.0207737 1 1 0.000CM0 0.0000000 0 1 0.0500000 0.0261937 1 1 0.016666? 0.0136037 1 1 0.0662500 0.0263631 1

~ ,

1*'

  • C.11iiH? 0.0;!iM7 1 1 0 M42HO 0. Zili31 1
".ifii" L M!hH .1  :.:iiHi* **HMO . 1 1
2. :!HHI ..:liki!: . .  : . :ii2'!O ' O. 02il156 1 1 2.: iH:, h ;3%!26 1 1 0.0491(i? 0.02722*2 1 1 TDR 1027 0.0!??M0 0.0254450 1 1 0.01i6i67 0.0136037 1 1 Rev. 1 h 0.0166667 0.0159499 1 1 0.0329167' O.0225821 1 1 Page 32 of 38 0.0495933 0.0263631 i 1 0.0333333 0.0214515 1 1 0.0166667 0.0159493 1 1 0.0!?0000 0.0209i33 1 1 p

0.0!000 % 0.0261945 1 1 0.0495933 0.0209909 1 1 O.0500000 0.0254460 1 1 0. N H167 0.0225821 1 1 0.233H33 0.0207747 1 1 0.0333333 0.0136037 i ATT.ib.

0.0!291(7 0.0!!!!34 1 1 0.0 0 0000 0.6000000 0 1 0.05M000 0.0266314 1 1 0.1000000 0.0324990 0 1 0.03:13H3 0.0223550 i 1 0.0662500 0.030($73 1 1 0.0333333 0.0215067 1 1 0.0ii6667 0.C2!4490 1 1 0.0333333 0.020??$7 i i 0.0229167 0.0300526 1 1

-0.016Ei67 0.0136037 1- 1 0.049!!)3 0.0263631 1 1 F 0.0333333 0.0215067 1 1 0.0662500.0.0300!26 1 i E .0.0333333 0.022?S50 1 1 0.0H2!00 _0.0306373 1 1 0.0666(67 0.0254490 1 1 0.0162!00 .0.01!9961 1 1 0.0662500 0.0263631 1 1 0.0662500 0.0310611 1 1 0.0329167 0.0300126 1 1 0.0iii667 0.0159499 1 1 0.04i5933 0.0209f4 1 1 0.0162500 0.0159?61 i 1 0.0991667 0.0372 W, v i 0.0491667 0.0273603 1 1 0.0166667 0.01!'e99 .i 1 6 0495933 0.0263631 1 1 0.0500000 0.M43985 1i v.0333333 0.0223950 1 1 7 0.1000000 0.0261937 0 1 0.0495933 0.0263631 1 1 O.06(6667 0.0 !"065 i 1 0.0533333 0.0324990 1 1 O.0333333 0.0207787 1 .1. 0.000C 'O 0.0000000 0 1 N

0.0500000 0.02!44t0 11 1 'O.0491667 ).0272272 1 1 0.0500000 0.0207787 1 1 0.0162500 0.0159961 1 1 g _0.0500000 0.0249995 1 1 0.0700000 0.0271995 1 1 0.0500000 -0.0254460- 1 1 0.0825000 0.0337969 1 1

@g -0.0M0000 0.0000000. 0 't 0.0162500 0.0159661 1 1 g~ 0.1166667 0.0342318 0 0 0.0833333 0.0207777 11

~+

0.0500MO 0.02544SO 1 1 0.0500000 0.0207787 1 1 10.0666667, 0.0299041' i 1 0.0329167 0.0224109 1 i O 0166667 0.0159499' 1 i.0.0000000 0.0000000 0- 1 0.016666760.013603? 11 0.0162500 0.0159961 1 1 0.033333360.0209633. 1 1 0.0333333 0.0223950 1 1 0.0333333 _ 0.0207787- 1 1. 0.0333333 '0.0207787 1. 1 0.0500000 0.0254480 1 0.0495833 0.0263631 1 1 P 0.0666667 0.0295156 -! _1 0.0500000 0.0261945 1 i F

0.0333333- O.020?633 'i 1 0.0933333_ 0.0299049 1- i
m 0.0333333 0.0209633: 1-1 0.0500000 0.0209633 1 1- <

0.0500000. 0.0254490- 1 1 0.0000000 0.0000000- 0 1, 0.0500000J0.0254430 i1 1_ 0.1325000 'O.0346967 0 0' x ~0.0333333 0.0215067 1 .1- 0.0166667O.0159490 1 1 m 0.0333333 0.0136037 1 1 -0.0333333 ' 0136037 1 1 0.0166667. 0.0136037 -1 1 0.0333333 v.0209633 1 1 0.0166667 0.0136037 1 1' 0.0829167 0.03068?3 1 1

-0.0666667 0.0295148= 1 _1 0.300000 0.02N430 1 1

'm l 0.0166667 : 0,0157065 1 1. 0.0825000 0.0304365 1 1 ..

0.0333333 .0.0215067 1 1= 0.0825000 .0.0222402 1 1-0.0333333 0.020777? 1 '1- 0.0491667~ 0.0272272 1 1 1 0.0833333 '0.0295156; i 14 0.0500000 0.0254480 1 1

. -0.0000000 0.0000000 ,0 1 0.0666667 0.0159498! 1 1

. 0.016666710.01570651 1_ i 0.0166667 0.0159499 1 1 0.0833333 -0.0324990. 1 1 0.0333333 0.0209633 1 1 0.0500000. 0.0261?45 -1 1 0.0933333 0.0299049 1 1 O.0500000f0.0261945_i 1 0.0495933,0.0275072.1 1 0.0662500 0.0295353E 1 1 0.0M 00001 0.0000000 0 1-0.016666? 0.0157065 1 1: 0.0833333 0.0215067 1 1 0.0500000 0.02!4480=.!! 1 0.0829167 - 0.0335668 1 1-4 '0.0333333; 0.0136007 1 1- 0.0166667 0.0157065 11 A Anms ^ u.=^4, e e a a u s:4 A a m a-= 4 4 d~.- s ._

A +

- i TDR 1037 Rev. 1 ,

Page 33 of 38 i

AU.[h

' 0.033333) 0.02150t? 1 1 0.VaasJ4J v.vsvreas 1 1 0,0666669 0.029M49 1 1 0.0495933 0.oPf?M4 i 1 ,

e 0.0662500 0.0300526 1 1 0.0000000 0.0000000 0 1 .

0.0333333 0.0209633 1 1 0.0991667 0.0333377 0 1 0.0666667 0.0295156 1 1 0.0166667 0.0136037 1 1 0.01(ift? 0.0159499 1 1 0.0M0000 0.0207?t7 i 1 0.0M0000 0.0266314 1 1 0.0029167 0.0335668 1 1 0.0M0000 0.020H33 1 1 0.0650333 0.0260700 1 1

0.0495033 0.0262166 1 1 0.0495033 0.0209909 1 1 0.0995033 0.0M2179 0 1 0.0642500 0.0300526 1 i . i 0.0666667 0.0284515 1 1 0.0666667 0.0159496 1 1 0.0333333 0.0223050 1 1 0.0650333 0.0260700 1 1

! 0.0500000 0.0266314 1 1 0.0325000 0.0222402 1 1 l' 0.0500000 0.0207787 1 1 0.0495033 0.0267973 1 1

[

- 0.0333333 0.0207787 1 1 0.0333333 0 J2077t? i i 0.0662500 0.0M6073 1 1 0.0029167 0.0900526 1 i

! 0.0500000 0.0254400 1 1 0.0166667 0.0159490 i i j- 0.0829167 0.0335660 1 1 0.0166667 0.0136037 1 i 1

) 0.0500000 0.0266314 1 1 0.0000000 0.0000000 0 1

{

i t

I 012/079.35

- . - , ~, .,,,, - , - , , , ,, a- .-- , . . . ,-- , ,.-.+,,na-a - - - - - , ,-..,e-m e - - ~ . - - - - - .-

3 7 5988tT451M TNI Nunalt 0F SulllT8 no e 5.

900487 L

  • drip sene and sanabed 9088T TDR 1027 >

IUHit I e drip tone onlyt VttY llD Rev. 1 )

8088t7 3 e sand beds SAD Page 34 of 38 '

$08987 4

  • rest of the spherel GOOD

$00887 5

  • cvilndert IIST THE number 0F PANtl$ IN $Ulltfl 1,2,3,4.51852015528 ATT, 2 1 tnt totsi nueter 0F PANILS e 100
  • AltVMt TOTAL NUMitt 0F 6 6 SAMPLt UNITS Il identical ICI IACH PANtl. 3 A N C) SEO CXClUCCD THE NUMitt 0F UNITS Ptt PANil nu s 600.

N M r N I N N B5tN' b '.3.4.5 IS 3000 12000 9000 3t200 4800 INTil t e Pt(bsd unit)I A CHARACTttl2Afl0N OF THE INTitt F0PULAfl0N.

31 0.05

$Ulltf Dl6TillVT10N no. 1:

0.2524407529 0.1262243765 '

0.0631121802 O.0050409751 0.0005040975

$Ulltf DllfillVT10N tio. 21 0.3924646782 0.0704929356 0.0392464678 0.0156985471 0.0078492936 P90P0tfl0N P1

  • 0.05015 P90F08710N P2 a 0.0510H33333 sampling without replacement i 48 NUMBit 0F PANILS TO 88 SAMPLID FOR subsets 1 5 = 3.12. 9. 32.4.

l TNB BOTTON HALF Of THE PANILS IN subsets i AND 5 Att IXCLUDID.

If AND CHLY IF.THtY Alt RANDOMLY SBLICTtD.

CONDITIONAL P90F08tl0N P1 a 0.043129s2963 .

. CONDITIONAL PROP 0Rfl0N P2 = 0.04181491401 l MAXINUM Of THE ISTIMAfstl 0.1203703704 1 1 50 0,1226851852 1 1 l NINIMON OF THE IlflHAft$1 00049000 l

AVilA48 0F TNI ttflHAfts: 0.04425562169 0.94 0.97 53.9 0.04344973545 0.94 0.95

$79 DIV 0F THt 18t!NAft8 0.02582932443 0.2386932566 0.171446604 1.702642035 0.02654310002 0.2306832546 0.2190429136 l

1 UPPtt TWO 519tD NORMAL 0.90 AND 0.95 CONflDtHCI LIMIT TOR CAlt 1 =

0.08627206074 0.09453330607 ..

LOWil TWO 8IDED NotMAL 0.90 AND 0.95 CONFIDINCE LIMIT F08 CAST 1 *

  • t.2009402438 *5 *0.2741276 tit *3 UPitt TWO llDID N0tNAL 0.90 AND 0.95 COHflDtNCE LINif FOR CAtt 2 =

0.0843H73604 0.09246374314 LOWit TWO 81DID NOIMAL 0.90 AND 0.95 CONFIDENCE LINif FOR Call 2 =

  • 6.94107206t *4 *8.03411355t*3 Pit hat) TEST 90 ft9T95 no. sampled p2(hau TEST 90 115795 0.0609018 1 1 54 0.0645145 i 1 0.0365741 1 1 .54 '0.0145tt$ 1 1 0.036Siti i 1 55 0.0370370 t i

.0.0000000 1 1 51 0.0100556 1 1 0.0643519 1 1 53 0.1226852 0 0 0.0?$9259 1 1 $3 0.0185195 1 i

^

4.s. ..e. . . .. .....es.. . . ,

m 0.035(852 1 1 55 0.0685185 1 1

e 0f050726 1. 1 S1 0.0277??8 1 1 O.0995370 0 0 53 0.0442963 1 1 TDR 1027 0.062HM i 1 54 0.0921296 0 1 Rov. 1 0.0634449 1 1 51 0.0828704 1 1 Page 35 of as 0.0370370 1 1 36 0.0277778 1 1 0.062M30 1 1 53 0.0277770 1 1 ATT. 2 0.0056401 1 1 52 0.0277770 1 1 0.0000000 1 1 52 0.0736111 1 1 0.0736111 1 1 50 0.0643519 1 1

, 0.0105185 1 1 54 0.0370370 1 1 0.0324074 1 1 55 0.0490741 1 1 0.0509259 1 1 55 0.0450333 1 1 0.0462963 1 1 54 0.0185185 1 1 0.0324074 1 1 55 0.0361111 1 1 0.0393519 1 1 53 0.0361111 1 1 0.0555556 1. 1 55 0.0550926 1 1 0.0185185 1 1 54 0.0555556 1 1 0.0370370 1 1 53 0.0643519 1 1 .

0.0370370 1 1 55 0.0462963 1 1 '

O.0138889 1 1 56 0.0365741 1 1

0.0550926 1 1 54 0.0365741 1 1 l 0.0277770 1 1 49 0.1009259 0 0 i

0.0648148 1 1 54 0.0277770 1 1 O.0416667 1 1 52 0.0462963 1 1 0.0393519 1 1 53 0.0638009 1 1 i L 0.0000000 1 1 54 0.0609015 1 1 0.0319444 1 1 55 0.0555556 1 1 0.0319444 1 1 56 - 0.032M74 11 0.0925926 0 1 52 0.0370370 1 1 0.0462963 1 1 54 0.1189015 0 0

  • O.0442963 1 1 53 0.0640148 1 1 0.0195185 1 1 53 0.032M74 1 1 0.032M74 1 1 55 0.0105105 1 i l 0.0370370 1 1 57 0.0609015 1 1 L 0.0570704 1 1 54 0.0324074 1 1 0.0643519 1 1 54 0.0462963 .1 1 j 0.0925926 0 1 54 0.0458333 1 1 0.0717593 11 54 0.0504630 1 1 l' O.0740741 1-1 54 0.0277770 1 1 I 0.0370370 1 1 53 0.0731401 1 1 l

0.0555556 1 1 57 0.0105105 1 1 0.0644140 1 1 57 0.0401952 1 1 0.0093593 1 1 54 0.0277779 1 1 0.0105195 1- 1 870 1 1-0.0324074 1 1' 38 " t~ 1 0.0640140 1 1 A0919444 1 1 0.0532M7 1 1* 'i 1 0.0092593 1 1 .0100601 1 1 0.0000000 1 -1 9t T O.0630009 1 1 0.0671296 1 1 53 0.0108185 1 1.

0.0370370 1 1 53 0.0130089 1 1 -

0.0555554 1 1 54 0.0277779 1 1 0.0277770 1 1 55 0.0000000 1 1 .

0.0370370 1 1 56 0.0599806 11 .

0.07M741. 1 1 56 0.0377770 1 1 0.0185195 1 1 55 0.0130889 1 1 l 0.0277778 1 1 52 0.0833333 1 1 0.0555554 1 1 54 0.0195105 1 1 0.0fG?195 1 1 54 0.0555556 1 1 0.010$105 1 1 54 0.083H33 1 1 0.076706 1 1 55 0.0458333 1 1 '

O.0M7322 11 54 0.033.9444 1 1

, $..:..n . . p 3 .m.e s . .

l > C l TDR 1027 Rev. 1 Page 36 o' 38 1

0.034"2 2 1 1 14 h.[?'i444 1 .

0.0195145 1 1 53 0.0000000 1 1 AE g 0.0707037 1 1 55 0.1046296 0 0 0.0570704 1 1 54 0.0319444 1 1 1

0.0370370 t 1 55 0.0092593 1 1 0.0324074 1 1 57 0.0416667 1 1 0.0504630 1 1 56 0.0605105 1 1 p 0.0166667 1 1 54 0.0000000 1 1

, 0.0105105 1 1 53 0.0105105 1 1 1

0.0740741 1 1 51 0.0450333 1 1 l

  • O.0105105 1 1 54 0.0000000 1 1 l 0.0462963 1 1 49 0.0277770 1 1 0.0537037 1 1 55 0.0370370 1 1 0.0509259 1 1 55 0.0402770 1 1 0.0310370 1 1 52 0.0105105 1 1 O.0000000 1 1 55 0.0020704 1 1 0.0324074 1 1 54 0.0324074 1 1 l

0.0000000 1 1 55 0.0000000 1 1 O.0555556 1 1 53 0.0615741 1 1 0.0370370 1 1 54 0.0033333 1 1 0.0925926 0 1 52 0.0509015 1 1 0.0209352 1 1 50 0.0319444- 1 1 l 0.0300009 1 1 55- 0.0185105 1 1 O.0450333 1 1 54 0.0464963 1 1 0.1203704 0 0 51 0.0105105 1 1 '

O.0722222 1 1 54 0.0458333 1 1 0.0000000 1 1 53 0.0939015 0 0 0.0324074 1 1 54 0.0324074 1 1 0.0000W0 1 1 51 0.0462963 1 1 0.0555556 1 1 53 0.0105105 1 1 0.0509259 1 1 52 0.0000000 1 1 i

1 012/079.38 L ,

- _ . - _ _ . . _ _ _ _ _ _ _ _ _ _ . . . _ . _ _ - - - _ . - , , . . ..-.- - , , , , - - _ . , . . - , ..._ n .- . . . - . , . . . . . . . - - _ . . . - .

o

.[

TDR 1027 llMPl!M Rev. 1 AllWMit TOTAL NUptli 0F 4 6 SAMPLI UNITS Il identical FOR BACH PANtt. Page 37 of 38 +

TNI Muntil 0F Uhift Pil PANil nu e 600.

798 total nweber 0F UNITS e 60.000.  !

INIll 4 e Pf(bad unit)8 A CNASACT!ll!At!0N OF tnt INT!It POPULATION.

. 0.05 *)

Pf0PCITION Pi e 0.050(1660047 NCM- STRAT@ D sa:Pltes without replacement Tut N'.'Fiti CF PANttl 70 It SAMPLID ll 60.

tnt ICTTOM waLF OF tnt PANtts IN TN! $4N) It) (20 PANtLI) All t trCLll TID. IF AND ONL7 IF TNEY Alt IAND0MLY $3LICT!D.

CON)lT!QNAL PROP 0ff!0N P1 = 0.05096296296 Mar! MUM 0F TNI flTIMAftli 0.1346153646 1 1 55 MINIMUM 0F TNI BlTIMAffli 0 0 0 44 AvtBAct et tnt 8171Maftli 0.0470419326 0.03 0.95 49.77 STD btV 0F TNI R$71Maftli 0.03059222540 0.3775251681 0.2190429136 2.407291113 UPPit TWO-llit) NORMAL 0.90 AND 0.95 CONF!btNCE LIMIT FOR **lt 1 =

0.09766751304 0.1066109375

  • LOWit TWO liitt NCIMAL 0.90 AND 0.95 CONFIDENCE LIMIT FOR CAlt 1 4.256412006t *3 *4.645011597t *3 pt(hau 788790 TitT95 no. sAnpled ,

0.0000000 0 1 51 ,

0.0196079 1 1 51 0.0576923 1 1 52 0.0212766 1 1 47 0.0000000 0 1 49 0.0196070 1 1 51 0.0392157 1 1 51 0.0100679 1 1 53 0.0377250 1 1 53 0.0000000 0 1 48

, 0.0196070 1 1 51 l

0.0200000 1 1 50 0.0612245 1 1 49 0.0566030 1 1 53 I' O.0408163 1 1 49,

! 0.0890392 0 1 51 0.0600000 1 1 50 0.0833333 1 1 48 0.1346154 0 0 52i' O.0408163 1 1 49' O.0000000 0 1 52 0.0425532 1 1 4' 0.06M000 t i 50 '*

.0.0425532 1 1 47 0.0364615 1 1-

!2 0.020l333 1 1 48 0.0588235 1 1 51 0.0784314 i 1 51 0.0!iiO!! 1 i 13 0.1086957 0 0 46 o.03a4619 1 1 52 0.0392157 1 1 !1 0.0576921 1 1  !!

i

%;sk.t - ..

.. wcr r s w-t 0.03W358 1 1 53 0 05?6v23 1 1 SI u n 8027 0.0033333 1 1 44 " 1 0.0800000 1 1 50 Page 38 of 38 I 0.0400000 1 1. 50 0.041 s e67 1 1 48

  • e. 0437290 1 1 47
. itiMO 1 1 So
. !1445 1 1 12 2.:(12245 1 1 49 o 2.;;41si? : 1 43
0. !*il23 1 1 477 3, 12

. 1?iO*1 1

  • 11
.:Tii)31 1 1 13
.*I"*!*) 1 1 14
.*11*171 1 1 4e

' . ,' X M00 0 1 D

.21346?? 1 1 13 3.035 411 1 1 52 0.0612.45 1 1 47 1

L 040M0? 1 1 10 0.0311064 1 1 47 l'

?.12000M 0 0 50 0.0588235 . 1 51 3.0634294 1 1 47 0.0000000 0 1 .49 I 0.0612245 1 1 49 T 0.0304615 1 1 12 0.0833333 1 1 48 0.0196078 1 1 11 0.0566034 1 1 53 0.0555556 1 1 54 0.0204082 1 1 49 0.0425532 1 1 47 0.0000000 0 1 54 0.0444444 1 1 45 0.0433333 1 1 44 3.0888889 1 1 45

%0112304 1 1 52 0.0212766 i 1 47 0.0638298 1 1 47 0.0425000 1 1 40 0.0566038 1 1 53 0.0784314 1 1 51 0.0016327 1 1 49 0.1224490 0 0 49 0.0227273 1 1 '44

-0.0000000 0 1.- 49 0.0600000 1 C M e-0.0033333 1,17 i G 0.0000000 0 Fw M 'a 0.0196079 1 8* 30 F 0.0000000 0 1 47 r 0.0769231 1 1 52 l ., 0.0196078 1 1 51 l 0.0222222 1 1 45 0.04H783 1 1 46 0.0308333 1 1 40 0.0400000 1 1 50 0.0101010 1 1 SS 0.02:2766 1 1 47 0.0304615 1 1 52 0.1111111 0 0 4?

0.0816327 1 1 49 o 0.0!!!299 1 1 47

_ _ _ _ _ , , . , , _ _ _ _ _ . - ~ . - ~

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