QC

/f-77 I

U.S. DEPARTMENT OF COMMERCE

Kational Technical Information Service

PB-266 238

Measurement

Assurance

Hationol Bureau of Standards, Washington, D C

Apr 77
NBSIR 77-1240

Measurement Assurance

J. M. Canneron

Institute for Basic Stan'Ja. ds

National Bureau of Stan-Jards

Washington, D.C. 20234

Aprii 1977

Final

Prepared for Office of Measurement Services

lnstft"<.'te io< Basic Standards

National Bureau of Standards

WashJngton, D.C. 20234

KATIOhML TECHNICAL
PB 266 238

N8SIR 77-1240

ifV

MEASUREMENT ASSURANCE li5Q>

.77-

J M Cameron

Institute *or Basic Standards

National Bureau of Standaids

Washington, D C. 20234

Research information Cenl-i

April 1977 «^mersDm:^, MD 20S99

Final

Prepared for Office of Measurement Services

Institute for Basic Standards

National Bureau of Standa'ds

Washington, D.C. 20234

\ L2K=ae.

U.S. DEPARTMENT OF COMMERCE. JuEnita M. Kreps, Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Acting Diractcr

REPRODUCED B» NATIONAL TECHNICAL

INFORAAATION SERVICE
U.i. Dt>'T. Or COMM

BIBLIOGRAPHIC DATA

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\. I'l m il A 1 K)\ OK Kl.l'OH 1 \0.

NBS IR 77-1240

2. ('»v'( Accosion

No.

3. Rcc ipi'.*ni *s Ac i. >.*.n)n No, i

4. 1 1 1 I t AM) SL a 1 1 n.i-; Measurement Assurance

5. fubl ii 31 ion Ddtr April 1977

6. P'. rforming Or^amzai ion ( oiiP •

J. M. Cameron

8. Performing Organ. Report No» '

9. 1'tKK.tHMlNG ORGANIZATION NAME AM) ADPRKSS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, O.C. 20234

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NBS

15. SUI PI.KMHNTARY NOThS

16. ABSTRACT (A 2 00- word or leaa tactual aummary of most significant inlotmation. U document includea » aigniticant

bibliography or literature survey, mentior\ it here.) Ths procedures by which one establishes that the uncertainty of individual

measurements is adequate to their needs have been given the title measurement

assurance. This note discusses t.^^e factors involved in achieving measurement

assurance, beginning with the base liie which serves as a standard or reference,

the determination of the uncertainty relative to this basis, and tne need for

control of the measurement process to assure the continuing validity of the

accepted process parameters.

17. KEY WORDS (si* to twe:ve entries, alphabetical order, capitalize only the lira: letter of the first key word unless « proper mime: separated by semicolons)

Measurement assurance: systematic error; uncertainty

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USCOMM-OC 29042-P74
Measurement Assurance

Introduction

A single measurement can be the basis for actions taken to maintain

our health, safety or the quality of our environment. It is important

therefore that the errcs of measurement be small enough so that the

actions taken are only negligibly affectf.'d by these errors. We

realize this necessity en a personal basis when we consider medical

measurements, or our exposure to radioactivity. In any government

regulatory action or measurement involved in legal actions it is also

obvious that the shadow of doubt surrounding the measurements should

be suitably small. But this is no less true for all other

measurefrients in science and industry and even though legal action may

rot be involved, the validity of scientific inference, the

effectiveness of process control, or the quality of production may

depend on adequate measurements [2].

Al lowable Limit s of Measurement Error

How does one achieve this condition--that the measurements are "good

enough" for their intended use? It would seem obvious that one has to

start with the need --i.e., deciding upon what is "good enough". There

are a number of cases where physiological restraints pro/ide the

definition such as in the allowable error in exposure to cobalt

radiation in cancer treatment or in the amount of pollutant entering a lake. In nuclear materials control the allowable error is a function

of the amount of material which would pose a hazard if diverted. In industrial production or commercial transactions, the error limit is

determined by a balance between the cost of better measurement and the

possible economic loss from poorer measurement.

By whatever path such requirements are arrived at, let us begin with

the assumption that the allowable error should not be outsidf; the

interval (-a, +b) relative to the quantity being measured. Our

problem is one of deciding whether the uncertainty of a single

measurement is wholly contained in an interval of that size. We

therefore need a means of assigning an uncertainty to a single

isolated measurement and, in fact, we need a perspective (i.e.,

physical and mathematical model) in which to view measurement so as tc

give operational meaning to the term "uncertainty."

Reference Base to Which Measurements Must Be Relate d

It is instructive to contemplate the possible "cross-examination" of a measurement if it were to become an important element in a legal

controversy. Two essential features emerge. First, that the

contending parties would have to agree on what (actually realizable)

measurement would be mutually acceptable. The logic of this seems unassailable--if one cannot state what measurement system v;ould be

1
accepted as "correct," then one would have no defensible way of

developing specifications or regulations involving such measurements.

Second, the scientific cross-examination by which one establishes the

"shadow of doubt" relative to this acceptable value gives one the

uncertainty to be attached to the measurement.

The consensus or generally accepted value can be given a particularly

simple meaning in dealing with measurements of such quantities as mass, volt, resistance, temperature, etc. One may require that

uncertainties be expressed relative tc the standards as maintained by

a local laboratory or, when appropriate, to the national standards as maintained by NBS. In othe'' cases, nationally accepted artifacts,

standard reference materials or in some CaS3S a particular measurement

process may constitute a reference base. One basic quality should not

be overlooked--an are operationally realizable. The confusion

engendered by introducing the te-.Tn "true value" as the correct but

unknowable value is thus avoided.

Properties of Measurement Processes

In discussing uncertainty, we must account for two characteristics of

measurement processes. First, repeated measurements of the same quantity oy the same measurement process will disagree and, second,

the limiting means of measurements by two different processes will

disagree. These observations lead to a perspective from which to view

measurement namely that the measurement be regarded as the "output" of

a process analogous to an industrial production process. In defining

the process, one must state the conditions under which a "repetition"

of the measurement would be made, analogous to defining the jonditions

of manufacture in an industrial process.

The need for this specification of the process becomes clear if one envisions the "cross-r/.t'.minatior" process. One would begin with such

questions as

Within what limits would an additional measurement by

the same instrument agree when meisuring some stable"

quantity?

Would the agreement be poorer if the time interval

between repftitions were increased?

What if different instruments from the same manu- facturer w'.'re used?

If two cr more types (or manufacturers) were used,

how much disagreement would expecteO?

To these can be added questions related to the conduct of the

measurement

.

2
What effect does geofnetry (orientation, etc.) have

on the measurement?

What about environmental conditions --temperature,

moisture, Ptc?

Is the result dependent on the procedure used?

Dc different operators show persistent differences

' in values?

Are there instrumental biases or differences due to

reference standards or calibrations?

The questions serve to define the measurement process--the process

whose "output" we seek to characterize.

The current understarding of a scientific or industrial process or of

a measurement process i'^ embodied in a physical model which explains

the interaction*^, of various factors, co'^rections for environmental or other effects, and the probability models necessary to account for the

fact that repetitions of the same event give rise to nonidentical

answers. For example, in noise level measurement one is involved with

assumptions regarding frequency response, weigh-ing networks, influence

of procedures and geometry, eind an accepted theory for making

corrections for temperature and other environmental factors. In mess

the properties of the cofiiparator (balance) the environmental effects,

and the procedure used ^11 enter into the description of the method.

One thus begins with the specification of a measurement method--the

detailed description of apparatus, procedures and conditions by which

one will measure seme quantity. Once the apparatus is assembled and

checked out, one has a measurement process whose output can be studied

to see if it conforms to the requirement for which it was created.

In industrial production one tries to produce identical items but

usually a measurement process is set up to measure a variety of

quantities and Ordinarily one does net measure the same quantity over

and over. One thus hdS the problem of sampling the output of the

measuring process so as to be able to make statements about the health

of the process relative to the needs. The needed redundancy can sometimes be achieved by remeasuring some of the items, or by

measuring a reference artifact periodically. It is essential that the

repetitions be done under the same diversity of conditions as the

regular measurements, and that the items being measured be typical of

the regular workload.

As an example, a sequence of measurements was made using two sound

level meters *o measure a sound of nominally 90 dB re 20 yPa. The

sound was generated by a loudspeaker fed broadband noise. On 16

3
different days measurements were made outdoors and over grass with the

loudspeaker in the same orientation and location relative to a building 2 rr behind the loudspeaker. The sound level meter was always

the same distance (10 m) from the loudspeaker and on a line

perpendicular to the face of the loudspeaker. Other than the grass,

the person holding the sound level meter, and the building to the rear

of the loudspeaker, there were no other reflecting surfaces or obstacles within 50 m. No measurements were made in the rain or in

winds exceeding a few km/hr. The results from these 16 repetitions

are shown in Figure 1. Typically, had duplicate measurements been

made on the same day they would have given results as shown in Figure

2.

1.5

1.0

<

> 0

-0.5

-1.0

McTER A

• MtTER B

+ 00S • •

1 !

• •O.N

1

•

1 1

•

I 1 1 •

1 5 10 15 1 5 10 15 DAY DAY

FIGURE 1: DAY-TO-DAY VARIATION IN METER READINGS.

<

1.5

1.0

B 0.5 -

0

•0.5

-1.0

1—1—

r

"T—I—

r

! I

I

1 1—I—I

1 r

J I I ' I I I I

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 DAY

Fir.liRE 2: DAV-TO-DAY VARIATION IN METER READINGS WITH MULTIPLE VALUES

PEP DAY. (COINCIDENT POINTS INDICATED BY NUMBERS.)

4
One now faces the question of how to describe the variation that

exists. Obviously there will be a different level of agreeme.it

expected between pairs on the same day, but this variation in no way

predicts that encountered from day-to-day. The issue is not so much

the statistical procedures to be U3ed--these will follow after one

defines the set of repetitions over which his conclusions muit apply.

For measuring the short term change in noise level, the .Jifference

between duplicates would apply; for any regulatory action, the day-today variation would have to be considered.

The crucial step in assessing th^ effects of random error -;s that of

defining the set of repetitions over which the measurement is to

apply. In the context of legal proceedings, one arrives at the degree

of credibility of evidence by questions designed to find out how far

the statement could be in error. In measurement, the uncertainty is

arrived at by determining the amount of disagreement expected in the

set of repetitions that would be appropriate in the context of the

intended use of the measurement.

The Concept of a Repetition of a Measurement

tvery ineasjrement has a set of conditions in which it is presumed to

be valid. At a very minimum, it is the set of repeated measurements

with the same instrument-operator procedure-configuration. (This is

the type of repetition one would envision in some process cont>'ol

oerations.) If the measurement is to be interchangeable with one made

at another location, the repetition would involve different

instrument-operator-procedure-environmc-nt configurations. (This type

of repetition is involved in producing items to satisfy a specification and of manufacturing generally.) When the measurement

is to be used for conformance to a health, safety, or environmental

regulation even different methods may be involved in a "repetition."

To evaluate a measurement process some redundancy needs to be built

into the syjtem to determine the process parameters. This redundancy

should be representative of the set of repetitions with which the

uncertainty statement is to apply. In NBS' measurements of mass, a check staraard is measured in parallel with the unknowns submitted for

calibration. One thus generates a sequence of measurements of the

same object covering an extended time period. From these results one

can answer questions relating to the agreement expected in a recal ibration and the operating characteristics of the measurement

process. In this simple case the check standard is treated exactly

the same way as the unknowns so that the properties of the process

•^elated to it are transferrable to the unknown.

The essential characteristic in estaolishing the validity of

measurement is predictabil itv that the variability remains at the same

level and that the process has not drifted of shifted abruptly from

its established values. One must build in redundancy in the form of a

5
control--the measurement of a reference quantity of known va1ue--or by

remeasuring some values by a reference method (or by an instrument

with considerably smaller uncertainty). In cases where the phenomenon

can be repeated, one can learn about random errors by remeasuring at a later time sufficiently far removed to guarantee independence.

In measuring an "unknown" one gets a single value, but one still is

faced with the need to make a statc^nent that allows for the scatter of

the results. If we had a sufficiently long record of measurements, we could set limits within which we were fairly certain that the next

measurement would lie. Such a statement should be based on a collection of independent determinations, each one similar in

character to the new observation, that is to say, so that each

observation of the collection and also the new observation can be

considered as random drawings from the same probability distribution.

These conditions will be satisfied if the collection of points is from

a sufficiently broad set of environmental and operating conditions to

allow all the random effects to which the process is subject to have a chance to exert their influence on the variability. Suitable

collections of data can be obtained by incorporating an appropriate

reference measurement into routine measurement procedures, provided

they are representative of the same variability to which the "unknown"

is subject. The statistical procedures for expressing the results

will depend on the structure of the data but they cannot overcome deficiencies in the representativeness of the values being used.

The results from the reference item provide the basis for detarmininq

the parameters of the measurement process and the properties are transferable. One is saying, in effect, if we could have measured the

"unknown" again and rgain, a sequence of values such as those for the

reference item would have heen obtained. Whether our single value is

above or below the mean we cannot say, but we are fairly certain It

would not differ by more than the bounds to the scatter of the values

on the rererance item.

The bound +R, to be used for the possible effect of random er-ors may

be as simple as +_3 (standard deviation) or may involve the combination

of many components of variance. Once the set of repetitions over which one's conclusions must apply is defined, the structure of the

random error bound can be determined.

Possible Offset of the Proces s

Once one has established that his measurement process is "in control"

from the point view of randci"n variation, there remains the question

of the possible offset of the process relative to other processes. It

is not helpful to speak of the offset from a "true value" whirh exists

only in thu mathematical or physical model of the process. The

usefulness of considering measurement in the context of legal

proceedings helps clear away some of the classical confusion about

6
errors of measurement. In a legal or regulatory setting, one is

forced to state what would be accepted as ccrrect such as coriiparison

(by a prescribed process) with national standards or with the results

from a designated laboratory or consensus of many laboratories.

The idea of defining uncertainty as the extent to which a measurement

is in doubt 'relative to a standard or process defined as correct finds

expression in the recent Nuclear Regulatory Cofimission statement [12]:

70.57(a) "Traceabil ity" means the ability to relate

ir.div LduaZ w.zcL6uAejmrU KdMilZi to national standards or nationally accepted measurement systems ... (italics added)

One could measure the offset of his process relative to the accepted

process, and make suitable correction*-, to eliminate the offset.

However, for most processes, one is content with setting bounds to the

possible offset due to factors such as:

Errors in the stjrting standards

Departures from sought -after Instrumentation (e.g.,

geometrical discrepancies)

Errors in procedures, environment, etc.

and other effects which are persistent. From properly designed

experiinents one can arrive at a limit to the possible extent of errors

from these sources in answer to the question, "If the process were set

up ab initio, how large a difference in their limiting means would be

reasonable?"

A bound to a number of factors can be determined as part of regular

measurement. For example, the effect of elevation on sound level

measurements could be evaluated by occasionally duplicating a measurement at a different height and taking an appropriate fraction

of the observed difference as the limit to the possible offset due to

any error in setting elevation. Figure 3 shows some results from

sound level mt-ters at two heights with the source at a constant

height.

c

o

51 -

mi

o

FIGURE 3: DIFFERENCE BETWEEN METER VALUES WITH CHANGE IN HEIGHT

7
Even if one has a functional relation, y = f(h), expressing the

dependence o'^ the result, y, on height, h, one still has to carry out

these measurements. The usual propagation of error approach involving

partial derivatives, etc., implies that all instruments are equally

dependent on the parameter under study, that there are .io effects

related to the factor except th i; contained in the formula. This can

be verified for a particular instrument by actually measuring its

response.

A sinilar comparison was made for a different or-'entation of the

instru.rent with respect to this signal source and is shown in Figure

4. The effect of orientation is negligible .""no one would not be

justified in adding an allowance for possible systematic error from

this source based on a theoretical calculation.

o 91p

" 90

ODIEIITAIION t 89

FIGURE 4: DIFFERENCE BETWEEN METER VALUES WITH A CHANGE IN ORIENTATION

From these measurements, one will have a set of bounds E] , E2» E3, ... to the possible offset or systematic error from the various factors.

The question as to how to rombine these to a single bound to the

possible offset depends on k.iowledge of the joint effects of tv;o or more factors and on the physical model assumed for the process. For

example, if the bounds E^ and Ej arise from independent random error

8
bounds, then it would be appropriate to combine them in quadrature,

i.e., /El + Zf. An error in t^:e model e.g., assjtr.ed linearity even when nonlinearity exists) would act as an additive error. The

properties of any combination rule can be evaluated and a selection

made of the most appropriate. The result will be an overall value, E,

for the possible offset for the limiting mean of the process from that

of the nationally accepted process.

I'pcertd vity

What can one say about the uncertainty of a measurement made by a process that may be offset from the nationally accepted process by some amount +E, and is subject to random errors bounded by +R? How

should these values be combined? To begin with, one could raTsc the

question, "If the random error could be made negligible, what

uncertainty wou^d one attach to a value from the process?" Clearly

the answer is H. The next question, "If, in addition, a random error

of size R is possible, what do we now say about the uncertainty?" The answer seems obv1ous--E and R are added to give an uncertainty of [E

- R].

But what if E were itself the result of only random errors? The answer depends or .hat one calls a repetition. By the way E is

defined. It i.* the bound for the systematic offset of the process and

although It may be arrived at from ccnsideration of random er»"ors, the

factor in.olved keeps the same (unknown) value throughout. Our

ignorance does not make It a random variable.

Consider the case of a mass standard. NBS' certificate states that

the uncertainty Is based entirely on random variation, the effects

from systematic errors being negligible. B«it unless one recalibrates,

the error due to calibration remains fixed in all measurements by the user.

The uncertainty of a measurement--*he widtli of its "shadow of doubt"

in a legal proceed1ng--must therefore be the sum of the random error

and systematic error limits.

Measuremer t Process Control

The essential feature for the validity of the uncertainty statement is

that the process remain in a state of statistical control. Once an out-of-control condition occurs, one has lost predictability and the

prpvious uncertainty statements are no longer valid.

To monitor the process some redundancy has to be built into the

system. A variety of techniques can be used to give assurance of

continued control. For example, one could periodically measure the same reference item cr artifact or one could make duplicate

measurenents on scrT.e production Items with enough delay to guarantee
independence. The American National Standards Institute Standard

N15.18 for mass measurement p0]i5 an example where this approach is

worked out in detail. But one has to verify more than just those

parameters related to random variations. One needs to build in tests

of the adequacy of the physical model by a variety of tests on the

process (e.g., by -epeating measurements under different conditions to

verify the adequacy of the corrections for such changes) as well as periodic redetermination of the bounas for systematic error. One thus

tests that the assumed model is still acceptable and that the

Parameters assigned to that model have not changed.

An excellent example of the efficacy of this approach is given by the

recent announcement [6] of discrepancies of 1 mg in the assignment of mass to aluminum kilogram standards. The mass measurement system has

long been shown to be nearly perfect for the usual standards. To

check up on the performance of the system at densities nearer to that

of most objects involved in practical meas'jremerit, an aluminum

kilogram was sent to laboratories incluoing several at high

elevation<;. It turns out that the difference between the mass of a stainless steel and an aluminum kilogram is significantly different at

different elevations. This uiiSJSDected property of the real

measurenient 'Lystem is now the subject of considerable study.

All measurements have some form of measurement assurance program

associated with them although, as with qualify control, we usually

reserve the term for a formal progr=im. In a formal program one treats

the whole process--beqinning with a study of the need, the development

of a measuring process and a procedure for determining and monitoring

Its pcfgrmance, and an evaluation of the effectiveness of the whole

effort. One needs a criterion of success to be able to determine

whether more of one'* current measurement activity or perhaps some Alternative would contribute nicst to the overall program, and this is

not necessarily provided by the smallness of the uncertainty for a measurement.

For example, when the requirement is for matched sets (e.g,, ball

bearings) or mated assembly parts, then it is usually cheaper and more

accurate to sort into finely divided classes and match for correctness

of fit rather than perform direct measurement of each part.

When the measurement requirements are stated in terms of the needs of

the system, (number of correctly matching parts, number of correctly

measured dor.imeters, etc.) one can measure success of the measurement

effort In terms of closeness to meeting those goals. Measurement

efficiency is thus judged in term? of the output of the organization

jather than by the count of che number of significant digits. Also,

one needs this measure of performance of the measurement effort to oe able !.o identify those areas which need improvement.

10
Examples of Measurement Assurance Programs in NBS Measurements

Two easily described measurement assurance programs are those in mass

and length. In routine calibration, a check standard is included with

each set of weigh'ngs and process control is maintained by monitoring

the value obtained for the cher.k sta-idard and of the random error ^rom

the least squares analysis [8, 9]. Control charts have been

maintained since 1963. In the calibration of gage blocks, similar

process control has been maintained since 1972 on both the

interferometric process by which the assignment of length to the NBS

master gage blocks is done and on the comparator process by which

length values are transferred to customer gage blocks. [1, 7]

Similar programs are in effect in all divisions, but not all

quantities involved in calibration have a formal program worthy of the

name, measurement assurance.

Examples of Measurement Assurance Programs At Other Laboratories

Only two examples of measurement assurance programs at other

laboratories have ever been reported. One at Autonetics [3] in length

and one at Mounds Laboratory in mass. Once the mass measurement

system for UFg is underway as part of the Safeguards program, NBS will

be able to document the efficacy of the approach in practical

measurement.

The N3S Measure-Tient Assurance Programs Offered As A Part Of

Our Calibration Service

Measurement Assurance Programs are listed as a calibration service in

mass, volt, resistence, capacitance, voltage ratio, watthour meters,

platinum resistance thermometry, and laser power. These are designed

to measure the offset of measurement processes for the calibration of

standards by other standards laboratories. These are applicable only

to those laboratories who maintain and calibrate standards in the same manner as NBS. [See 11, 5, 13.]

These procedures enable a laboratory to determine the offset between

its process of calibrating standards and that of NBS.

Need For Measurement Assurance Program For Practical Measurement

The UFg cylinder program for Safeguards [lo] is an example of NBS'

service in providing a direct method for measuring the offset of

practical measurement processes from that accepted as correct, namely

mass measurement by NBS. Investigation of the need and possible

mechanisms or artifacts for monitoring the offsat of practical

measurements in quantities such as voltage, resistance, le- ih,

radioactivity is underway. (For examples of the application of these

principles to sound level meters, see [5].)

11
In personnel dosimetry procedures arc being worked out [14] to monitor

the output of firms providing such services. In this case, a table of

allowable limits of uncertainty are based on physiological

considerations. Process oararneters are to be determined by an initial

study. Routine monitoring will be used to confirm that the process is

"in control" at those levels, otherwise the parameters are redetermined ab initio. These "consistency" or "in control" criteria

replace the usual one-timi2 round robin approach. The amount of effort

needed to establish this predictability is a function of the risk and

costs of wrong decisions.

In industrial measurement we could ask

If some critical measurements on the production line were repeated would the two measurements agree?

How much bad material is passed, or good material rejected

because of errors in measurement?

To those who have not properly answered these questions, dollar

savings and improved product quality are possible without redesign or changes in production procedures.

Is our faith in instruments justified? Implicit fdith in the

correctness of instruments means that product variability (as

determined by these instruments) 1s attributed to variability in

cofiiponents, raw materials or even poor design. One wonders how many

times this has led to expensive changes in production procedure's

without apparent improvement because the variability actually arose in

the measurements themselves.

How often has the installation and methods of use degraded the output

of an instrument capable of much more accuracy than is required when

handled properly? Without some surveillance of the actual

measurements, one would ntver know.

One wonders how often a product is redesigned because measurement

error has led to the decision that the product does not conform to

specifications.

The result of this ""ook at measurement is measurement assurance--the

quality control of measurement. If adequate control exists, then one

can 'lOok elsewhere for improvements in the product line. If it does

not, then one has the possibility of savings without changing

production procedures.

Some fern of redundancy must be built '•nto the process to answer these

questions.

12
References

[I] John S. . Beers, "A Gage Block Measurement Process Using Single

Wavelength Interferometrv," MBS Monograph 152, December 1975

[2] J. M. Cameron, "Measurement Assurance," Review of Standards and

Specifications Section of Journal of Quality Technology, Vol.. 8,

No. 1, pp. 53-55, January 19/6

[3] J. A. Hall, "Dimensional Measurement Assurance Programs,"

Autonetics Report No. X73-1 146/031 , presentation at 1973

Conference of the National Conferance of Standards Laboratories

at the National Bureau of Standards, Gaithersburg, Md., November

1973

[4] Edward 8. Magrab, "Environmental Effects on Microphones and Type

II Sound Level Meters," NBS Technical Note 931, October 1976

[5] N. Michael Oldham, "A Measurement Assurance Program for Electric

Energy," NBS Technical Note 930, September 1976

[6] P. E. Pontius, "Mass Measurement: A Study of Anomalies," Science

190 , pp. 379-380, October 1975

[7] P. E. Pontius, "Measurement Assurance Program--A Case Study:

Length Msasurements. Part i. Long Gage Blocks (5 in. to 20

in.)," NBS Monograph 149, November 1975

[8] P. E. Pontius, "Measuremeiit Philosophy of the Pilot Program for

Mass Calibration," NBS Technical Note 288, May 1966

[9] P. E. Pontius, "Notes on the Fundamentals of Measurement and

Measurement as a Production Process," NBSIR 74-545, September

1974

[10] "Mass Calibration Techniques for Nuclear Material Control,"

Nl 5. 18-1975, American National Standards Institute, New York, New

York

[II] "Measurement Analysis Program in Mass," NBS Technical News

Bulletin, September 1970

[12] "Measurement Control Program for Special Nuclear Materials

Control and Accounting (10 CFR 70.57)," Federal Register , Vol.

40, No. 155, pp. 33651-33653. August 1975

[13] 'New Calibration Service for the Volt," NBS Technical News

Bulletin, pp. 46-47, February 197i

[14] "Proposed Standard--Criteria for Testing Personnel -Dosimatry

Performance," Health-Physics Society, HPSSC WG/15, October 1976

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