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Forwards Attachments to 870810 Further Answers to Comanche Peak Review Team (Cprt) Interrogatories (Set 12),including Calculations of Cprt Sampling Plan.Related Correspondence
	ML20238F435
Person / Time
Site:	Comanche Peak
Issue date:	08/17/1987
From:	Eggeling W; ROPES & GRAY, TEXAS UTILITIES ELECTRIC CO. (TU ELECTRIC)
To:	; NRC OFFICE OF THE SECRETARY (SECY)
References
	CON-#387-4283 OL, NUDOCS 8709160155
	Download: ML20238F435 (50)
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ret.ATED CORRESPONDOtCB

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L 225 FRANKLIN STREET BOSTON, MASSACHUSETTS O2110

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30 MENNEDY PLAZA TELEX NUMBER 940519 ROPGRALOR BSN 8003 TWE NTV-5 ECONO STREET, N.W P R O /IDE NCE, R. i. 02 903 TELEX NUMBER 95f 973 ROPES GRAY BSN ; t' WASHING 70NitEC.2OO37 f 400 52 -e400 TELtcOPERs teirl423-e377 (sirt 423 784 Oi'!. 4 ')(202! 429-seOO TE LECOPIER' i400 521-0910 T E L E CO PIE R:8202! 429-1629

NTER N AtiONAL (er7) 423-6905 August 17, 1987

' Office.of the Secretary U.S. Nuclear Regulatory Commission i Washington, D.C. 20555 ATTENTION: Docketing and' Service Branch Re: Texas Utilities Electric Company et al.

_ Docket No. 50-445-OL & 50-446-OL

Dear Sir:

In "Further Answers to CPRT Interrogatories (Set No.

12) ", .which was filed Menday, August 10, 1987, reference is made to three attachments. Unfortunately these attachments

.were not included with the submitted document. Enclosed-are three copies of each of the attachments.

Very truly you William S. Egge ig WSE/plw

Enclosures:

Attachment A "CPRT Sampling Plans -- Addendum"

. Attachment B " Developing Sampling Plans for TRT Issues" Attachment C " Sample Plans for Finite Populations & 100" cc: Certificate of Service 8709160155 870817 PDR ADOCK 05000445 3 0 PDR: C

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so. *i N 12/12/84 (y Page 1 of 8 f.

MEMO- .

To: CPRT Team Leaders with Sampling Problems From: Fred Webster

Subject:

. DEVELOPING SAMPLING PLANS AND RANDOM SAMPLES FOR TRT ISSUES

/

1.0 INTRODUCTION

The purpose of this memo is to provide general guidance in the development of sampling plans for TRT issues requiring sampling, and to outline the basic method to be used in generating random samples from a population.

What is discussed in this memo applies-to sampling plans for TRT issues related-to either inspection by. attributes or tolerance limits of populations. Most of the TRT. issues requiring sampling fall into one of these two categories. If other types of sampling problems arise, they must .;

be dealt with.on a case-by-case basis, 2.0 SAMPLING !LANS FOR INSPECTION BY ATTRIBUTES l Sampling inspection by attributes is concerned with classifying articles j (e.g. heat shrinkable cable insulation sleeves Train-C conduit runs, etc.)

as defective or non-defective. The inte is type of sampling is to establish, with some level of confidence,Athe percentage of defective

' articles in the entire population of articles. It is therefore essential 1

that the sample be drawn in a random manner. Note that a sample is random j if every article in the population has an equal chance of being selected.

This may easily bn accomplished by using a table of random numbers to generate the simple-(see Section 4.0). Human attempts to randomize a sample, without.such aids often result in biased samples.

Certain risks must be assumed if sampling inspection is to be used rather ;

than 100 percent inspection. A graph of these risks, plotted as a function of the Fraction Defective (FD) in the population is called the operating characteristic (OC) curve.

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12/12/8L Page 2 of 8 [

2.0 SAMPLING PLANS FOR INSPECTION BY ATTRIBUTES (Cont'd)

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Q 0 05 S u 0.W E c.ol 0 02 0 0b 0.04 9.0 5 FRACTtoM DEF&c.TIVE Figure 1 Example OC Curve If the Fraction Defective in the population is low, then it is desirable to have a high probability of accepting the population, based on the random sample. On the other hand, if the Fraction Defective is large, it is desirable to have a low probability of accepting the population (or alternatively, a high probability of rejecting the population), based on the random sample. These two types of risks are known as producer risk and consumer risk, respectively, and are illustrated on the example OC curve in Figure 1 as points A and B.

Sampling problems posed by the TRT issues, which fall into the category of inspection by attribute, are related to consumer risk, in which the NRC (representing the public interest) is the consumer. In other vords, the NRC is interested in TUCCO developing sampling plans which result in a high probability of them rejecting a population of articles which has a large Fraction Defective (e.g. 0.05 FD may be considered large). Thus, a sampling plan which has a 95 percent confidence level on the 95 percentile value is interpreted as meaning that, based on the sample, there is at least a 0.95 probability that a Fraction Defective in the population of 0.05 or more vill be detected and the population rejected.

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Page 3 of 8 j/

a 2.0 SAr Ti .s PLANS FOR INSPECTION BY ATTRIBUTES (Cont'd)

MIL-STD 105D is a set of sampling plans which are oriented toward producer risk rather than the consumer risk. Generally speaking, use of the MIL-STD 105D, without consideration of the specified consumer risk, may result in larger than' desired consumer risk, particularly for small populations.

However, if the Limiting Quality Table VII-A of the MIL-STD 105D is used to L determine the sample size code letter and AQL consistent with the desired .

consumer risk, then the MIL-STD 105D single or double sampling plan tables can be used to determine an appropriate sample size and appropriate acceptance and: rejection numbers. For example, using a 0.05 probability of

-acceptance-and a 0.05 FD and going to Table VII-A, we find'a sample size code letter, K,~and an AQL of 0.65. Taking this information into Table II-A, the sample plan corresponds to a sample size of 125 with an acceptance number of 2.

As an alternative to using MIL-STD 105D to develop sampling plans, Table 1 may be used to determine the sample sizes and corresponding acceptance n'.wbers which are consistent with a 95' percent confidence level on the 95, 97.5, and 99 percentile levels (i.e. 0.05, 0.025, and 0.01 Fraction Defective). These sampling pipra are based on an assumption of an infin'ite population size and are conser.ative when compared with sampling plans based on finite populations. Note that for a 0.05 Fraction Defective the minimum : sample size is 60 with an acceptance number of zero. _ This means that out of a random sample of 60 articles inspected, there can be no 1 I

defective articles. If defective articles are found, the sampic size may be increased.in the hope that no more defectives are found, or the population can be 100 percent inspected.

It is suggested that Table 1 be used as a guide, even for small I

populations. Use of MIL-STD 105D for small populations will result in sample sizes which are even larger that those listed in Table 1. For l reference, Attachment 1 shows a set of OC curves which correspond to the sampling plans listed in Table 1.

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Page 4 of 8 f/

2.0 SAMPLING PLANS FOR INSPECTION BY ATTRIBUTES (Cont'd)

TABLE 1 !

SINGLE SAMPLING PLANS FOR 0.05 PROBABILITY OF ACCEPI.'.NCE*

SAMPLE SIZE ACCEPTANCE NO.

0.05 FD 0.025 FD 0.01 FD 60** 120 300 0 95 190 474 1 126 252 630 2 155 310 775 3 183 366 915 4

. 210 421 1051 5 237 474 1184 6 263 526 1315 7 339 678 glM 10

Reference:

A.-H. Bowker, and G. J. Lieberman, " Engineering Statistics",

2nd edition, Prentice-Hall, 1972, page 538.

- For populations of 100 or. fewer articles the sample size may be reduced to 45, with an acceptance number of zero.

3.0 SAMPLING PLANS FOR TOLERANCE LIMITS The acceptable quality of a population of items or quantity of material'is often specified by setting either an upper or lower bound value based on a certain percentage of the population falling below or above this bound.

When an upper or lower bound is specified in statistical terms it is called a tolerance limit. A tolerance limit has the property that a certain percentage of the population of values (e.g. 90 percent) may be expected to fall above or below this bound with some level of confidence (e.g. 95

~

percent confidence), Tolerance limits are usually based on the assumption that the underlying population distribution is either normal or log-normal.

There exist tolerance limits which are in(ependent of the form of the underlying population distribution, bewever they are of limited practicability since they require very large samples in order to make o reasonable confidence statements. Sampling plans outlined here are based on the assumption that the underlying population distributions are reasonably approximated by the normal or log-normal distributions.

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' 12/12/84 i Page 5-of 8 3.0. SAMPLING PLANS FOR TOLERANCE LIMITS (Cont'd) . 1 A tolerance limit is defined as ! i KS, where X is the sampi average and S is the sample standard deviation. The tolerance factor, K, is dependent on.

the sample size and the specified population percentage above or below the litnit, and the desired level of confidence (e.g. the 95 percent confidence I level). On'ce the confidence level has been selected and the population percentage specified, the sample size is only a function of the tolerance

{

factor, K. To lower the tolerance factor, it is necessary to increase the sample size. The relationship for several population percentages is listed in Table 2. A graphical representation of this relationship is shown in Attachment 2.

i It should be ur:derstood that there is no unique sample size for any particular problem. However, it is obvious from Table 2 that it becomes increasingly difficult to lower the tolerance factor as the sample size increases. From a practical point of view, sample sizes between 50 and 100 provide reasonable tolerance factors for the sampling effort.

It is' recommended that, for TRT issues related to tolerance limits (e.g.

concrete strength), sampling plans be developed by first determining through engineering, materials, or other types of arguments whether it is reasonable to assume the underlying population distribution to be normal or log-normal. If this assumption is reasonable, then it is recommended that, as a minimum, a sample size of 50 be obtained. The actual sample size ;

selected, however, should take into account the difficulty in obtaining the sample and how sensitive the resulting conclusions are to the actual tolerance limit.

Any tolerance limit problems, for which the underlying pvpulation distribution cannot be reasonably assumed to be normal or log-normal, must be handled on a case-by-case basis.

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Page 6 of 8-

[j 3.0. SAMPLING PLANS FOR TOLERANCE LIMITS (Cont'd) .

TABLE 2 SAMPLE SIZE VERSUS TOLERANCE LIMIT i FACTORS, K FOR 95 PERCENT CONFIDENCE LEVEL (Tot'ai Limit =.X t KS)

First Fifth Tenth Fiftieth Sample Size Percentile

Percentile

Percentile

Percentile **

5 5.75 4.21 3.41 0.90 .

10 3.98 2.91 2.36 0.56 -l 15 3.52 2.57 2.07 0.45 20 3.30 2.40 1.93 0.38 25 3.16 2.29 1.84 0.34 l 30 3.06 2.22 1.78 0.31 35 2.99 2.17 1.73 0.28 40 2.94 2.13 1.70 0.26 50 2.86 2.07 1.65 0.24 70 2.77 1.99 1.58' O.20 100 2.68 1.93 1.53 0.17 300 2.52 1.80 1.42 0.10 a 2.33 1.65 1.28 0.00

Reference:

D. B. Owen, " Handbook of Statistical Tables", Addison-Wesley, 1962, page 126.

- Based on approximate relationship K a (u,+ xu [(I- )/n + 3 + (1- ).

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- 4.0; GENERATING RANDOM SAMPLES It is genera 11y' impractical or undesirable from a time and expense point of view to examine an entire population of articles oriquantity of material.. One may, however, sample part of it and, on the basis of this

. limited investigation, make inferences regarding the entire population.

The question then is how the' sample should be selected.

There-are basically two ways to select samples, one is to use engineering.

judgement and select areas or items that are likely to be.the most critical, the other 1s to randomly sample the population. Inferences based !

,n the former approach must .also be based on engineering judgements or arguments. Inferences based on random sampling are statistical.- In either case, the inferences cannot be 100 percent certain without 100 percent

~

sampling..

.The procedure for generating a random sample begins by.first defining the

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unit size or article (e.g. a truck load of concrete, a conduit run, a conductor termination, etc.), then determining the total. number of these units:in the population. Note that a population, so defined, may actually be'a subpopulation which has certain specified attributes. Each unit or article in the population must be assigned an unique sequential number, 1 through N, where N is the total number of units in the population.- A table of random digitr is then'used to develop a random sequence of units from R the population. Table 3 outlines the complete procedure.

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i .Page 8 of 8 4.0L GENERATING' RANDOM SAMPLES (Cont'd) . !

1 TABLE 3

' Procedure For Generating Random Sample From Population

'1. Determine population size, N,.'and number each article sequentially, 1, 2,

.....N.

2. Start at top of a table of random digits, such as that referenced below, and perform the following steps for each random digit, until the desired sample size is obtained. !

i

3. Multiply the population size, N, by the random digit, RN , after placing a decimal in front of the five digit number.

4. Retain onl'y the integer part of the above product and add 1. .This will define the i N article to be included in the random sample.

5. It'is usually a good idea to generate a longer list of randomly selected articles in case a particular article is inaccessible in the field, or in .

case the same article is selected more than once.

Example: Generate a sample of 300 items from a populacion of size 3791.

Random Digits

Population Size Random Sample RN y = .04146 x 3791 = 13/.17 =* 157 + 1 = 158 RN = .23432 x 3791 = 888.31 =* 388 + 1 = 889 2

RN = .74381 x 3791 = 2,619.78 =* 2,819 + 1 - 2,820 3

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= .59221 x 3791 = 2,245.07 =* 2,245 + 1 = 2,246 )

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These random digits are from Page 355 of "A Million Random Digits" by The Rand Corporation.

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ML20238F435

Contents

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Dear Sir:

Enclosures:

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1.0 INTRODUCTION

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ML20238F435

Text

Dear Sir:

Enclosures:

Subject:

1.0 INTRODUCTION

Reference:

Reference:

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