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A1 11 00989979

Croarkin, Carroll/Measurement assurance QC100 .U556 V163;1979 C.I NBS-PUB-C 1979

1> J

NBS MONOGRAPH 163

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards

Measurement Assurance

for Gage Blocks

—QC—

100

.U556

NO. 163

1979
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress March 3, 1901. The

Bureau's overall goal is to strengthen and advance the Nation's science and technology and

facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in

trade, and (4) technical services to promote public safety. The Bureau's technical work is performed by the National Measurement Laboratory, the National Engineering Laboratory,

and the Institute for Computer Sciences and Technology.

THE NATIONAL MEASUREMENT LABORATORY provides the national system of

physical and chemical and materials measurement; coordinates the system with measurement

systems of other nations and furnishes essential services leading to accurate and uniform

physical and chemical measurement throughout the Nation's scientific community, industry,

and commerce; conducts materials research leading to improved methods of measurement,

standards, and data on the properties of materials needed by industry, commerce, educational

institutions, and Government; provides advisory and research services to other Government

Agencies; develops, produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

Absolute Physical Quantities' — Radiation Research — Thermodynamics and

Molecular Science — Analytical Chemistry — Materials Science.

THE NATIONAL ENGINEERING LABORATORY provides technology and technical

services to users in the public and private sectors to address national needs and to solve

national problems in the public interest; conducts research in engineering and appHed science

in support of objectives in these efforts; builds and maintains competence in the necessary

disciplines required to carry out this research and technical service; develops engineering data

and measurement capabilities; provides engineering measurement traceability services; develops test methods and proposes engineering standards and code changes; develops and

proposes new engineering practices; and develops and improves mechanisms to transfer

results of its research to the utlimate user. The Laboratory consists of the following centers:

Applied Mathematics — Electronics and Electrical Engineering^ — Mechanical

Engineering and Process Technology' — Building Technology — Fire Research —

Consumer Product Technology — Field Methods.

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts

research and provides scientific and technical services to aid Federal Agencies in the selection,

acquisition, application, and use of computer technology to improve effectiveness and

economy in Government operations in accordance with Public Law 89-306 (40 U.S.C. 759),

relevant Executive Orders, and other directives; carries out this mission by managing the

Federal Information Processing Standards Program, developing Federal ADP standards

guidelines, and managing Federal participation in ADP voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal Agencies; and

provides the technical foundation for computer-related policies of the Federal Government.

The Institute consists of the following divisions:

Systems and Software — Computer Systems Engineering — Information Technology.

'Headquarters and Laboratories at Gaithersburg, Maryland, unless otherwise noted; mailing address Washington, D.C. 20234. Some divisions within the center are located at Boulder, Colorado, 80303.

The National Bureau of Standards was reorganized, effective April 9, 1978.
Measurement Assurance for

Gage Blocks ^

Carroll Croarkin

Statistical Engineering Division

Center for Applied Mathematics

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

John Beers and Clyde Tucker

Mechanical Processes Division

Center for Mechanical Engineering and

Process Technology

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

With an Introduction by

J. M. Cameron

Retired

National Bureau of Standards

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

Jordan J. Baruch, Assistant Secretary for Science and Technology

S NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued February 1979
Library of Congress Catalog Card Number 78—600162

National Bureau of Standards Monograph 163

Nat. Bur. Stand. (U.S.), Mono. 163, 78 pages (Feb. 1979)

CODEN: NBSMA6

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1979

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Stock No. 003-003-02023-1 Price $2.50

(Add 25 percent additional for other than U.S. mailing)
TABLE OF CONTENTS

PAGE

1. Introduction

1.1 Statement of the Problem 1 1.2 The Measurement Process 3

2. Who Should Participate in an NBS-Sponsored Gage Block

Measurement Assurance Program? 10

3. Procedures for Gage Block Measurement Assurance 11

3.1 General --Choosing an Appropriate Program 11

3.2 One Set of Standards, Single Measurements on

Unknowns, One Set of Control Blocks 13

Figure l--Worksheet 3.2.2 (Process Parameters:

Accepted Values of Controls and Standard 17

Deviations)

Figure 2--Worksheet 3.2.3 (Observed Value of

Control Compared to Accepted Value of 18

Control

)

Figure 3--Worksheet 3.2.4 (Accepted Values of

Process Parameters Compared to New

Values for Process Parameters, k Blocks 20

in a Group)

Figure 4—Worksheet 3.2.5 (Values of NBS Blocks

From Laboratory Process Compared to

Values Assigned at NBS, k Blocks in a 22

Group)

Figure 5--Report of Test 24

3.3 Test Set Measured Against Two Standard Sets:

Control on the Difference Between Standards 27

Figure 6--Worksheet 3.3.2 (Process Parameters:

Accepted Values of the Control and

Group Standard Deviation, k Blocks in 31

a Group)

Figure 7--Worksheet 3.3.3 (Observed Values of

Control and Standard Deviations Compared

to Accepted Values, k Blocks in a Group) 32

Figure 8--Worksheet 3.3.4 (New Values of Process

Parameters Compared to Accepted Values, 34

k Blocks in a Group)

Figure 9--Worksheet 3.3.5 (Values of NBS Blocks

From Laboratory Process Compared to 36

Values Assigned by NBS, k Blocks in a Group)

Figure lO-Report of Test 38

111
3.4 Two Test Sets and Two Standard Sets in a Drift Eliminating Design Involving Eight

Observations, Difference Between Standards 41

as Control

Figure ll--Worksheet 3.4.2 (Process Parameters:

Accepted Values of Control, Within

and Total Standard Deviations, k 45

Blocks in a Group)

Figure 1 2--Worksheet 3.4.3 (Observed Value for

Control and Within Standard Deviation 46

Compared to Accepted Value)

Figure 13--Worksheet 3.4.4 (New Values for Process

Parameters Compared to Accepted Values) 48

Figure 14—Worksheet 3.4.5 (Values of NBS Blocks

From Laboratory Process Compared to 50

Values Assigned by NBS)

Figure 15--Report of Test 52

4. Operating a Measurement Assurance Program 55

4.1 Equipment and Environment 55

Figure 16--Elements of a Comparator 56

Figure 17--Errors Resulting From Comparator 56

Design

4.2 Measurement Techniques 58

4.3 Computation and Analysis of Data 60

4.4 Control Charts 60

4.5 Access to the National Standards 60

4.6 Procedures for Correcting Out-of-Control 60

Conditions

Figure 18--0bserved Difference Between 1-Inch

Gage Blocks Used as Check Standard 61

Figure 19--0bserved Within Standard Deviations

on 1-Inch Check Standard 61

Figure 20--0bserved Differences Between 6-Inch

Gage Blocks Used as Check Standard 61

Figure 21 --Observed Within Standard Deviations

on 5-Inch Check Standard 61

4.7 Upgrading the Process 62

Table I--F Values, Upper 1% Probability Level 63

References • 64

Appendix A--Trend Eliminating Design 65

Appendix B--Interferometric Gage Block Comparator 69
Figure B. 1 --Observed Value of Control Compared

to Accepted Value of Control 73

Figure B.2--Report of Test 74

V

MEASUREMENT ASSURANCE FOR GAGE BLOCKS

by

M. Carroll Croarkin

and

John Beers and Clyde Tucker

With an Introduction by

J. M. Cameron

This monograph is intended for those who need to know on a continuing

basis the uncertainty of their gage block calibration procedure. A

general discussion of the philosophy of measurement assurance is given

first. Then three levels of measurement assurance programs are

outlined showing how control over the measurement process can be

maintained and how the offset (or systematic error) from the unit of

length maintained by the National Bureau of Standards can be made

negl igible.

Key Words: Calibration; gage blocks; length; measurement assurance;

measurement process control; systematic error; uncertainty

1. What is a Measurement Assurance Program?

(An Introduction by J. M. Cameron)

1.1 Statement of the Problem

Measurement assurance is the name given to the procedures by which one

ascertains that individual measurements are "good enough" for their

intended purpose. Our focus has to be on individual measurements

because a single measurement can be the basis for actions taken to

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

important that the errors of measurement be small enough so that the

actions taken are only negligibly affected by these errors. We

realize this necessity on 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

measurements in science and industry, and even though legal action may

1
not be involved, the validity of scientific inference, the

effectiveness of process control, or the quality of production may

depend on adequate measurements.

The measurement assurance programs described in this monograph relate

specifically to measurement processes in which the length of a gage

block is assigned relative to one or more reference standards.

Calibration of customer's gage blocks by the National Bureau of

Standards is an example of such a process as are calibrations done by

other laboratories for the public or for production quality control

within their own organization. The objective of these measurement

assurance programs is to demonstrate on a continuing basis that the

uncertainty of each measurement is suitably small relative to its end

use.

The term "good enough" needs to be given operational meaning and this

can only be done after one has a framework for describing the quality

of measurements. To do this we will need to know

. the allowable limits of measurement error

. the reference base to which the measurements must be related

. the properties of the measurement process (extent of random

variation, possible offset from the reference base)

. a means for assigning uncertainty to a measurement.

1.1.1 Allowable Limits of Measurement Error

How does one achieve the 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 the limits to be used arise quite

naturally. For example, physiological restraints provide the

definition for 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.

In gage block calibration, the limits are often given by an announced

"accuracy" claim or result from an hierarchal approach in which

smaller accuracies are required of "higher level" laboratories.

Ideally the limits would be based on actual need in production or

qual ity control

.

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

the assumption that the allowable error should not be outside the

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

2
problem is one of deciding whether the uncertainty of a single

measurement is wholly contained in an interval of that size.

1.1.2 Reference Base to Which Measurements Must Be Related

It is instructive to contemplate what might happen if a measurement

were to become an important element in a legal controversy. Two

essential features should arise. 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 would be accepted as "correct,"

then one would have no defensible way of developing specifications or

regulations involving such measurements. Second, the uncertainty to

be attached to the measurement would be established by a form of

"cross-examination" by which one would determine the "shadow of doubt"

relative to this acceptable value.

The consensus or generally accepted value can be given a particularly

simple meaning in dealing with measurements of such quantities as

length, mass, voltage, resistance, temperature, etc. One may require

that uncertainties be expressed relative to the standards as

maintained by a local laboratory or, when appropriate, to the national

standards as maintained by NBS. In other cases, nationally accepted

artifacts, standard reference materials or in some cases a particular

measurement process may constitute a reference base. One basic

quality of all these examples should not be overlool<ed--al 1 are

operationally realizable. The confusion engendered by introducing the

term "true value" as the correct but unknowable value is thus avoided.

1.2 The Measurement Process

1.2.1 Properties of Measurement Processes

In discussing uncertainty, we must account for two characteristics of

measurement processes. First, repeated measurements of the same

quantity by the same measurement process will disagree and, second,

the limiting means of measurements by two different processes will

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

1 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 conditions of manufacture in an industrial process.

The need for this specification of the process becomes clear if one

envisions the "cross-examination" process. One would begin with such

questions as

Within what limits would an additional measurement by

the same instrument agree?

3
Would the agreement be poorer if the time interval

between repetitions were increased?

If two or more types (or manufacturers) of comparators were used,

how much disagreement would be expected?

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

measurement.

What about environmental conditions--temperature,

moisture, etc.?

Is the result dependent on the procedure used?

Do different operators show persistent differences

in values?

Are there instrumental biases or differences due to

reference standards or calibrations?

The questions force one to define the measurement process--the process

whose "output" we seek to characterize. Once the measurement method

is agreed upon and set into operation, one then has 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.

1.2.2 The Measurement Method

The current understanding of a scientific or industrial process or of

a measurement process is embodied in a physical model which explains

the interactions of various factors, corrections 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.

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

detailed description of apparatus, procedures and conditions by which

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

checked out, a measurement process exists whose output can be studied

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

1.2.3 Random Variation

One is accustomed to random variation as it occurs in industrial

production in an attempt to produce identical items. In measurement.

4
each item to be measured is different and unless some redundancy is

built in there will be no repetitions from which to disentangle the

random error from differences between items.

A number of methods can be used to achieve the needed redundancy.

. Some measurements on test items could be repeated after a few minutes.

. Some measurements on test items could be repeated after one

or more days.

. A reference object could be remeasured periodically.

. A check standard could be measured in parallel with the test

i tem

.

The crucial step in assessing the effects of random error is 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 for the intended use of the

measurement. If repetitions are always done within a few minutes of

each other, one would expect much better agreement than if they were

run days or weeks apart. The short term variability is appropriate

for process control purposes, but the uncertainty attached to the

value for a test item must allow the day-to-day variation to be

responsive to such questions as "Within what limits would one expect

the value to lie if the item were re-submitted at a later date?"

1.2.4 The Concept of Measurement Repetition

Every measurement 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 expected in some process control operations.)

If the measurement is to be interchangeable with one made at another

location, the repetition would involve different instrument-operatorprocedure-environment configurations. (This type of repetition occurs

in producing items to satisfy a specification and in manufacturing

generally.) In gage block calibration, the "repetition" involves at

least the level of variability which would be encountered if the value

were determined at intervals of one week or longer.

To evaluate a measurement process some redundancy needs to be built

into the system to determine the process parameters. This redundancy

should be representative of the set of repetitions to which the

uncertainty statement is to apply. In the NBS gage block measurement

program, a check standard is measured along with the unknowns

submitted for calibration. One thus generates a sequence of

measurements of the same object covering an extended time period.

5
From these results one can answer questions about 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 related to it are transferrable to the unknown.

1.2.5 Building Redundancy Into the System

The essential characteristic needed to establish the validity of

measurement is predictability of the process, i.e., that the

variability remains at the same level and that the process is not

drifting or shifting abruptly from its established values. The

evidence of predictability must come from redundant measurement of

"control" or reference blocks of known value which have properties

similar to those of the regular workload in order to verify this

condition.

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

faced with the need to make a statement that allows for the

anticipated scatter of the results. If we had a sufficiently long

record of measurements, we could predict the 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 data collections can be obtained by

incorporating an appropriate reference measurement into routine

measurement procedures, provided such measurements 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 used.

Results from the control item provide the basis for determining the

parameters of the measurement process and verifying that the

properties are transferable to measurements on test items. One is

saying, in effect, if we could have measured the "unknown" again and

again, a sequence of values such as those for the control item would

have been 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 control item.

The bound +R, to be used for the possible effect of random errors may

be as simple as +3 standard deviations or may involve the combination

of many components of variance. Once the set of repetitions over

6
which one's conclusions must apply is defined, the structure of the

random error bound can be determined.

The question of how much redundancy is enough is difficult to answer.

The observer could measure a "control" block after each 10 test

blocks, he could measure every block against two standards or he could

do an "experiment" (as NBS does) in which both a control is measured

and a check on process variability is also made. Each of these

approaches have computable operating characteristics relative to

various forms which lack of process control could take--all give a high degree of protection against large changes in comparator scaling

whereas a single "bad" value (e.g., due to a burr) on a test block

would go unnoticed. If one knew which departures from ideal

conditions were most likely to occur, he could design a procedure to

protect against such occurrances.

1.2.6 Possible Offset of the Process

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

from the point of view of random 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" which exists

only in the mathematical or physical model of the process.

Considering measurement in the context of legal proceedings helps

clear away some of the classical confusion about errors of

measurement. In a legal or regulatory setting, one is forced to state

what would be accepted as a correct answer such as one which agrees in

a comparison (by a prescribed process) with national standards or with

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 Commission statement [14]:

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

^ndiv-idLiaZ rmcu>uAm2,nt n.zA>uJiUi to national standards or

nationally accepted measurement systems ... (italics added)

In gage block measurement, the use of standards whose uncertainty is

given relative to the length standards maintained by NBS eliminates

the considerable effort required to document the uncertainty of

measurements using interferometry alone. One still is confronted with

the problem of setting bounds to the possible offset due to factors

such as:

Errors in the starting standards

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

geometrical discrepancies)

7
Errors in procedures, environment, etc.

and other effects which are persistent. From properly designed

experiments 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 InJjUjo, how large a difference in the limiting means of the two

processes would be reasonable?"

A bound to the possible offset from many of the important factors can

be determined as part of a regular measurement process by running some

of the controls under different conditions, operators, instruments and

analyzing the results to see if significant differences appear.

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

The question as to how to combine these into a single bound to the

possible offset depends on knowledge of the joint effects of two or

more factors and on the physical model assumed for the process. For

example, if the bounds E] and E2 arise from independent random error

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

i.e., /Ef + E2. An error in the model (e.g., assumed linearity even

when nonlinearity exists) would act as an additive error. The

properties of proposed combination rules 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.

1.2.7 Uncertainty

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 raise the

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

uncertainty would one attach to a value from the process?" Clearly

the answer is +E. 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 obvious--E and R are added to give an uncertainty of +[^

+ R].

But what if E were itself the result of only random errors? The

answer depends on what one calls a repetition. By the way E is

defined, it is the bound for the systematic offset of the process and

although it may be arrived at from consideration of random errors, the

factor involved keeps the same (unknown) value throughout. Our

ignorance does not make it a random variable in our process.

The uncertainty of a measurement--the width of its "shadow of doubt"

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

and systematic error limits.

8
1.2.8 Measurement Process Control

The essential requirement 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 previous uncertainty statements are no longer

valid.* The following sections of this monograph present techniques

for monitoring the gage block measurement processes to assure that the

process parameters have not changed. But one has to verify more than

just those parameters related to random variations and possible offset

from national values. One needs to build in tests of the adequacy of

the physical model by a variety of tests on the process (e.g., by

repeating measurements under different conditions to verify the

adequacy of the corrections for such changes) as well as periodic

redetermination of the bounds for systematic error. One thus tests

that the assumed model is still acceptable and that the parameters

assigned to that model have not changed.

When measurement requirements are stated in terms of system needs

(number of correctly matching parts, number of correctly measured

dosimeters, etc.), one can measure success of the measurement effort

in terms of closeness to meeting those goals. Measurement efficiency

is thus judged in terms of the output of the organization rather than

by counting the number of significant digits. Also, one needs this

measure of performance of the measurement effort to be able to

identify those areas which need improvement. In gage block

calibration, one ordinarily does not see the use to which the blocks

are subjected and has only the requested uncertainty as a goal.

All measurements have some form of measurement assurance program

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

reserve the term for a formal program. In a formal program one treats

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

of a measuring process and a procedure for determining and monitoring

its performance, and an evaluation of the effectiveness of the whole

effort. A criterion of success is needed to determine whether more

effort should be put into one's current measurement activity or

whether perhaps some alternative would contribute more to the overall

program. An appropriate criterion is not necessarily provided by the

smallness of the uncertainty for a measurement.

*The practice of using the values of the statistical parameters from a single set of data in an uncertainty statement (e.g., confidence

intervals based on the Student-t distribution) is not defendable

unless there is a reasonable amount of evidence that the observed

values can be regarded as random variables from the assumed stable

probability distribution. The apparent exactness of these methods

tends to obscure the fact that their validity is critically dependent

on the need for randomness and independence of the measurements,

qualities not easily demonstrated for a single isolated set of

measurements.

9
2. who Should Participate in an NBS-Sponsored Gage Block Measurement

Assurance Program?

Measurement assurance allows participating laboratories who maintain a continuous and documented check on their calibration process to relate

their proccess to the national unit of length maintained by NBS.

Laboratories who will benefit from this NBS service fall into two

groups:

(1) Industrial laboratories who must prove the dimensional precision

of their manufacturing process and its relationship to the length

unit

(2) Laboratories who perform calibrations for customers and who are

asked to prove that they provide an acceptable level of

calibration accuracy.

It is possible that, where calibrations for customers are provided,

two calibration levels could be offered; one employing the widely

used "size check" (usually a single comparison which is adequate for

many purposes) and the other employing the more involved procedures

described in this monograph with documented uncertainty statements.

Many laboratories do not need direct intercomparison with NBS as part

of their measurement assurance program either because their accuracy

requirements are not stringent or because only "in-house" consistency

is required. Instead, a modest program of intercomparisons involving

their reference set and a working set will give evidence of control.

See section 3.2 for a method of accomplishing this goal.

In making a decision about participating in the NBS program, the

potential benefits should be weighed against the investment of time

and effort necessary to make it effective.

10
3. Procedures for Gage Block Measurement Assurance

3.1 General

3.1.1 Choosing an Appropriate Program

Three different levels (options) of measurement assurance are

described in the following sections. All three provide a format for

the calibration of gage blocks and "controls" to assure the continued

validity of uncertainty statements.

Briefly the three options are as follows: Option 1 (Section 3.2)

describes the simplest technique in which a single measurement is made

on each block, and an occasional control block is introduced into the

calibration process. Option 2 (Section 3.3) describes a procedure in

which duplicate measurements are made on each block by comparing each

block to two standard blocks. Option 3 (Section 3.4) describes a program for calibrating two test blocks against two standard blocks by

a drift eliminating design. The three options contain many common

elements, and the sections are written to be self -complete.

The choice of a program for a particular laboratory depends on a number of factors including (1) the availability of gage block sets,

equipment, and trained personnel; (2) the availability of time to

spend on the program, and (3) the accuracy requirements for the

calibrations. Options 1, 2, and 3 require progressively greater

investments of time and effort, and generally yield progressively

better process control. It may be advantageous to start with option 1 and upgrade to option 2 or 3 if necessitated by inadequate results.

It is important in selecting the appropriate level to keep in mind

that the program must become a regular part of the calibration

procedure.

3.1.2 Methodology

The basic method is to incorporate the measurements of the "controls"

into the regular working routine of the laboratory on a continuing

basis so that the properties of the measurement process which are

ascribable to this set of blocks can be attributed to the entire

calibration procedure.

Included in each option are procedures for (1) establishing process

parameters; (2) routine monitoring to assure process control; (3)

updating process parameters; and (4) maintaining the tie of the

process to national standards. A worksheet is provided for each of

the foregoing procedures showing the necessary calculations and

statistical tests.

Instead of a detailed explanation of the methods of process control,

the worksheets are intended to guide the user through the various

11
procedures. Sample data and calculations are given in such a way that

one can follow the example through the four steps outlined above that

are the essence of a measurement assurance program.

3.1.3 Statistical Surveillance

Continuous monitoring of the process is necessary to insure that

predictions based on the accepted values of the process parameters are

valid and that the process remains in a state of control. Statistical

surveillance is maintained on the accepted values for the controls and

the associated random error components by the following means. After

each calibration run, the observed value of the control block(s) is

checked against its accepted value by comparing a test statistic, "t"

to the critical value 3.0. This test corresponds to the .003

probability level for a normal distribution; i.e., assuming the

observations come from a normal distribution with known variance. For

observations from a normal distribution with unknown variance, the

test statistic is distributed as Student's t. Similarly the random

error components are checked against their accepted values using a test statistic based on the F distribution. Critical values of F

which correspond to the .01 probability level are given in Table I (page 63). See reference [9] for a discussion of the applications of

the t and F distributions in metrology.

If the criteria for both of these tests are satisfied, the process is

regarded as being in control and the calibrated values for the unknown

blocks and associated uncertainties are accepted as valid. Otherwise,

some remedial action is indicated. Usually the calibration is

repeated before more extensive steps are taken, but this is discussed

in the appropriate sections.

3.1.4 Special Procedures for Interferometry and Long Gage Blocks

(Over 4 Inches)

Procedures described in this monograph apply primarily to calibrations

done with conventional electro-mechanical gage block comparators.

Fringe counting interferometric gage block comparators are a special

case because they can be used either as comparators in conjunction

with standard blocks or they can be used to measure test blocks

directly without reference to standard blocks. When one of these

instruments is used as a comparator, all procedures in the body of

this monograph apply. This is true even where only a few standard

blocks are used to cover the full size range and the length

differences between standard and test blocks are consequently large.

When fringe counting interferometry is used to measure test blocks

directly, procedures are somewhat different as described in Appendix

B. The Appendix B procedures are also valid for static interferometry

where test blocks are wrung to optical flats and measured in a Kosters

type or a Fizeau type gage block interferometer.

12
The procedures outlined are intended for use primarily on short blocks

(blocks up to 4 inches). The suggestions for measurement procedures,

handling techniques and environmental controls which are covered in

Section 4 deal with both short and long blocks. However, because long

blocks are sometimes subject to rapid secular changes, the statistical

analyses may have to be modified to allow for this condition. See

reference [10] for a discussion of analysis of long block data.

3 . 2 One Set of Standards , Single Measurements on Unknowns , One

Set of Control Blocks

3.2.1 The Measurement Process

In the simplest and perhaps most common procedure for gage block

calibration the value for an unknown is assigned by measuring the

difference in length between a standard block and the unknown using a comparator (which may be either a mechanical comparator or a fringe

counting interferometric comparator). In some processes duplicate

measurements are made as a check on gross errors. Unless the second

set of measurements are separated far enough in time to be

statistically independent, the differences should not be used in

setting bounds for the process random error.

The random errors associated with the process are of two kinds; those

arising from repetitions in the short term (a few minutes) and those

involving long term differences (day-to-day, week-to-week, etc.) The

random error appropriate for the calibration process is that

associated with the repeated measurement of a control block over a sufficiently long time period to insure that all factors affecting

variability have a chance to exert their influence.

Because of temperature effects, the amount of variation in the

measurement process is usually length dependent. For this reason and

for convenience of working group size, the usual set of blocks (80 or

so blocks in the 0.050 to 4 in. range) should be treated as a number

of subsets of up to 20 blocks each. At NBS the six groups listed

below are used:

Nominal Length Approximate

Group (Inches) No. of

I 0.050 to 0.09375 4

II 0.100 to 0.107 20

III 0.108 to 0.126 20

IV 0.127 to 0.146 20

V 0.147 to 0.500 15

VI 0.550 to 4.000 13

Redundancy is introduced into the system by repeatedly including the

control block in the measurement procedure. The control blocks should

13
be treated exactly as test blocks measuring them in proper size

sequence along with the test set. The control set should be made up

of at least one block from each group with more blocks of the larger

sizes. A suggested set of control blocks is:

No. of

Nominal Size Control

Group (Inches) K

I 0.05 1 II 0.1 1 III 0.125 1 IV 0.140 1 V 0.25, 0.50 2

VI 0.75. 1.0, 2.0, 4.0 4

One would expect the same variability for all control blocks in a group so that the standard deviations* computed for each of the

control blocks in a group could be combined into one overall standard

deviation for the group. If S], . . . S|^ are the standard deviations

for the k blocks in a group with degrees of freedom v] , . . . respectively, then

/v,s? + ... + V. s?

s.d. (group) = / -LJ

^

/ V-j + . . . +

3.2.2 Establishing Process Parameters

To determine initial accepted values** for the controls and for the

random error component, all the blocks in the control set should be

measured by the usual process, say 6 times, with a few days between

repetitions.

*The standard deviation of a single observation is given by

where

the r-j is the difference between each observation and the average of n observations. The quantity n-1 is called the degrees of freedom

associated with s.

**The term "value" for a gage block means the deviation from nominal

size (measured length minus nominal length) at 20* C.

14
From that initial data, an average and a standard deviation should be

computed for each control block. The accepted values for the control

and for the random error component will be the average value for the

block and the standard deviation for the group as indicated above.

These will be the starting accepted values for the process. A portion

of a typical worksheet showing starting values for two blocks in a control set is given in Figure 1. Examples given in the following

sections are based on these two blocks and their parameters. All data

in the examples is hypothetical and is intended only to explain the

methodology.

3.2.3 Maintaining Process Control

After the process parameters have been established, control is

maintained by checking the control value after each calibration run

against the accepted control value.

A sample worksheet (see Figure 2) details how this is done and shows

the appropriate statistical test for determining whether or not the

process is in control.

3.2.4 Updating Process Parameters

As information collects on the regularly used control blocks, the

accepted values for these blocks should be updated. If either of the

process parameters has changed from its starting value as indicated by

the t-test or F-test, a new process parameter must be computed based

only on the current data. Otherwise the process will be considered to

be continuous, and the data will be combined. A sample worksheet

showing how this is done is given in Figure 3.

The frequency of updating will depend on the workload but should be

done initially after 5 or 10 values and then at intervals dictated by

convenience (e.g., every 6 months or a year).

3.2.5 Relationship to National Standards

It is important to know if a process produces values which are

consistent with the national standards as maintained by NBS. A

convenient method for testing the whole system is afforded by using

two calibrated sets loaned to the laboratory by NBS. If each of these

sets is measured as a test set in the calibration procedure, one will

have the independent check needed to test for consistency with NBS.

The data should be taken by the regular calibration process. Two

complete calibrations should be done a day or two apart.

Laboratories with the capability of writing their own documented test

report based on their measurements of the NBS sets are encouraged to

do so. In this case NBS will provide the two calibrated sets of

blocks, their current assigned values and associated uncertainties.

15
The table in Figure 4 summarizes the analysis of the data and shows

whether or not there is a significant offset from the NBS process. If

the offset is significant, the values for the laboratory reference

standards and their associated uncertainties should be corrected as

shown in the suggested "Report of Test" form in Figure 5. In effect

this is a method for each laboratory to calibrate its own standards.

3.2.6 Uncertainty

The uncertainty, +U, associated with any test block calibrated by this

process, assuming the process is in control, is given by

U = E + 3Sg

where E is the assigned uncertainty of the standard block, and sq is

the accepted group standard deviation for that block size (see Figure

4). This assumes that the standard blocks have documented

uncertainties e.g., if they were calibrated at NBS . (For

convenience one may use the maximum uncertainty found in the group so

as to report a single uncertainty value for the whole group.)

3.2.7 Summary

In sections 3.2.3 and 3.2.5 tests are described which determine if the

process is in control. The actions which can be taken when one of

these tests indicates an out-of-control condition are described in

section 4.6. In the absence of a specific format for out-of-control

conditions, it should be noted that once predictability is lost, no

statements should be made about the condition of the process. Until

the process parameters have been re-established or some satisfactory

corrective action has been taken, any uncertainty statements which are

issued should be designated as provisional.

16
FIGURE 1—WORKSHEET 3.2.2

PROCESS PARAMETERS: ACCEPTED VALUES OF CONTROLS

AND STANDARD DEVIATIONS

Values in Microinches at 20 °C

Nominal Average Value No. of Standard Group*

Size of Control Repetitions Deviation Standard Deviation

( inches)

Group II 0.10000

Group V 0.150

16.7

16.2

1.34

1.75

1.34

1.75

Id

i=l k = no. of control blocks in the group (in this case k = 1).

The degrees of freedom associated with Sg are k(n-l),

17
FIGURE 2--W0RKSHEET 3.2.3

OBSERVED VALUE OF CONTROL COMPARED TO ACCEPTED VALUE OF CONTROL

Values in Microinches at 20 °C

Nominal Comparator Value Value of

Size Ident. Readings Diff. of Std. Block

(Inches)

Test Standard X-S V+d

X S d V L

Group II 0.10000 Test 19.0 17.0 2.5** 17.5 20.0

0.10000 Control 17.0 16.0 0.5** 17.5 18.0}

0.10010 Test 13.5 10.5 3.0 11.0 14.0

0.10020 Test 18.8 17.0 1.8 16.6 18.4

Group V 0.147 Test 20.0 18.5 1.5 18.3 19.8

0.148 Test 19.5 17.8 1.7 18.2 19.9

0.150 Test 19.5 18.0 0.9** 17.0 17.9

I 0. 150 C ontrol 20.2 19.2 1.6** 17.0 18.6 | 0.200 Test 20.0 18.3 1.7 19.5 21.2

*If t >_ 3, process is out of control for that group. Repeat entire group.

**Use average of S,^^^ and S^^^,^^^ , i.e., d = X - 1/2 (S^^^^ + S^ontrol^'

Values of V and E are assigned values (e.g., from NBS calibration). All other

values are from participant's process.

18
FIGURE 2--continued

Accepted Value Accepted t Uncertainty Limit to Uncertainty of

of Control Group S.D. Test* of Std. Random Error Test Block

L-Lj/Sg 3S3 E + R

U Sp t E R U

C G

1.8 4.0 5.8

16.7 1.34 1.0

1.8 4.0 5.8

1.8 4.0 5.8

2.3 5.2 7.5

2.3 5.2 7.5

2.3 5.2 7.5

16.2 1.75 1.7

2.3 5.2 7.5

19
FIGURE 3--W0RKSHEET 3.2.4

ACCEPTED VALUES OF PROCESS PARAMETERS COMPARED TO NEW VALUES FOR PROCESS PARAMETERS,

k BLOCKS IN A GROUP

Values in Microinches at 20 °C

Starting Values New Values

Nominal

Size Control Number Group S.D. Control Number Group S.D.

(Inches)

L

' c "2

Group 0.10000

II

|< = 1 Combined

16.7 6

1.34

15.2 12

2.12

(^•"J^P 0.150 16.2 6 18.3 12

k=l Combined 1.75 1.59

*If t ^ 3, the new value L^ should replace L^ for the control

;

otherwise, use combined value L.

'I''' 2. 01 ^^'^ ^1 ^""^ "^2 degrees of freedom, the new value of s^ should replace

Sg as the group standard deviation; otherwise, use the combined standard deviation.

The critical value, F

qi , can be found in Table I where y-] = k(n2-l) and

Y2 = k(n^-l).

20
FIGURE 3--continued

Combined

t Value F Degrees

Test* Control Test** Combined S.D. of Freedom

Lc-L;I "iW; ,

/ (n^-l)s|.(n ^-l)s,I 2

G '^"l 2 '12

t L F s^ Y

2.2 15.7

2.5 1.91 16

2.4 17.6

0.8 1.64 16

1

21
FIGURE 4--W0RKSHEET 3.2.5

VALUES OF NBS BLOCKS FROM LABORATORY PROCESS COMPARED TO VALUES

ASSIGNED AT NBS, k BLOCKS IN A GROUP

Values in Microinches at 20 °C

Nominal Calibrated Accepted

Size Assigned Values Values Differences Group S.D.

(Inches) NBS-, NBS2 NBS^ NBS2 N^-W^ N2-W2

Average of

2 Values

^1 W2 ^1 N2 ^1 '2

Group II 0.10000 51 .5 50.3 53.08 51.82 1 .58 1.52

k=3 0.1001 55.2 56.5 51.42 52.68 -3.78 -3.82

0.1002 52.8 51.4 50.20 48.90 -2.60 -2.50

Combined 1.91

Group V k=2

0.150

0.160

52.8

54.2

52.9

62.7

52.72

51.82

52.42

59.68

-0.08

-2.38

-0.48

-3.02

Combined 1.64

*If t >_ 3, process is out of control and a new value for the laboratory reference block

should be determined if the standard deviation is in control.

**If F ^ F Qi

for k and y degrees of freedom, process is out of control. The critical

value, F p,-, , can be found in Table I where Yt = k and = y.

22
FIGURE 4--continued

t Observed F Combined

D.F. Test* Difference Group S.D. Test** Group S.D. D.F.

Id^+d^l/Sg d^-d^ fF—- S.VSg^ ys|+ks| Y+k

^ k

Y t D ¥

1.6 0.06

4.0* 0.04

2.7 -0.10

16 0.07 0.0 1.75 19

0.3 0.40

3.3* 0.64

16 0.53 0.1 1.56 18

23
FIGURE 5

REPORT OF TEST

of

Length Calibrations From ^to Inches

Using

NBS Gage Block Sets ^and

PARTICIPATING LABORATORY

Duplicate measurements made by the participating laboratory on NBS Gage Block Sets

and made by calibrating each NBS set against a standard set during a regular

calibration procedure gave the following results at 20 °C (values are in microinches)

A. Standard Deviations

Accepted SD OF From Test DF Test Combined SD DF

Group Sg X-j X2 F s^

Conclusions from the F-test:

(a) If F < F Qi

for X-j and X^ degrees of freedom, the process is in control, and the

standard deviation used in the uncertainty statement is s^.

(b) If F >^ F

QI

for X-j and X2 degrees of freedom, the process is out of control, and the

uncertainty statement is omitted.

NOTE: Standard deviations s^, s^, and s- are found in Figure 4.

24
FIGURE 5--continued

B. Offset of Participating Laboratory's Process from NBS

From NBS Process From This Test

Nominal Assigned Values Uncertainties Calibrated Values t Size NBS^ NBS2 NBS^ NBS2 NBS^ NBS2 Offset Test

(Inches) l/2{(Ni+N2)-(W^+W2)

}

Nominal Laboratory Standards Corrected for Offset Uncertainty

Size Assigned Value Uncertainty Assigned Value Uncertainty Test Block

(Inches) V^^A "^^c ^i^^z

/2 2

V E V E' U

Conclusions from t test:

(a) If t < 3, there is no offset from the NBS process, and the assigned value and the

uncertainty of the standard is unchanged.

(b) If t ^ 3, there is an offset from the NBS process, and the assigned value of the

standard should be corrected by A. The uncertainty of the standard is E'. The uncertainty for any test block is calculated from E or E' whichever is

appropriate, i.e., U = E' + 3Sq.

NOTE: The computations of the F and t statistics are found in Figure 4.

25

3 . 3 Test Set Measured Against Two Standard Sets : Control on the

Difference Between Standards

3.3.1 Measurement Process

To introduce redundancy into a calibration system, duplicate

measurements are made on each unknown, X, by comparing X to two

standard blocks Si and S2 in the order X S-| S2 X. This will not only

provide a check on gross errors, but the difference between the two

standard blocks can be used to test process control. By continuous

examination of this difference, the stability of the measurement

process and of the standard blocks themselves can be kept under

surveillance so that decisions about the condition of the process can

be made after each calibration run.

The random errors associated with the process are of two kinds; those

arising from repetitions in the short term, and those involving long

term or day-to-day differences. The random error appropriate in this

case is that associated with the repeated measurement of a control

"block" over a sufficiently long time period to insure that all

factors affecting total variability have a chance to exert their

influence. (The control "block" is actually the difference between

the two standard blocks.)

Because of temperature effects, the variation is usually length

dependent. For this reason, and for convenience of working group size

the usual set of blocks (80 or so blocks in the 0.05 to 4 inch range)

should be treated as a number of subsets of up to 20 blocks each, and

at NBS the following six groupings are used.

Group

Nominal Length

(Inches)

Approximate

No. of Blocks

I II

III

IV

V

VI

0.050 to 0.09375

0.100 to 0.107

0.108 to 0.126

0.127 to 0.146

0.147 to 0.500

0.550 to 4.000

4

20

20

20

15

13

27
Variability should be approximately the same for all blocks in a group

so that one can combine the standard deviations* computed for each of

the blocks in a group into one overall value of the standard deviation

for the group. If S], . . . sk are the standard deviations for the k

blocks in a group with degrees of freedom v] , . . . vk respectively.

3.3.2 Establishing Process Parameters

Before starting process control, it will be necessary to establish an

initial accepted value** for the control, S-| - $2 , and a value for th

random error component. To do this the control set should be measured

by the usual process, say 6 times, with a few days between

repetitions. Then the average value for the control, S] - $2, and the

standard deviation associated with the difference should be computed

for each pair of standard blocks.

The accepted starting values for the control and random error

component will be the average and group standard deviation as

indicated above. Figure 6 details a portion of a typical worksheet

showing the starting values for two groups of blocks in the set.

Examples given in the following sections are based on these two groups

and their parameters. All data in the examples is hypothetical and is

intended only to explain the methodology.

The standard deviation of a single observation is given by

where the r^ is the difference between each observation and the average

of n observations. The quantity n-1 is called the degrees of freedom

associated with s.

**The term "value" for a gage block means the deviation from nominal

size (measured length minus nominal length) at 20 ''C. The value for

the control in this case is the difference in length between the two

standards (S] - $2) at 20 °C.

28
3.3.3 Maintaining Control

After the process parameters have been established, control is

maintained by checking the observed value for each parameter after

each calibration against its accepted value.

A portion of a typical worksheet is given in Figure 7 detailing the

tests for determining whether or not the process is in a state of

statistical control.

3.3.4 Updating Process Parameters

As information collects on the control blocks which are used

regularly, the values for the process parameters should be updated as

shown in Figure 8. If either of the process parameters has changed

from its starting value as indicated by the t-test or F-test, a new

process parameter must be computed based only on the current data. If

the process parameters have not changed, the process will be

considered to be continuous, and the data will be combined. A portion

of a typical worksheet (Figure 8) details how this is done.

The frequency of updating will depend on the workload but should be

done after 5 or 10 values initially and then at intervals dictated by

convenience (e.g., every six months or a year).

3.3.5 Relationship to National Standards

The process should produce values which are consistent with the

national system as maintained by NBS. In order to test the entire

system, NBS is prepared to send each participating laboratory two

calibrated sets when requested, presumably at intervals of one or two

years. Each of these two sets should be calibrated twice by the

laboratory using its regular calibration procedure thereby giving the

independent check necessary for verifying consistency.

Laboratories with the capability of writing their own test reports

based on their measurements of the NBS sets are encouraged to do so.

In this case NBS will provide the two calibrated sets of blocks, their

current assigned values and associated The table in Figure 9

summarizes the analysis of the data and shows whether or not there is

a signficant offset from the NBS process. If the offset is

significant, the values for the laboratory reference standards and

their associated uncertainties should be corrected as shown in the

suggested "Report of Test" form in Figure 10. In effect this is a method for each laboratory to calibrate its own standards.

29
3.3.6 Uncertainty

The uncertainty, +U, associated with the average value of any test

block which has been calibrated twice, assuming the measurement

process is in control, is given by

Ut+U, 3Sp

U = -1—1+ -i2 2

where Lli and U2 are the assigned uncertainties of the standard sets

Si and S2 respectively, and sq is the accepted group standard deviation*

for that block size (see Figure 9). This assumes that the standard

blocks have documented uncertainties (e.g., if they were calibrated at

NBS). For convenience one may use the maximum uncertainty in the

group so as to report a single uncertainty for the entire group.

3.3.7 Summary

In the foregoing sections, tests are given to determine if the process

average has shifted and if the variability of the process has changed.

The actions which can be taken when one of these tests indicates an

out-of-control condition are described in section 4.6. In the absence

of a specific format for out-of-control conditions, it should be noted

that once predictability is lost, no statements should be made about

the condition of the process. In some cases the standard blocks may

have actually changed and may need to be recalibrated. In others the

process may have changed and new process parameters must be

determined. Until the process parameters have been reestablished or

some satisfactory corrective action has been taken, any uncertainty

statements which are issued should be designated as provisional.

*Note that sq is the standard deviation of the difference between the

two standard blocks Si and S2. The standard deviation of a single

observation from the process is sq//2".

30
FIGURE 6—WORKSHEET 3.3.2

PROCESS PARAMETERS: ACCEPTED VALUE OF THE CONTROL AND GROUP STANDARD

DEVIATION, k BLOCKS IN A GROUP

Values in Microinches at 20 °C

Nominal Control No. of Observed S.D. Group Degrees of

Size Average Value Repetitions of Control S.D. Freedom

(Inches)

of S]-S2

i

zs.2 k(n-l)

Group II

k=4

0.10000

0.10005

0.10010

0.10020

Combined

0.20

-1.25

0.32

0.10

0.50

0.37

1.12

0.54

0.70 20

Group V

k=5

0.147

0.148

0.149

0.150

0.200

Combined

1.86

4.13

1.38

1.00

0.43

1.01

0.94

0.92

1.46

0.54

1.02 25

31
FIGURE 7—WORKSHEET 3.3.3

OBSERVED VALUES OF CONTROL AND STANDARD DEVIATIONS

COMPARED TO ACCEPTED VALUES, k BLOCKS IN A GROUP

Values in Microinches at 20 °C

Accepted

Value

Nominal of

Size Comparator Readings Control Control

(Inches)

Test Std. Std. Test

X-S^ X-S2 ^2"^1

X h ^2 X ^1 d2 C Lc D

Group II U. 1 UUUU 20 0 Id. y 17. 2 d \ .{J J. 1 3. cS U. / -U. c u. y k=4 0.10005 23.1 22.0 22.9 23.8 1.1 0.9 -0.2 -1.2 1.0

0.10010 19 0 16.7 16. 0 20.1 2.3 4.1 1.8 -0.3 2.1

0.10020 20 3 18.0 17. 1 19.9 2.3 2.8 0.5 0.1 0.4

Combined

Group V 0.147 21 3 20.7 16. 0 21.2 0.6 5.2 4.6 1.9 2.7

k=5 0.148 23 6 20.7 23. 5 23.2 2.9 -0.3 -3.2 -4.1 0.9

0.149 15 7 15.1 17. 2 16.6 0.6 -0.6 -1.2 -1.4 0.2

0.150 20 0 15.4 15. 0 19.9 4.6 4.9 0.3 1.0 -0.7

0.200 16 7 15.8 15. 2 15.7 0.9 0.5 -0.4 0.4 -0.8

Combi ned

*If t >_ 3, the process is out of control. Remeasure blocks and test again. |D| means the absolute

value of D.

**If F >_ F Qp for k and y degrees of freedom, process is out of control. Remeasure all blocks in

group and test again. The critical value, F

qi , can be found in Table I (page 63) where Y] = k and

Y2 = Y- If t < 3 and F < qi , process is in control. Accept value for test block of l/2(di+d2+Vi+^

where V-j and V2 are assigned values for standards S-j and $2.

***Ui and Up are the assigned uncertainties of standards S-, and S^.

32
FIGURE 7--continued

Observed Accepted

S.D. of S.D. of t F Uncertainty of Limit to Uncertainty of

Group Group D.F. Test* Test** Starting Std. Random Error Test Block

zdT2 |D|/Sq s2/s2 1/2(U^+U2)*** 3Sg/2 E + R ~T~

Sj Sg Y t F E R U

1.3 1.8 1.0 2.8

1.4 1.8 1.0 2.8

3.0* 1.8 1.0 2.8

0.6 1.8 1.0 2.8

1.26 0.70 20 3.2

2.6 2.3 1.5 3.8

0.9 2.3 1.5 3.8

0.2 2.3 1.5 3.8

0.7 2.3 1.5 3.8

0.8 2.3 1.5 3.8

1.36 1.02 25 1.8

33
FIGURE 8—WORKSHEET 3.3.4

NEW VALUES OF PROCESS PARAMETERS COMPARED TO ACCEPTED VALUES

k BLOCKS IN A GROUP

Values in Microinches at 20 °C

Nominal

Size Control

Starting Values

Group S.D. No. Control

New Values

Group S.D. No.

(Inches)

s„

G 1 L' s iG

n^'2

Group II 0.10000 -0.2 6 -0.3 12

k=4 0.10005 -1.2 6 -1.0 12

0.10010 -0.3 6 -0.2 12

0.10020 0.1 6 -0.9 12

Combined 0.70 1.16

Group V 0.147 1.9 6 4.7 12

k=5 0.148 -4.1 6 -3.5 12

0.149 -1.4 6 -2.1 12

0.150 1.0 6 0.4 12

0.200 0.4 6 1.0 12

Combined 1.02 1.34

*If t >_ 3, the new value L^ should replace L^ for the control; otherwise, use the

combined value L^.

**If F >_ F

Qi

for k(n2-l) and k(ni-l) degrees of freedom, the new value Sg should

replace s^ as the group standard deviation; otherwise, combine the new and starting

value into a combined group standard deviation. The critical value, F

gi

, can be

found in Table I where y-] = k(n2-l) and Y2 = kCn-j-l).

***If F >_ F

Qi

for k(ni-l) and k(n2-l) degrees of freedom, the new value Sg should

replace s^; otherwise, use the combined group standard deviation. The critical

value, F g-j , can be found in Table I where Y] = k(ni-l) and Y2 ~ k(n2-l).

34
FIGURE 8--continued

Combined

t Value F F Degrees of

Test* Control Test** Test*** Combined Group S.D. Freedom

HThHT^ X X /k(ni-l)s^3.k(n2-l)s'2 k{.^.n^-2)

/T7T "r"2

Sp/—+ — G n-j n2

0.3 -0.3

0.6 1.1

0.3 -0.2

2.9 -0.5

5.5* *

1.2 -3.7

1.4 -1.9

1.2 0.6

1.2 0.8

^G" V k(n^+n2-2)

F F Sp

C G

2.7 0.4 1.04 64

1.7 0.6 1.25 80

35
FIGURE 9—WORKSHEET 3.3.5

VALUES OF NBS BLOCKS FROM LABORATORY PROCESS COMPARED TO

VALUES ASSIGNED BY NBS, k BLOCKS IN A GROUP

Values in Microinches at 20 °C

Nominal Values Assigned Average of 4

Size by NBS Calibrated Values Sum Difference

(Inches) NBS^ NBS2 NBS^ NBS2 (N^+N2)-(V^+V2) (N^-N2)-(V^-V2)

h '2 ^1 S D

0,,130 51.5 50.3 53.1 51.8 3.1 0.1

0,.135 55.2 56.5 51.4 52.7 -7.6 0.0

.145 52.8 51.4 50.2 48.9 -5.1 -0.1

,200 52.8 52.9 52.7 52.4 -0.6 0.4

,350 54.2 62.7 51.8 59.7 -5.4 0.6

Combined (K=5)

*If t >_ 3, process is out of control and a new value for the laboratory reference

block should be determined if the standard deviation is in control. |S| means

the absolute value of S. *If F >_ F Q,] for k and y degrees of freedom, process is out of control. The critical

value, F

qi , can be found in Table I where y-| = k and Y2 ~ y- oi

the accepted and observed standard deviations as shown.

36
FIGURE 9--continued

Accepted

Group S. D. D.F.

Observed

Group S.D.

t

Test*

F Test**

Combined

Group S.D.

Total

D.F.

\ k ^G ^G V k+Y

5.0*

12.2*

8.2*

1.0

8.6*

Y t F

1.25 80 0.66 0.3 1.23 85

37
FIGURE 10

REPORT OF TEST

of

Length Calibrations From ^to Inches

Using

NBS Gage Block Sets ^and

PARTICIPATING LABORATORY

Duplicate measurements made by the participating laboratory on NBS Gage Block Sets

and ^made by calibrating each NBS set against two standard sets during a regular

calibration procedure gave the following results at 20 °C (values are in microinches)

A. Standard Deviations

Accepted SD DF From Test OF Test Combined SD DF

Group Sg A-j Sj^ X2 F_ s^

Conclusions from the F-test:

(a) If F < F Qi

for X-j and X2 degrees of freedom, the process is in control, and the

standard deviation used in the uncertainty statement is s^,.

(b) If F i F

Qi

for X-j and X2 degrees of freedom, the process is out of control and the

uncertainty statement is omitted.

NOTE: Standard deviations Sp, s,. and Sp are found in Figure 9.

38
FIGURE 10--continued

B. Offset of Participating Laboratory's Process from NBS

From NBS Process From This Test

Nominal

Size

Assigned Values Uncertainties

NBS^ NBS2 NBS^ NBS2

Calibrated Values

NBS^ NBS2

Offset t

Test

( Tnrhps ) 1/2{(N,+N„)-(W,+W^)}

—

W2 R^ R2

— — — —

^1 ^2 A t

—

Nominal Laboratory Standards

— _ — —

Corrected for Offset Uncertainty

Size Assigned Values Uncertainties Assigned Values

S-i $2

Uncertainties Test Block

^1 ^2

(Inches) Vn+A V,+A

V^ V2 U-, U2 V] V^ U] U^ U

Conclusions from t-test:

(a) If t < 3, there is no offset from the NBS process, and the assigned value and

uncertainty of each standard are unchanged.

(b) If t >^ 3, there is an offset from the NBS process, and the assigned value of each

standard should be corrected by A. The uncertainties associated with V-l and Vo are

and U2 where

1 3s 12 = U^ = 2" +^1 +^2 ^ ^ • '^^^ uncertainty for any test block is

calculated from and U, or [}\ and U^ whichever is appropriate, i.e.,

U^ + u; 3s, '

'

NOTE: The computations of the F and t statistics are found in Figure 9.

39

3.4 Two Test Sets and Two Standard Sets In A Drift Eliminating Design

Involving Eight Observations , Difference Between Standards As

Control

3.4.1 Measurement Process

Laboratories doing high precision work can benefit from a drift

eliminating design using eight observations to intercompare two test

blocks with two standard blocks. Redundancy is built into this design.

In addition, any linear drift effect caused by comparator time

dependence will be balanced out. The differences between the block

pairs of the two standard sets Si and S2 will serve as controls and will

allow the stability of the measurement process and of the standard

blocks themselves to be monitored.

The random errors associated with the process are of two kinds;

namely, a short term component called "within" variability and a long

term component called "total" variability.

The within variability, a^, is readily demonstrated in a repeated

sequence of measurements made over a short time. This quantity is

used for a day to day check on the process variability.

The total variability of the process, a^, reflects both short term and

long term variability. It is found by examining the measurement

process over a sufficiently long time period to insure that all

factors affecting variability have a chance to exert their influence.

It is used in a statistical t-test to identify any shift in the

control value for the process.

Because of the effect of temperature on block length, variations are

usually length dependent. For this reason, and for convenience of

working group size, the overall set of blocks (80 or so blocks in the

0.05 to 4 inch range) should be treated as a number of groups of up to

20 blocks each. The following six groupings are recommended.

Group

Nominal Length

(Inches)

Approximate

No. of Blocks

I II

III

IV

V

VI

0.050 to 0.09375

0.100 to 0.107

0.108 to 0.126

0.127 to 0.146

0.147 to 0.500

0.550 to 4.000

4

20

20

20

15

13

41
The group is selected so that variability of all blocks in a group is

expected to be the same. Then the standard deviations computed for

each block in a group can be combined into an overall group standard

deviation. If s-|, . . . s^ are the standard deviations of the k blocks

in a group with degrees of freedom V"| , . . . v|< respectively, then

3.4.2 Establishing Process Parameters

Before starting the control process, it will be necessary to establish

initial accepted values* for the controls and initial values for the

random error components. To do this, at least six calibration runs

should be made using the control blocks in the trend-eliminating

design. The calibrations should be separated by several days. The

measurement sequence for the trend-eliminating design along with the

equations for finding the least squares estimates of the controls and

the within standard deviation and the pooled within standard deviation

are given in Appendix A. See [7] for a more complete analysis of

trend-eliminating designs.

The average value of the control, the pooled within standard

deviation, and the total standard deviation** are computed for each

pair of standards. Then the random error components are combined into

a group within standard deviation and a group total standard deviation

as shown in 3.4.1. These values and the average value of the control

are the starting process parameters.

Figure 6 details a portion of a typical worksheet showing the starting

values for two groups of blocks in the set. Examples given in the

following sections are based on these two groups and their parameters.

All data in the examples is hypothetical and is intended only to

explain the methodology.

*The term "value" for a gage block means the deviation from nominal

size (measured length minus nominal length) at 20 ^'C. The value for

the control in this case is the difference in length between the two

standards (S] - $2) at 20 °C.

**The total standard deviation for the control is given by

where r-j is the difference between each value of the control and the

average of n values. The quantity n-1 is called the degrees of

freedom associated with as.d. (group)

42
3.4.3 Maintaining Process Control

After the process parameters have been established, control is

maintained by checking the observed value of the control S-j - $2 and

the within standard deviation a;^ for each calibration run against their

accepted values.

A typical section of a worksheet for making these comparisons showing

the appropriate statistical tests is given in Figure 12.

3.4.4 Updating Process Parameters

Periodically as data accumulates on the control set, the output

produced by the process is compared to the accepted process

parameters. If one of the parameters has changed as indicated by a ttest or F-test, a new value for the parameters must be determined

based only on the current data; otherwise, the process will be

considered to be continuous, and the data will be combined. The

worksheet in Figure 13 details this procedure and shows the

appropriate statistical tests.

Initially the process should be updated after five or six calibrations

and then as convenience dictates (every six months or yearly).

3.4.5 Relationship to National Standards

The process should produce values which are consistent with the

national system as maintained by NBS. In order to test the entire

system, NBS is prepared to send each participating laboratory two

calibrated sets when requested, presumably at intervals of one or two

years. These sets should each be calibrated twi ce by the laboratory

using the trend-eliminating design procedure thereby giving the

independent check necessary for verifying consistency.

Laboratories with the capabilitiy of writing their own test reports

based on their measurements of the NBS sets are encouraged to do so.

In this case, NBS will provide the two calibrated sets of blocks,

their current assigned values and associated uncertainties. The table

in Figure 14 summarizes the analysis of the data and shows whether or

not there is a significant offset from the NBS process. If the offset

is significant, the values for the laboratory reference standards and

their associated uncertainties should be corrected as shown in the

suggested "Report of Test" form in Figure 15. In effect this is a method for each laboratory to calibrate its own standards.

3.4.6 Uncertainty

The uncertainty +U associated with the value assigned to any test

block which has Feen calibrated using the trend-eliminating design is

given by

43
where Ui and U2 are the assigned uncertainties in the calibration of the

standard sets S-j and $2 respectively, and Sq is the accepted total group

standard deviation for that block size and sq is the accepted within

group standard deviation (see Figure 14). Tnis assumes that the

standard blocks have documented uncertainties (e.g., if they were

calibrated at NBS.) For convenience one may use the maximum

uncertainty in the group so as to report a single uncertainty for the

entire group. An explanation of the computation of the uncertainty

can be found in [7].

3.4.7 Summary

In the foregoing sections several statistical tests are described

which determine if the process mean has shifted and if the variability

of the process has changed. Actions which can be taken when one of

these tests indicates an out-of-control condition are described in

Section 4.6. In the absence of specific format instructions for outof-control conditions, it should be understood that once

predictability is lost, no statements should be made about the

condition of the process. Any uncertainty statements which are issued

should be designated as provisional until the process is again under

control

.

44
FIGURE 11—WORKSHEET 3.4.2

PROCESS PARAMETERS: ACCEPTED VALUES OF CONTROL, WITHIN AND TOTAL

STANDARD DEVIATIONS, k BLOCKS IN A GROUP

Values in Microinches at 20 °C

Q-Ln 3 II o ^

0.147 0.10 6 0.65 0.34

0.148 0.20 6 0.23 0.62

0.149 0.04 6 0.48 0.64

0.150 0.21 6 0.51 0.34

0.200 0.20 6 0.30 0.48

Combined 30 0.46 120

Accepted Pooled Group

Nominal Value of No. of Within Within Degrees of Total Group Degrees of

Size Control Reps. S.D. S.D. Freedom S.D. Total S.D. Freedom

(Inches) Average ZC? 4kn s(L_) IwT l<(n-l)

L^ n C Sg 6 S ag y

0.10000 0.5 6 0.22 0.93 ^ 0.10005 -0.1 6 0.28 0.54

%1 0.1001 -0.4 6 0.39 0.36

1"^ 0.1002 -0.0 6 0.41 0.26

Combined 24 0.33 96 0.58 20

0.50 25

45
FIGURE 12—WORKSHEET 3.4.3

OBSERVED VALUE FOR CONTROL AND WITHIN STANDARD DEVIATION COMPARED TO ACCEPTED VALUE

(SEE APPENDIX A FOR COMPUTATIONS)

Values in Microinches at 20 °C

Accepted Values

Accepted Observed Group

Nominal Value Within Within

Size Control of Control S.D. S.D. D.F.

Group

Total

S.D. D.F.

(Inches)

Group II 0.10000

0.10005

0.1001

0.1002

Combined

c

2.5

0.0

-0.5

-0.6

c

0.5

-0.1

-0.4

-0.0

"w

0.48

0.16

0.30

0.50

0.33 96 0.58 20

Group V 0.147

0.148

0.149

0.150

0.200

Combined

0.8

-0.2

0.5

0.5

-0.5

0.1

0.2

0.0

0.2

0.2

0.59

0.61

0.33

0.62

0.43

0.46 120 0.50 25

*If t >_ 3, process is out of control for that block. Remeasure and test again.

If F ^ F

gi

for 4 and

The critical value, F

**If F ^ F

Qi

for 4 and 6 degrees of freedom, process is out of control for that block.

g-| , can be found in Table I where Yt = 4 anda

***Ui and U^ are the assigned uncertainties of the two standard blocks.

46
FIGURE 12—continued

t F Uncertainty Limit to Uncertainty of

Test* Test** of Restraint Random Error Test Block

l^c-Lcl/^G l/2(Ui + U2)-* 3/3e^ - 1 s^ TT^

l 5

t F E R U

3.4* 2.1 1.8 1.5 3.3

0.2 0.2 1.8 1.5 3.3

0.2 0.8 1.8 1.5 3.3

1.0 2.3 1.8 1.5 3.3

1.4 1.6 2.3 1.3 3.6

0.8 1.8 2.3 1.3 3.6

1.0 0.5 2.3 1.3 3.6

0.6 1.8 2.3 1.3 3.6

1.4 0.9 2.3 1.3 3.6

47
FIGURE 13—WORKSHEET 3.4.4

NEW VALUES FOR PROCESS PARAMETERS COMPARED TO ACCEPTED VALUES

Values in Microinches at 20 °C

Nominal

Size

Starting Values

Control No.

Group Group

Within Total

S.D. S.D.

New Values

Control No.

Group Group

Within Total t S.D. S.D. Test* Average

(Inches)

agA/n^j+T/n^ "l^"2

0.10000

^0.10005

go. 1001

S 0,1002

0.5

-0.1

-0.4

0.0

Combined (k=4) 0.33 0.58

1.0

-0.8

0.1

-0.2

12

12

12

12

0.31 0.47

1.7

2.4

1.7

0.7

0.8

-0.6

-0.1

-0.1

0.147

0.148

Q_o 0.150

0.200

0.1

0.2

0.0

0.2

0.2

-0.5

-1.3

0.5

-0.2

-0.2

12

12

12

12

12

2.4

6,0*

2.0

1 .6

1.6

-0.3

*

0.3

-0.1

-0.1

Combined (k=5) 0.46 0.50 0.23 0.65

where S-^ = 4kni , 62 4kn,

*If t^ 3, the new value for_the control L' is significantly different from L and should replace L^;

otherwise, use the average L^.

**If F > F m for 4kno and 4knT degrees of freedom, replace Sp by si; otherwise, use the combined

value-s 2 1 ^

' G ^ G

c ***If F 2: F

Qi

for k(n2-l) and k(n,-l) degrees of freedom, replace 5- by 5^; otherwise, use the

combined' value 5^.

/If F 2 F Q-] for 4kn-| and 4kn2 degrees of freedom, replace Sg by s^; otherwise use the combined

value s^:

//If F 2 F

Qi

for k(n^-l) and k(n2-l) degrees of freedom, replace by o^; otherwise, use the

combined' val ue 5 . c The critical values, F q-j , mentioned above can be found in Table I. The y-] in the table refers to the first number of decrees of freedom and to the second.

48
FIGURE 13--continued

Combined

F F F F Group Degrees of

Test** Test*** Test / Test // Within S.D. Freedom

Combined

Group

Total S.D.

Degrees of

Freedom

^g'/^g' s2/s'2 / 5^s^.6,s^^ 4k(n^+n2) (n^-l)52+(n2-l)5g2 k(n^+n2-2)

0.9 0.7 1.1 1.5 0,32 288 0.51 64

0.2 1.7 4.0/ 0.6 0.61 80

49
FIGURE 14--W0RKSHEET 3.4.5

VALUES OF NBS BLOCKS FROM LABORATORY PROCESS COMPARED TO

VALUES ASSIGNED BY NBS

Values in Microinches at 20 °C

Nominal Values Assigned Average of

Size by NBS Two Calibrations Sum

(Inches) NBS-, NBS2 NBS^ NBS2 (Ni+N2)-(W^+W2)

W2 ^1

1 C S

Group II 0.10000 19,,00 19,.56 19.00 18.32 -1 .24

0.10005 17..00 18,.20 17.51 18.23 0.54

0.1001 13..50 13,,37 14.53 13.68 1 .34

0.1002 18.,80 17,.83 18.55 17.20 -0.88

Combined

Group V 0.147 21 .,30 18 .77 21 .20 18.01 -0.86

0.148 23.,60 27 .71 23.29 25.69 -2.33

0.149 15,,70 16 .22 16.62 15.45 0.15

0.150 20,,00 19 .69 19.99 19.45 -0.25

0.200 16,.70 16,.71 15.70 16.01 -1.70

Combined

*If z >: 3, process is out of control and new values for the laboratory reference

blocks should be determined if the standard deviations are in control.

*If F 2: F Q,j for 4 and y degrees of freedom, process is out of control.

The critical value F q-j can be found in Table I where Y] = 4 and Y2 " Y50
FIGURE 14--continuecl

Observed Accepted Accepted F Within S.D. Within S.D. D.F. Total S.D. Test* Test**

W b

^G Y z F

0.35 2.5 1.2

0.59 1.1 3.4

0.79 2.7' 6.1**

0.24 1.8 0.6

0.32 288 0.51

0.33 1 .4 2.1

1.02 3.8* 19.7**

0.32 0.2 1.9

0.40 0.4 3.0

0.51 2.8 4.9**

0.23 240 0.61

51
FIGURE 15

REPORT OF TEST

of

Length Calibrations From ^to Inches

Using

NBS Gage Block Sets ^and

PARTICIPATING LABORATORY

Duplicate measurements made by this laboratory on NBS Gage Block Sets ^and made by

calibrating each NBS set against two standard sets during a regular calibration procedure

gave the following results at 20 °C (values are in microinches)

A. Standard Deviations

F Group Accepted Standard Deviations From This Test Test Combined

Within DF Total DF Within DF 5|/s^ Within DF

Sg A-, Og X2 S|>^ A3

Conclusions from F-test:

(a) If F < F

Qi

for A^ and A-j degrees of freedom, the process is in control, and the

within standard deviation used in the uncertainty statement is S^.

(b) I'f F >^ F

Qi

for A^ and A-j degrees of freedom, the process is out of control, and the

uncertainty statement is omitted.

NOTE: Standard deviations s^, ap, s., and s^ are found in Figure 14.

52
FIGURE 15--continued

B. Offset of Participating Laboratory's Process from NBS

From NBS Process r rom 1 n 1

b

Toe + Nominal Assigned Values Uncertainties Cal ibrated Values t Size NBS^ NBS^ NBS-j NBS^ NBS^ NBS2 Offset Test

(Inches) 1/2{(N^+N2)-(W^+W2)}

1 W R^ R2 A—

t—

iNOim na i Laboratory Standards Corrected for Offset Uncertainty

Size Assigned Values Uncertainties Assigned Values Uncertainties Test Block

^2 ^1 ^2 h h

(Inches) V^+A V2+A

'2 ^1 ^2 ^2 U' u^ U

Conclusions from t-test:

(a) If t < 3, there is no offset from the NBS process, and the assigned values of the

standards are unchanged. The uncertainties are U-j and U2 respectively.

(b) If t ^ 3, there is an offset from the NBS process, and the assigned value of each

standard should be corrected by A. The uncertainties associated with Vj and V2 are

U\ and Uo where: ,

The uncertainty for any test block is calculated from U-j and U2 or Uj and U2 whichever

is appropriate, i.e., U^+U2

3 /^ga _ 1 ^2

U = 2/ 6

^•

NOTE: The computations of the F and t statistics are found in Figure 14.

53

4 Operating a Measurement Assurance Program

4.1 Equipment and Environment

4.1.1 The Comparator

There are a number of suitable comparator designs and a typical one is

shown schematically in Figure 16. An upper stylus and a lower stylus

contact the gaging faces of a block supported on an anvil. Each

stylus is attached to a differential transformer core. An integrated

signal from these two transducers is displayed on a meter graduated in

length units (usual ly microinches) . In the simplest comparison, the

difference in length between two gage blocks is obtained by inserting

the blocks, one at a time, between the stylus tips and taking the

difference between the two readings.

An important comparator feature is the point-to-point measurement

along an axis through the gaging point of the block. Other suitable

comparator designs use only one transducer but by various means insure

the point-to-point measurement. Single-transducer comparators are

susceptible to errors when measuring burred or non-flat blocks (see

Figure 17) if they do not have provisions for point-to-point measurement.

For the most precise measurements, it is important that the comparator

stylus contact the defined gage point of the block. A metal or

plastic bar about 1/4 inch thick can be fastened to the anvil (with

laboratory wax if no other means is provided) behind the stylus and

positioned to stop the gage blocks so the stylus will contact the gage

point. The bar can be L-shaped to position the gage block both

laterally and transversely if desired and special configurations can

be devised for comparing blocks of different shapes.

4.1.2 Gage Block Requirements

Nearly all gage blocks are either square or rectangular in cross

section, but a few are circular in cross section. Any of these cross

sections are easily handled in intercomparison procedures on short

blocks (sizes up to 4 inches). Long blocks (over 4 inches) of the

rectangular cross section are prone to tipping in vertical

comparators.

Transferring the length unit to a gage block by intercomparison does

not require rigorous constraints on the flatness and parallelism of

its gaging faces because the transfer is made only along a single line

through the block. Gage block use, however, may be more demanding on

the geometry of the gaging faces. A separate paper covers the

measurement of flatness and parallelism [1].

55
TRANSDUCER CORE

PRIMARY COIL

SECONDARY COILS

MEASURING STYLUS

GAGE BLOCK

ANVIL

MEASURING STYLUS

.REED SPRINGS

FIGURE 16: ELEMENTS OF A MECHANICAL COMPARATOR OF LENGTHS

ERROR WITH WARPED BLOCKS ERROR WITH BURRS

FIGURE 17: ERROR RESULTING FROM COMPARATOR DESIGN

56
Thermal expansion coefficients are generally taken from bulk values,

and these may vary by as much as 10% from actual values for gage

blocks. This problem can be circumvented in the intercomparison

process by insuring that blocks being intercompared are close to 20''C.

If non-standard temperatures are used, the coefficients must be known

unless the attendant systematic errors are tolerable.

4.1.3 Environment

A temperature controlled laboratory is necessary for intercomparisons

of the highest precision. The degree of temperature control needed

depends on the length of the blocks being compared, differences in

coefficients of thermal expansion among the blocks, and the limiting

uncertainty required of the measurements. At NBS, short blocks are

intercompared in a temperature controlled laboratory at 20°C + 0.25°C.

Long blocks are intercompared in a laboratory at 20°C + 0.05°C.*

Relative humidity should be held below 50% to prevent corrosion of

blocks and instruments.

4.1.4 Temperature Effects and Their Control

A large uncertainty in the comparison process can be introduced by

temperature effects. For example, a temperature difference of 0.5°C

between two one-inch steel blocks will cause an error of nearly 6

micro-inches in the comparison. Two causes of temperature differences

between blocks are sometimes overlooked:

(1) Room temperature gradients or nearby heat sources such as

electronic equipment can cause significant temperature

differences between blocks even when they are stored relatively

close to each other before comparison.

(2) Blocks with different surface finishes on their non-gaging faces

can absorb radiant heat at different rates and reach different

equilibrium temperatures. The magnitude of these effects is

proportional to gage block length.

A number of remedies are available to alleviate temperature gradients.

For short blocks the remedies are quite simple. For example, store

the blocks, both standards and unknowns, on a thermal equalization

plate of smooth surface and good heat conductivity close to the

comparator but away from heat sources. Also, use tweezers or tongs to

handle the blocks and use a systematic, rythmic block handling

technique in the comparison procedure to insure a nearly identical

thermal environment for each block.

*Note: This does not mean that every laboratory needs this level of

temperature control

.

57
4.2 Measurement Techniques

The sequence of observations for each of the three program options has

been described in sections 3.2.1, 3.3.1, and 3.4.1. This section will

concentrate on techniques that have been found to be important in

achieving good results.

4.2.1 Block Preparation

The master and test blocks must be thoroughly cleaned, examined, and

deburred using procedures in reference [13]. The identification

numbers are recorded for inclusion in the test report or records.

4.2.2 Comparator Preparation

The instrument anvil should be deburred and cleaned. The comparator

transducer pressure, magnification and alignment should be checked.

Periodic cleaning of the instrument anvil during the work day is

recommended to help reduce the number of spurious readings that result

from minute particles that can contaminate the anvil surface.

4.2.3 Block Storage

Short blocks are arranged on a thermal equalization plate next to the

comparator. From here they can be moved to the comparator anvil by

groups at the time of comparison. There is some thermal advantage,

for sizes from about 0.3 inch to 4 inches, to leaving the blocks on

the plate at all times except when the block is being inserted in the

comparator for measurement. Alternatively, a group can be moved to

the comparator anvil and allowed to equalize there for an appropriate

period.

Long gage blocks are stored in a group on the comparator anvil after

preparation. Additional long blocks that are to be measured during

the day are prepared and placed on a thermal equalization plate next

to the instrument. As comparisons of one group are completed a new

size group can be moved from the plate to the anvil and allowed to

equalize before comparison. All gage blocks are oriented on the

comparator with the top surface uppermost.

4.2.4 Thermal Equalization Time

Equalization time varies with block size, treatment and allowable

measurement uncertainty. Blocks prepared in advance and kept in the

gaging area are placed on the equalization plate, or in the case of

long blocks, moved from the equalization plate to the comparator

anvil. They may then be intercompared using the following table as a first approximation.

58
Block Size

(inches)

Equalization Time

(minutes)

0.100 to 0.250

0.300 to 1.000

2.000 to 20.000

30

60

90

Experiments establishing optimum equalization times should be

conducted in your own laboratory because of the many variables

involved and differing measurement uncertainty requirements.

4.2.5 Temperature Measurement

Temperature measurements can be made with a calibrated mercury-inglass thermometer. The thermometer is mounted on the block storage

plate in the case of short blocks and on the instrument anvil for the

long blocks. The more sophisticated temperature measuring devices

such as thermocouples and thermistors are very useful for detecting

gradients and inequalities.

4.2.6 Handling Techniques

The success of intercomparisons is largely dependent upon block

handling techniques. Proper technique includes the insertion of all

blocks between the styli in a like manner. The operator should

develop a rhythm, after acquiring some experience with the process,

that will ensure that each pair of blocks is handled for approximately

the same length of time as all other pairs in the series.

A camel's hair brush or an air bulb is useful for sweeping or blowing

dust particles from the blocks and the anvil just before insertion.

The short blocks are moved about by grasping them with rubber tipped

10-inch tweezers. When handling square style blocks, the tips of a pair of tweezers may be bent to accommodate this configuration.

The sequence of observations in option 3 was developed to compensate

instrument and temperature drifts, but it still relies on equal

handling of blocks for good results.

4.2.7 Temperature and Deformation Corrections

Deformation corrections for various stylus radii and pressures [3],

can be applied to the observations when blocks of different materials

are compared if the correction is of sufficient magnitude to be

significant.

Temperature corrections are applied to all blocks above 0.350 inch in

size when the blocks are of different materials. This size limit can

be raised if larger uncertainties are acceptable.

59
4.3 Computation and Analysis of Data

NBS staff members will be available to help participants with

computations and analysis of the results especially in the early

stages of the program, but extensive services of this type must be

done on an at-cost basis. Our general aim is to make participants as

self sufficient as possible.

Laboratories wishing to receive a signed and documented NBS test

report should submit their data and worksheets to Mr. Clyde Tucker,

Room B104, Metrology Bldg., NBS, Washington, D.C. 20234.

Responsibility for the calculations and resulting report will be

assumed by NBS.

4.4 Control Charts

A useful tool for monitoring the progress of the measurement process

is the control chart. This is a graphical presentation of the output

from the calibration process on a continuing basis.

After each calibration the value of the control and the associated

standard deviation(s) should be plotted against a time scale.

The chart of the control block values should have the control limits

marked so that an out-of-control value is immediately visible (see

Figure 18). It is also the quickest means of spotting a change in the

size of the control block with time (see Figure 20) and should be

carefully monitored especially for block sizes of one inch and longer.

The chart of the standard deviations provides visual evidence of the

within day process variation (see Figure 19) and makes it possible to

ascertain when a change in the process has occurred (see Figure 21).

4.5 Access to the National Standards

One or two sets of NBS reference standard gage blocks will be loaned

to each participant at periodic intervals for measurement. The period

will be governed by the performance and history of the participant's

process. A time limitation may be imposed because of demand for these

sets. Participants may chose to send their standard sets to NBS for

periodic calibration instead of using the loaned sets.

4.6 Procedures for Correcting Out-of-Control Conditions

If the process is found to be out-of-control by an F-test, repeat the

offending measurements to determine if the condition persists. If it

persists, look for:

(1) Comparator malfunction

(2) Dust or other contamination on the gage blocks

60
FIGURE 18 OBSERVED DIFFERENCE BETWEEN 1-INCH GAGE

BLOCKS USED AS CHECK STANDARD

Values in Microinches

• Upper Limits w

•••

•

• •

Mean * —i -

•

• •

Lower Limits

12 24

IVIONTHS 36

29.5

29.0

28.5

28.0

27.5

27,0

FIGURE 20 OBSERVED DIFFERENCES BETWEEN 6-INCH GAGE

BLOCKS USED AS CHECK STANDARD

Values in IVIicroinches

•A* •

24 48

IVIONTHS

64

FIGURE 19 OBSERVED WITHIN STANDARD DEVIATIONS ON 1-INCH CHECK STANDARD

Values in Microinches

• •

12 24

IVIONTHS

36

2.5

2.0

1.5

1.0

.5

FIGURE 21 OBSERVED WITHIN STANDARD DEVIATIONS

ON 5-INCH CHECK STANDARD

Values in IVIicroinches

24 48

MONTHS

64

61
(3) Temperature problems, in blocks over 0.5 inch, such as too short

an equalization time, heat source (including operator) too close

to the comparator, and temperature difference between gage block

equalization plate and the comparator.

(4) Lack of finesse in gage block handling during comparisons.

If the process is found to be out of control by a t-test:

(1) Look for dirt or burrs on the blocks (stoning may help).

(2) Look at block history for evidence of steady drift toward out-ofcontrol condition. This would indicate a length change and a need to recompute the accepted difference and possibly a recalibration against NBS standards.

(3) If a large number of block sizes are out of control, check

comparator calibration and function.

(4) For blocks larger than 0.5 inch, look for temperature differences

between the blocks.

4.7 Upgrading the Process

A process may perform within the established control pattern but still

not be adequate to the assigned goal. Some or all of the following

changes may be made to improve the process:

(1) Upgrade the quality of the standard sets by purchasing new

blocks.

(2) Obtain a better comparator if one is available.

(3) Improve temperature conditions by removing heat sources from

vicinity of comparator, isolating operator from comparator by

shielding, improving temperature control in lab, etc.

(4) Improve handling techniques during comparisons by equalizing time

each block is handled, taking greater care about cleanliness,

etc.

(5) Switch to option 3 (see Section 3.4) if not already using it.

ACKNOWLEDGEMENTS

The authors wish to thank Mr. J. M. Cameron for his help and guidance

in preparing this document and Mrs. Kay Etzler and Mrs. Barbara Uglik

for their typing skill and patience through many revisions of the

manuscript.

62
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63
REFERENCES

[I] Beers, J. S. & Tucker, C. D., "Gage Block Flatness and

Parallelism Measurement," NBSIR 72-239, 1973.

[2] Beers, J. S. & Tucker, C. D. "Intercomparison Procedures for Gage

Blocks Using Electromechanical Comparators," NBSIR 76-979, 1976.

[3] Beers, J. S. & Taylor, J. E., "Contact Deformation in Gage Block

Comparisons," NBS Technical Note 962, 1978.

[4] Beers, J. S., "A Gage Block Measurement Process Using Single

Wavelength Interferometry," NBS Monograph 152, December 1975.

[5] Cameron, J. M., "Measurement Assurance," NBSIR 77-1240, April

1977.

[6] Cameron, J. M., "Measurement Assurance," Journal of Quality

Technology, Vol. 8, No. 1, pp. 53-55, January 1976.

[7] Cameron, J. M. & Hailes, Geraldine E., "Designs for the

Calibration of Small Groups of Standards in the Pressence of

Drift," NBS Technical Note 844, August 1974.

[8] Cameron, J. M., Croarkin, M. C, Raybold, R. C, "Designs for the

Calibration of Standards of Mass," NBS Technical Note 952, June

1977.

[9] Ku, Harry H., "Statistical Concepts in Metrology," Precision

Measurement and Calibration , NBS SP 300, Vol. 1, pp. 296-330.

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

Length Measurements, Part 1. Long Gage Blocks (5 In. to 20 In.),"

NBS Monograph 149, November 1975.

[II] Pontius, P.E., "Measurement Philosophy of the Pilot Program for

Mass Calibration," Technical Note 288, May 1966.

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

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

1974.

[13] Tucker, C. D., "Preparations for Gage Block Comparison

Measurements," NBSIR 74-523, 1974.

[14] "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.

64
APPENDIX A

TREND ELIMINATING DESIGN

Let the two test sets be designated by A and B and the two standard

sets by S] and $2. The design involves making the following observations

in the order given:

- - $2

Z2 = B -

Z3 = A - B

^4 ~ ^2 ' ^

The least squares estimates of the standards S-] and $2 are given by:

S-i = 2V^5Zi - 2Z2 - Z3 - 2Z4 - Szg - 2zg + 3Zj + 2Zg + 12K}

1 S2 = J^-^^^ + 2Z2 + Z3 + 2Z4 + Szg + 2Zg - 3Zy - 2Zg + 12K}

The estimate of the difference L^ = Si - So is

c I 2

The estimates for the test blocks are:

A = Y^i-z-^ + 2z2 + 5Z3 - 6Z4 - + 2zg - 7Zj + 6Zg + 12K}

B = ^ {z-| + 6Z2 - 5Z3 - 2z^ - 7z^ + 6Zg - z^ + 2Zg + 12K}

where K is the assigned value of S-] plus the assigned value of S2.

65
The variances of the parameters are given by:

wherea^ is the within process variance whose least squares estimate is

given oy:

8

E dev.^

> - i=i

w

4

dev-i

1 " {49z^ 7Z2 . 21z^ + 49Z5 + 49zg - 7z^ + 21zg}

dev2 1 " TO {-7Z-, + 87Z2 + 13Z3 - 5Z4 + 33Z5 - ^l^s + 53Z7 + 35zg}

dev3

1 168

{-7z^ + 13Z2 + 89Z3 + 25Z4 - 39Z5 + 37zg + 57zy - 7zg}

dev^ 1 - 168 {21z^ 5Z2 + 25Z2 + IIIZ4 - 27Zg + 3Zg - 23z^ + 63Zg}

deVg

1 - 168 {49z^ + 33z2 - 39^3 - 27Z4 + 97Zg + 25Zg + 9z^ + 21Zg}

devg

1 168

{49z^ 41

Z2 + 37Z3 + 3Z4 + 25Z5 + 103Zg + I3Z7 - 21Zg}

devy 1 " TO" {-7z^ + 53z2 - 23Z4 + 9Z5 + 13Zg + 73Z7 - 7Zg}

devg

1 168 {21z^ + 35z2 - '^z' 63z^ + 21Zg - 21zg - Iz-j + 63Zg}

The pooled within standard deviation for n calibrations would be

The following data was taken on two test blocks A and B and two

standard blocks S] and $2 using the trend eliminating design over a six month period.

66
DATA ON FOUR BLOCKS OF NOMINAL SIZE 0.500 INCHES

Corrections in Microinches

Observations Run 1 2 3

S-i -S^ 55.9 51.7 54.0 51.1 53.9 50.2

B-St

1 56.3 55.9 52.1 54.2 52.0 53.5

A - B 56.0 56.5 51.2 52.2 55.7 51.0

S2-A 51.9 55.2 51.1 52.2 50.8 56.0

S2-B 52.0 56.8 51.2 52.8 51.0 51.4

B-S^ 57.0 56.0 52.7 54.3 51.7 54.9

S-|-A 56.1 56.0 54.7 52.0 54.7 54.9

A-S2 56.2 52.2 52.1 51.5 56.3 51.8

4 5 6

53.0 50.0 56.0 54.0 52.8 51.3

54.0 53.2 55.0 56.0 55.3 53.0

63.2 54.2 54.8 55.8 51.1 55.9

00 . u \jC . C OH- . C. 0 1 .

0

50.2 54.5 52.0 55.0 50.3 55.5

54.8 53.8 55.0 55.5 56.0 53.1

53.8 63.0 55.0 53.8 53.1 51.9

63.0 50.2 53.8 52.2 52.0 50.3

67
The least squares estimates of the parameters are as follows:

Run r\U 1

1

1

1

dt , nnuu

A

"^4 1

1

. 1 1

AsRD

/SU

w

407

C 51 5? 18

-i 3 fin 5R ?1 SI ?1

At •J • Uc. 54 Q8 537

5 2.82 52.54 53.32 .525

6 1.98 51.84 56.22 .729

If this group of measurements is the basis for the starting values

in a measurement assurance program, then the value of the control

Lc " ^1 " ^2 would be the average 3.11; the pooled within standard

deviation would be ^ = 0.606 and the total standard deviation 0.696.

68
APPENDIX B

B.l Interferometn'c Gage Block Comparator , No Standards , One or More

Measurements on Unknowns, One Set of Control Blocks

B.1.1 The Measurement Process

Test blocks can be measured directly in terms of light wavelengths.

This can be done with fringe counting interferometric comparators, or

static interferometers of the Kosters or Fizeau types. In most

processes duplicate measurements are made. Unless the second set of

measurements are separated far enough in time to be statistically

independent, the differences should not be used in setting bounds for

the process random error.

The random errors associated with the process are of two kinds: those

arising from repetitions in the short term (a few minutes) and those

involving long-term differences (day to day, week to week, etc.). The

random error appropriate for regular calibration is that associated

with the repeated measurement of a control block over a sufficiently

long time period to insure that all factors affecting variability have

a chance to use their influence. The amount of variation in the

measurement process is usually length dependent because of temperature

effects on the blocks and because of ambient air conditions affecting

the wavelength. For this reason and for convenience of working group

size, the usual set of blocks (80 or so blocks in the 0.050 to 4 in.

range) should be treated as a number of subsets of up to 20 blocks

each. At NBS the six groups listed below are used:

Nominal Length Approximate

Group ( Inches) No . of Blocks

I 0.050 to 0.09375 4

II 0.100 to 0.107 20

III 0.108 to 0.126 20

IV 0.127 to 0.146 20

V 0.147 to 0.500 15

VI 0.550 to 4.000 13

Redundancy is introduced into the system by repeatedly including a control block in the measurement procedure. The control set should be

made up of at least one block from each group with more blocks of the

larger sizes. A suggested set of control blocks is:

69
Group

Nominal Size

(Inches)

No. of

Control Blocks

K

I II

III

IV

V

VI

0.05

0.1

0.125

0.140

0.25, 0.50

0.75, 1.0, 2.0, 4.0

2

4

One would expect the same variability for all control blocks in a group so that the standard deviations* computed for each of the

control blocks in a group could be combined into one overall standard

deviation for the group. If S], . . . S|^ are the standard deviations

for the k blocks in a group with degrees of freedom v-] , . . . respectively, then

B.1.2 Establishing Process Parameters

To determine initial accepted values** for the controls and for the

random error component, all the blocks in the control set should be

measured by the usual process, say 6 times, with a few days between

repetitions.

From that initial data, an average and a standard deviation should be

computed for each control block. The accepted values for the control

and for the random error component will be the average value for the

block and the standard deviation for the group as indicated above.

These will be the starting accepted values for the process. A portion

of a typical worksheet showing starting values for two blocks in a control set is given in Figure 1 (page 17 ). Examples given in the

following sections are based on these two blocks and their parameters.

All data in the examples is illustrative and is intended only to

explain the methodology.

*The standard deviation of a single observation is given by

the r^- is the difference between each observation and the average of

n observations. The quantity n-1 is called the degrees of freedom

associated with s.

**The term "value" for a gage block means the deviation from nominal

size (measured length minus nominal length) at 20 "C.

70

/ n-1

where
B.1.3 Maintaining Process Control

After the process parameters have been established, control is

maintained by checking the control value after each calibration run

against the accepted control value. A sample worksheet (see Figure 1)

details how this is done and shows the appropriate statistical tests

for determining whether or not the process is in control.

B.1.4 Updating Process Parameters

As information collects on the regularly used control blocks, the

accepted values for these blocks should be updated. A sample

worksheet showing how this is done is given in Figure 3 (page 20).

The frequency of updating will depend on the workload but should be

done after 5 or 10 values initially and then at intervals dictated by

convenience (e.g., every 6 months or a year).

B.1.5 Relationship to National Standards

It is important to know if a process produces values which are

consistent with the National standards as maintained by NBS. A

convenient method for testing the whole system is afforded by using

two calibrated sets loaned to the laboratory by NBS (or two NBS

calibrated sets owned by the laboratory). These need not be complete

sets but could be small sets consisting of a size distribution of

blocks similar to the control set. If each of these sets is measured

as a test set in the calibration procedure, one will have the

independent check needed to test for consistency with NBS. The data

should be taken by the regular calibration process. Two complete

calibrations should be done a day or two apart.

Laboratories with the capability of writing their own documented test

report based on their measurements of the NBS sets are encouraged to

do so. In this case NBS will provide the two calibrated sets of

blocks, and their current assigned values. The table in Figure 4

(page 22) summarizes the analysis of the data and shows whether or not

there is a significant offset from the NBS process. If the offset is

significant, the values for the laboratory reference standards and

their associated uncertainties should be corrected as shown in the

suggested "Report of Test" form in Figure B.2. In effect this gives

each laboratory a method for determining the offset from the NBS

process.

B.1.6 Uncertainty

The uncertainty, +U, associated with any test block calibrated by this

process, assuming the process is in control, is given by

U = E + 3sg

71
where E is the offset between the laboratory's process and the NBS

process (see Figure B.2), and sq is the accepted group standard

deviation for that block size (see Figure 4). For convenience one may

use the maximum uncertainty found in the group so as to report a single uncertainty value for the whole group.

B.1.7 Summary

In sections B.1.3 and B.1.5 tests are described which determine if the

process is in control. In the absence of a specific format for outof -control conditions, it should be noted that once predictability is

lost, no statements should be made about the condition of the process.

Until the process parameters have been re-established or some

satisfactory corrective action has been taken, any uncertainty

statements which are issued should be designated as provisional.

Nearly all of the statements made in section 4 (Operating a Measurement Assurance Program) apply to the interferometric technique

as well. If the process is found to be out-of -control by an F-test or

a t-test, the trouble sources listed in section 4.6 are valid, but a number of other sources need to be added if a length dependent systemat

error is revealed when the NBS reference sets are measured. These

error sources, unique to interferometers, are:

(1) Air temperature measurement

(2) Barometric pressure measurement

(3) Humidity measurement

(4) Vacuum wavelength of the light source

(5) Wavelength correction formula in which the above parameters are

used

(6) Gage block temperature measurement

(7) Misalignment of the optical axis with the measurement axis of the

interferometer

(8) Offset of the optical axis from the measurement axis of the

interferometer (Abbe offset).

A full discussion of an interferometric measurement process and its

error sources is in reference [4]

72
FIGURE B.l

OBSERVED VALUE OF CONTROL COMPARED TO ACCEPTED VALUE OF CONTROL

Values in Microinches at 20 °C

Nominal

Size Ident.

Interferometer

Readings

Value of

Block

Arrpn1"pH

Value

of Control

ArrpnfpH

Group

S.D.

t Test*

Limit to

Random Error

(Inches) ' C ' u 3Sp

X L ^Gt R

0.10000 Test 100020.0 20.0 4.0

I—

1

t—t 0.10000 Control 100019.0 19.0 16.7 1.34 1.0

Q.O 0.10010 Test 100114.0 14.0 4.0

s- 0.10020 Test 100218.4 18.4 4.0

0.147 Test 147019.8 19.8 5.2

>

0.148 Test 148019.9 19.9 5.2

o.

Z3 0.150 Test 150017.9 17.9 5.2

O

s- 0.150 Control 150018.6 18.6 16.2 1.75 1.4

0.200 Test , 200021.2 21.2 5.2

*If t >^ 3, process is out of control for that group. Repeat entire group.

73
FIGURE B.2

REPORT OF TEST

of

Length Calibrations From ^to Inches

Using

NBS Gage Block Sets ^and

PARTICIPATING LABORATORY

Duplicate measurements made by the participating laboratory on NBS Gage Block Sets

and ^made by calibrating each NBS set against a standard set during a regular

calibration procedure gave the following results at 20 °C (values used are in microinches)

A. Standard Deviations

Accepted SD DF From Test DF Test Combined SD DF

Group Sg X-j Sj^j X2 F s^ X^

Conclusions from the F-test:

(a) If F < F Qi

for X^ and X^ degrees of freedom, the process is in control, and the

standard deviation used in the uncertainty statement is s^.

(b) If F >_ F Qifor X-j and X^^ degrees of freedom, the process is out of control, and the

uncertainty statement is omitted.

NOTE: Standard deviations Sp, s^ and s^ are found in Figure 4.

74
FIGURE B.2--continued

B. Offset of Participating Laboratory's Process from NBS

Nominal

Size

From NBS Process From This Test

Assigned Values Calibrated Values

NBS^ NBS2 NBS^ NBSg Offset

t Test

Uncertainty

Test Block

( Inches

)

1/2{(N^+N2)-(W^+W2)}

W

2

N E t U

Conclusions from t test:

(a) If t < 3, there is no offset from the NBS process, and the systematic error E is

negl igible.

(b) If t >_ 3, there is an offset from the NBS process, and the systematic error E should

be added to the random error limit 3s^ to get the uncertainty for any test block.

NOTE: The computations of the F and t statistics are found in Figure 4.

75
tiBS-114A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBS Monograph 163

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Measurement Assurance for Gage Blocks

5. Publication Date February 1979

6. Performing Organization Code

7. AUTHOR(S)

Carroll Croarkin, John Beers, and Clyde Tucker

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No.

11. Contract/Grant Nc

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP) 13. Type of Report & Period

Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 78-600162

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

bibliography or literature survey, mention it here.)

This monograph is intended for those who need to know on a continuing basis the

uncertainty of their gage block calibration procedure. A general discussion of

the philosophy of measurement assurance is given first. Then three levels of

measurement assurance programs are outlined showing how control over the measurement process can be maintained and how the offset (or systematic error) from the

unit of length maintained by the National Bureau of Standards can be made negligible.

__m.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper .(J name; separated by semicolons

)

Calibration; gage blocks; length; measurement assurance; measurement process control;

systematic error; uncertainty

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