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NBS!R 81-2219

Inventory Difference Calculations:

Problems and Possibilities

James A. Lechner

Center for Applied Mathematics

National Engineering Laboratory

U.S. Department of Commerce

National Bureau of Standards

Wasnington, DC 20234

February 1 981

Final Reoort

red for: Nuclear Regulatory Commission

hington, DC 20555

ATIONAL BUKEAU

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NBSIR 81-2219

APR 6 1981

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INVENTORY DIFFERENCE CALCULATIONS:

PROBLEMS AND POSSIBILITIES

James A. Lechner

Center for Applied Mathematics

National Engineering Laboratory

U.S. Department of Commerce

National Bureau of Standards

Washington, DC 20234

February 1 981

Final Report

Prepared for: U.S. Nuclear Regulatory Commission

Washington, DC 20555

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
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INVENTORY DIFFERENCE CALCULATIONS: PROBLEMS AI'TD POSSIBILITIES

by J. A. Lechner

The origin, development, and termination of the "error study" task funded

by the Nuclear Regulatory Commission at the National Bureau of Standards is

presented in this report.

Other reports which grew (at least partially) out of this study are

listed, and related to the intent of this study.

A general approach to the calculation of Inventory Difference (ID) and its

Limit of Error (LEID) was devised and refined through visits to a selected

fuel-fabrication facility. This approach is discussed, with emphasis on the

importance of having measurements "under control" and on the possibility of

automating the computations. The concepts of "measurement process" and

"Measurement Assurance Program" are also discussed, and their importance

shown. Possible problem areas, both those observed at the studied facility

and others, are given, along with possible directions for resolution.

Finally, new approaches to the calculation of ID and LEID being developed

elsewhere are described, and their relation to the approach being considered

herein is elucidated.
2

1. Incroduction and history.

In 1978 the National Bureau of Standards agreed to perform a task for the

Nuclear Regulatory Commission. The purpose of this task was to investigate

the nature of systematic errors. The task plan called for evaluating data

currently available, to see if these data were sufficient to characterize the

distribution of the systematic error components in material accounting. If

the data were found to be sufficient, then they were to be used to perform the

study and evaluate the characteristics of the systematic error components. If

the data were found to be insufficient, then the measurement processes

themselves were to be studied, and a determination was to be made of what

would be necessary to properly evaluate the systematic errors. Several steps

were envisioned. First, one licensee was to be chosen, acceptable to both NBS

and NRC. The study was to be initiated with this licensee. At the conclusion

of this phase, a report would be written, detailing the findings there and

tentative generalizations to other licensees. The next step would be to

verify these generalizations with smaller spot studies at other licensees.

Visits to the selected licensee began in December 1978. There were a

total of six visits, of one or two days each, by one or two NBS personnel. In

September 1979, after the sixth visit, it became apparent that there was a

misunderstanding developing. The NRC inspectors were getting the impression

that NBS had been hired by the licensee to correct some deficiencies noted in

their material accounting system. At this point it was decided that there

should be no communication between NBS and the licensee until this matter had

been clarified. No further communication has occurred since that time.

There have been several discussions between NBS and the sponsor at NRC,

and attempts to initiate communication between NBS and the inspectors at

NPX. This communication has not materialized. Funds have been
3

cut several times. Finally, the effort was terminated, with reports still to

be written, and some of the necessary information still not obtained.

However, a considerable effort has gone into this study. Although the desired

finished product has not been obtained, useful things have been learned at the

licensee's facility. In addition, as a result of what was learned there,

other studies have been carried forth, designed to improve the material

accounting process. These are reported separately, and will be described

only in general terms in this report. A general approach to material

accounting, which allows for more systematic treatment of both the random and

the systematic errors involved, was originated during the course of this

study. It will be presented in this report. Its relationship to other

approaches that have recently appeared will also be described. The concepts

of measurement process and of measurement assurance program are also

discussed, because they are vital to proper measurement control. Possible

problem areas with this approach, both those observed at the studied facility

and others, are given, along with possible directions for resolution.

2. Specific problems suggested by visits to the facility.

2.1 A fundamental problem, here as well as elsewhere in our experience, is

the lack of a solid basis for the assessment of errors. This is due in part

to the sophistication necessary to assess errors properly, and in part to

insufficiency of data. This whole subject will be considered in Sections 3

and 4, because it is intimately connected to the idea of measurement as a

process , and to the related concept of measurement assurance.

2.2 Another class of problems in calculating Limit of Error (LE) involves

cancellation. The Inventory Difference (ID) is defined as ID = (Beginning

Inventory) + (Receipts) - (Shipments) - (Ending Inventory), or ID = BI +

R - S - El. It is well-known that items appearing in both
4

Beginning Inventory and Ending Inventory cancel out of the equation for

Inventory Difference, and thus contribute nothing to the LE. But items in BI

and Shipments (S), or Receipts (R) and El, or R and S, should also cancel.

Furthermore, in some processes there is no chemical change to fuel material

during the manufacturing process. Thus the accounting is by element , with

percent U235 being the same for outgoing as for incoming material. (It may

even be that percent U is the same, too.) In such a case, there can be no

contribution to LE from the isotopic (and maybe also the chemistry) error,

since the same value is used. If this sort of process represents a large

portion of throughput, then the effect is significant. Of course, the

fraction of material which gets recovered will be shipped with different

chemistry and isotopic values, so that both input and output

chemistry/isotopic errors apply to that fraction. The consideration here is

similar to that applied in Reference [1], example 6.E, page 202ff where the

isotopic error applies not to the entire throughput, but only to the ID. In

our case, it applies not to the entire throughput but only to the ID and to

all material which goes to R.ecovery.

2.3 It appears that oversimplified formulas may be in use for combining

variances. In particular, at the facility studied, (BI + R -S -EI)^ is

calculated by material type , and multiplied by the appropriate (relative)

systematic error variance. This is not correct, even if done separately for

each value of the variance. It needs to be done separately for each separate

value of the systematic error (even though the actual values are not knotvni).

For example, suppose that four made-up standards are used during the inventory

period, and that the quantities (BI+R-S-EI) measured with each standard are

+50, -70, +100, -70, which total to +10. Assuming that the errors in
5

making up the standards are independent, the (relative) systematic error

variance for these errors should be multiplied by (50)^ + (-70)^ + (100)^ +

(-70)2 = 22,300, not by 102 = 100, to obtain the contribution to LE from this

error. (If the amounts were the same magnitudes but all positive, the

correct multiplier is still 22,300, but the incorrect figure is 84,100. Thus

the miscalculation could be in either direction.)

Finally, note that the total quantities measured with each standard

should be used; this includes all types of material.

2.4 Problems also appear with the random error variance. For example, at the

studied facility, the term (Blt-ypg)^ ^^^rand type^/^ appears. This is valid

only when cancellation has been done properly, in the equation for ID, and

when every item in the BI is of the same magnitude and subject to the same

variance. If the magnitudes are different, but the (relative) error is the

same, the formula will underestimate the total error. The effect is not

serious for magnitudes in the same general size range. ^vhen the items differ

from the mean item size by + 10 percent at most, the resulting variance is

underestimated by at most 1/2 percent. However, when the differences can be

as large as + 40 percent, the resulting variance is underestimated by up to 8

percent. Another problem arises, however, if the relative errors are not the

same. For instance, if a scale has the same random error variance regardless

of the weight, then the error variance is n’o^ where n is the number of items

weighed and a is not a relative error but an absolute error (i.e., is not in

percent but in grams). What one wants, in general, is simply the sum of the
6

absolute variances (i.e., in grams squared) for all the items weighed that

period. (This is assuming that the ID involves simply the sum of the weights.

For more complicated relationships, the usual propagation of error formulas

can be applied.)

3. Measurement control and measurement assurance.

Measurements are the result of a process . Material is input to the

process, and numbers are produced by the process. We may distinguish two

modes of operation. If a given item is measured repetitively, the situation

corresponds to a manufacturing process attempting to produce identical items.

If on the other hand, a sequence of different items are measured, it is like

a custom manufacturing process filling orders for different sizes of an item.

In the manufacturing process, the items produced will not be precisely the

specified size(s), although the errors will be detected only if a sufficiently

accurate inspection is performed. Likewise, measurements are not exact.

However, there is a difference: when measuring unknowns, one has no

specification against which to measure errors. For the manufacturing process,

the quality is monitored by measuring the errors (actual value minus

specification value) accurately for selected items. For a measurement

process, one could imagine a more accurate measurement method (a "reference

method" in a sense), used to measure the error made by the measurement process

on selected items. Alternatively (and usually more conveniently) one could

remeasure one or more specific items ("check standards") from time to time.

The resulting measurement values can be treated just like the measurement

errors in the manufacturing process, except that sometimes one does not know

the "true value" for these check standards.
7

How are these values to be treated? In industry they are usually plotted

on a "control chart", which embodies decision rules for flagging problems or

potential problems in the manufacturing process. Similarly, measurements on a

check standard can be used to flag problems or potential problems in the

measurement process. Such use is called "measurement control" or "measurement

assurance", short for measurement quality control or measurement quality

assurance. Quality control has been the subject of many publications, from

the early work of Shewhart [2], through the ASTM Manual of 1976 [3] and the

Quality Control Handbook [4], to more recent work ([5], for example).

The starting point for measurement control is the attainment of a "state

of statistical control" in the measurement process. Quoting Ref. 6, "...

until a measurement operation ... has attained a state of statistical control

it cannot be regarded in any logical sense as measuring anything at all." A

sufficient condition for this state of control is that the errors in

successive measurements are independent, identically distributed random

variables. Generalization to situations more like much actual practice are

discussed in Ref. [6], where the concept of "multistage statistical control”

is expounded. This covers cases where there are certain components of error

which remain fixed for periods of time but vary randomly between periods.

Examples are periodic calibration and made-up standards.

To properly understand and use this approach, it is helpful to discuss the

concepts of systematic error and random error. We start with the idea of a

"limiting mean". This is a hypothetical value, the value that would be

approached by the average as one takes more and more measurements under

conditions specified as well as one knows how to specify: instrument,
8

operator, reference solutions, environment, etc. By definition, the

difference between a given measurement and the limiting mean under the

same conditions is a random error; and the difference between the limiting

mean and the desired value (the "true value", possibly defined relative to a

national standard) is the systematic error. Now this systematic error can be

seen to depend on, among other things, the instrument, the operator, the

temperature (and/or other environmental conditions), and perhaps even on the

item itself. (This latter situation occurs, for example, when different

barrels of scrap, containing the same amount of special nuclear material,

will produce different (but stable) values on a drum counter because of

geometry or other such factors. It also occurs when a calibration curve is

used, because the inaccuracy in the curve is different for different amounts

of material.) In this case, we have "item-dependent errors". A more complete

discussion will be found in another of the reports growing out of this

contract (Ref. [7]).

Assume the complication of item-dependency does not exist. One must still

face up to the presence of systematic error which varies: over time, between

operators, etc. One way to keep tabs on the process, i.e., to "assure" that

both the systematic error and the random error are under control, is to use a

"measurement assurance program". This usually involves frequent measurement

of check standards, and occasional measurement of artifacts (whose true values

are unknown to the participant) in exactly the same way that production

measurements are made. The errors in measurements of the artifact are then an

indication of systematic error in the measurement process. More detail on the

measurement assurance program approach is to be found in References [8], [9],

and [10]; the latter is concerned specifically with calibration.
9

In the absence of sufficient data of the type just mentioned, it is

impossible to produce valid and "tight" uncertainty statements. More

specifically, until the different sources of variation are properly assessed,

the only valid estimates of uncertainty (and thus the estimates of LE) are

larger than they need be.

4. Grassroots material accounting.

The inventory difference (ID) is a number, defined as (Beginning

Inventory + Receipts - Shipments - Ending Inventory). It is calculated from

other numbers, each one eventually expressible (in general) in terms of

measurements of some sort:

ID = f (x]_, X2, ...» x^)

where N may be several hundred (or even several thousand).

If the errors in all the xj_ are independent, with mean zero and known

2

variance Oj_, then (to a first approximation, and assuming the function f is

well behaved)

var(ID) = I

/_3f \

^ Oi • i=l

In this case, computation of the limit of error, LEID, is straightforward

(although probably tedious) if Oj_’s and _3f_' s are determinable. If the

3xj_

errors are not independent, but do have mean zero, we need the covariance

matrix of the set of xj^:

N var ID = ^ , i,j 3xi 3x^

= 1

where E cov (xj_, xj), and

2
10

4.1 Systematic errors.

But what happens when there are "systematic" errors? First, we need to be

clear about the meaning of the term "systematic". It has long been applied to

uncorrected biases, such as, the error due to an incorrect half life

value. Hardly anyone will object to this use of the term. It has come to

be applied to "components of variance", as for example when a new bottle of

reagent is used each week, and the contribution due to the reagent variability

is called a "short term systematic". Here a problem ensues: systematic

errors have traditionally been thought of as (unknown) constants , but here

they vary from day to day or week to week. For better or worse, this usage is

by now thoroughly ingrained in the Safeguards community. Furthermore, the

term "systematic error variance" is in common use, even in cases where the

error a constant. In this case, the term sometimes refers to the variance

of the systematic error remaining after a (randomly determined) correction is

applied, as in recalibration. Since the error remaining is the difference

between the original (systematic) error and a random variable, it is also a

random variable; its variance is identical to the variance of the (random)

correction. Unfortunately, the term seems to imply that the systematic error

itself is random, even when it is not. Furthermore, when the correction is

deemed too small to apply, the "systematic error variance" is still

recommended ([1]) to characterize the uncertainty due to that source of

error. No clear justification exists for this approach. It is true that the

variance of the correction estimate somehow measures how far from zero the

true error could reasonably be expected to be, so that probabilistic limits on

its extent can be derived. However, the error (whatever its true value is) is

not necessarily a random error. The only truly appropriate way to handle such

errors is to study them in enough detail and over enough time to characterize
11

their behavior. If a rule is used to determine when to "correct", then that

rule must be considered also, so that the characteristics of the error that

results (from applying or not applying corrections according to the rule) can

be accurately modeled. One more point of possible confusion needs to be

mentioned. Take, for example, the case of the reagent bottles. The bottleto-bottle differences correspond to systematic errors. Suppose these

differences were actually randomly distributed with variance a^. This is then

the "variance of the systematic error". Its value depends on the procedures

which produced the bottles, and has nothing to do with the operations at the

user’s plant. Now suppose the value for a particular bottle is estimated

(using a known standard) from a sequence of n independent determinations.

If the variance of one determination is (say) then the variance of the

0

average of n determinations will be a^/n. This quantity, which is also the

0

variance of the estimate of the systematic error of a given bottle, is the

"systematic error variance"; it is unrelated to o^, and depends only on n

and the accuracy of the n determinations. It is important to be careful

which meaning is being used.

4.2 Independent case.

Now consider the situation where each of the has, in addition to a +

random error, a defined pair of limits, say Aj_) , on its systematic error.

If the systematic errors are unconnected, in the sense that knowing the actual

systematic error for one of the x^ tells us nothing about the actual error for

the others, the situation can be handled by splitting the Xj_ into two groups,

based on the sign of 3f . We simply substitute Xj_+Aj^ for Xj_ if 3f > 0,

3xj_ 3xj_

and Xj_ + Aj_ for x^ if 3f < 0, and calculate the new

value of f; and then repeat, using the other error limit for each Xj_. This
12

procedure gives two values of f, whose differences from the original value

are the limits of error due to the systematics; to these, one needs to add

the appropriate multiple of the standard deviation of the ID.

4.3 Dependent case; removing correlation.

Finally, if the systematics are not "independent", the contribution from

systematic error is more complicated. For example, f(x) might include xj^g “

xii, where in reality xj^g = Y + Z and x^ = W + Z, and the systematic error

affects only Z. In terms of the x's, the treatment above would inflate one of

the x's and deflate the other by the appropriate limits for systematic error.

In terms of Y, Z, and W, however, it is obvious that the effect of systematic

error on this part of ID is negligible: if systematic error inflates xj^g, it

must inflate xj[]_ also, thus canceling out. This example shows the importance

of expressing the measurements in terms of the basic error components.

Incidentally, the same technique may also be applied when different

measurement errors are correlated because they share a common component (for

example, an error due to system setup, standards, operators, etc.). Note that

the effect of the error is not removed; the resulting correlation is removed,

thus simplifying the determination of valid LE's.

Another source of correlation is the use of calibration curves: each

determination using the curve is a function of the (randomly-determined)

parameters of the fitted curve, so that all the readings taken in an interval

between recalibrations are correlated. In some cases, there is not even a

closed-form expression for the inverse function, so it is not possible to

express these values precisely in terms of the parameters. In fact, even for

cases where the inverse curve is expressible in closed form, it does not
13

necessarily follow that the determinations even have finite variance. It is

clear that calibration curves could cause complications, for which further

work would be required. A recent report [11] on calibration goes into

more detail.

The approach outlined above will avoid many pitfalls due to correlation,

and will enable the explicit consideration of systematic error bounds. It is

still necessary, of course, to obtain these bounds; for this, a statisticallydesigned study will usually be necessary.

4.4 Implementation.

The suggested approach, in simplest terms, is to express everything in the

equation for ID in terms of the basic measurements which contribute errors,

and then to collect terms so that the effect of each error can be clearly

seen. Is this practical? Can one manage to accomplish this in a

manufacturing facility, where the operating personnel who make measurements

and do calculations are not statisticians? Perhaps so. Most facilities have

already computerized their material accounting. The incorporation of a

capability to perform the LE evaluation seems feasible. One approach will now

be outlined, by example.

The computer system is assumed to have symbol manipulation capability.

It will contain the actual numbers determined by various measuring systems,

and distinct index numbers for each. it will also contain two other

categories of information. One is a catalog of error information for the

"basic" measurements in the system, which will contain the variance of the

random component of error for that measurement and the limits (positive and

negative) of systematic error for that measurement. The other is a list of

symbolic expressions which express every other number in terms of the basic

measurements

.

Now let us see by example how this would work.
14

Consider first an "assigned value" for an in-house mass standard, labeled

(say) sl7 in the computer file. The only significance of the number sl7 is

that there were 16 other values assigned to standards before this (not

necessarily all for this standard). If there is no component of error common

to this and to other measurements -e.g., this is the only standard calibrated

against a given NBS standard, and the calibration was done in such a way that

the assigned value has a random error independent of any other determinations

and a systematic error dependent only on the NBS standard's value -then it

qualifies as a "basic measurement". It would appear in the catalog (or

rather, its index number would appear in the catalog) accompanied by values

for the random-error variance and the appropriate systematic-error limits.

Now suppose this value were used, together with a comparative weighing

sequence, to determine the weight of a product item. Further, let us suppose

that the item is the 24th product item measured, and denote its measured value

by p24. The operator would, of course, enter the measured value into the

system, together with its index number, perhaps by entering the equation "p24

= 41.235". Now for this item, this number is all that is necessary to compute

the ID. However, more is needed to compute a LE: the system needs to know

the error characteristics of this number. So the operator also needs to input

a symbolic expression to let the system know what to do with the number.

He writes something like "p24 = sl7 + d36", which expresses the relationship

between the determination p24 and the components which were used to obtain it,

namely the assigned value sl7 and a difference which was obtained in the

comparative weighings. I have labeled this difference d36, as if there were

35 other differences before it. It is, of course, the difference
15

between the average product weight and the average weight of the standard in

the sequence. Note that it qualifies as a "basic measurement" (under

reasonable assumptions), because its systematic error is zero and its random

error is independent of any other determination (as long as only one product

item was present in the difference sequence). But the computer needs to know

this. Therefore, the operator must also catalog the symbol d36, by inserting

into the system catalog this symbol, the random error variance, and the

systematic error limits (zero in this case).

Proceeding in this fashion, one can keep a real-time check on the

consistency of information entered. At the end of the accounting period,

the computer can look at the equation for ID, determine the coefficients of

the first-order expansion in terms of each variable around its measured value,

and compute the contribution to LE due to errors in each variable in turn.

This report is not the place to present a finished system, because the

contract did not fund such an effort. However, let's extend the example one

step more. Suppose that not one but three different product items are weighed

in one sequence with the in-house standard. Then the corresponding three

differences are correlated, since they all contain the same terra for the

average weight of the standard. The treatment is only slightly more

complicated, however. Instead of entering the differences as "basic

measurements", the operator enters the three averages w36, w37, and w38

corresponding to the product cylinders, and the one average w39 corresponding

to the standard, and the symbolic equations "p24 = sl7 + w36 - w39",

"p25 = sl7 + w37 - w39", and "p26 = sl7 + w38 - w39"; and he catalogs all four

of these weights as basic variables, with the appropriate random error
16

variance and with no systematic error. (Actually, there is a systematic error

in each weight, but by design this error is identical for each weight, and

cancels out.) One might instead define variables corresponding to the

systematic error, especially if one didn’t know that these errors cancel out.

The point is that it is not enough to use the same systematic error limits,

since that approach would allow for systematic error in both terms independently instead of cancelling it out.

Finally, a few brief words about two other approaches in the literature.

There are two somewhat similar programs which have been publicized recently;

NUMSAS (see [12] and references cited there) and a program used by General

Electric (Wilmington) [13]. In both, random and systematic errors are both

taken to be characterized by a variance, with the mean assumed to be zero.

The only errors considered are weighing, analytical, and sampling.

Furthermore, the amount of SNM in each batch is assumed to be expressible as

(bulk measurement) x (uranium factor) x (enrichment factor). The difference

between the two is that the former models each transaction as a true value

plus random error plus systematic error, and allows for coromon systematic

errors by simply using the same error variable for all transactions which

share that value of error; the latter stratifies the error sources, one error

type at a time, by magnitude of the error variance. Thus it seems that the

former allows for more detailed treatment of errors, while the latter shortens

the computation by combining transactions. Neither allows for absolute limits

the systematic errors; neither allows for unusual computations (like corrections based on residue analyses); and possibly, neither allows for the kind

of partial cancellation that occurs when the same isotopic fraction is used

for input as for (a large share of) output. However, these two programs

are already operational.
REFERENCES

1. Jaech, John L. (1973). Statistical Methods in Nuclear Material Control . TID-26298, US Atomic Energy Commission.

2. Shewhart, W.A. (1931). Economic Control of Quality of Manufactured

Product . Van Nostrand, New York.

3. American Society for Testing and Materials, 1976. ASTM Manual on Presentation of Data and Control Chart Analysis , ASTM STP 15D.

4. Juran, J.M. , Editor (1974). Quality Control Handbook - Third Edition . McGraw-Hill, New York.

5. Schumacher, R.B.F. (1979). Measurement Assurance Through Control Charts

33rd Ann. Tech. Conf. Trans ., pub. by Am. Soc. for Quality Control.

6. Eisenhart, Churchill (1963). Realistic Evaluation of the Precision and

Accuracy of Instrument Calibration Systems. Journal of Research of the

National Bureau of Standards-C, 67 161-187. Reprinted in Precision

Measurement and Calibration , H.H. Ku, Ed., SP300 - v. 1, US Govt.

Printing Office, Washington, DC, 1969.

7. Liggett, Walter L. (1980). Assessing Errors Related to Characteristics

of the Items Measured. Nuclear Materials Management IX .

8. Cameron, J.M. (1977). Measurement Assurance . NBSIR 77-1240, National

Bureau of Standards.

9. Belanger, Brian, Ed. (1981). Measurement Quality Control and the Use of

NBS Measurement Assurance Program (ILAP) Services . NBS Handbook (in

preparation)

.

10. ANSI/ASQC Quality Standard on Calibration Systems and Measurements , in

preparation. Appendix on systematic and random errors, control charts

and check standards.

11. Lechner, James A., Reeve, Charles P. , and Spiegelman, Clifford H. (1980)

A New Method of Assigning Uncertainty in Volume Calibration . NBSIR 80-

2151. National Bureau of Standards, Washington, DC.

12. Argentesi, Flavio, Franklin, Michael (1979). Monte Carlo simulation of

MUF distribution for application to Euratom Safeguards, pp. 677-689 in

Measurement Technology for Safeguards and Materials Control , edited by

T.R. Canada and B.S. Carpenter. NBS SP-582. National Bureau of

Standards, Washington, DC.

13. Shu, F., Watson, J., Dudding, K. and Meenan, P. (1979). The Design of a Limits-of-Error of Inventory Difference (LEID) Computation Program.

Nuclear Materials Management VIII, 39-44.
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PUBLICATION OR

REPORT NO.

2. Performing Organ. Report NoJ 3.

NBSIR 31-2219

Publication Date

FE3RUA11Y ’981

4. TITLE AND SUBTITLE

INVENTORY DIFFERENCE CALCULATIONS: PROBLEMS AND POSSIBILITIES

5. AUTHOR(S)

J. A. Lechner

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

national bureau of standards

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9.

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

J.S. Nuclear Regulatory Commission

Washington, DC 20555

10.

SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bliography or literature survey, mention it here)

The origin, development, and termination of the "error study" task funded

by the Nuclear Regulatory Commission at the National Bureau of Standards is

presented in this report.

Other reports which grew (at least partially) out of this study are listed, and related to the intent of this study.

A general approach to the calculation of Inventory Difference (ID) and its

Limit of Error (LEID) was devised and refined through visits to a selected

fuel-fabrication facility. This approach is discussed, with emphasis on the

importance of having measurements "under control" and on the possibility of

automating the computations. The concepts of "measurement process" and

"Measurement Assurance Program" are also discussed, and their importance shown.

Possible problem areas, both those observed at the studied facility and others,

are given, along with possible directions for resolution.

Finally, new approaches to the calculation of ID and LEID being developed

elsewhere are described, and their relation to the approach being considered

herein elucidated.

12.

KEY WORDS (Six to twelve entries; alphabeti cal order; capitalize only proper names; and separate key words by semicolon sj inventory difference; limit of error; material accounting; Nuclear

Regulatory Commission; systematic error.

13.

AVAILABILITY

I I Unlimited

I -^f^For Official Distribution. Do Not Release to NTIS

i ! Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

15. Price

USCOmm-OC 5043-P90