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Pontius, P. E/Measurement assurance prog QC100 .U556 V149;PT1;1975 C.I NBS-PUB-C

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

Measurement Assurance Profifram—

Case Study:

Length Measurements.

Part 1. Long Gage Blocks

(b in ZU m)
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 consists of the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology,

the Institute for Computer Sciences and Technology, and the Office for Information Programs.

THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United

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THE INSTITUTE FOR MATERIALS RESEARCH conducts materials research leading to improved methods of measurement, standards, and data on the properties of well-characterized

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2 Located at Boulder, Colorado 80302.
V, f>F STANDABD8

JAN 1 4 1976

Measurement Assurance ProgramA Case Study: Length Measurements. ' n». m

Part 1. Long Gage Blocks (5 in to 20 in) f^-is

Paul E. Pontius

Institute for Basic Standards

National Bureau of Standards

Washington, D.C. 20234

U.S. DEPARTMENT OF COMMERCE, Rogers C. B. Morton, Secretary

James A. Baker, III, Under Secrefary

Dr. Betsy Ancker-Johnson, Assisfani Secrefary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acfing Director

Issued November 1975
Library of Congress Cataloging in Publication Data

Pontius, P. E. Measurement Assurance Program, a Case Study.

(NBS Monograph; 149

Includes bibliographical references. CONTENTS: Pt. 1. Long gage blocks (5 in to 20 in)

Supt. of Docs. No.: C 13.44:149

1. Physical Measurements. 2. Length Measurement. I. Title.

II. Series: United States. National Bureau of Standards. Monograph; 149

QC100.U556 No. 149, etc. [QC39] 389'.08s [530'.8] 74-31143

National Bureau of Standards Monograph 149

Nat. Bur. Stand. (U.S.), Monogr. 149, 75 pages (Nov. 1975)

CODEN: NBSMA6

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1975

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

(Order by SD Catalog No. C13.44: 149). Price $1.35 (Add 25 percent additional for other than U.S. mailing)

Stock Number 003-003-01390
Contents

PAGE

1. Introduction 1

2. A Comparison — Traditional metrology and measurement assurance programs 2

3. Variability — Two approaches 3

4. Summarizing history 6

4.1. Predicted values 6

4.2. Supporting evidence 12

4.3. Estabhshing "Old" accepted interferometric values 14

5. A new point of departure 16

5.1. Definitions 16

5.2. Single wavelength interferometry 18

5.3. The comparison process 20

5.4. Transfer techniques , 21

5.5. Thermal conditions 23

5.6. "Practical" and "Virtual" surfaces 25

6. Developing a measurement process 28

6.1. Restraint requirements 28

6.2. Predicted values (process I) ... 31

6.3. Process II performance parameters 35

6.4. Closure 37

6.5. Process surveillance 39

7. Measurement process in action 45

7.1. Uncertainty of the transferred value 45

7.2. Verifying the uncertainty 47

7.3. Other measurement processes 47

7.4. Operational "Addition" 50

8. Summary 51

9. References 54

10. Appendix 1. Definition and use of length value assigned to a block or artifact 55

11. Appendix 2. Gage block intercomparison designs 57

12. Appendix 3. Gage block interferometry 59

13. Appendix 4. The gage block comparator 63

'4. Appendix 5. Introduction to the report of calibration 65

iii

The Measurement Assurance Program —

A Case Study:

Length Measurements

Part I — Long Gage Blocks (5 in to 20 in)

P. E. Pontius

The differences between the methods of traditional metrology and the measurement assurance programs are briefly discussed. The historical data relative to long gage blocks (5 in to 20 in) are analysed

to provide a basis for comparison with results from new measurement processes formulated in ac- cordance with the philosophies of the measurement assurance programs. The results from the new

processes are in agreement with the work of the past. The current length values assigned and asso- ciated uncertainties are shown for selected long gage blocks used in the dissemination of length by

the National Bureau of Standards. These long gage blocks are a part of a growing collection of similar well characterized artifact standards for use in comparative measurement processes. The methods

and techniques used in developing the new measurement process are discussed in some detail. It is the author's intent that, in addition to the technical content, this paper be largely tutorial in the area

of measurement process analysis. This paper is, in essence, a report on the extension of the techniques

first suggested in NBS Monograph 103 "Realistic Uncertainties and the Mass Measurement Process"

to the area of length measurement.

Key words: Measurement algorithm; measurement assurance; measurement process; measurement

unit; process variability; uncertainty.

1. Introduction

The National Bureau of Standards has been

engaged for some time in the development of length

measurement processes which are in accordance

with the philosophies of the Measurement Assurance

Program (MAP). One of the ultimate goals in this

work is the optimization of the uncertainty ^ of the

values assigned to artifact length standards, such as gage block. Work to this end requires not only a reevaluation of the manner in which values are assigned, but also a complete characterization of

the measurement processes of both the National

Bureau of Standards and the users of the calibration

service. Eventually all of the National Bureau of

Standards length measuring processes wiU be

modified. This paper covers the progress to date on

the long gage blocks (from 5 to 20 in in length).

Currently, the basis for the values reported by

the National Bureau of Standards are the values

assigned to a group of gage blocks which are normally called "Starting Standards." These values

have been assigned by interferometric methods

using a stabiUzed laser as a light source. The

wavelength of the laser hght has been estabhshed.

' The term uncertainly is used to designate a quantitative statement of the bounds

fpr error assoicated with a particular measurement resuh. An optimized uncertainty

results from a selection of measurement methods and processes which, in combination, conserve measurement effort yet provide demonstrable evidence that the uncertainty

is realistic regardless of the number of transfers between the user and the defined

standard. A realistic uncertainty is, in turn, the basis for judging the adequacy of a given measurement result relative to the manner in which the result is to be used.

and is monitored periodically with indirect reference

to the present defining Krypton radiation.^ Values

assigned to other blocks are determined from

comparative measurement data. At the present

time, comparators with contacting transducers

are being used, however, any well characterized

comparative process would be suitable. All new

procedures include features which permit the

estabhshment of meaningful process performance

parameters, as well as means to monitor the

process performance over time. The purpose of

this paper is to verify the closure between the

"old" process and the "new" process, and to describe the present "points of departure" upon

which some of the current assigned length values

are based.

This paper is organized as follows: Section 2

presents some of the philosophical differences

between traditional metrology and the measurement

assurance programs. Section 3 examines in detail a typical list of "error budget" items in the hght of

the measurement assurance program philosophy.

Section 4 is a review of the calibration history of

selected gage blocks. The historical data are ana- lysed to estabhsh a predicted value at a given time

and an estimated uncertainty of that value. The

predicted value will be used to verify continuity

with the "new" process results. Section 5 discusses

* Direct calibration of the laser wavelength against 86Kr is possible, but is relatively tedious and expensive. The procedure used is a heterodyne comparison of the stabilized He-Ne laser with an iodine stabilized laser. This procedure is both rapid and precise, with measurement errors at or below 1 part in 10* easily achieved [i].

1
the new procedures, the interferometric and comparative process, and also some of the supplementary studies relating to systematic errors. Section 6 demonstrates that there is continuity and

discusses the development of the "new" measure- ment process. Section 7 summarizes the perform- ance to date of this "new" process. Section 8 is a

closing summary.

2. A Comparison — Traditional Metrology versus Measurement Assurance Programs

Traditional metrology, almost exclusively con- cerned with the propagation of measurement units,

regarded measurement as a reahzation of the highly

idealized process by which the quantity being measured was defined. Each measurement was in essence a "work of art," the result being accepted

mainly on the basis of the method used and the

reputation of the person making the measurement.

The traditionahst knew that placing severe restrictions on the characteristics of objects being measured, and on the measurement environment, would

reduce errors from such sources. While his stature

among his peers was directly related to the small- ness of the uncertainty associated with his work,

he did not always have the means to estabhsh rea- hstic uncertainty statements. When his measure- ments related to practical measurement processes, in

many cases, his results were considered correct

by "definition." His uncertainty statements were

largely a matter of judgment, sometimes with a disclaimer stating that the result was applicable

only in his laboratory at the time of the measurement. Nonetheless, while he had difficulty in relating to practical measurements, his dihgence and

attention to detail provide a basis for a different

approach.

The dividing fine between the era of traditional

metrology and the era of measurement assurance programs is clearly associated with the development and increasing accessibihty of large computers. Even with simple comparison procedures,

the traditionahst had to make long, detailed hand

computations. A large percentage of his time was

spent in concentrating on mathematical procedures,

checking and double checking hand computations.

In order to simplify the computations, tables were

constructed for a variety of things such as air density, and "fringe fractions" per microinch departure

from nominal value for a variety of spectral sources under standard conditions. As a consequence the

measurement processes became married to the ta- bles. Now, through the computer, one has in effect

tables for all possible combinations of variables. In

addition, matrix manipulation, statistical analysis,

control charts, correlation studies, and the hke are immediately available. Both the philosophy and

scope of the measurement assurance programs are a direct result of being able to store and recall

large amounts of data, and to analyze and format

the results in many different ways.

One can think of aU of the measurement processes

in our technical society as parts of measurement

systems — length measurement systems, mass

measurement systems,^ and so on. Within these

systems, measurements are made to accomphsh a wide variety of functions. The measurement

processes are merely tools, subject to an equally

wide variety of value judgments. It is the quahty

of the measurements made by these processes that are of primary concern. One would like to have

assurance that each individual measurement within

the system is correct enough for its intended use. When the measurement result is necessary to the

successful completion of the task at hand, then if length or mass (or whatever) measurements are to have real meaning, one must be able to make the

required measurements on the object of interest

in an environment appropriate to the particular

task.

The measurement process is a production

process, the product being numbers which represent

certain characteristics of the item or phenomenon

under study. The uncertainty at a given location is related to the output of the whole process — the

instrument, the operator, the procedure, etc. Once

one accepts the concept of measurement as a

production process rather than a "work of art," one can introduce redundancy into the procedures

which can be used to ascertain parameters which

are descriptive of the process performance characteristics and to monitor the process performance.

For example, comparing one gage block with two

"master" blocks, and averaging the results, will

establish a number for the length of the block. In

the past the redundancy of this method was used to check for "bad" measurements and almost never to estabhsh properties of the process. Such a procedure could also give information about the

process, namely the observed difference between

the two "masters." Comparing two gage blocks

with two "masters" according to a measurement

design provides, with httle additional effort, not

only a value for each of the two blocks, but also a "check" on the constancy of the "masters," an

estimate of the short term process precision, and

in time, an estimate of the long term process

variabihty. The first procedure in which a single

gage block is compared to two "masters" requires

only simple arithmetic operations. The second

procedure requires sophisticated data processing

which has only been available within the last ten

years.

^The initial work leading lo the development of measurement assurance programs

in calibration was in the area of mass measurement. This work is described in part in references [2, 3, and 4].

2
The complexity of a measurement assurance program depends upon the purpose a particular

measurement is to serve. The program analysis

relies on data actually generated by each measure- ment process; therefore, the process performance

parameters are valid descriptors of the expected

process performance. Procedural steps incorporated

in routine measurements provide data which, in

turn, can be checked against parameter estimates

to give a continuing assurance that the process

performance is as expected. For processes supporting modest requirements, these procedural steps can be very simple. As the requirements become

more stringent, obviously the monitoring procedures

become more complex.

Assigning a value which is to be used as the length

of a gage block and determining the uncertainty of

that value is not a simple task. The properties of the

block, as a function of time and temperature, are determined using a process whose behavior must be

monitored as a function of procedural, instrumental,

or environmental changes. In addition, there are parameters related to the optical or mechanical

process which need to be measured to provide

bounds for the departures from the assumed

physical model. Also, one needs to have vaUd estimates for the various components of variabiHty

from which one can make the proper combination

for bounds to random error. To achieve the objective, one needs a sequence of measurements over a

sufficiently long time span to allow the influence of

various perturbations to exert their full influence on the process. This leads to valid estimates of the

effects of random error. By properly combining

these with systematic study of the eff"ect on the

output of controlled changes in certain factors and

correlation studies of the eff"ects involving those

factors not subject to control, one arrives at a realistic uncertainty statement.

Having completely characterized one process, in

terms of process definition and appropriate performance parameters, the characterization of other

similar processes consists mostly of determining

the numerical values for the various performance

parameters. These parameters determine realistic

uncertainty statements which permit meaningful

comparison of results from diff"erent locations.

The measurement assurance approach enables one to clearly establish the limitations of a particular

method of measurement. In cases where the re- quired uncertainty of measurement for a particular

task is unusually small, the program will provide

some guidance as to possible actions which may

produce satisfactory results. The program provides

a means to monitor the performance of various

measurement processes throughout the system.

One result from the program is a clear definition of

the level at which various factors significantly

affect the uncertainty. This information, together

with a clear definition of process performance re- quirements, can be used to grossly simphfy many

existing measurement processes and procedures.

3. Variability— Two Approaches

As a point of departure, all length measurement

processes are, directly or indirectly, comparative

operations. Even the most simple concept of such a measurement contains certain implicit assumptions:

(a) a constancy in the basis for the ordering or comparing;

(b) a stability in the equipment, procedures,

operator and the like which are used to make

the measurement; and

(c) a stability in the object, effect or property

being observed.

Quantitative ordering implies an invariant basis

for the ordering, thus a long term constancy in a standard unit and a stability in the realization of a standard unit, is necessary. In a similar manner, the

property to be measured must also be stable. If a measurement process detects a difference between

two things, it is expected that repeated measures

of that difference should agree reasonably well. In

the absence of severe external influence, one does

not expect things to change rapidly.

There is a difference between stability and

constancy in context with the above. Repeated

measurements over time can exhibit a random hke

variabiUty about a constant value, or about a time

dependent value. In either case, if the results are not erratic (with no unexpected changes), the

process is considered to be stable. The objects

being compared may have constant values, or may

be changing at a uniform rate, or may be changing

at different rates. For continuity, time dependent

terms must be included in quantitative descriptors

for both objects being compared. Stable changes with

time can be extrapolated in the same manner that one "extrapolates" a constant value over time. The

extrapolations can be verified whenever desired by

making additional measurements. Constancy, then,

merely means that the coefficients of time dependent terms are essentially zero. Gage blocks

which are changing at a constant rate are considered

to be stable. This is not to say that features such as constancy, and perhaps geometry, are not desirable

for certain usage, but only that such features are not necessary restrictions on the ability to make

good and useful measurments.

Two quantitative descriptors are used to describe

the process variability, and ultimately, to establish

the bounds for the limit of error. A given measure3
ment process is continually affected by perturbations from a variety of sources. The random like

variability of the collection of repeated measure- ments is a result of these perturbations. One

descriptor, designated random error, includes

effects from both cyclic perturbations such as might

be associated with the environment and variabihty

associated with operating procedures. The random

variability imphes a probability distribution for

which one can set limits such that the range of

variabihty in the collection is not hkely to exceed

certain bounds. The second descriptor,, designated

systematic error, S.E., includes the use of constants

which are in error as well as discrepancies from

certain operational techniques. The S.E., expressed

as a single number, is an estimate of the offset

of the measurement result from some defined

process average. These two descriptors, called the

process performance parameters, are factors in

assessing the worth of a result relative to a particular

requirement.

The random error estimate reflects the effects

of cycUc perturbations which are constantly changing whether the process is being used or not.* These effects can be grouped into two categories:

short term effects which vary through one or more

cycles in the course of a single measurement or measurements made over a short time interval, and

long term effects in which the period of the effect

is at least , as long as the time required for a given

sequence of measurements.

A second category of short term effects are those

which are instantaneous, or step-hke, in nature.

In many cases, "shocks" on the instrument, or variations in the manner in which various objects

are introduced to the instrument, cause changes in

the instrument configuration which affect the

instrument indication. The effects appear as minute,

and sometimes not so minute, instrument reading

scale shifts. The thickness of the film between

two gage blocks which have been "wrung" together

is an example of a step-hke source of variability.

While for each "wring" there is a finite film thickness, for repeated "wrings," the film thickness is never quite the same.

In terms of measurement process performance,

the within-group variabihty expressed as a standard

deviation, aw, reflects the combined short term

effects. In many cases, ctw represents an optimum

process performance. The within-group variabihty

of the measurement process is the most famiUar

process parameter as it is easily demonstrated in a repeated sequence of measurements of the same

thing in a very short time interval. Practically aU

important measurements are repeated several

times. The magnitude of the within-group variabihty

is generally established by the degree to which

certain types of perturbations are controlled and by

factors such as the operator skills, quahty of the

instrument, and attention to detail procedure. In

most cases one cannot identify sources of perturbations which contribute to within-group variabihty.

Process improvement in terms of reducing crw is obtained perhaps more frequently by trial and error than by design. The adequacy of a given process

relative to a particular requirement is often judged

on the basis of the within-group variabihty. Such a judgment, however, may be erroneous. The total variability is the variabihty of a long

sequence of data which reflects the effects of aU

possible perturbations. Repeating a given measure- ment over a time interval sufficiently long to reflect

the influence of all possible perturbations estabhshes a total process standard deviation, ctt, which

reflects both the short term and the long term ran- dom variabihty.^

With a sufficiently long sequence of data, one

should be able to identify the sources of the largest

perturbation through supplemental measurements

and correlation studies. Having identified the source

of the largest perturbation, the magnitude of its effect on the measurement can be minimized, with a consequent reduction in the magnitude of err- Frequently one is tempted to ideahze the process in

order to reduce the total variabihty, that is, to estabhsh a carefully controlled environment and use only

selected artifacts. Such actions are self-defeating in

terms of understanding the measurement process.

A more appropriate action, provided one has

sufficient motivation and resources, is to modify the

process to account for the variabihty associated

with all the perturbations that can be identified.

There are several different classes of Systematic

Errors. Perhaps the most famihar class of S.E. is associated with instrument reading scale offset. Such S.E.'s are not present in comparative meas- urements provided that the instrument indication can be related to the measurement unit, and

provided that the instrument response is reasonably

hnear over the range of difference which must be

measured. A second class of S.E.'s is associated

with supplemental data such as barometric pressure,

temperature and relative humidity measurements

which are in turn combined to determine air

density, index of refraction and the hke. Each of the

supplemental measurements is, in essence, a separate distinct measurement process with both

random variabihty and systematic effects. The

'Reference [5] ai-i figure 24 in section 7.1 show that the collection of values obtained by sampling at random times the value of the sum of as few as four sinusoidal functions, each of equal amphtude, but of periods differing by a factor of 10, has the appearance

of a normal distribution for even moderate sized sequences of observations.

^ The total process variability, ar, can be thought of as the sum of the variabilities of all of the perturbations that affect the process, that is, o-r^o-i^-Hra^H-. - . . (Tn^. For one class of perturbation with variabiUties (Ti to (r.n, which are those with very

short periods and with nearly equal amplitudes, it may not be possible to identify the

individual perturbations. The variabihty from these perturbations combine to form a threshold variabihty tr^. Other perturbations, with variabiUties (Tm+i to an, may be

identifiable if the magnitudes are sufficiently large. These effects combine to form a between time component of variability a-p. The total variability is then <jT^ = (r^^+<T^\

4
random variability of the supplemental measure- ments is, of course, reflected in the total process

variability. The S.E.'s associated with supplemental data must be carefully considered.

One action, which is rarely practical, would be

to "randomize" the S.E. by using different instruments, operators, environmental or other factors.

Thus, the variation from these sources becomes

part of the random error. A more practical procedure

is to evaluate the S.E. associated with an instrument

(or other factor) by direct experiment. When the

change in response, such as, for example, that

introduced by a temperature error of 0.1 degree,

is a small fraction of the standard deviation of the

process, a rather large number of measurements

is required to establish the effect with a reasonable

degree of assurance. Bearing in mind that an

average of n measurements has a standard deviation

of times that of the original measurements,

in order to determine an effect of size one standard

deviation with an uncertainty (3 standard deviations)

of half of its size one would need about 36 measurements. (If one relaxes the uncertainty requirement

for the average to a value equal to the standard

deviation of the process, then 9 measurements

would be required.)

With evidence that the individual supplementary

measurements are satisfactory, the next concern

is the manner in which supplementary data are combined and used to adjust the observed data.

For example, having adjusted the data for thermal

expansion, one would not expect a collection of

values over time to correlate with the temperature

measurements for each individual value in the

collection. A collection of values from repeated

measurements should be tested for correlation

with each of the supplementary measurements, and

their various combinations, as appropriate. If

correlation is indicated, either the supplementary

measurement is not being made at the appropriate

location, or the manner in which the supplementary

measurements are combined does not describe the

effect that is actually occurring. Corrective action

is necessary. Low correlation does not necessarily

indicate that there are no S.E.'s present, but only

that for the supplementary measurements which

have been made, the magnitude of the combined

S.E.'s is not large relative to the total standard

deviation of the process.

There may be long term systematic error effects

from sources not associated with the current

supplemental measurements. It is relatively easy

to demonstrate the presence or absence of such

effects, but it may be difficult to reduce their

magnitudes. If one has available a collection of

values over a long time span, one can compare the

standard deviation as computed for small numbers

of sequential values over short time spans with the

standard deviation of the total collection.® While

reasonable agreement is expected, frequently such

is not the case. If the magnitude of the effect is sufficiently large, the collection of values may

indicate grouping, with the group means appearing

as random variability about the process average.

If the distribution of the collection of values appears

to be bi-modal, one should look for a large long

term cyclic effect. Until the source of such variabihty is identified, and appropriate action taken

to modify the process, the total standard deviation

must be used as the descriptor of the random

variability of the process.

The purpose for measuring gage blocks is to as- sign numbers representing the lengths of the blocks

in such a way that the numbers will be useful to others. The reason for characterizing the measure- ment process is to assign meaningful error bounds,

or uncertainties, to the numbers representing the

lengths. The magnitude of the uncertainty is established by the error bounds of the local measurement

process and the error of the accessible unit. In most

mass and length measurements, access to the unit

is through an artifact which has been assigned a length, or mass, value by another measurement

process. In the case of mass, for example, the

international prototype kilogram is defined to have

zero unit error. With a proces operating in a state

of control, that is, with no known systematic effects

unaccounted for, and with the international prototype kilogram to introduce the unit, the uncertainty

is only a function of the process standard deviation,

either o-w^ or cry. One may report a single measurement, or the

average of n measurements. Few, however, can

afford the time and effort to make a very large number of measurements. As a consequence, the

"reported" result is always offset from the process

average by some amount. This offset is called a systematic error and can be either plus or minus.

When the object as measured above and its assigned

value are used to provide access to the unit in

another process, this systematic error, which is associated with the unit, in combination with the

random variabiUty of the second process, is the

uncertainty of the result from the second process.

For all well characterized measurement processes,

the S.E. associated with the accessible unit is the

only S.E. component in the uncertainty, all other

identifiable S.E.'s having been accounted for in the

process.

Fortunately, most measurement processes for a given parameter are similar so that the complete

* The use of comparison designs, described later in this paper and discussed in detail in reference [6], facilitates this type of analysis. The within group variability,

0"w, is computed for the prescribed sequence of measurements. Each measurement

sequence includes in effect a "check standard" which is measured over and over again

with similar measurement. The total stand.ard deviation is computed for the collection of values for the "check standard." The inequality (Tt>K(Tu, is taken as evidence of the existence of a long term systematic effect, perhaps as yet unidentified. The term K

in the above relation accounts for the fact that the "reported" value of the "check

standard" from the observations required by the design is not a "single value" but, in

effect, is, the average of "n" measurements in the design sequence while (Tw is ihe standard deviation of a "single measurement."

5
characterization and documentation of a typical

process over the range of objects and environments

in which the measurements are usually made substantially shortens the time required for characterizing other processes. As a practical Umit, few

can afford the time and effort to identify perturbations related to either the between-group variabihty

of S.E. components (as previously discussed)

with effects of magnitude less than one standard

deviation of the within-group variabihty. In the end,

the uncertainty associated with a sequence of operations defined to be a measurement is determined in

part by the larger of <tw and ctt and by the S.E.

components associated with the unit. The uncertainty statement must also include the S.E.'s which

are not accounted for in the measurement process

for reasons of convenience.^

One traditional method for determining the limit

of error, or uncertainty, of a measurement result is the use of an error budget. In this method, one

compiles a listing of all known sources of error which might affect the measurement result. Table 1,

[7] shows a rather complete list of the usual error budget items associated with measurement proc- esses used to assign length values to gage blocks.

In the traditional method, one makes a theoretical

analysis of the algorithm and "engineering adjustments" to provide estimates of the magnitude of the

expected variabihty term by term. Such estimates

would then be combined in some manner to obtain an estimate of the total expected error bounds.

While the error budget analysis may be helpful in

some kinds of measurement, it is not unusual to find the results of measurements of the same thing

which disagree in excess of the error bounds estabUshed in this manner. In a repetitive measurement

process, such as the caUbration of gage blocks, one

can verify experimentally the magnitude of the

significant effects contributing to the process

variabihty.

The items normally considered in an error budget

can be further developed into categories according

to the way in which they are most hkely to affect the

uncertainty. One category would contain items

which relate to S.E.'s; another category would re- late to (Tw; and the third category would relate to

(Xb or (Tt. To illustrate the nature of these categories, table 1 also shows a tentative disposition in

terms of a measurement assurance program selected

to: (1) disseminate a physical embodiment of a length unit; (2) characterize a measurement process

in such a manner that reahstic uncertainties can

be estabhshed for the assigned values; and (3)

provide a basis for sorting with respect to other

properties desired for a particular usage (i.e.,

deviation from desired nominal value).

The items included in table 1 are divided roughly

equally between being contributors to the withingroup variabihty, and the between-group variabihty.

All but two can be monitored or evaluated by a

judicious choice of a comparison design, to be used

over time so that all of the perturbations can exert

their full effect on the measurement process. The

two exceptions are the uncertainties associated with

the assigned starting values, or restraint values, and

the conversion of the present instrument indications

to length units.

4. Summarizing History

4.1. Predicted Values

To assure continuity in the transition to a meas- urement process formulated on the basis of a measurement assurance program, some tie between

the old and the liew process must be estabhshed.

If, for a given block, a predicted value based on

historical data can be estabhshed, a reasonable

estimate of the uncertainty of this value can

provide a basis for comparison with a current

value produced by a new process. The difference

between the old and the new values relative to the uncertainty of each would clearly verify the

continuity, or discontinuity, of the measurement

system. To start, an analysis of historical data is necessary to estabhsh an estimate of the predicted

length for each block (as defined in appendix 1), at a specific temperature and at a specific time,

together with an estimate of the uncertainty of

that value. Such a task has been completed for

two groups of long gage blocks (nominal lengths

ranging from 5 in to 20 in).

The first set to be discussed includes the following blocks, the number following "NBS" being the

serial number, and the dash number being the

nominal length in inches and (.) being the short

designator (read as "one dot"):

NBS-M136-5 (.)

-M115A-6(.)

-W202A-7(.)

-M103A-8(.)

NBS-M109A-10(.)

-M135A-12(.)

-M109A-16(.)

-A157-20 (.)

' In many cases acceptable limits relative to a particular usage are large with respect

to measurement process capabilities. In the interest of conserving measurement effort, detailed corrections for S.E.'s are frequently ignored. When such is the case, the

effect of the ignored S.E.'s must be included in the uncertainty statement.

^^Figures in brackets indicate references on page 54.

A cursory review of the cahbration history in- dicates a reasonably stable (not erratic) condition

since approximately 1956. Measurement data, if in existence prior to this date, were not considered

in this analysis. Where necessary, the historical

data have been adjusted to reflect redefinitions

of the inch and of the practical temperature scale

[8, 9]. For comparison, over this time period, the

announced uncertainty associated with gage block

cahbration was ± l/u, in per inch of length. It was

privately felt that a more reahstic estimate might

be ±5fx in for 5 in through 10 in, ±6/a in for 12

in, ±8^1 in for 16 in and ±10/u in for 20 in. With

few exceptions, for the individual blocks, the

deviations from the fitted line shown are well

6
TABLE 1 Error Budget

Spectral Sources Krypton 86 "Red-orange line exact by definition limited by

practical considerations to about .01 ppn in

Disposition

Used only in scanning interferometer under conditions which

realize the defined length as closely as possible. Defined out.

Stabilized Laser

(Laitb-dip)

Working Sources

Index of Refraction

Standard Ctonditions

Standard to Actual

Ccffiditions

Index of Refracticm

Standard to Actual

Conditions

Interferometer

Instrument

"Spectral lines necessary for exact fraction interferoraetry.

"Lairp construction features" "Lanp operating conditions"

"Change with age, stability"

Uncertainty associated with the assigned vacuum wavelength

"Accepted vacuum wavelengths determined by limited

experijnental measurements and reproducibility. Hg 198 - .05 ppm; Cd 114 - .07 ppm. Lanp construct tion features . Lamp operating conditions . "

"Conversion vacuum wavelength to standard conditions using Edlen, Barrell and Sears relation. Alternate irethod using refractateter having un- certainties dependent on use and design."

"Conversion to actual for small range of variable,

if spectral dispersion is used rather than approximations, equations can be considered to introduoe negligible errors. Errors from measuring environ- nental conditions are:"

a. Barcmetric pressure error (mmHg) xO . 36pEm;

typical top quality mercury manometer

.05 cal. uncertainty + .OSirm sd reading;

{.05+3X.05) .36=.07ppm.

b. Air temperature error, (deg C)x.93ppm,- 05° typical thermometer cal. uncertainty

+ .015sd reading; (.05+3x.015) = .09ppm.

c. Humidity (vapor pressure) error (iTiTiHg)x.05 ppm; typical cal. uncertainty liiim, reading error negligible (5% rh) ; lx.05-.05ppm.

d. OO2 content assumed standard usually.

e. Other impurities in air which affect index of refraction.

"Slit width and cfcliquity.

Exact fraction interferonetry used only to determine integral

fringe order. Discarded.

Lamp performance monitored relative to stable lasers. A

problem only to those who assign vacuum wavelengths to other

spectral sources. Discarded.

Vacuum wavelength assigned on the basis of comparison on scanning

interferoTeter with red-orange line of Kr 86. Periodic checks verify stability. Uncertainty of no practical conoem with the

U.S. interconparison of stable lasers on international basis

under way, with undoubted outcome of replacing the Kr 86 definition. S.E. contribution negligible.

Used only in exact fraction interferometry to determine, or

verify the integral fring order nuirber when necessary.

Discarded.

Use latest assessment of Edlen formulas, converting directly from vacuan to actual conditions. Error in functional form systematic

to whole system. Verify by closure.

This group of items is considered to be a source for between-group

variability. It is assumed that, by using the calibration data, the observed data would produce results that tend to a limiting irean which would not differ significantly from th^ real value. That is, the desired paraneter such as air temperature is nearly as often

indicated high as well as low, and the process can detect very small

changes. Correlation studies between the measured temperature and

the final results will indicate the presenos of significant vari- ability due to air tenperature measurement problems locally. Closure

tests may indicate systematic differences between different measure- ment processes. The same applies to baroiEtric pressure and humidity. Between corrponent.

Insofar as CO2 content and other inpurities, local process variability, either long or short term, relates to the difference betk'een the local environment and the assumed standard air. With sufficiently

precise processes, closure test might show up differences between

processes, if it were possible to determine the composition of the

local environment in an easy way. The nature of these changes is only new beginning to be studied as a part of pollution studies. Verify by closure.

Use best recarmended formulas, if significant relative to precision of process. Could be checked with closure studies.

Envircmient

and Seti:p

Interpreting

Interference Pattern

"AligraiEnt, angle of incidenoe; dimensional stability of instrument;

vibration, illumination."

"Planeness of wave front; syiitnetry of interference

pattern; (coatings, noncorpensation , obliquity) ; linearity of viewing optics; contrast and light

level of interference pattern; method of estima- tion of fringe fraction."

First oonsideration is magnitude of effect relative to a precision of

process. If effect significant, must adjust carefully. Other factors affect the within-group variability.

Certain items are obviously a part of the instrunent design and the presence, or absence, of significant effects can only be determined by closure. The use of the laser light source eliminates many of

the problems of the past. Fringe interpretation by means of photointerpretation allows a more versatile approach to the problem. The present procedure uses multiple points to extrapolate to the gaging

point. The use of scanning equipnent may permit determining departures from a defined point at other selected points. Fortunately,

the interpretive process is relative, thus as long as film changes do not destroy the relative position of the image, there is no prc±)lem. Within-grotp oonponent.

7
TABLE 1 (continued)

Item

Interference Length of Block

Phase "Basic material properties, apparently due to

finish.

Disposition

Select prxjoedures to minindze. If departure fran defined process

introduces significant changes, be prepared to determine and adopt

appropriate correction factors. Verify by closure.

Wringing Film Defined out . Process variability affected in part by variability

of wringing film. Studies under way to try to characterize wringing film, the mechanism, and to develop techniques to minimize

variability.

Coefficient of Thermal ExpansionPrecise ccmparative processes will allcw experimental determination of coefficient of expansion for each block with sufficient precision

to be useful over a wide range of temperature. While it is conceded that a reasonably constant temperature is desirable during the

course of a series of interoonparisons , only convention says that

the tenperature must be 20 "C. Between conponent.

Tenperature "Realization of IPTS; teirperature systan

calibration; physical thenral contact

thermometer to block."

Variability block to environnent affects between-time variability. Temperature differences between blocks during caiparison affects within-group variability.

CoT^ression

,

Bending

"Atnospheric pressure; mechanically applied

forces; gravity forces; magnetic forces; material constants such as Young's Modulus, Poisson Ratio."

Minimized by definition of attitude of block at time of measurement. Nbgnitude predictable and of conosm only when significant relative

to process precision. These items perhaps ntore troublesome in the area of dimensional technology. Defined out.

Geometry "Parallelism effect on reading and defini- tion of length; flatness; gecxretry of

interface with wringing.

Only real constraint on parallelism is that associated with deter- mining fringe fraction. Photointrepretation permits a much wider

latitude for variation than interpolation by direct observation. Flatness, and interface, affect the attitude of the block at the time of measurement. Failure to reproduce in attitude is a betweentime CCTnponent of variability.

Mechanical Cbmparison

Stylus "Ete formation, material constants and variation in surface finish." For blocks of similar materials, contributes only to the withinvariability. For blocks of different materials, contributes to

total variability. Data adjustKent may be necessary.

Tenperature "Iteirperature coefficient, tenperature difference." Contributes only to the within-group variability. Judicious choice of ccnparison design will minimize effect. Can Treasure tenperature

differences and coirrect if neoessary.

Stability

"Bending and corpressive forces, variation in material constants , ODirpression clamps . "

"Stability of apparent length with time of

ccnparison of both block and instrunent."

In a coiparative operation, contributes to within-group variability

only.

Minimized by judicious choice of design. Contributes to within-group

variability.

Environment "Adverse environnent conditions; rapid thermal lag

problems; vibration electrical interference, etc.

Design "Anvil-stylus design relations to length definition, effect of flatness of block and anvil."

Gecnetry "Effect of parallelism errors of block on measure- ment regarding gage point definition and inter- action to squareness of sides to ends."

Alignment "Effects of alignment of instrument measuring

tips; block seating, burrs, parallelism errors."

Indication "Magnification of comparator indication." Establishing conversion indication to length

units.

Either defined out, or brought under control in initial assessnent of

process performance.

Minimized by conparative operation. Contributes to within-group

variability.

By specifying the measurement and the attitude of the block at the time of measurement, this is defined out. Further tests may be necessary to establish suitability of block for uses other than transfer of length

unit.

Alignment effects minimized by comparative operation. Block seating

variability contributes to within-group variability. De-burring, etc. a part of a definite "premeasurement" procedure.

Magnification must be such that sate variability is indicated in re- peated measurements of the rrost stable object. Conversion of scale

units to length units cannot readily be made a part of the measurenent

at this time. I^thods are under study which will permit verification in i the course of the neasurement. For the present, this must be accepted i as a systematic error. The magnitude of the error may be insignificant over the range of small differences normally encountered if the callj bration is done carefully. i

I

I

8
within these limits indicating that perhaps more

care than normal was exercised in assigning values

to these blocks.

Figure 1 shows assigned values for the above

blocks over the time interval 1956 and 1971. The

values shown are expressed as corrections or departures from nominal length where the assigned length, L, equals the nominal length, A'^, plus the correction F,v The assigned values were

used as "exact," as indicated by the straight dashed

lines, until such time that a later value was determined. The points are spaced along the X

axis according to the date of the particular document from which they were obtained. Figure 2

NBS M136-5 ( • I

NBS M109A-10 I )

30

(/J. in)

25

J I I \ L. 1957

NBS M115A-6 ( • I

30

26

_l I i I I I L J I L

1957

NBS W202A-7 | •

) 20

10 LJ \ 1 L. 1957 NBS M103A-8 (

50

45

1957 59 61 63 65 67 69 71 1957 59 61 63 65 67 69 71

Figure 1. Historical assigned values, NBS(.)

9
shows the measurement history for a similar set,

the USN blocks, over the same time interval

[10]. Again, the deviations from the fitted line are vfeU within the previously stated hmits.

The values shown were computed from data

produced by an interferometric measurement

process which utiUzed hght sources of different

wavelengths. (For the purpose of this report, such

a procedure is called multiple wavelength interferometry.) While it is known that varying amounts

of measurement effort are associated with the

values shown in these figures, it is accepted that

each value is the result of work which was done

by careful, dedicated metrologists and, as a con- sequence, there is no reason to beheve that any one is more reliable than the others. As a rule,

each block was monitored by comparison with

other known blocks, therefore no particular time

increment was used to determine when a "re- cahbration effort" was required.

The general patterns of the historical values

for both the NBS ( . ) blocks in figure 1 and for the

USN blocks in figure 2 indicate a constant change in

length over the time period covered. In order to establish an appropriate tentative "predicted

value," a fine of the form:

{Y,^,t)={Y^,to) + Ki {t-to)

was fitted to the data. In this relation the correction

to nominal length at any time t, {Yn^i), is a function of the correction at an arbitrary time, to, (Fat, to), the rate of change in microinches per year, Ki,

and the time interval in years {t — to)- In the case of the NBS 7(.) and 8(.), as shown

in figure 1, and the USN-7, shown in figure 2, it was decided that Ki = 0, thus the predicted value

at any date is taken as the average. For the NBS

12(.), it is not clear whether there were measur'ement process problems or whether the block was

USN R317A-5 USN V215A-10

Figure 2. Historical assigned values, USN.

10
really changing. In this case, both the average and

the fitted line were used to establish tentative

values. In the case of NBS 20(.), only two points were available so that the estimate of K\ is very

weak. A summary of the predicted values and uncertainties for the date 1 July 1971 (7/1/71) is shown

in table 2. The uncertainty of the predicted value, as shown

by the parallel Unes above and below the point of

intersection with the time line 7/1/71 in figures 1 and 2, is a function of the number of points in each

collection, the degree of extrapolation beyond the

time span encompassed by these points, and the

standard deviation of the fit [11].

The uncertainty of the predicted value is computed by the relation

where n = the number of points in the collection;

t= time/date of the prediction;

F = average time/date (location of the

centroid of time span covered by

the measurement history, that is t=^tiln);

ti = time/date associated with each of

the n values;

cr = process standard deviation (s.d.

about the fitted line); and = s.d. of predicted value at time*.

A summary of the predicted values and uncertainties, (ScT/s), is shown in table 2. For each

block, an estimated standard deviation, s, has

been computed from the deviations of points from

fitted lines shown. For both the NBS (.) and the

USN reference blocks, s is plotted as a function

of length in figures 3 and 4. The dashed line in

figure 3 is an estimate of cr based on both sets of

reference standards since the two sets are similar

in all respects. The term crC, as defined in table 2,

has been smoothed in figure 4 to obtain an estimate

of CTiS for the NBS (.) group of blocks, cr^ for the

USN blocks is estimated in figure 5. The uncertainties of the predicted values for the USN

blocks is somewhat smaller than those associated

with the predicted values of the NBS (.) blocks

because the USN blocks were measured more

frequently over the same time span.

TABLE 2 Suitmary of the Analysis of Historic Data

Block

Ident. 7/01/71 Predicted Value

No. Points oC

3a„

B n

^BS(.) M136-5 29.5 5 .44 .62 .78 .48 .4 1.2 mi5A-6 28.2 5 .76 .75 .78 .58 .52 1.6 M202A-7 15.4 4 1.63 .87 .33 .29 .64 1.9 M103A-8 47.2 5 1.25 1.0 .73 2.2 M109A-10 55.8 5 1.38 1.22 .78 .95 .95 2.8 M135A-12 68.8/76.0* 1.45 .33 .48 1.16 3.5 m09A-16 66.8 5 2.16 1.92 .80 1.53 1.59 4.8 A157-20 -0.2 2 2.4 2.02 6.1

USN

R317A-5 19.5 8 .89 .62 .43 .27 .27 .8 U157A-6 14.1 7 .38 .75 .48 .37 .35 1.1 T229A-7 43.7 8 .95 .87 .43 .37 .4 1.2 W186A-8 18.5 7 1.04 1.0 .46 .46 .47 1.4 Y215A-10 14.9 7 .4 1.22 .46 .56 .6 1.8 U136A-12 38.7 7 1.0 1.45 .48 .7 .73 2.2 W234A-16 15.5 7 1.4 1.92 .48 .92 1.0 3.0 W198A-20 37.0 6 2.2 2.4 .53 1.3 1.26 3.8

a = estimated process standard deviation (figure 5) A, ^7/1/71

Og = estimated standard deviation of predicted value (figures 6 and 7)

'°B = estimated uncertainty of predicted value

* 68.8 based on average

76.0 based on cotiputed rate of change

11
2.0

crml

1.0

/

/ o /

/

/

/

+ o /

^ /

/

o f

/

lAA L

5 6 7 8 10 12 16 NOMINAL LENGTH

20

2(dev.)2

n-2

o USN

+ NBS (•) process stondard deviation as estimated

from i., deviation of points from fitted

line.

Figure 3. Process standard deviation, historical.

2.0

crC ,cr^

{fj. in)

1.0

/

/

"

7f /

/

/

/

• / • -/

5 6 7 8 10 12 16 20

NOMINAL LENGTH

c = J_ ^

(t7/l/7|-t)'

n 2(t:-t)^

a- Q ^Standard deviation of predicted value

at time t= 7/1/71 (NBS (.) BLOCKS)

1.0

/X in

C

=

5 6 7 8 10 12 16 NOMINAL LENGTH20

2(ti -t )'

;3=Standard deviation of predicted value

at tinne t= 7/1/71 (USN BLOCKS)

Figure 5. S.D. of predicted value, USN.

Figure 4. S.D. of predicted value, NBS{.).

4.2. Supporting Evidence

To verify the reasonableness of the uncertainty

of the predicted values, an effort was made to review all of the measurement history relating

to the NBS(.) blocks. In figure 6, as many in- dependent value estimates as could be found or established are shown on the date the measure- ments were made. Where appropriate, the predicted value line and the predicted value for

7/1/71 together with the uncertainty limits of

that value are shown. As before, all early data

have been adjusted for changes in definition of the

temperature scale and the inch.

The short horizontal line symbols represent

independent values as determined by multiple

wavelength interferometry, an independent meas- urement being defined as the length obtained for one wringing to an appropriate platen. The "re- ported" values shown in figure 1 are the average

values from a collection of such independent

measurements. Because the time lag between

making the measurements and preparing the

report was, in some cases, very long, the location

12
NBS A157A-20 ( .

1962 64 66 68 70 72

Figure 6. Historical data, NBS{.).

13
of the symbols on figure 6 reflect a realistic picture

of process performance over time.

The results indicated by the triangular symbols

on the left side of the figures are values relative to a line scale. Mr. B. Page made a careful compari- son of the NBS (.) blocks with various intervals on a well known 40 inch line scale [12]. In this work

the separation between scribed lines on each of two

"cap" blocks was determined first with the "cap"

blocks wrung together, then with the "cap" blocks

wrung onto the ends of the gage blocks. The dif- ference between the two separations was ascribed

to be the length of the gage block. This was a

difficult, tedious set of measurements, which, in

effect related the gage block length to the traditional meter bar.

The most reveahng information is indicated by

the small open symbols. In all interferometric

measurements which are made by the traditional

methods,^ the length, L, of the object is related to the difference in the length of two appropriate

optical paths by the relation: L = {N + f) {kl2)

In this relation is an integer, / is a fraction,

and the sum, (N+f), is the difference in path

lengths expressed in wavelengths. The term \

is the appropriate wavelength of the light source expressed in length units. The interferometer

provides an estimate for the fringe fraction, /,

thus for each object there are A'^ possible solutions,

only one of which is correct. Observing the same

object with light sources of several different

wavelengths (multiple wavelength interferometry)

introduces some redundancy which can be used to substantially decrease the number of possible

solutions. Even so, the separation between possible solutions is commensurate with the number

of wavelengths available, and in most cases it is necessary to establish an estimate of the integral

number of fringes by some other means. Prior

to 1971, a mechanical comparison with "known"

blocks was used to determine the approximate

integral fringe order. ^ Since the redundancy of

multiple wavelength interferometry could resolve over a range of several fringes, there were

no stringent requirements on the mechanical

comparison.*"

As a consequence of the above procedure, for

each set of gage blocks which was calibrated by

the old interferometric process, the data included

a set of mechanical difference measurements with

respect to the NBS (.) blocks. Accepting the

^Two methods for using interferometry are described in some detail in appendix 3. The traditional method, sometimes called static interferometry, or multiple wavelength interferometry, has normally been used to assign length values to selected objects by metrology laboratories. This method should not be confused with "fringe counting" interferometry, in which one element of the interferometer is moved along

the interval of interest. *The mechanical comparison process is described in detail in appendix 4. ''In the past, a value assigned on the basis of mechanical comparison was de- termined by simply comparing the "unknown" with one or more "knowns." With the exception of values referred to in this paragraph, all other comparison values in this paper are based on comparison designs discussed in Section 5.

interferometric values as the best estimates of the

lengths of the blocks under test, these values,

together with the mechanical difference measurements, provide, in essence, "new values" for the

NBS (.) blocks, as shown by the small open circle

symbols. In all cases, these "feedback" values

do not deviate from the fitted lines, or average

value where appropriate, in excess of the most

optimistic uncertainty estimates previously Usted.

This evidence suggests that the long, tedious in- terferometric measurements did Uttle more than

"verify" that values as transferred from the NBS (.) blocks were appropriate. This evidence also suggests that the inherent precision and simplicity of

the mechanical comparison process was being

ignored.

The small circular symbols with the horizontal

hues, immediately to the left of the "7/1/71" time

lines in figure 6 provide additional evidence to support the routine use of a mechanical transfer

process. Because of the good agreement between

the historical values and the "feedback" values

as described above, formal mechanical comparisons were made, following the procedures

described in section 5.3. The values indicated by

the 0 symbols are the values for the NBS (.) blocks

relative to the USN historical predicted values.

This work is summarized in table 3.

4.3. Establishing "Old" Accepted

Interferometric Values

The supporting evidence for the NBS 12{.)

seems to indicate that the proper vsdue is between

the average value and the predicted value based

on the estimated slope. In all other cases, the

supporting evidence seems to verify the predicted

values. It is of interest to note that values estabhshed by one-to-one mechanical comparisons used

in the old interferometric process, by a defined

single interferometric measurement, by the "cap

block" method with reference to a line scale, and

by the more sophisticated intercomparison designs, appear to fall within limits which are not at

all unreasonable with reference to the uncertainty

of the predicted value.

The assignment of accepted "old" interferometric values is shown in table 4. With minor

changes, as explained, these are essentially the

same as the tentative values of table 2. The estimates of the coefficient Ki, the rate of change of

length in microinches per year, are computed in

table 5. These estimates wiU be subject to considerable discussion, and some revision, later in

this paper.

Finally, the NBS (.) blocks and the USN blocks

have been used in pairs in many mechanical comparisons. One output of the design is the difference

as measured mechanically, between the NBS (.)

14
TABLE 3

Summary of USN and ^BS(.) Predicted Values and ms(.) Values

Assigned Relative to USN Value by Mechanical Coirparison

Nominal

Size

TTCM UoLM Predicted

Value Uncertainty

\Tt3C { \ Relative to NBS ( .

)

Predicted

Value A

Uncertainty

NBS Predicted

Value

(in)* Yd) Yd)

5 19.5 .8 29.1 29.5 - .4 1.2

OO "3 ±. Z 2y . u - . 5

6 14.1 1.1 28.8 28.2 + .6 1.6

0 Q 1 + .5

Z<5 . J

J.+ 1

. 1

7 43.7 1.2 15.5 15.4 + .1 1.9

.0 14 . b - . 8

8 18.5 1.4 48.4 47.2 +1.2 2.2

ft / . t) J- A

'±1.1 + . D

10 14.9 1.8 57.1 55.8 +1.3 2.8

c;^; Q DO . y +1.

1

+i . X

12 38.7 2.2 72.4 68.8/76.0 - 3.5 70.8 - 70.3 -

J . u DO . O

J-+ A. 4A O 4 . o OO 0 U 66.6 - .2

20 37.0 3.8 4.0 -.2 4.2 6.1

3.7 3.9 1.7 1.9 2.5 2.7

1.3 1.5 1.8 2.0 2.7 2.9

2.7 2.9 2.3 2.5

* Except for nominal size, all values in uin

** 3 degrees of freedcm in each measurement

TABLE k mS(.) ACCEPTED PREDICTED VALUES BASED ON HISTORICAL DATA AND MECHANICAL COMPARISONS

- NBS(.)

Ngjinal -Accepted

Size Value

Estimated

Uncertainty Source Yd)

5 29.5 1.2 Table 2

6 28.3 1.6 Table 2

7 14.9 1.9 Average NBS Relative to USN - Table 3

8 47.9 2.2 Average NBS Relative to USN - Table 3

10 56.0 2.8 Minor Adjustment Based on Difference Measurements

(55.8 fran Table 2, 51.0 Average frcin Table 3)

12 70.8 3.5 Minor Adjustment Based on Difference Measurenents

(Uncertainty fran Table 2, 71.2 Average fran Table 3)

16 66.8 4.8 Table 2

20 1.6 6.1 Minor Adjustment Based on Difference Measurements

(-.2 from Table 2, 2.5 Average fran Table 3)

15
TABLE 5 Time-Rate of Change of Length

Difference Difference Ki Nominal Block Values from Granhs (uin) (yin) No. of (Slope Size Ident. 1/1/71 1/1/58 l/i/62 '71- '58 '71- '62 Days yin/yr.

NBS( .

5 MI36 29.5 25.6 3.9 1)718 .300

6 ^al5A 28.2 26.1 2.1 il748 .162

7 W202A* 0

8 Ift03A* 0 10 M109A 55.8 53.5 2.3 1)718 .177

12 M135A* 0 16 m09A 66.9 6i).0 2.8 1)71)8 .215 20 AI57 -.2 12.3 -12.5 3287 -I.D78

* Data doss not indicate conclusively changes of length

vfith time, K, is assumed to be zero for these bloclts.

TABLE 6

(.) - USN (Ti-pical)

NOTiinal Size

Computed

Diff. Between

Predicted Values

Measured Diff. by Ccnparison A

Estimated

Uncertainty of

Corputed Diff.

5 7.4 9.0 1.6 1.6

6 15.2 14.4 -0.8 1.7

7 -28.5 -28.9 -0.4 2.2

8 29.7 29.4 -0.3 2.4

10 41.0 41.8 +0.8 2.6

12 31.6 31.8 0.2 2.9

16 50.2 50.2 0 3.5

20 -36.7 -35.2 1.5 4.2

A = [(Measured Diff, by Comparison) - (Computed Diff. Between Predicted Values)]

and USN block. These differences should agree

with the difference between the accepted "old"

interferometric values. While this point will be

discussed in detail later, a typical comparison of

the computed difference between the predicted

values and the measured difference as determined

in comparisons is given in table 6.

5. A New Point of Departure

5.1. Definitions

Two noncoincident terminators along a specified

coordinate axis determine a length interval. Three

such intervals are of interest. For the defined unit,

the interval is the wavelength of a specified radiation, the terminators being defined by interferometry, and the coordinate axis being defined by the

axis of the interferometer. Practical access to this

unit is through artifacts typified by the hne scale

and the gage block. For the line scale, the terminators are lines marked on a reasonably flat surface.

The coordinate axis is usually defined relative to some additional markings on the scale surface.

For the gage block, the terminators and the co- ordinate axis are related to the geometric form

of the block. The length interval embodied in both

types of artifacts must be related to the defined

unit with error limits compatible with the manner in which the artifacts are to be used.

In theory, relating the line scale to the defined

unit is a simple displacement measurement. A

suitable detector initially centered on one terminator can be moved along a parallel coordinate

axis to a position centered on the other terminator.

The movement, or displacement, can be measured

in terms of the wavelength of some suitable light

source, and this in turn is assigned to be the length

of the interval defined on the face of the artifact.

This is a symmetrical measurement in that the

detector can approach the terminators from either

direction, searching, if necessary, for some re- producible "center." In practice, such a measure- ment over a long interval is difficult primarily

because of the lack of rigidity of both the ar- tifact and the measuring equipment.

In the case of the gage block, terminators and

the coordinate axis are not precisely defined

by the geometry of the block. The fact that the

terminators are on opposite faces of the block

with the coordinate axis going through the block

means that the sensing device can only approach

a terminator from one direction, and as a con- sequence, no sensing device can approach both

terminators from the same direction. Such a meas- urement is called a separation measurement.

For measurements of this type, the measurement

process must be defined in such a way that the sens- ing device can approach both terminators from

the same direction, and the nonsymmetry of the

sensing device relative to the terminator must be

considered.

Traditionally, gage blocks are made in ordered

sizes so that they can be assembled in stacks to create a variety of artifact lengths. This suggests

that the desired length could be considered to be

the separation between two parallel planes, one

being the surface of the block, and the other being

the surface to which it is mated. Wringing the block

16
to a suitably large flat surface not only simulates one

usage, but also establishes a terminator surface

which can be approached from the same direction

as the terminator surface on the opposite end of

the block. If both terminator surfaces, that is the

block and the flat or platen, have very nearly the

same optical properties, the problems introduced by

lack of symmetry will be minimized.

The degree of flatness of the two terminator

surfaces, and the degree to which the two surfaces

are parallel are manufacturing value judgments.

Descriptors for "out of flat" and "out of paraUel"

involving non-flat surfaces are, at best, semiquantitative. (The traditional method of determining these descriptors is given in reference [13].)

For the purpose of measurement, a specific terminator, or "gaging point," is designated on the

visible, or "top," surface of the block. The assigned

length is the separation between a point and a

plane, the point being the defined "gaging point,"

and the plane being a suitable platen surface which

is in close proximity, that is "wrung," to the bottom

surface of the block. In order to assign a length

value to an object such as a gage block, the sur- faces must be sufficiently flat to produce an in- terferogram which can be interpreted and to obtain an acceptable "wring" with similar objects and

appropriate platens.

The length assigned to a block or an object at some time, to, and at some temperature. To, can be

expressed in two ways as shown for a 5 in block:

Block length

^Lm{to,To) =4.999 975 in

= {Nom + Ym{toJo) =(5 -0.000 025) in

where the subscript m designates the measurement

process used to determine the value, and "Nom"

designates the nominal size of the object. (In this

paper m is assigned the symbol H for values determined by the historical multiple wavelength

interferometric process, as discussed in section

4.1.; I for the new single wavelength interferometric process to be described in section 5.2.; and II for the transfer of values by mechanical comparison as described in section 5.3.)

The past practice had been to limit "Nom"

to certain selected numbers. With Nom—Ym{to,To

less than e, an arbitrarily small tolerance limit, in

many practical uses Im {to, To) is assumed to be

zero. Also, the coefficient of change with time had

been eliminated by discarding blocks which show

change. The temperature at the time of compari- son has been controlled so that T is very nearly

equal to Tg. The present intent is to emphasize

Lm{t,T) without restriction on the magnitude of

Y, time, temperature or material.

The block length at any time, t, and at any

temperature, T, can be expressed by the relation:

Lm {t,T)=Lm{to,To)

+ Ki{t-to) {l-hK2{T-To))±{S(T + S.E.)

where Ki is the natural rate of change of length

with time, K2 is the thermal coefficient of expansion, cr is the appropriate estimator of the random

variabihty of process m, and S.E. is the appropriate

systematic error estimate for process m. Each term

in this relation is discussed in detail in appendix 1. The parameters in the above formula cannot all be determined in a single sequence of measurements. Ki must be estimated from historical data.

The formula shown assumes the uncertainty of

K2, the coefficient of thermal expansion, to be

small relative to the precision of the process. The

numerical value of K2 currently used, as in the past,

is appropriate only because laboratory conditions

are held very close to 20 °C, the accepted temperature, for reporting lengths. In terms of usage,

however, the formula should be vahd over a temperature range of at least 5 °C. To achieve this,

some future efforts must be directed toward es- tablishing block transient thermal characteristics,

block temperature and appropriate coefficients of

expansion.

With the present state of the interferometer

technology, there is no way to introduce a re- dundancy into the measurements other than

straightforward repetition. Each interferometric

measurement produces an independent estimate

of a length relative to a wavelength scale. Under

this condition the amount of work necessary to estabhsh realistic estimates of uncertainty of the

values, as evidenced by this paper, makes it economically impossible to consider such measure- ments as routine. A more practical means must

be used to transfer the unit from the defining

wavelength to the point of use. The procedural operations in the new measure- ment process are, in essence, merely refinements of

earlier techniques diff^ering mainly in the order in

which they are performed. (See fig. 7.) Initial

value assignment to reference standard blocks is the output of an interferometric measurement

process. The transfer of a length unit as represented

by this assigned value to another block is based

on direct comparison which at the present is done

with contacting comparators. This sequence has

been chosen because of the relative standard

deviations of the two processes, that of the interferometric process being somewhat larger than

that of the mechanical process. In order to not degrade the transfer in the comparative processes,

the new NBS interferometric process is limited to the measurement of NBS reference standards and

other similar objects which support the total

length measuring system.

17
NO N( )

( )

Control BlocksPROCESS

I

Yi() Y, (•)

Process

Characteristics

(Yji(-)-Yn(--))

Outline of NBS Gage Block Calibration

Method

Figure 7. Outline NBS gage block calibration.

Process I is a single wavelength interferometric

measurement process. The inputs to Process I are: the reference blocks, that is the (.) and (..)

blocks; a light source of known wavelength A.o; and the length of theReference blocks expressed in

integral "fringes", Ni.) and N{..). The process

outputs are estimates of length expressed as cor- rections to a nominal value, Yi{.) and Yi(..), nor- malized to a temperature of 20 °C. The state of

control of the measurement process is established

partly by collections of measurements of the

(.) and (..) reference blocks, and partly by measure- ments on selected "control" blocks which have

been chosen to emphasize certain types of systematic errors which might be present in the

results.

Process II is a transfer process based on dif- ferences as determined by comparison. The ref- erence blocks, (.) and (..), their accepted values,

Yi{.) and and the associated uncertainties,

together with the "unknown" blocks (x) and (y)

which may or may not be similar to (.) and (..), are the inputs to Process II. One output is the

values for the "unknown", Yuix) and Yniy)

at temperature 20 °C, together with appropriate

uncertainties. Control outputs are an estimate of

the process standard deviation, s, which will

eventually establish an accepted process standard

deviation, cr, and a measured difference between

the reference blocks, (y„(.) — (Fn(. .)). It must

be demonstrated that Process II wiU operate in a

state of control, and that the characteristics of like

processes are similar. It must be verified that the

measured differences determined by Process II agree with the computed differences obtained from

Process I, within the uncertainty of both processes.

5.2. Single Wavelength Interferometry

One shortcoming associated with all static

interferometric measurement processes (see appendix 3) is that one can only observe fractional

fringe differences between the fringe patterns

associated with the top of the block, and the platen

to which it is "wrung." The integral number of

fringes associated with the fraction, to express the

length of the block or artifact, must be estabUshed

by other means. Initially, one rehed on thq skiU

of a master craftsman to construct a set of blocks

such that the deviation from selected nominal

values was very small. The redundancy of multiple

wavelength interferometry provided a means to resolve these small differences. For longer lengths,

or differences, one was faced with the problem of

multiple solutions, the length equivalent between

solutions generally increasing with the number of

different wavelengths used. In general the accepted

solution was the one which was closest to some

initial estimate of the length, or difference, provided

the uncertainty of this estimate was considerably

less than the interval between possible solutions.

To assign values to long blocks by these methods

to the level of uncertainty historically stated was

a monumental task. In effect the measurement was

a stepping process involving a sequence of blocks

having length differences commensurate with the

coherence of the available Light sources. The coherence of stabilized laser light sources removes previous hmitations on the length of the

optical path, thus simpUfying the interferometric

measurement of long blocks. The stabilized laser

is also easy to operate and the intensity of the light

beam, even with small apertures, makes the

photographing of "fringe patterns" practical. The

assignment of the wavelength to the laser radiation can be made with reference to the defining

radiation of Krypton, or some other suitable well

characterized radiation. The details of the in- terferometric process as currently used are described in reference [14].

For computational purposes, a single measure- ment for Process I is defined by the following

steps:

(1) Wring block to appropriate platen.

(2) Photograph fringe pattern.

(3) Compute the length from the average of four

independent photo interpretations for the

fraction /, and the effective A..

18
(4) Several hours later repeat steps (2) and (3).

(5) The single measurement is the average of

the values computed in steps (3) and (4).

The complexity of the process is such that it cannot be readily modified to utihze the power of

intercomparison designs as a means of monitoring

the state of control. The required redundancy,

however, can be obtained from repeated measure- ment of the same set of objects. Control blocks, or "check standards," in the form of three gage

blocks permanently wrung to suitable platens were

chosen. Repeated measurements of the three

blocks, at frequent but random intervals, provided

sequences of data suitable for monitoring the

process. The "check standards" are not removed

from the platens between measurements, therefore,

the variability introduced by the wringing process

is not reflected in the control data.

The chosen "check standards" consist of a 0.150

in chrome-carbide block, a 10 in summation of

cervit blocks (4 in + 4 in + 2 in), and a 10 in steel

block. In interpreting the accumulated data, the

variability associated with the long steel block

should approximate the variability associated

with the normal process output, except for wringing film variability. The variabihty of the cervit

block should reflect length dependent variability

not associated with temperature. The variability

of the chrome-carbide block should represent a

sort of ultimate performance. Repeated measure- ment on other objects, such as the reference

blocks, should provide data for evaluating the

effects of wringing.

The initial work with the interferometric process

described above was to establish values for the

NBS(.) and NBS(. .) groups of reference blocks.

For the (.) group, the "tentative" values were

taken from table 4 in section 4.3, and for the

(..) group, from table 14 in section 6.1. This work

is summarized in table 7. A tentative estimate of

the uncertainty of a single value was computed

using successive differences, as shown in table 7

and figure 8. (This initial estimate of process

precision, s = 0.635 ^t in, will be revised later in

this paper as additional measurements are made.)

In the course of the above work, frequent meas- urements of the control blocks were made at random times. The results of some of these measure- ments are shown in figure 9. The initial wide variabihty reflects in part the performance of the

interferometric process during the measurements

of the (.) and (..) blocks. Analysis of this data

provided guidance toward improving the process

precision. (See sec. 7.1.) After process improvement,

the results of measurements on the three control

blocks appear weU behaved. The details of this

improvement are discussed in reference [14]. It is of interest to note that in the course of obtainc

TABLE 7 Sunroary New Interfercmetric Process Data

(PROCESS I, (January 1972)

Block

Ident.

1/01/73 n

V —

1 1+1

{ y —Y ^ 2

' 1 ^i+l'

3s

yin

NBS ( . .

)

H178-5 0.9 3 .15 .02 1.1

.45 .2

Z.J. 2 . 95 _9 1.35

. o 2 1. 05 1.1 1.35

7/ . 14

T

Z. J.1 QSO a Z J. • -3 J

Hi AQ— 1 ft -1 4 2

- 1

. X . 01 1. 35

2 _ _ 7 . 49 1.35

HIS 5—16 10.

2 -.25 .06 1.35

nx*40 jiU 21.7 2 -1.2 1.44 1. 35

NBS(.)

M136-5 29.3 2 -.1 .01 1.35

M115A-6 29.4 2 -.2 .04 1. 35 M202A-7 15.5 1 1.9

M103A-8 50.7 1 1.9

M109A-10 58.4 1 1:9

M135A-12 71.9 1 1.9

M109A-16 67.7 1 1.9

A157-20 1.1 1 1.9

2 = 8.07

07

2x11 = .635

SUCCESSIVE DIFFERENCES

0.635 /A in

2.01-

1.0

+ 0.0

iii -1.0

II < - 2.0

I I I 1 _L _L ±

5 6 7 8 10 12 16 NOMINAL LENGTH

20

Estimate of interferometric process

precision by successive differences.

Figure 8. Interferometric process precision by successive

differences.

19
21 f20 :

19

18 '

10 HCH STEEL

28 —

27 —

25 —

24L

10 INCH CERVIT

• •*••.'!._

'

I .—. *. . . • ' . .

... . «»'.«.» . .

,

• • i i • • i i • • i • • • i i • • • • • n 0 —

.150 INCH CHROME CARBIDE Early Interferometric Process Control BiocK Values

(Y, IN MICROINCHES PLOTTED IN SEQUENCE)

Figure 9. Early interferometric process control block data.

ing improved performance, the change in average

values for the control blocks was insignificant.

Future measurements will reflect the benefits of

the changes made.

5.3. The Comparison Process

At the present time, by far the largest usage of

long gage blocks is associated with various types of

contacting comparators such as described in

appendix 4. The use of these comparators provides a

precision of measurement compatible with most

requirements. The precision of some comparative

processes can be substantially smaller than the

precision of the interferometric process. A measure- ment process designed around this type of in- strument will not only provide a means to transfer

the unit, but wiU also provide guidance to similar

processes in which the transfer standards are used to measure other objects.

In formulating a measurement process one must

define (1) the manner in which the instrument

indication is related to the measurement unit,

and (2) the sequence of operations which are to be

used for a "single measurement." The announced,

or reported, result can be from a "single measure- ment" or the average of several "single measure- ments." For groups of similar objects, an

intercomparison design provides a redundancy

which is more efficient than a specified number of

"single measurements" for each of the objects in

the group. For example, to obtain a result which

is the average of 4 "single measurements" for

each of two "unknowns" with reference to two

"knowns" would require 16 "single measurements." With the use of a comparison design,

the same redundancy can be obtained with 6 or 8

"single measurements", depending on how the

design is formulated. In addition, other desirable

features can be incorporated into the design.

Initial studies were made using a comparison

sequence designated ABBA (sometimes called a double substitution comparison). In this sequence,

object A is inserted in the comparator producing

an observation Oi; object B is inserted to produce

O2; and then the sequence is repeated in reverse

order. This can be illustrated as:

Observation Separation Interval

01 S-A

02 S-B + d

03 S-B + 2d

04 S-A + 3d

where S is the unknown separation of the comparator

head and anvil and d is an assumed uniform incremental drift occurring in the interval between the

observations. If the sequence is made on a reasonably uniform time scale, Unear drifts are eliminated

in computing the estimate:

20
{A-B)^Ki0i + 0,-02-03)l2

The differences in instrument indication in the

above relations are converted to length units by the

constant K. In most cases, the instrument is adjusted before making the comparisons so that

K~l, and, as a consequence, the observed differ- ences are assumed to be expressed in microinches.

The repetition of the difference measurement in reverse order eliminates the effects of linear drifts, or trends, d, in the announced difference, (A—B).

The above set of observation equations can be

solved for average linear drift or trend:

somewhat more efficient than the design shown

above

10

(-30,-02 + 03 + 304).

While the ABBA "single measurement" in- corporates trend elimination, the design described

in appendix 2 does not. After some experiences

with this combination, because of short time intervals required to make the necessary comparisons,

it was felt that trend elemination should be in- corporated in the design. A trend elimination design

involving 8 measurements was adopted.^*

The use of this design resulted in a decrease in

standard deviation for the 12, 16 and 20 in blocks,

therefore, the "trend elimination" design was used

for the work described in this paper.

An analysis of many series of measurements

indicated that the computed linear drift, d, was

essentially zero. This was ascribed to the stability

of the comparators, and the short amount of time

required to make the required comparisons. The

comparison repeated in reverse order appeared to be a wasted effort. As a consequence, the "single"

measurement is now defined as AB (sometimes

called a single substitution comparison), where:

^ = S + Oi

5 = S + 02 + c?

where d for all practical purposes is zero, and:

{A-B)-^K{0,-Q2).

Currently (Since January 1974) the gage block

measurements are made with the AB "single

measurement" and the following design which is

' The design used (later replaced) was as follows:

(.) (. .) (x) (y)

A(\)

A{2) A(3)

A{*) A (5) A (6) A(V

A (8) R

C

+

- -I-

+ -

+

(•) (• •) (x) (y)

.4(1) 1 +

A 1 0\ +

AA{6) 1 +

^(4) 1 +

^(5) +

A{6) +

A{1) +

A{S) +

R + +

C +

This design is described in detail in reference [6]. Generally speaking, the current requirement that

all items being compared have the same nominal

length is due to the limited on-scale range of the

comparators and not a limitation of the comparison

design. These, or similar, designs can be used with

large "on-scale" range comparators now under

construction, with minor changes in the definition

of a "single" measurement for comparators with

"on-scale" ranges of several inches.

5.4. Transfer Techniques

Developing a measurement technique is, to a

certain extent, trial and error. Initially, a sequence

of operations is established based on one's best

judgment. Minor procedural changes may be

necessary to achieve the desired results — a sequence

of repeated measurements which tend to cluster

about a limiting mean and are free of identifiable

trends, groupings or abrupt changes. The distribution of the initial collection of values is a characteristic of the process. In most cases, an adequate

descriptor of this distribution is the standard

deviation. The standard deviation of the initial

collection becomes a "yardstick" against which one

can assess the effect of changes in the sequence of

operations. Introducing changes one at a time will

give sequences of results in which the standard

deviation is either significantly larger than, about the

same as, or significantly smaller than the initial

standard deviation. By appropriate action, one

finally determines a detailed procedure which produces results within acceptable limits and free from

correlation with all known sources of variability. At

this point predictive limits, within which it is almost

certain that the next measurement result will fall, can be based on actual process performance. Each

new measurement verifies the validity of these

limits.

The expected variability of the result from a design is a function of the standard

deviation of a "single measurement" and the redundancy incorporated in the design.

If the standard deviation of a "single measurement" is o". for the design shown, the standard deviation of the value of one unknown is 0.52o". A comparable standard

deviation for the previous design is approximately O.SSa".

21
PROCESS E DEVELOPMENT

(6 IN. BLOCKS, I. )-(..!, SEPT. 1971 TO JULY 1972)

o SINGLE MEASUREMENT BY DESIGN A COMPUTED PROCESS I

Figure 10. Process development. (6(.)-6(. .))•

A typical sequence of results during the process

formulation period is shown in figure 10. The

measurements were made in a slightly pressurized,

temperature controlled room in which the level of

illumination is held quite low. (While such faciUties are not unique to NBS, the environment is re- stricted and may be significantly different than that

in which other facilities must work with long blocks.)

Many things were tried between the first measure- ments and the operational measurements, not all of which were significant in terms of improved

performance. Clearly, in the beginning (from

November 9, 1971 until March 22, 1972) the differ- ences between the two "known" or restraint blocks

as determined in the comparative process were

widely scattered and offset from the expected

difference as determined from the accepted

interferometric values.

Having achieved a performance in which the

process appears to be weU-behaved with a mean

difference at least in the neighborhood of the

expected difference, one can proceed with the

process development. A frequently overlooked step

is to purposely change procedures in an attempt to degrade the process performance. This technique

will clearly identify the significant elements of the

process. Factors studied in the development interval

shown include methods of placing the block in the

comparator, agreement between operators, time

interval allowed for temperature equihbrium, and

location of comparator indicating system. In

addition, the contact pressure and "readout"

caUbration were checked at frequent intervals.

It was found that once the blocks had initifilly

reached a state of temperature equilibrium with the

environment, time intervals between sequences of

measurements could be reduced from in excess of

4 hours to about 30 min without degrading the result.

The stabiUty of the process is demonstrated by its

2.0

1,8

1.6

S.D.

(/i in)

1.4

1.2

1.0

0.8

0.6

0.4

0 2

• 0%

o o

o

°

O Ooo„ o

+ + + ++ ++ + ++

tj. + + +

+

+

+

" Reference [15] describes the procedures necessary to verify that the comparator

is operating properly. Reference [16] describes the procedural detail now used in the NBS comparison process. ABC

OPERATORS

Figure 11. Operator standard deviation.

22
performance through the development stage, as shown in figure 10, since many things were tried

between the first measurements and the operational

measurements.

One essential requirement is that all operators

must be able to follow the procedures and produce

consistent results. Figure 11 illustrates the standard deviations obtained by three different operators

for sequences of like measurement. In the end, it was decided that careful block handling, attention

to cleaning details, and a light stoning of the surfaces

of the block and comparator anvil were essential

elements in achieving a state of control.

Process simpUfication is a continuing task. One

is constantly searching for methods or procedures

which conserve measurement effort without degrading the process performance. There is no "one

way" to carry out the detailed procedures which

would be applicable to all measurement processes.

On the other hand, the detailed procedures used in a process are a part of the defined measurement.

Ideas from other measurement processes can be

adopted after there is verification that such procedures do not degrade the performance of one's

own process.

5.5. Thermal Conditions

It has long been suspected that the largest source of variability in the measurement of long

blocks has been thermal effects. Errors from this source can enter the measurement in two ways, as a systematic effect or offset, and as a source of

randomhke variabihty. For example, the temperature of the sensor may be offset from the average

temperature of the block. The phase and magnitude

of temperature variability at the sensor may also

differ from changes occurring in the temperature of

the block. It is most important that blocks be at very nearly the same temperature at the time of

comparison. Equalization must occur in a uniform

temperature environment (no significant horizontal

temperature gradient).

Block temperature changes occur because of both

conduction and radiation. For example, a warm

block is usually placed on a cool surface plate, in an airstream, to come into temperature equilibrium

with the measurement environment. Most of the

initial temperature change is probably a result of

conduction from the block to the air and the surface

plate. Some is due to radiation. Having reached

thermal equihbrium with a particular environment,

the same block, when exposed to a heat source such

as a light or operator in close proximity, will immediately start to change in temperature. Such

changes are largely associated with radiation.

The systematic effects are usually minimized by

making all measurements in a controlled temperature environment. The base temperature can be set

sufficiently close to the accepted reporting temperature, 20 °C, so that the uncertainty in the

thermal coefficient of expansion of the block

material is not significant. It is recognized that this

practice restricts the usefulness of the number

assigned to the blocks. One of the ongoing programs is the development of procedures to verify, or estabhsh if necessary, coefficients of expansion

for each block sufficient for use over a temperature

range of 20 to 25 °C with minimum degradation of

uncertainty of the computed values for temperatures

in this range.

Blocks are normally stored on the instrument

platen to permit temperature equihbration, and

then handled with special tongs when making the

comparisons. The comparators are partially en- closed with barriers made from insulating material

to minimize the effects of horizontal thermal gradients. From the start, reflective coated mylar smocks

have been worn by the operators to minimize radiation effects. The level of illumination in the measure- ment laboratory is quite low, and as a consequence

Httle attention was given to the finish on the non- gaging surfaces of the blocks.

The agreement between the results of measure- ments repeated in various laboratories is a part of

process development. In one early study, the

differences between two 16-inch blocks as determined by NBS and by a cooperating laboratory were

not in agreement. This is shown by the data from

September 6, 1970 to April 3, 1971 in figure 12.

Many things were checked to determine a plausible

explanation, it finally being decided that the discrepancy might be associated with the markedly

different finish on the nongaging surfaces of the two

blocks (one was bright and the other was dull and

mattelike), and the difference in illumination in the

two laboratories (one was practically dark and the

other a well lighted general purpose lab). If one assumes that a steady state block temperature is based on equilibrium in heat flow to and from the

block, all other things being equal, the differential

block temperature would not be the same under the

two conditions, the hghted lab and the dark lab.^^

Between April 3, 1971 and August 23, 1972,

studies were made on the thermal response of blocks

subjected to a radiant energy shock (in the form of

turning on and off a fluorescent light located a few

feet from the block while measuring the block

temperature). It was found that a wrapping of two

(or more) layers of gold-coated mylar film essentially

made test blocks with different finish on the non- gaging surfaces appear to have uniform thermal

" A continuing question with regard to long blocks concerns the ahiUty to demonstrate closure at temperatures other than 20 XI. At the present time it is assumed that the linear coefficient of expansion of the (.) and (. .) reference blocks, and all similar blocks, is 11.5 /iin/in/"C, a "handbook" value. A temperature change of 5 °C is a change

of 1150 fjL in for a 20 in block. The present uncertainty of the predicted values at 20 *C

is approximately in. (See table 31 in section 6.5.) In order to demonstrate closure

at 25 ''C, the error in the differential coefficient of expansion must be substantially

less than 3/a in. It may well be necessary, if such closure is required, to determine by

separate experiment the coefficient of expansion for each block. A similar experience is described by .1. C. Moody in reference [18].

23
CONDITION

I K I

o

n I H

• o

o

o o

0 0

o°0

0

* •

•

•

•

o

o — o

o

<p o o

• o

•

°

o

..

•

o

SEPT

19 70

NOV. DEC.

°oOO

O '^o

MARCH

1971 APRIL

o

AUGUST

1972 SEPT.

(5-18)

o

SEPT.

(20-22)

16 in. BLOCKS, (2902-HI55), PROCESS 01

CONDITION I - LOW LIGHT LEVEL

CONDITION H- HIGH LIGHT LEVEL

o UNLIKE FINISH

• "LIKE" FINISH (WRAPPED)

Figure 12. Values for 16 in block determined in laboratories.

surface properties. That is, blocks which responded

differently in the unwrapped condition would re- spond very nearly ahke in the wrapped condition

when subject to the same "thermal shock" [16].

The procedure of routinely wrapping long blocks

was adopted.

Some time later, it was decided to repeat the

initial experiment. The same 16 in blocks were compared in both the "wrapped" and "unwrapped"

condition in the same two laboratories. The results are shown in figure 12 over the dates 8/23/72 to 9/22/72. The dashed hne shown is the approximate

average of the "unwrapped" values obtained at NBS over the period September to December

1970. The hmits shown are based on current process

performance parameters (January 1974). The

March 1971 "unwrapped" values under condition

II are clearly outside of these Umits. Three 1972

values are "borderline", two "wrapped" and one "unwrapped." One "unwrapped" value is clearly

out of these limits. While these measurements do

not show a significant difference between the

"wrapped" and "unwrapped" results in the well

hghted laboratory, all long blocks are measured

in the "wrapped" condition at NBS.

A sequence of measurements was made on a group of 8 in blocks, including the 8(.) and the 8(. .), in which an attempt was made to monitor the

change in temperature of each block in the course

of the series of comparisons. Differential temperatures were measured with thermocouples located

in the holes of the "hoke" type blocks. Plastic

plugs were used to reduce any "chimney" effect.

The data was reduced in two ways: first by assuming

all of the blocks to be at the ambient temperature

of the laboratory, and then by normalizing the data

to a fixed temperature using the differential temperatures and the assumed coefficients of expansion.

A statistical analysis of the result, summarized in

table 8, does not indicate any significant difference

between the two methods. The scheduled sequence

of measurements required by the comparison design can be completed in a matter of minutes. Each

block is handled about the same amount of time.

For these reasons, the actual change in temperature

is small, and further, if all blocks are of the same

Table 8. The comparison of results between assuming the temperatures of the blocks to be ambient, and adjusting the data by means of differential temperature measurements to the temperature of the first block.

Differential temperature

Uncorrected correction data made

Number of measurements 112 98

Average diff. (8(.)-8(. .)) 44.24 44.29

.072 .073

.763 .726 3.45 3.60

24
material as is the usual case, and the temperature

change for each block is about the same, the results are not affected. Inasmuch as monitoring the temperature of each block is a difficult procedure, the

practice has been discontinued.

The present procedure is to place the wrapped

long blocks in the comparator for a period of time

to allow thermal equihbration. This is usually done

the evening before the scheduled measurements. To

evaluate the effect of time intervals between meas- urement series on a given group of blocks of the

same nominal size, a sequence of five series of

intercomparisons have been made on a given day

with a four-hour interval between the first and

second, a two-hour interval between the second and

third, a one-hour interval between the third and

fourth, and a half-hour interval between the fourth

and fifth. This has been done many times, using

blocks of all sizes. There is no obvious correlation

between the results and the elapsed time interval.

Only four blocks of the same nominal size can be

stored in the present comparator. The success

of these studies, however, indicates that, with

adequate storage for 32 blocks, the series of comparisons for each size could foUow in sequence

with nominal delay.

5.6. "Practical" and "Virtual" Surfaces

Two types of surfaces are of interest in all measurements involving gage blocks, "practical"

surfaces, and "virtual" surfaces. "Practical"

surfaces establish the position of the gage block

relative to a mating object. The "virtual" surface

relates to the method of surface detection. The

"practical" surface is established by the geometry

of the mating surfaces and the procedural steps used

in bringing the objects together. Each method of

surface detection rehes on a different reaction in the

interface between the object surface and the

detector, and as a consequence each method has

its own "virtual" surface. For these reasons, the

"virtual" surface and the "practical" surface can

never be in coincidence. For a given block, the

degree to which the separation between the two

is a factor in the measurement depends upon the

precision of the particular measurement process.

In both Process I and Process II measurements,

the position of the block relative to the platen, or

anvil, is estabhshed by the "practical" surface

located between the bottom of the block and the

mating object. In Process I, the "virtual" surface

of the gaging face is estabhshed by the mechanism

which causes a hght beam to be reflected from a

relatively smooth, contaminated metallic or nonmetallic surface. In the Process II measurements,

the "virtual" surface is located in the interface

between the surface of the contacting probe and

the deformed surface of the gaging face, the

deformation occurring because of the force acting on the probe.

The nature of the gage block surface in a normal

environment is quite complex. From the outside

and progressing inward, with perhaps no one layer

being completely continuous, one would expect

to find a layer of more or less tightly bound dust

particles, residue from some intentional "cleaning"

procedure, a layer of fluid or semifluid material

consisting of residue from polishing or other surface

treatments and previous environments in which the

block has been, and interface of cleavage planes,

attached pieces of shattered grains, oxides, nitrides

and the like and finally the basic material of the

block. The detailed geometric features of a large area of such a surface estabhsh in part the "practical" surface. A quantitative description of such

a surface must, at the present, be inferred from

nondestructive tests over small portions of the area. In essence, there are only two practical tests; the

abihty to wring to other blocks and platens, and the

abihty to observe interference fringes.

The nature of how two surfaces come into contact can be illustrated by first considering how a planar

surface would come into contact with a surface such

as illustrated in figure 13. If the area of the planar

surface is small, the "practical" surface would be

established by the highest elevation points, a, b,

and c. For a larger planar surface, contact would be

made at a' , b' and c', and for a still larger area, the

contact is at a" ,b" and c " . Clearly, only the maximum elevation peaks on the rough surface are involved. The depths of the valleys are immaterial.

In such a situation, the "practical" surface is estabhshed by the three highest peaks on the rough object

which lie within the projected area of the mating

planar surface.

Some insight as to the location of the "practical"

surface between two mating surfaces can be obtained in the following manner.'^ Let a surface be

represented by a grid in which the deviation of each

element of the grid above some reference plane is aij=^C + Nij{fJi, cr^) where Niji/JL, cr^) is selected

at random from a table of normal deviates with

average, (x, and variance cr^. With two such surfaces,

arranged so that the reference planes are parallel

and separated by an amount jo (no contact), one

can reduce y until contact is obtained. A pair of

mating rows from the grids representing two sur- faces is shown in figure 14. At this point, the

separation between the summation a,j + 6a/

(where bki represents the profile of the mating

surface) is a maximum value for the initial, or

"first", contact between the two surfaces. A

future reduction in y will identify the "second"

contact, the "third" contact, and so on.^^

Siddall and Willey, reference [17], discuss a different approach in which surface

traces are matched. " For simplicity, it is assumed that the two elements which maite initial contact "compress."

25
Figure 13. Contact between "random" surface and ideal plane.

(Courtesy of Gould Measurement Systems).

REFERENCE PLANE B—

a|, = C +Nii {i±,<T^)

VL i -REFERENCE PLANE A—

MODEL OF CONTACTING SURFACES

Figure 14. Model surface contact.

In the above simulation, for C=10, iVij(0, 1),

and Nki{0, 1) the maximum expected separation

at initial contact, (aij + bki), would be of the order

of (10 + 3(7+ 10 + 3(t) —26. Table 9 summarizes

the results for 100 pairs of 10 X 10 grids, and 20

pairs of 30 X 30 grids. The table indicates the value

of y for "first", "second" and "third" contacts.

The degree of "interpenetration" and possible

"tilt" is reflected in the results. As long as the sur- face areas are large, the degree of penetration wiU

be a function of the elevation of the peaks above

some reference plane for the "smoothest" block.

This infers a stable, reproducible "practical"

surface in the interface between the bottom of the

block and the comparator anvil provided that both

26
Table 9 Maximum Separation Between Random Surfaces

(ftodel)

For 10 X 10 Grid, 100 Pairs (20 OOP Random Numbers)

"First" "Second" "Ihird"

Contact Contact Contact

Maximum 25.2 24.0 23.5

Minumum 22.6 22.2 21.8

Average 23.5 23.3 22.5

For 30 X 30 Grid, 20 Pairs (36 OOP Randan Numbers)

"First" "Second" "Third"

Contact Contact Contact

Maximum 25.5 24.8 24.4

Minumum 23.6 23.6 23.5

Average 24.5 24.2 24.0

surfaces are clean and free of "burrs." (The blocks

and the comparator anvil are cleaned and "stoned"

lightly prior to all Process II measurements).

The nature of the "practical" surface in the

interface between the block surface and mating

platen is altered by the presence of a "wringing"

fluid. For a given measurement, the film thickness

in the interface, whatever it might be, is included

in the initial assignment of a length value by an

interferometric process. The variability of a collection of repeated measurements reflects in part the

variability of this film thickness. The development

of micro-scratches in the surface of the block by

virtue of the sliding action necessary to make the

"wring" indicates that, at least part of the time,

there is an interpenetration of the two surfaces

similar to the previous argument. Eventually,

surfaces deteriorate to the point that they will no longer "wring." While there is a possibility

that some of the damage may occur because of the

abrasive action of foreign material on the surfaces,

this suggests that for minimum or "zero" film

thickness, the "practical" surface between the block

and the platen is essentially the same as the

practical surface between the block and the

comparator anvil.

The maximum "film thickness" is largely a matter

of operator "feel" at the time of making the "wring."

As a consequence of this added variability, the

position of the gage block on the comparator anvil

may well be more reproducible than its position as "wrung" on a platen. The standard deviations of

the two processes tend to support this conclusion.

("Wringing film thickness" is discussed further

in section 7.4.) The practice, after cleaning and

"stoning" the long blocks, is to "wring" to a quartz

flat and judge the quality of the "wring" by its appearance as viewed through the flat. If all is

in order, the quartz flat is removed and the block

immediately "wrung" to the appropriate platen.

Because of the operations necessary to obtain

a highly reflective surface, figure 15 may be more

representative of the block surface profile. In

Process I measurements, light waves are reflected

from such a surface. Typical gage block interferograms are shown in figure 16 [18]. The presence

of surface scratches is evident in most of the interferograms, but the surface from which the light

appears to come is not in coincidence with the

"practical" surface of the gaging face.

In the case of reflected light, the location of

the "virtual" surface is thought to be a function

of the roughness of the surface and reaction of the

light with the surface molecules. In the first case,

interference occurs over a large area so that, with

the exception of the edges of the fringe, the detailed

surface profile is not revealed. It is sometimes

assumed that the reflection plane is located about

midway between the peaks and the valleys. In

the second case, in the process of absorbing and

reradiating the incident light beams, the phase

relation between the incident and reflected ray

may be changed. The net result of the two effects,

which are inseparable, is a "virtual" reflecting

surface which cannot be in coincidence with the

"practical" surface.

In the Process I measurements, the "reflecting

virtual" surfaces are located at both the gaging

face and the platen face. As long as the separation

between the "virtual" surface and the "practical"

surface on both of these faces is nearly the same,

the separation between the two "virtual" surfaces

is essentially the same as the separation between

the two "practical" surfaces. Defining S(g) as the separation between the "virtual" surface and the

"practical" surface of the gaging face, and S (p) as a like separation at the platen face, one is concerned

as to the significance of [S(g) — S(p)] relative to

the precision of the measurement process, for

various combinations of blocks and platens. Early

studies on short gage blocks under 4 in, reported in

reference [19], utilized the "slave block" technique.

Later studies used short blocks of various manufacture and two steel platens with different surface

finishes. In both cases there was no evidence to indicate that S (g) # Sip). In the Process I measurements of long gage blocks, the platens used

are made from the same type of material and have

the same surface finish as the blocks. It is assumed

that S ig) = S{p). (This is not the case when the

results from a steel platen are compared with the

results from a quartz platen [20].)

The "virtual" surface in the Process II measure- ments is in the interface between the surface of

the contact probe and the deformed gaging surface

of the block, as shown in appendix 4. Defining the

separation between this surface and the "practical"

surface of the block as penetration, one is concerned

with the difference in penetration, /3, from block

27
Figure 15. "Typical" gage block profile. (Courtesy of Gould

Measurement Systems).

to block. Factors which determine the magnitude

of the penetration are the geometry and physical

characteristics of the contacting probe, the geometry

and physical characteristics of the block surface,

and the contact force. In the transfer of the length

of one block to another, as long as both blocks

respond in a similar manner to a fixed force on

a given probe, j8 is essentially zero, and the dif- ference in separation between the "virtual" sur- faces of the blocks and the reference plane of the

comparator is very nearly the same as the difference

in separation between the "practical" surfaces of

the blocks and the reference plane.

Commercially available long gage blocks are made

from through-hardening steel, such as Type W-1

tool steel or Type 52100 steel. Blocks made from

such steels, when properly heat-treated, are

sufficiently hard for resistance to wear, can be

polished to obtain a suitable surface finish, and

exhibit a high degree of stability with time [21].

The physical properties of these materials are very

nearly the same. One would expect the penetration

of a given comparator probe on any pair of steel

blocks to be about the same so that /3 would be

very nearly zero. The closure studies between

the Process I and Process II measurements, discussed in section 6, verify that is not large relative

to the precision of the process. It is assumed that

/3 — 0, therefore the small variation in penetration

across the surface of the block, and from block to block, is a component of the process variability.

This assumption is not true when transferring the

value from a steel block to a block made from

grossly different material. Gage blocks of nominal

length 4 in, and under are commercially available

in cervit, chrome-carbide, tungsten-carbide, as well as steel, therefore a detailed discussion of j8

is included in reference [20].

6. Developing a Measurement

Process

6.1. Restraint Requirements

The comparison designs discussed in section 5.3

require two "known" blocks in each sequence of

comparisons. The length values assigned to these

"known" blocks introduce the measurement unit

into the process. That is, the sum of the values for

the "knowns" is the restraint for the least squares

solution used to determine values for each of the

four blocks in the particular measurement sequence.

28
iwiiiwiiiigii<i|iiiwiiiii^

iWM«iW»iWl>i ili.ii¥<i<ii

m

0 ?.Af.

a, - 0 'SC-fi i;"

m

|illiipiiiiii.<>i»iii^^

WW

Mfr. 4 CX.A. = 0.40^' i"

Figure 16. Gage block surface interferograms.

29
Using two "known" blocks to introduce the unit

rather than one provides a means for monitoring one with reference to the other and also provides

a collection of "repeated" measurements which,

in turn, reflects the long term performance of the

process. Accepting the NBS (.) blocks as one group

of "knowns," the task is to estabhsh suitable values

for a second set (the NBS (..) blocks) with the "new"

interferometric process. In order to do this, the

continuity of the results from the historical interferometric measurements and the "new" interferometric process must be demonstrated.

For one group of reference blocks, the NBS (.) group, table 10 compares the predicted historical

values discussed in section 4.3 with the values

estabhshed by the "new" interferometric process

(Process I) discussed in section 5.2. With one

exception, the area of doubt associated with the

historical predicted value encompasses the new

process value. For the 8 (.), the uncertainty bands

overlap. Within the precision of both processes,

continuity appears to be preserved. As an additional

check on the continuity of the two processes, table

11 compares the historical values established for

the USN blocks with values for selected blocks

established by the "new" process. Again, for the

blocks which were measured by the new process,

the difference between the two sets of values is less than the uncertainty of the historical value.

On the basis of this evidence, it was concluded that

the change from one process to the other did not

affect the continuity of the measurements.

The NBS (.) blocks, together with predicted values

based on "new" process measurements, are accepted as part of the restraint. The task is now

to establish acceptable values from the second set of blocks necessary to complete the restraint. From

this point on, all values discussed in the paper are from the "new" process.

The NBS(. .) group of blocks was selected for

the second required set of reference blocks. The

(. .) set consists of the following blocks:

NBS H178-5(. .) H132-6(. .) H105-7(. .) H143-8(. .)

NBS H148-10(. .) H249-12(. .) H155-16(. .) H146-20'(. .)

These are relatively new blocks which were used

in conjunction with multiple wavelength interferom-

(a) (b) 7/01/71 1/01/72 Predicted Value Average Value

Block Based on from Dif fUNC* UNC**

Ident. Historical Data New Process (a) -(b) 7/01/71 1/01/72

NBS ( .

Ml 36-29.5 29.3 .2 1.2 1.4 M115A-6 28.3 29.4 -1.1 1.6 1.4 M202A-7 14.9 15.5 - .6 1.9 1.9 M103A-8 47.9 50.7 -2.8 2.2 1.9 M109A-10 56.0 58.4 -2.4 2.8 1.9 M135A-12 70.8 71.9 -1.1 3.5 1.9 M109A-16 66.8 67.7 + .1 4.8 1.9 A157-20 1.6 1.1 + .5 6.1 1.9

* OF PREDICTED VALUE (SEE TABLE 4)

** OF AVERAGE (SEE TABLE 7

TABLE 11 Summary of Conparlson USN, "Old" vs "New" Values

Block Block

Serial No. Nominal Size Yj^(7/1/71,20) UNC Yj( 1/1/72, 20) UNC n

R317A-5 5 in 19.5 0.8 19.7 1.3 U157A-6 6 11).

1.1 11.3 1.3 T229A-7 7 1)3.7 1.2 W186A-8 8 18.5 1.1) 19.6 1.3 V215A-10 10 11).

1.8 U136A-12 12 38.7 2.2 W23tA-16 16 15.5 3.0 W198A-20 20 37.0 3.8 39.1 1.1

Yjj (SEE TABLE 2)

TABLE 12 NBS(..) Reference Standards with Reference to NBS ( .

(Mechanical Comparison with Restraint for Solution on Value for NBS ( . ) Only)

NBS(.) Values*

Nominal

Size (Restraint)

NBS ( . .

^11

Diff

11/71

Series

12/71

Series Avg. NBS{. .)Y^ Values*

5 29.3 1.1 - .2 .45 .9 - .45

6 29.4 -2.9 -1.3 -2.1 -2.1 0

7 15.5 -5.8 -4.3 -5.0 -5.8 + .8

8 50.7 6.8 8.1 7.4 7.4 0 10 58.4 -1.8 -2.0 -1.9 -1.4 - .5 12 71.9 14.2 14.9 14.6 14.9 - .3 13.4

16 67.1 10.2 10.7 10.4 10.3 .1 20 1.1 18.9 16.5 17.6 21.7 -4.1

17.7 17.2

* See Table 7 ** 4 degrees of freedom per series

30
TABLE 13

NBS(.) and (..) Accepted Values, Sums and Differences, November 22, 1972

Y Values-Nov. 22 . 1972 Restraint "Check"

Nominal

I (.) Group (

) Group

Y

II YII Size Ave n A HVtr n " A (.)+(..) (.)-(..) UNO*

5 29.0 5 -.3 1.1 6 +.2 30.1 27.9 .54

6 29.1 4 -.3 -2.4 4 -.3 26.7 31.5 .72

7 15.0 3 .1 -5.7 ^ .1 9.9 21.3 .90

8 50.6 3 -.1 6.5 4 -.9 57.1 43.6 1.02

10 58.4 3 0 -2.0 4 -.6 56.4 60.4 1.38

12 72.3 3 .4 15.0 4 .1 87.3 57.3 1.50

16 67.3 4 -.4 9.9 4 -.4 77.2 57.4 2.01

20 2.9 6 1.8 21.0 6 -.7 23.9 -18.1 2.31

n Number of independent values in average.

A Change from Table 12.

* Uncertainty for both ((.)+(..)) and ((.)-(,.)).

3.0

2.0

[fj. in)

1.0

s.d. of old process (figure 5)

s.d from differences (figure 8)

s.d. of new Process I

_(.635)

1_2 L

5 6 7 8 10 12 16 NOMINAL LENGTH

20

Z (dev)^ NPROCESS I STANDARD DEVIATION (NOV. 1972)

Figure 17. Process 1 standard deviation.

etry but which had no previous history of values

assigned by the "old" process. By virtue of the

closure between the two processes discussed above,

the average values from the "new" process (see

table 7) were accepted as the tentative values for

the NBS (. .) blocks. Intercomparison measure- ments with reference to the NBS ( . ) blocks, summarized in table 12, were made to verify closure

between the transfer values relative to the NBS ( . ) assigned values, and the tentative interferometric

values. With the exception of the 20 in blocks,

the agreement is remarkably close. The discrepancy

at the 20 in level is considered acceptable in

view of the small number of measurements available for the assignment of values to both the 20(.) and

the 20(. .) blocks.

With additional measurement data available, the

accepted values for the individual blocks, the sums

and difference for the pairs, and the process uncertainty in use in September 1972, are shown in

table 13. The estimated uncertainty tabulated in

table 13 is 3(V2)o-, where a is from the "fitted"

hne on figure 17. The points plotted in figure 17

are the computed standard deviation of the collections of values for each of the ( . ) and (. .) blocks

and the appropriate USN blocks. The dash-dot hne,

(7 = 0.635, is the original estimate estabhshed in

figure 8. The dashed hne is the estimated process

standard deviation for the "old" process established

in figure 5.

6.2. Predicted Values (Process I)

Partly as a practical expedient, and partly

because it was thought that the relatively small

rates of change would not be apparent over the short

time span associated with "new" process measurements, changes with time have not been considered

up to now. Under the assumption that the length

of all of the blocks change with time, the average

value is not the best estimate of current or future

values. It is necessary to predict appropriate values

for individual blocks, sums and differences, together

with appropriate uncertainties, over some reasonable time interval. Because closure is an important

criteria for judgment, it is necessary to have reahstic

estimates of uncertainty for the predicted values.

This and the following two sections are devoted

to estabhshing and verifying reaUstic rates of

change.

In the case of the NBS (.) blocks, with a long

history of measurement, significant rates of change

31
(a) EDICTED VALUE

(3 POINTS)

(b)

NEW PREDICTED VALUE

re POINTS)

(c)

are readily apparent in the historical data. For the

NBS (. .) blocks, with no long history of measurement,

estimates of rates of change must be based on data over a short time span. As the data base increases,

confidence in both the predicted values and the

rate of change will increase. To iUustrate, in figure

18(a), a rate of change, or slope, is computed on

the basis of three hypothetical measurements over

a particular time span. From the fitted line, one

can determine a predicted value for any given time.

With a reasonable estimate of the process standard

deviation, the uncertainty of the "predicted value" can be computed from the formula used in section

4.1. Because the extrapolation time interval is large relative to the "data" time interval, the uncertainty of the predicted value, and the rate of

change, is large. This is analogous to the Process

I collection of data for the (.) blocks and the (. .) blocks.

With additional data points, as shown in figure

18(b), the uncertainty of the predicted value is somewhat smaller since the extrapolation interval

is a smaller function of the new data base. Finally,

with still more data available, such as shown in

figure 18(c), the data bank covers a sufficiently

long time interval that the uncertainty of the predicted value extrapolated over some relatively

small time increment approaches the "uncertainty

of the mean." At this point, the slope, or rate of

change, is reasonably well known. This is analogous

to the situation as additional Process I measure- ments are made.

Figure 18(c) is analogous to the historical data

from the ( . ) blocks.

All of the values available up to June 1972 are shown in table 14. For each block, the value Y{1)

is the correction to nominal length as obtained by

NEW PREDICTED VALUE

(9 POINTS)

Figure 18. (a) Predicted value, 3 data points, (6) predicted

value, 6 data points, and (c) predicted value, 9 data points.

UNCERTAINTY OF PREDICTED VALUE

(A'S ARE DIFFERENCE BETWEEN "OLD" 8 "NEW" PREDICTED VALUES)

32
Table 14. Summary of predicted value computations.

Ml 36 5.00000000

H178 5.00000000

M115A 6.00000000

H312 6.00000000

W202A 7.00000000

H105 7.00000000

M103A 8.00000000

HI^3 8.00000000

M109A 10.00000000

H148 10.00000000

M135A 12,00000000

H249 12.00000000

M109A 16.00000000

H155 16.00000000

(_

^ A157 20.00000000

H146 20.00000000

UA I t K t b

8 24 71 -.01

10 18 71 .02

3 6 72 -.04

3 7 72 .27

3 8 72 -. 23

9 13 71 . 15

9 30 71 -.27

10 15 71 . 12

3 6 72 -.40

3 7 72 . 10

3 8 72 . 30

8 25 71 .03

10 18 71 -.04

3 15 72 -. 30

3 16 72 .31

9 14 71 .45

9 29 71 -.49

3 15 72 -.38

3 16 72 . 42

8 26 71 .00

12 72 -.35

<* 13 72 . 35

9 15 71 .59

9 28 71 -.62

4 12 72 -.18

4 13 72 .22

9 3 71 .00

4 5 72 -.40

4 6 72 .40

9 10 71 .87

9 27 71 -.95

4 5 72 .04

4 6 72 . 04

9 1" 71 .0 1 4 21 72 -.60

4 24 72 .60

9 9 71 -.09

9 26 71 .10

4 21 72 -.21

4 24 72 .20

8 31 71 -.00

5 17 72 . 30

5 18 72 -.30

9 8 71 -.63

9 24 71 .t)7

5 17 72 -.22

5 18 72 .18

8 27 71 .06

8 28 71 -.04

4 28 72 - I. 12

5 3 72 1.10

9 7 71 -. 1

1

9 22 71 . 14

4 28 72 -.97

5 3 72 .94

8 30 71 -. 02

3 12 72 .65

3 13 72 -.17

3 20 72 -.46

9 2 71 -.54

9 23 71 . 61

3 12 72 . 10

3 13 72 -. 19

3 20 72 .02

KKtU 3blO KKtU

29.31 1.49837242

29.18 1.10141098

28.84 1.05066556

28.83 1.05666725

28. 83 1.06272294

1.05 1.17258103

1.07 1.05748172

1.08 .96562185

1.20 1.05533223

1.20 1.06179731

1.20 1.06830278

29.37 1.49013871

29.24 1.12024894

28.90 1.28731512

28.89 1.29437192

-2.05 1.35908125

-2.11 1.25014015

-2.82 1.29983598

-2.82 1.30710523

15.50 1.84499115

15.65 1.30179745

15.65 1.30743296

-5.79 1.34569207

-5.78 1.26352671

-5.62 1.30030192

-5.62 1.30712561

50.60 1. 84498999

50.60 1.30161662

50.60 1.30761462

7.43 1.35931462

7.35 1.24990916

6.46 1.30024020

6.46 1.30668136

58. 39 1. 84492531

58.40 1.29636528

58.40 1.31291182

-1.31 1.35483630

-1.40 1.25433275

-2.59 1.29476681

-2.60 1.31251545

71. 80 1. 84499304

72.50 1.30212003

72.50 1.30710903

14.93 1.34686165

14.93 1.26235954

15.02 1.30128424

15.02 1.30656852

67.74 1.30717546

67.74 1.30191566

66.92 1.29146101

66.90 1.31775805

10.31 1.34b79803

10.26 1.26227620

9.57 1.28983255

9.56 1.31801963

1.42 1.84412411

3.95 1.04944718

3.97 1.05456385

4.06 1.09261698

21.74 1.37626223

21.69 1.23092210

21.30 1.04716051

21.29 1.05269817

21.28 1.09273252

X t n* Y 1 1

)

13. o411 29 . 30

13. 7690 29 .20

14. 1808 28 .80

14. 1836 29 .10

14. 1863 28 .60

13. 6932 1 . 20

13. 7397 .80

13. 7808 1 .20

14. 1808 . 80

14. 1836 1 .30

14. 1863 1 . 50

13. 6438 29 .40

1 3. 7890 29 .20

14. 2055 28 .60

14. 2082 29. 20

13. 6959 -1 .60

13. 7370 -2 .60

14. 2055 - 3 .20

14. 2082 -2 .40

1 3. 6466 15 . 50

14. 2795 15 . 30

14. 2822 16 .00

13. 6986 -5 .20

13. 7342 -6 .40

14. 2795 -5 . 80

14. 2822 -5 .40

13. 6658 50 .60

14. 2603 50. 20

14. 2630 51 .00

1 3 . 68 49 8 .30

U. 7315 6 .40

14. 2603 6. 50

l-t. 2630 6 .50

13. 6603 58 .40

14. 3041 57 .80

14. 3123 59 .00

13. 6822 -1 . 40

13. 7288 -1 .30

14. 3041 -2 .80

14. 3123 -2 .40

13.6603 71 .80

14. 3753 72 . 80

14. 3781 72 .20

13. 6795 14 .30

13. 7233 15 .60

14. 3753 14 .80

14. 3781 15 -20

13. 6493 67 .80

13. 6521 67 .70

14.3233 65 . 80

14. 3370 68 . 00

1 3. 6767 10 .20

13. 7178 10 .40

14. 3233 8 .60

14. 3370 10 .50

13.6575 1 .40

14. 1973 4 .60

14.2000 3.80

14. 2192 3 .60

13. 6630 21 . 20

13. 7205 22 .30

14. 1973 21 .40

14. 2000 21 .10

14. 2192 21 . 30

•Time in years measured from 1958.

33
Table 15, Process I pooled standard deviation and block rate of change. S.D.=standarddeviationofindividualmeasurement;XBAR = averagelime; YEAR = average of all values; A = intercept; B = slope; SDB = standard deviation of slope.

ER NO NOMINAL S. D. N XSAK YSAK A B SDB T=8/SD8

Ml 36 5.00 000000 .6 1500000 5 13. 9961o'>08 28 , 9999995 2 4 1. 35402060 - .88267193 I. 1 741 6480 - .75 1 74449

HI 78 5. 00000000 .61500000 6 13. 96073031 1 .1333333 3 -3. 044972 36 .29928991 U 1 1 95 05 2 7 . 26734122

M115A 6.00 000000 .6 1500000 13. 9616<.370 29 .09999990 40. 77057743 - .83590285 1 . 22742754 - .68 10201 1 H312 6. 00000000 .61500000 13. 9616*370 -2 .44999999 18. 53376698 -1 .5029582

1. 25184469 -1.20059478

W202A 7 . 00 00 0 0 0 0 .61500000 3 069<.062 7 15 .5999^990 12. 222 1 16 1 1 .24008717 1. 1 3 7 5 7 1 06 . 202 16657

HI 05 7.00000000 . 6 1500000 * 13. 99863005 -5 .69999993 -9. 73748553 .28842006 108859476 .26494712

M1034 6 . 00 00 0 0 0 0 . 61500000 3 1'.. 06301355 50 .59999943 50. 53418207 .00468020 1. 26401 1 17 .00370266

Hl'»3 8 .00000000 . 6 1500000 <t 1 3. 9B'.931 35 6 . 9249999 5 30. 3413 3935 -1 .67439789 1 . 109293 I 3 -1 .50942779

M10 94 I 0. 00 000000 . 6 1500000 3 !<.. 09223723 58 .3999996 2 58. 1503 35 79 .0 177164 J 1. 162401 74 .01524123

HI "iS 1 o.oooooooo .6 1500000 l*.. 0068491

- 1 .97499999 26. 83147764 -2 . 05659941 1 . 01 877393 -2.01370045

H13 5A 12.00000000 . 61500U00 3 !<.. 137899*0 72 .2666664 I 58. 48655987 .97469271 1. 051331 16 .92710341

HZ*"* 1 2.00000000 .61500000 <> K. 03904092 14 .97499 990 I 3. 04558635 .13743201 90968765 . 1 5107604

MlOqA 16. 00000000 .61500000 13. 99041080 67 .3249998

84. 37028885 - 1 .21835519 90504555 -1 .34618106

H155 16.00000000 . 6 1 500000 I'l. 01369846 9.92499995 25. 895506 14 -1 .13963535 )706 1710 -1.17413484

Al 57 20.00 000000 .61500000 I'*. 06849 301 3 .34999996 -62. 73942280 4 .69769025 1. 2951 8704 3.62703615**

20.00000000 .61500000 5 13. 99999976 21 .45999956 33. 14868593 .83490620 1. 0895 56 14 -. 76628102

the defined interferometric process. The column

X{1) is a time coordinate for the date of measure- ment referred to an arbitrary "zero" time. The

predicted value for each date is that from a least

squares straight line fit of F as a function of Z. The

residual is the difference (7(1 ) —Predicted). The

3 sigma predicted column is computed by the

formula given in section 4.1. It should be noted that

the 3 sigma predicted value is smallest near the

centroid of the time span covered by the data. The

process standard deviation used for these computations is 6- = 0.615 from table 15. Table 15 shows, for each block, the pooled

standard deviation (i.e., computed from all of the

residuals in table 14) and the number of measure- ments which have been made for each block.

XBAR is the location of the centroid of the points

according to time from an arbitrary time "zero".

YEAR is the average of all of the available points

for each block. A is the intercept value at an

arbitrary time "zero" (1 Jan. 1958). B is the computed slope or rate of change in microinches per

year. The test, T= B/SDB, is computed from B

and the standard deviation of B, SDB. Except for

A157 (20( . )), r<3, thus at the present level of

precision and over the time interval of these

measurements, the rate of change does not appear

to be significant. It is of interest to note that the

"pooled" standard deviation, o- = 0.615 microinches,

is in good agreement with the estimate, (t = 0.635

microinches computed from earlier successive

differences (see figure 8). The rate of change data are summarized in table

16. The rate of change for the NBS ( . ) blocks based on new data can be compared with the historical

data from table 5. In order to check on the appropriateness of the rate of change estimates for the

(. .) blocks in figures 19(a) and (b), all of the available measurement history is shown with respect to a prediction fine drawn through the July 1, 1973

(7/1/73) predicted value. The small open circles,

and the small circles with the horizontal lines have

the same meaning as before. (See sec. 4.2) The

point on the 1972 line, and associated uncertainty

limits, are the tentative accepted values from

-10 Li I

I - I I I - Lj I I 1 1 I I 1968 70 72 74 1968 70 72 74 Figure 19. (a) Measurement data, NBS{. .)5, 6, 7,8, 10 and 12.

NBS H146-20 ()

35r

NBS H155-16 (••!

ol_i I I I I

I

I 15l_i 1 1 1

1 1 1 1968 70 72 74 1968 70 72 74 Figure 19. (b) Measurement data, NBS{. .) 16 and 20.

34
table 7. For the 7(. .) and the 20(. .) the supporting

data appear to differ substantially from the change

estimate in table 16. In all other cases, the supporting data seem to substantiate the new estimate,

or to be inconclusive.

TABLE 16

Estimated Rate of Change (yin/yr)

(.) and (..) Reference Blocks

Rate of Change Based on: Block Historical New

Ident. Data* Data

(•)

136-5 .300 - .883

XJ-jA D .162 - .836

202A-7 0 .240

103A-8 0 .005

109A-10 .177 .018

135A-12 0 .974

109A-16 .215 -1.218

157-20 -1.47-8 4.680

(••)

178-5 .300

312-6 -1.503

105-7 .288

143-8 -1.674

148-10 -2.057

249-12 .137

155-16 -1.140

146-20 - .835

* Prom Table 5

TABLE 17 Conparison of Predicted Process I Values with

Average Process I Values Which Have Been Used in Process II

* Based on historical rate of change. * Based on Process I rate of change estimates.

Table 17 shows a comparison of the predicted

values, accounting for change with time, for 7/1/73

with all previous "accepted," or average, values.

Table 18 hsts the predicted values for the sums and

differences, as required in the comparison process,

together with the uncertainty of these values based

on the "pooled" standard deviation for the process.

These predicted values are monitored in two

ways. First, it is expected that the results from

future Process I measurements will verify the prediction. For example, referring to the A's in figure

18, a value predicted back to the time of the last

prediction (based on the smaller data base) is a check on the continuity of the data.

Second, a value predicted forward in time based on the increased data base provides the necessary

restraint data for Process II, and the difference

measurements from Process II should verify the

differences between the appropriate Process I predicted values. Failure in either case is an indication of the existence of a problem. One, or both,

blocks may have changed in an unexpected manner,

or the predicted values are in error. The values

shown in tables 16 and 18 will be revised later in

this paper as a result of both additional Process

I measurement data, and Process II difference

measurements.

TABLE 18

Predicted Sum and Difference Process I Values

for July 1, 1973 as of December 1972

SUM DIFF

(.) + (..) (.)-(..) UNC*

31.0370 27.8489 1.58

24.5889 34.1131 1.84

10.3330 20.8670 2.00

54.9882 46.2118 2.00

53.5988 63.6904 2.00

87.4424 57.0909 2.00

75.8741 59.4118 1.84

21.6850 -18.7303 1.75

* Applies to both SUM and DIFF

6.3. Process II Performance Parameters

In order to compare results from Process I, such as the computed difference ((.)—(. .)), with

Process II results, the measured difference ((.)—

(. .)), it is necessary to estabUsh Process II performance parameters. The Process II within-group

standard deviation, and total standard deviation,

in addition to being used to monitor the process

performance determine in part the uncertciinty to be associated with the process output. Initially,

the magnitude of these parameters is unknown. In

practice, one starts with estimates based on short

Block

Ident.

Accepted

Historical

Value

Accepted

Value

2/23/72

Accepted

Value

12/8/72

Predicted

Value

7/1/73

(.) 136-5

115A-6

202A-7

103A-8

109A-10

135A-12

109A-16

157A-20

29.5

28.3

14.9

47.9 56.0

70.8 66.8

1.6

29.3

29.4

15.5

50.7 58.4

71.9 67.7

1.1

29.0 29.1

15.6

50.6

58.4 72.3

67.3

2.9

29.4*

29.4

15.6

50.6

58.6 72.3

67.6

1.5

(..) 178.5

312-6

105-7

143-8

148-10

249-12

155-16

146-20

0.9 -2.1

-5.8

7.4 -1.4

14.9 10.3

21.7

1.1 -2.4

-5.7

7.0 -2.0

15.0 9.9 21.0

1.6** -4.8

-5.3

4.4 -5.0

15.2

8.2 20.2

35
sequences of repeated measurements and then

modifies the estimates as a history of process

performance develops. If all is going well, the

estimates approach long term stable values which

become the accepted parameters for the particular

process.

The redundancy of the intercomparison design

provides the mechanism for establishing the

within-group standard deviation which is the standardard deviation of a "single" comparison computed

as shown in appendix 3 and reference [6]. For

the designs used each estimate of the within-group

standard deviation is based on 5 degrees of freedom.

These estimates, combined for many series of

measurements, establish the accepted withingroup standard deviation, ctw, as shown in table

19. Since there is no immediately apparent reason why the accepted standard deviation for the 6 in,

7 in, 10 in, and 12 in blocks should be less than

that for the 5 in and 8 in blocks, for control purposes,

the accepted standard deviation was "rounded"

as shown. In like manner, the accepted standard

deviation for control purposes for the 16 in and

20 in blocks was also "rounded."

TABLE 19 Within Group Standard Deviation, Ccrnparative Procsss

Accepted S.D.

Ncmincil

Size

No. of

Series*

Obser ved

S.D.

for

Control Purposes

5 in 77 .50 .5

6 in 132 .39 .5

7 in 89 .42 .5

8 in 173 .5 .5

10 in 72 .41 .5

12 in 73 .48 .5

16 in 52 .49 .8

20 in 62 .67 .8

* 4 degrees of freedan per series

For each new sequence of measurements, the

computed or observed standard deviation is tested

for conformity with the existing distribution by

computing an "F ratio:"

F = ((Observed S.D.)/(Accepted S.D.))^

If the "F ratio" exceeds a suitable Umit, an "outof-control" situation for that particular sequence

of comparisons is indicated, and the measurements

must be repeated. If the accepted standard deviation, (Tw, really reflects the process performance,

few measurements will have to be repeated. On

the other hand, a few "out-of-control" measure- ments occurring in sequence following a long

sequence of "in-control" measurements are an

almost sure sign of process troubles.

The difference, ((.) — (. .)), is determined in

every comparison measurement series. For a given

pair of reference blocks, this difference should be

reasonably well behaved, and similar to all other

difference measurements required in the particular

design. A collection of measurements of this dif- ference reflects the total variability of the process

over the time span of the collection. The standard

deviation of such a collection is the total standard

deviation, err, of the process. The total standard

deviation reflects the difference between the variabihty accounted for in the measurement algorithm,

the within-group standard deviation, and the variabiUty from all sources which affect the process

over time. The total standard deviation is a measure

of the ability of the process to repeat a given

measurement.

As an initial estimate, the accepted Process II difference between the reference blocks was the

average of a collection of measured differences.

Each series of measurements produces a new

value for this difference. The new value is checked

for conformity with the existing collection by

computing a ratio:"

i = (New Obs. Diff. -Accepted Difif.)/ (Accepted Total S.D.)

For t values exceeding suitable limits, the process is considered "out of control." On the assumption

that the estimates of the accepted difference

and the accepted total standard deviation are proper, an "out of control" signal indicates that one or the other of the reference blocks has changed

or, for some reason or other, the process is not

measuring the appropriate differences.

The accepted total standard deviation as of July

1973 is tabulated in table 20. On the initial assumpTiffiLE 20

Itital, or Process, Standard Deviation, Cotparative Process

tion that difference is constant, the average measured ((.)—(. .)) is tabulated together with the number of values in each average. These averages are the

Accepted S.D. S.D. (.)-(..)* No. of Total for of Block Designation Average Series S.D.** Oontrol Mean m36-5 - H178-5 28.5 61 .46 .5 .059 M115A-6 - H312-6 32.1 111 .47 .5 .045 M202A-7 - H105-7 22.0 58 .34 .5 .045

^4103A-8 - H143-8 44.2 112 .76 .8 .072 ^a09A-10 - H148-10 61.4 66 .65 .8 .081 ^a35A-12 - H249-12 57.0 62 .91 .8 .115 M109A-16 - H155-16 57.5 40 .79 .8 .125 A157-20 - H146-20 -16.5 54 1.14 1.1 .156

Ttentative pending check on closure between Process (!) and Prooess (II)

berrrpes of freedon Is one less than the number of series.

36
"Accepted Differences" used in computing the

ratio." The total standard deviation, for control

purposes, was "rounded" as indicated.

6.4. Closure

When a particular measurement is made by each

of two different measurement processes, it must be

shown that the two results "close." If both processes

are indeed measuring the same thing, as a minimum,

the uncertainty limits associated with each result

should overlap. Process II, the comparison process,

measures the difference ((.) — (. .))II directly.

Process I, the "new" interferometric process,

estabhshed values for each of the ( . ) and (. .) blocks from which the difference ((.) — (. .))I can be computed. These two sets of differences are tabulated in table 21. The uncertainty of the differ- ence as shown for ((.) — (. .))Iis from table 18.

The uncertainty as shown for ((.) — (. .))II is 3 times the standard deviation of the mean, from

table 20. For the 6 in blocks, [((.)-(• .))I-

((.) - (. .))II] = 34.1 - 32.1 = 2.0 > (Unci + UnciT) =

(1.84 + 0.135), therefore the results do not "close."

The same is true for the 10 in blocks. Closure is marginal for the 8 in, 16 in and 20 in blocks.

TABLE 21

Closure, Process (I) and Process (II)

Process (I) Process (II)

Nominal

Size (.)-(..) Uncertainty

of Diff.

Average

(.)-(••)

3 S.D.

of Mean

(Predicted July 1973) (Table 18)

5 in 27.8 1.58 28.5 .177

6 in 34.1 1.84 32.1 .135*

7 in 20.9 2.00 22.0 .135

8 in 46.2 2.00 44.2 .216

10 in 63.7 2.00 61.4 .243*

12 in 57.1 2.00 57.0 .345

16 in 59.4 1.84 57.5 .375

20 in -18.7 1.75 -16.5 .468

* Differences, as established by Process (I) and Process (II),

do not agree within expected limits.

In retrospect, for the (.) blocks the rate of change

used to establish the predicted values was based

on a long history, (table 5), and even if some

of the historical points have questionable uncertainty hmits, the time span covered (with the

exception of the 20 in block) adds confidence in

the rate of change. On the other hand, for the (. .) blocks the rate of change used was from the small

collection of Process I data. In the case of Process

II, the average difference ((.) — (. .)) is based on

a large collection of values, the difference being

determined in every sequence of measurements.

In table 21, the computed difference between the

predicted Process I values has been compared with

the average Process II difference. While the

precision of Process II is smaller than that of

Process I, because of the short time span covered

by these measurements, initially it did not seem

hkely that one could detect the rate of change of

the differences between two blocks.

The ((.) — (. .)) data from Process II was

analyzed to determine the rate of change of the

difference, the standard deviation of this rate of

change, and a predicted difference for July 1973

(7/73) and January 1974. The results of this analysis are summarized in table 22. In the case of the 5 in,

8 in, 10 in, and 20 in blocks, the rate of change is not

significant relative to the standard deviation of the

rate of change. The standard deviation of the collection and of the fit are essentially the same. For the

rest of the blocks, the rate of change is considered

to be significant relative to the S.D. of the rate of

change (slope). This is further verified by the fact

that the standard deviation about the fitted hne is smaller than the standard deviation of the

collection.

TABLE 22 Analysis of Process II ((.)-(..)) Data

(Same Data as Used in Table 20)

Assuming Oiange With Time i: Assuming Constant^

Natiinal Fitted S.D. Accepted * Size Slope Slope Slope S.D. S.D.

5 in .038 .195 0 .468 .465

6 in .907 .178 .907 .472 .522

7 in 1.465 .259 1.465 .592 .679

8 in .191 .266 0 .803 .802

10 in - .088 .264 0 .718 .715

12 in - .815 .330 - .815 1.059 1.087

16 in -1.588 .388 -1.588 .900 1.000

20 in .404 .410 0 1.175 1.087

* Of collection about fitted line

** Relative to average value, no fitting

TABLE 23 Sumrary Rate of Change Conputation

Hist.

Process I Estimate

Process I Cornputed

Process II (Measured) New

Estimate

Moninal

Size (.) (.) (..) (.)-(..) (.)-(..) (..)

(a) (b) ((a) -(b)) (c) ((a) -(c))

5 in .300 - .883 + .300 - .005 0 .30

6 in .162 - .836 -1.503 1.666 .90671 - .74

7 in 0 .240 .288 - .288 1.46455 -1.47

8 in 0 .005 -1.674 +1.674 0 0

10 in .177 .018 -2.057 +2.231 0 .18

12 in 0 .974 .137 - .137 - .81543 - .82

16 in .215 -1.218 -1.140 1.351 -1.58771 1.80

20 in -1.478 4.680 - .835 - .473 0 -1.48

From Table 16

37
Table 24 Predicted Values, 7/73 and 1/74, Based on Rate of Qiange Ooitputations

7/1/73 3 S.D. of 7/1/73 7/1/73

Nominal Identification Predicted Value Predicted Value Predicted Sum Predicted Difference

Size (.) (..) (.) {..) (.) and (..) {.) + (..) {.) - (..)

5.000000 M136 H178 29.44 1.59 1.12 31.03 27.86

b . UUUUUU ?ai5A H312 29.35 - 3.59 ZD* /D 7.000000 W202A H105 15.60 - 7.90 1.41 7.70 23.50

g. 000000 M103A H143 50.60 6.93 1.41 57.53 43.68

10.000000 M109A H148 58.64 - 1.72 1.41 56.93 60.36 12.000000 M135A H249 72.27 16.17 1.41 88.43 56.10 16.000000 tll09A H155 67.64 12.60 1.30 80.24 55.05 20.000000 A157 H146 1.48 19.50 1.24 20.98 -18.02

1/1/74 3 S.D. of 1/1/74 1/1/74

Ncxninal Identification Predicted Value Predicted Value Predicted Sum Predicted Difference

Size {.) (..) (.) (..) (.) and (..) (.) + (..) (.) - (..)

5.000000 M136 H178 29.59 1.73 1.12 31.32 27.86 6.000000 rai5A H312 29.43 - 3.97 1.30 25.47 33.40 7.000000 W202A H105 15.60 - 8.63 1.41 6.97 24.23

8.000000 ^4103A H143 50.60 6.93 1.41 57.53 43.68

iSj • UUUUuU M109A H148 58.73 - 1.63 1.41 0 / xu fin "^fi 12.000000 f4135A H249 72.27 16.57 1.41 88.84 55.69 16.000000 M109A H155 67.75 13.50 1.30 81.25 54.25 20.000000 A157 H146 .82 18.84 1.24 19.67 -18.02 o "average" diff.

60 • PREDICTED DIFF (7/73)

o PREDICTED DIFF . (7/73) PROCESS 1

Uncertainty of Sum

and Difference

1.58

1.84

2.00

2.00 2,00

2.00 1.84

1.75

Uncertainty of Sum

and Difference

1.58

1.84

2.00 2.00 2.00

2.00 1.84 1.75

58

56

54

(2)«

(2)«

„2).(2)

• (2)

(2)i -<>

(4)t

(3)«

K2)

• (2) 6

16 IN. BLOCKS, (,)-(..), PROCESS TL

(3/3/72 TO 5/8/73)

Figure 20. Closure, 16{{.) — (. .)), Processes I and II.

All of the rate of change data for the (.) and

(. .) blocks and the difference ((.) — (. .)) data are shown in table 23. The Process I estimate of rate

of change for the (.) blocks does not agree very well

with the historical data. The same is true for the

rate of change of the difference from Process I as compared to the measured rate of change of

the difference from Process II. Under the assumption that the cause was the small Process I data

base, it was decided that the (.) rate of change based

on historical values should be retained, and that

the best estimate of the rate of change for the {. .) blocks would be that computed from the historical

Process I data for the blocks and the measurement

Process II data for the differences.

Using the rate of change data from column (1)

and column (6) of table 23, new Process I predicted

values were determined for 7/73 and 1/74, as shown

in table 24. As a typical example, the results for

the 16 in blocks, which previously did not close,

38
are shown in figure 20. Clearly the predicted Process

II difference is well within the uncertainty of the

difference computed from the Process I predicted

values using the rate of change data from table 23.

The closure is now as expected for the 5 in through

the 16 in blocks, as shown in table 25. The closure

at the 20 in level is still marginal.

TABLE 25

Summary of Closure

(Predicted July 1973)

Nominal

Size

Process (I) Computed Dlff. Uncertainty

Process (11) Predicted Diff. Uncertainty*

5 27.86 1.58 28.46 .15**

6 32.94 1.84 32.90 .15*

7 23.50 2.00 22.98 .20*

8 43.68 2.00 44.14 .17**

10 60.36 2.00 61.35 .22**

12 56.10 2.00 56.31 .33*

16 55.05 1.84 55.98 .36*

20 -18.02 1.75 -16.46 .36**

* 3 S.D. of predicted difference

** 3 S.D. of mean

At the 20 in level, the greatest confidence at this time is in the Process II((.)— (. .)) by virtue of

the number of measurements which have been

made. This, however, does not help in establishing

the value of either 20(.) or 20(. .). Figure 1 of section

4 indicates only two values prior to establishing the

new interferometric process, therefore the historical

rate of change of 20(.) is highly subject to question.

There were no prior interferometric values for 20(. .). As an expedient action, values for the sum and

difference as shown in table 18 were accepted

for use in Process II measurements. The uncertainty

of the predicted July 1973 values for the sum and

difference value at the 20 in level, as shown in

table 18, was increased by 2fjL in to account for the

uncertainty in the rate of change estimates. As

a parallel action, additional measurements were

started both on the 20(.) and the 20(. .). The result

of this is discussed in the next section.

6.5. Process Surveillance

Process surveillance is a continuing operation. In

the case of Process I, it is expected that any new

value, with appropriate uncertainty, will be in agreement with the current predicted value. Further, each

new value adds to the data base used to establish

the next predicted value such as was shown in

figure 19. If such agreement is obtained, the vahdity

of the predicted value is verified. If such is not the

case, either the measurement process or the object

has changed. The "out of control" situation requires

study to determine what has happened so that

necessary actions can be taken to again establish an "in control" situation.

Because of the mar^nal closure at the 20 in level, a single Process I measurement was made on each

of the 20(.) and 20(. .) blocks (measurements of

July 9, 1973 in table 27). The difference between

the results was ((.) — (. .)) = — 16.0 microinches.

The estimated uncertainty of this difference is ±2.5 microinches, computed by the relation

(3V2)cr where (x was taken from figure 18. In

figure 21 this value is compared with Process II difference measurements, the average Process II difference (from table 20), and the July 1973 Process

I predicted difference from table 25, each with

appropriate uncertainties. Clearly, the new measure- ment data alone is not precise enough to resolve

the question.

Additional Process I measurements were made

on each of the 20 in blocks, and aU of the newly

determined values were added to the existing data

bank. New predicted values, computed differences,

and rates of change were determined for these

blocks, as summarized in table 26. The new July 1,

1973 predicted difference computed from Process I values, — 16.06 microinches, is now in good agreement with the Process II measured difference, — 16.45 microinches, as shown in figure 23.0n the

basis of this analysis, the July 1973 predicted values

for the 5 in through 16 in blocks shown in table 24,

and for the 20 in blocks, in table 26, were accepted

for use as restraints for Process II.

Table 26 Sunmary 20 ( . ) and ( .

. ) Predicted Values

Previous

7/1/73 Predicted

Value

Previous Assumed

Slope

Estimate

• 7/1/73 Measured

VaJ.ues

New

7/1/73 Predicted

Value UNC

Slope

Estiinate

20(.) 1.48 -1.308 1.3 1.31.762 1.24 - .990

20(..) 19.50 -1.308 17.2 18.0

17.822 1.24 -2.387

Surmary 7/1/73

Sum = (.) + {..) = 19.58 Diff = (.) - (..) =-16.06 Rate of change 1.397 pin/yr

UNC of Sum and Diff. = 1.8

In the fall of 1973, additional Process I measure- ments were made on the 5 in through 16 in blocks.

Using the expanded data base, as shown in table

27, new estimates of the process standard deviation

and the rates of change were made, as shown in

table 28. On the basis of the "pooled" standard

deviation, 0.642, three blocks, H105-7(. .), H148-

10(. .) and H146-20(. .), showed significant rates

of change. The data for each block was also analyzed

to determine the standard deviation about its "fitted" line. From this it was evident that the s.d.'s are length dependent. The use of the "pooled"

s.d. in such a circumstance has the effect of predicting pessimistic uncertainty limits for the shorter

39
12

O AVERAGE DIFF. • PROCESS I, COMPUTED DIFF. FROM PREDICTED VALUES BASED ON VALUES

BEFORE 1973

A PROCESS I, COMPUTED DIFF. FROM ONE.

SET OF 1973 MEASUREMENTS

PROCESS r, COMPUTED DIFF. FROM PREDICTED VALUES BASED ON ALL

MEASUREMENTS

16 -0-

-20 ±

20 IN. BLOCKS, (.)-(..), PROCESS H

(3/6/72 TO 5/14/73)

Figure 21. Closure, 20((.) — (. .)), Processes I and II.

blocks, and optimistic limits for the longer blocks.

The process standard deviation was fitted, by the

method of least squares, to a line of the form s.d.—

pL. Values from this hne, as shown in the table 29

column labeled S.D., were used to recheck the

rates of change. With the new process precision, one more block, H312-6(. .), indicates a significant rate of change. It is of interest to note that the

process standard deviations shown in table 29

are very nearly the same as shown in figure 17,

section 6.1. Using the larger data base and the new process

s.d. estimates, predicted values were established

for 7/1/73. These values are compared with the

values which formed the restraint on Process II in the fall of 1973 in table 30. The agreement is within the combined uncertainty limits. Predicted

values, and appropriate Process I restraint data

based only on Process I measurements, were

estabhshed for 1/1/74, and 7/1/74, as shown in

table 31. The appropriate Process II data is shown

in table 32. The agreement between the differences

((.)—(. .)) as determined by both Process I and

Process II is shown in table 33. On January 1,

1974, the values shown were accepted as the

restraints on Process II. These values will be used

until July 1, 1974, at which time the 7/1/74 value

will be used. Additional Process I measurements

will be made in the fall of 1974, at which time the

values will be "updated," first by checking back to the 7/1/74 values, then by predicting forward for

both a six months and a one year period.

The Process II data on the difference (.) — (. .), initially used to estabhsh rates of change, is now

used in a different manner. Since the difference

between the two reference blocks is determined in

every Process II measurement, there is a very large

amount of data on the measured differences. In

early 1974, all of this data was analyzed to determine

a "predicted" measured difference for 1/1/74.

The predicted Process II measured difference is compared with the computed Process I difference

in table 33. With the exception of the 5 in level, the

agreement between the two processes is clearly

within the expected hmits. The marginal agreement

at the 5 in level may indicate that the 0.95 uncertainty of the Process I computed difference is a little optimistic.

40
Table 27. Process I data through September 1973.

M136 5.00000000

H178 5.00000000

MU5A 5.00000000

H312 5.00000000

W202A 7.00 000 0 00

H105 7.00000000

m03A 8.00000000

Hl<i3 8.000000U0

H109A 10.00000000

H148 10.00000000

M135A 12.00000000

H2*9 12.00000000

H109A 16.00000000

H155 15.00000000

A157 20.00000000

H145 20.00000000

8 24 71 . 18 29. 12 .44729495 13.5411 29.30

10 18 71 . 12 29.08 .40707047 13. 7890 29. 20

3 6 72 -.17 28.97 .32709971 14. 1808 28 . 80

3 7 72 .13 28.97 . 32672425 14. 1835 29.10

3 8 72 -.37 28.97 .32635185 14. 1863 26.60

9 5 73 .05 28.55 .55864410 1 5. 67 12 28.60

9 7 73 .05 28.55 .55043653 1 5. 5757 28. 60

9 13 71 .00 1.20 .38671374 13. 5932 1.20

9 30 71 -.38 1. 18 . 37524648 1 3. 7397 .80

10 15 71 .03 1.17 . 36551 706 13. 7808 1 .20

3 5 72 -.25 1-05 .29674699 14. 1808 .80

3 7 72 .25 1.05 .29648054 14. 1836 1. 30

3 8 72 .45 1-05 .29621738 14. 1863 1 .50

9 5 73 . 10 -60 .55793002 15. 5712 .70

9 7 73 -.20 .50 .55968714 1 5. 5767 .40

8 25 71 .24 29. 16 . 5 7410409 13-6438 29.40

10 18 71 .05 29.15 .52578718 13. 7890 29.20

3 15 72 -.50 29. 10 .42056881 14. 2055 28.60

3 16 72 . 10 29.10 .42009815 14. 2082 29.20

8 29 73 .05 28.95 .56422637 15.6548 29.00

8 30 73 .05 28.95 . 56527818 1 5. 6575 29. 00

9 14 71 .64 -2.24 .55651485 13. 69 59 -1 .60

9 29 71 -.33 -2.27 . 54290299 13. 7370 -2.60

3 15 72 -.52 -2.58 .42063475 14. 2055 -3. 20

3 15 72 .19 -2.59 .42016304 14 . 2082 -2.40

8 29 73 -.04 -3. 56 .65474203 1 5. 6548 -3.60

8 30 73 .16 -3.56 .66579553 15.6575 -3.40

8 26 71 -.23 15.73 . 84005621 13. 6466 15.50

12 72 -.18 15.43 .57447319 14. 2795 15. 30

4 13 72 . 52 15.48 .57367142 14. 2822 16 .00

8 21 73 .05 14.95 . 78495288 15. 6329 15.00

8 22 73 -.15 14.95 .78527992 1 5. 6356 14.80

9 15 71 . 15 -5. 3 5 .67490634 13. 6986 -5.20

9 28 71 -1. 00 -5. 40 .65014295 13. 7342 -6 .40

4 12 72 .40 -6.20 . 4698 7276 14. 2795 -5.80

13 72 .80 -5.20 .48938058 14.2822 -5.40

8 21 73 -. 32 -8. 18 . 78308550 15. 6329 -8.50

B 22 73 -.02 -8-18 .78436027 15. 6356 -8.20

9 3 71 -.09 50. 59 .93686 561 13. 5658 50.60

<» 5 72 -.33 50. 5 3 .65594131 14. 2603 50.20

6 72 .47 50. 53 .65500934 14.2530 51.00

8 23 73 . 13 50. 1 7 . 88820929 15. 6384 50.30

3 28 73 -.17 50. 1 7 .89569559 15. 5521 50.00

9 10 71 1.19 7. 11 .76265827 13. 6849 8.30

9 27 71 -.59 7.09 . 741 18 396 13. 7315 5.40

4 5 72 -.37 6.87 .55647095 14. 2603 6.50

4 6 72 -. 37 5. 87 . 55590144 14. 2530 5.50

8 23 73 .31 6.29 .88482391 15. 6384 5. 50

8 28 73 -.08 5.28 .89195498 15.6521 5.20

9 1 71 -.06 58.46 1 .20521970 13. 6603 58.40

4 21 72 -.55 58. 35 . 81255757 14. 3041 57.80

4 24 72 .55 58. 35 .80924487 14. 3123 59.0 0

8 15 73 -. 12 58. 12 1 . 1 1280546 15. 6164 58.00

8 16 73 .08 58. 12 1. 1 1472857 15. 5192 58.20

9 9 71 . 19 -1.59 .97305609 13. 6822 -1.40

9 25 71 . 34 -1.64 .94512025 13.7288 -1 .30

4 21 72 -.59 -2.21 ,69053131 14. 3041 -2.60

4 24 72 -. 18 -2.22 .68860428 14. 3123 -2. 40

8 15 73 -.08 -3. 52 1. 10762404 15. 6154 -3.50

8 16 73 .32 -3.52 I- 10944539 15. 6192 -3.20

8 31 71 -.61 72.41 1.49285778 13.6603 71 .80

5 17 72 .78 72-02 . 9594051

7

14. 3753 72. 80

5 18 72 . 19 72. 01 .95811283 14. 3781 72.20

8 13 73 . 07 71. 33 1. 32885 1 1

2

15.5110 71 .40

8 14 73 -.43 71.33 1.33119936 15. 6137 70. 90

9 8 71 -.74 15.04 1. 19357648 I 3. 6795 14. 30

9 24 71 .57 15.03 1.16109239 13. 7233 15.60

5 17 72 -. 06 14. 85 .81827080 14. 3753 14.80

5 18 72 .34 14.86 .81763773 14. 3781 15. 20

8 13 73 . 44 14. 56 I. 32066737 15.6110 15.00

8 14 73 -.56 14.56 1. 32286757 15. 6137 14.00

8 27 71 .15 57.55 1.55581940 13.6493 67.80

8 28 71 .05 57. 55 1. 56305913 1 3. 6521 67. 70

4 28 72 -1.25 67.06 1.08108890 14. 3233 65. 80

5 3 72 .95 57.05 1.07705037 14. 3370 68.00

7 12 73 . 10 66. 00 1. 74337101 15. 5260 66. 1 0

7 I 3 73 .00 66. 00 1 . 74633643 15. 52 88 66.00

9 7 71 . 19 10. 01 1. 57265292 1 3. 5757 10-20

9 22 71 . 39 10.01 1.53078017 13. 7178 10. 40

4 28 72 -1.39 9.99 1 .08747844 14. 3233 8.60

5 3 72 -51 9.99 1. 08290522 14. 33 70 10.50

7 12 73 .05 9.95 1. 75076 166 1 5. 5250 10.00

7 13 73 . 25 9.95 1. 75380018 15. 5288 10. 20

8 30 71 -2. 12 3.52 2.12566841 13. 5575 1 .40

3 12 72 1.59 3.01 I. 47846642 1 4. 1973 4.60

3 13 72 .80 3.00 1.47619784 14. 2000 3.80

3 20 72 .61 2. 99 1.4507161

1

14. 2192 3.50

7 9 73 -.44 1.74 2.22950065 15-5178 1. 30

7 1

1

73 -.44 1.74 2.23770985 15. 5233 1.30

9 2 71 -1.00 22.20 1. 79572752 13. 6630 21.20

9 23 71 .24 22.06 1. 72537805 13. 7205 22.30

3 12 72 . 48 20.92 1. 28946503 14. 1973 21 .40

3 13 72 . 18 20.92 1-28801 192 14. 2000 21.10

3 20 72 .43 20-87 1.27827047 14.2192 21.30

7 9 73 -.57 17.77 2-21398526 15. 5178 17.20

7 11 73 .24 17-76 2.22 176322 15. 5233 18.00

41
Table 28. Process 1 standard deviation and block rate of change computations through September 1973.

See Table 15 for meaning of column headings.

5t R NO Nrty 1 N A L S. D, N X R A H YHA R A B SDB T- 8/SDB

Ml 36 S • 00 000 000 . 2 1 "579567 7 1 4 a 4755 3 773 28.88571358 32. 9322 3906 - . 2 79542 35 . 1 041 1625 -2 .68490598

00 00 0 0 0 0 , 2 96 2 00 85 1 * • 38904083 ,98749999 5, 296731 3 3 - . 29961 910 . 1 3656049 -2 . 1 9403940

Ml 1 5A 6 ,00000000 , 2R5823 16 6 1 4 , 52646365 29 .06666660 30, 61 824822 - , I 0681 056 .14 15 1 073 . 754 78770

H3I2 6 , 00000000 , 4 904 9272 6 14 . 52648365 -2 ,,79999995 6, 96 1 20870 -.671 95950 .2431 31 56 -2 . 7637691

7 . 00 000000 ,3561 1541 5 1 4. 6953421

1 5 ,, 31CQQ98 1 2 1 . 04999971 - ,38991947 . I 9886784 -1 . 96 06964

HI 05 7 ,00 oonooo .69405091 6 1 4 . 54383540 -6 ,,5833332 5 14. 699045 1

-1 .46332642 ,352071 65 -4 , 15633130»»

M103A 6 .00 000000 .35695536 5 t 4 , 695890150 ,,4 1999960 54. 29846048 - .26391 467 ,19626350 -1 ,33099663

HI 63 8 ,00 000000 . 7527782f* 6 1 4 . 53835595 6 ,,7499994 a 1 2. 8H094354 -.421 7091

.37720064 -1 , 1 1 799434

M 1 09A 1 0 .00 000000 . 50056331 5 1 4, 70246542 5 8 ,.27C<)9q26 60, 88251 352 - . 1 7701 2 10 , 28555798 .6 1 9681 49 HM8 1 0 . on 000000 , 4000494"' 6 14. 54 383528 -2 ,,4499999 6 1 2. 03702903 - ,996094 I 4 , 2045581 5 -4 .869491 34»»

M 1 35A 1 2 ,00 000000 .f 3595 ?'85 5 14. '2767103 71 ,. B19 99 97 4 80. 0 t 9251 82 - .55^72438 .3702 1 064 -I .50380355

H2 1 2 . Of 000000 ,e 1 I 4 8O02 6 1 4 . 5^^ 34 700 1 1 4 ,. 81 666660 18. 44053245 -.24-183259 , 3 1 54 6 1 8

. 78878830 MIOQA 1 6 . Of. 000 00 0 , 79493372 6 1 4 , 502 73 94 3 66 ,89999962 79. 65 187836 - .87927383 . 4 1 629779 -2 , 1 02 02 83 7

Hi ^5 I 6 , OO 00.0 000 ,781 856 79 6 14, 51826453 9 ,.9833332 3 10. 42036641 -.030 10230 . 42054037 ,0 71 58006

Al ?7 2 0 . ocoooooo 1 . 45 303530 6 14. 55251 098 2 ,,6666666 3 1 6. 61056948 - ,958 17648 , 83 J81 634 -1 , 1 491 481 I HI 46 20 ,00000000 .6 I 379633 7 I 4 , 43444 1 92 20 ,, 357 1424 5 5 4. 62744598 -2 .38605932 , 3225 3424 - 7 ,4 0404904

Table 29. Accepted Process I standard deviation^ January 15, 1974.

See Table 15 for meanings of column headings.

SER NO NOMINAL S.D- N XBAR ySAR A B SOB T=B/soa

Ml 36 5. 00000000 . 2 7000000 7 1*. 47553778 28. 0857135 8 32. 93223906 .27954235 13026854 -2 . 14589289

HI 78 5. 00000000 .27000000 8 1*. 33904083 98749999 5. 298731 33 .29961910 12448085 -2 .40594937

6. 00000000 .32000000 6 1*. 52648365 29 .0666666 0 30. 61824822 . 1 068 1050 15843165 .67417440

H312 b. 00000000 .32000000 6 526'.8365 -2. 7999999 5 6. 96120870 .67195950 15862029 -4 .23627704»»

W202A 7. OOGOOOOO . 38000000 5 I*. 6953'.218 15. 3 199993 I 21. 0499997.38991947 21220587 -I .83745846

HI 05 7. 00000000 .38000000 6 14. 54383540 -6. 58333325 14. 6990451

-1 .46332642 19276284 -7 .59133035**

M1034 8. 00000000 .*3000000 5 14. 69589019 50. 41999960 54. 29846048 .26391467 23885873 -1 .10489857

Hl'.S 8. 00000000 .<.3000000 6 14. 538 35595 6. 7499993 8 12. 88094354 .42170819 21546355 -1 .95721361

M109A I 0. 00 000000 . 54000000 5 14. 70246542 58. 27999926 60.88251352 .17701210 30805555 . 57461 098

10. 00000000 • 5'>000000 6 14. 54383528 -2. 44999996 12. 03702903 .995094 14 2761 1935 -3 .60747671»»

M13 5a 12. 00000000 .65000000 5 14. 72767 103 71 . 81999874 80. 019251 82 .55572433 3 783 852 1 -1 .47131543

H?4q 12. OOGOOOOO .65000000 6 14. 56347001 14. 81666660 18. 44053245 .24883259 33532929 . 74205443

M109A 16. 00000000 .86000000 6 14. 50273943 66. 89999902 79. 651 87836 .37927383 4525 3596 -1 .94299215

H 155 1 6. 00 000000 .86000000 6 14. 51820453 9. 9833332 3 10.42036641 .03010230 46257155 .05507599

4157 20. 00000000 1 . 08000000 6 14. 55251098 2. 6666666 3 16. 61056948 .95817843 51975208 - 1 . 54606739

HI '.6 20. 00 000000 1.08000000 7 14. 43444192 20 . 357 14245 54. 82744598 -2 .38805932 56 75 123 1 -4 .20794272«»

42
Table 30

Conparison of 7/1/73 Predic±ed Values

Predicted Predicted'^ Delta

Serial NoTUJial Value Value Predicted

Nmrber Size (71-72 Data) 3 S.D. (71-73 Data) 3 S.D. Value

136 5.0 29.44 1.11 28.60 .67 .84

178 5.0 1.59 1.11 .66 .67 .93

115 6.0 29.35 1.30 28.96 .80 .39

312 6.0 - 3.59 1.30 - 3.45 .80 - .14

7.0 15.60 1.41 15.01 .98 .59

105 7 n - 7.90 T ill 1-41 - 7.98 .96 .08

103 8.0 50.60 1.41 50.21 1.10 .39

143 o n o.U b. y J ±. ft-L D . JD 1 no . Jo

109 10.0 58.64 1.41 58.14 1.40 .50

148 10.0 - 1.72 1.41 - 3.40 1.38 1.68

135 12.0 72.27 1.41 71.39 1.69 .88

249 12.0 16.17 1.41 14.58 1.65 1.56

109 16.0 67.64 1.30 66.03 2.29 1.61

155 16.0 12.60 1.30 9.95 2.31 2.65

157 20.0 1.48 1.24 1.76 3.00 - .38

146 20.0 19.50 1.24 17.82 2.94 1.68

Based on 71-72 Process I Data Supplemented with Process II (.)-(..) Data

Predicted Values Based on 71-73 Process I Data

Table 31. Accepted Process I data for (.) and (. .) reference blocks, January and July 1974.

NOM. SIZE IDENT tFICATION 1- 1-74 PREO VAL 3SIG PREO VAL 1- 1-74 PR ED SUM 1- 1-74 PREO DIFF JNC OF SI (.1 (..) (.) ( . .) ( . ) ( . . 1 ( .)4^( ..)

5.000000 M136 H178 28.46 .50 -67 .67 28.96 27-95 .95

6. 000000 M115A H312 28.91 -3.79 .80 .80 25. 1 2 32-70 1.14

7.000000 M202A H105 14-81 -8.7 2 -98 .96 6. 09 23.53 1.37

8.000000 M103A H143 50.08 6. 13 1. 10 1.08 56.2 1 43-94 1.54

10. 000000 M109A Hl't8 58-05 -3.90 1.40 1.38 54. 15 61. 95 1.97

12.000000 M135A H249 71.11 14.46 1.69 I .65 85.57 56.65 2.36

16. 000000 M109A H155 65.58 9.94 2. 29 2.31 75.52 55.64 3.26

20. 000000 A157 H146 1.28 16.61 3.00 2.94 17.89 -15-33 4.20

NOH. SIZE IDENTIFICATION 7- 1-74 PR ED VAL 3SIG PRED VAL 7- 1-74 PREO SUM 7- 1-74 PRED DIFF UNC OF SUM

(.1 (..) ( . ) (. .1 (.) (. . i {.)*{..) >

5. 000000 M136 H178 28.32 .36 .85 .84 28.68 27.96 1.19

6.000000 H115A H312 28.86 -4. 12 1. 01 1.02 24.73 32.98 1.44

7. 000000 W202A H105 14.62 -9.44 1-25 1 .22 5.18 24.06 1.75

8.000000 H103A H143 49.94 5.92 1.41 1-37 55.87 44.02 1.97

10. 000000 M109A H148 57.96 -4.39 1.8 1 1.75 53.57 62.36 2.51

12. 000000 M135A H249 70.84 14.34 2- 19 2.10 85-17 56.50 3.03

16.000000 M109A H155 65.15 9.92 2. 90 2.94 75.07 55.22 4.13

20. 000000 A157 H146 .80 15.43 3.85 3.72 16.24 -14.6 3 5.35

43
Table 32. Accepted Process II data for (.) and ( ) reference blocks. January 1974.

VALUES (M ICROINCHES ) FOR REFERENCE BLOCKS AND PROCESS PARAMETERS AS OF FEB 74

FOR USE IN CALIBRATION OF TEST BLOCKS BY MECHANICAL I NT ERCO MP AR I SON

CHECK

L ENGT H lOENTIF ICATION RESTRAINT UNCERTAI NTY STANDARD S.D. S.D

(. ) (.)*{..

)

(.)-(..) ( Wl THIN) ( TOTAI

5.000000 M136 H178 28.963 .946 28.460 .47 .54

6. 000000 Ml 15A H312 25.117 1 . 1 37 33.476 .47 .59

7.000000 W202A H105 6.092 1. 372 23. 562 .47 .6 3

8.000000 M103A H143 56.208 1. 544 44.212 .47 .67

10.000000 M109A H 148 54. 147 1 .966 61.373 .47 .76

12.000000 M135A H249 85. 569 2.363 56. 908 .47 .85

16. 000000 Ml 09A H155 75.520 3.257 57. 282 .57 1.02

20.000000 A157 H146 17. 889 4. 201 -16.484 .72 1.20

Table 33

Cotparison {{.)-{..), Process I and Process II, January 1974

Ncminal

Size

Process

(.)-(..)

I

UNC

Process II (For 1-1-74)

(.)-(..) Itotal S.D. D.F. 3S.D. Mean 4

5 27.95 .95 28.460 .489 90 .153 -.51

6 32.70 1.14 33.476 .525 97 .513 - .78

7 23.53 1.37 23.562 . .543 106 .546 - .03

8 43.94 1.54 44.212 .753 309 .129 - .27

10 61.95 1.97 61.373 .729 88 .231 .58

12 56.65 2.36 56.908 1.104 89 .348 - .26

16 55.64 3.26 57.282 1.072 71 .378 -1.24

20 -15.33 4.20 -16.484 1.054 94 .324 1.15

A is the difference between computed Process !((.)-(..)) and the

measured Process II ((.)-(..))

44
7. Measurement Process in Action

7.1. Uncertainty of the Transferred Value

The concept of a measurement system requires

that values assigned to represent certain characteristics of objects be reasonably unique and

repeatable over time and changes in location. It

is expected that sequences of measurements of

the same thing made at various times and at different locations show evidence of convergence

to the same limiting mean. Uncertainty statements

are, in essence, predictors of the degree to which

such closure can be attained. Failure to agree within

uncertainty hmits is an indication that the two

processes are fundamentally different, or that

the uncertainty statement does not adequately

describe the error bounds. For a practical measurement, the measurement algorithm, or the mathematical model of the measurement process, can- not possibly reflect all of the sources of variability.

The instrument or comparator cannot differentiate

between a real change and all of the perturbations which change the indication in the same manner as a change in the object. Nonetheless, it is important to know the bounds for the variability

which occurs in the course of making measurements. Redundancy, either by repeated measure- ments or incorporated in a particular measurement

process, provides a means for assessing this

variability.

In order to illustrate the nature of a realistic

uncertainty statement, consider first the collection

of simulated measurement data in figure 22. The

data shown reflects the effects of variabihty from

four cyclic sources over the time period necessary

for 300 measurements. This data has the appearance

of coming from a reasonably well behaved measure- ment process. There are no apparent trends and

there is little evidence of grouping. The 3 s.d. limits appear to be bounds for process variability.

One would surely expect the next measurement

result to be within these prescribed limits. Further,

if the next measurement was defined to be the av- erage of n independent measurements, one would

expect this average to agree with the average shown

within 3is.d./( y/n)- Without knowledge of independent parameters which are proportional to the

magnitude of each source of variability, there is no way to further analyze this data. The random

component of the uncertainty of the result would

be a function of the s.d. and the definition of the

result (i.e., single measurement, or the average of n measurements).

<

>

r

1

... 1 . —t

1 PARAMETER A

PARAMETER B

PARAMETER C

70

60

UJ^ 40 <

>

100 200 RUN NUMBER

Figure 22. Simulated measurement data.

PARAMETER D

Figure 23. Simulated measurement data analysis.

45
In this process simulation, there are identifiable

parameters which are proportional to the effects of sources contributing to the process variability.

Recording the parameter values along with each

measurement result permits the use of correlation

studies to further evaluate the process. In figure 23,

the parameter for each source of variability is plotted against the appropriate measurement result.

For parameters B, C, and D, there is little evidence

of correlation. While the variability of these parameters contributes to the process variability, one

cannot differentiate between their respective contributions. Clearly, there is a correlation with parameter A. This correlation indicates that a "between

time" variability associated with parameter A is influencing the measurement results. The effect

is systematic, that is, the result is high when the

parameter value is high, and vice versa. It should

be noted, however, that in spite of the existence of

the systematic effect, the initial Sar limit is still an

appropriate bound for the process variability.

If, over the sequence of the 300 measurements,

the variability of the result reflects the maximum

excursion of each parameter in this and all similar

measurement processes, the initial s.d. is an appropriate basis for a realistic uncertainty statement.

This includes one parameter frequently overlooked,

a change in location. The variability of a given

parameter in one facility, such as air density,

may be only a small fraction of the variability of

the same parameter over all locations. Other parameters may be related only to changes in location. If,

under the conditions stated above, the performance

of the process is adequate for the intended use of

the results, there would be no reason for change.

On the other hand, having identified the source of

variability, action can be taken to reduce the magnitude of the systematic effect with a resulting

decrease in process s.d. as shown in figure 24.

70|-

60 -

50 ^ . .

_ UJ . . Z> !_!;"',"^^^'

_I 40 - • < . > ....

30 • ;

20 -

loU 1 1 L 100 200 300 RUN NUMBER

Figure 24. Simulated measurement data — systematic effect minimized.

The two measurement processes used to assign

values to "working" gage blocks are described by

the above simulation. Process II, the comparison,

is like the process described by figure 22. Each value

from Process II is the result of a sequence of measurements over a short time span (about 5 minutes)

so that conditions do not change very much. One

would normally expect that the standard deviation

of the collection of repeated measurements, (.)—(. .), would be a function of the redundancy of the design

and the within-group standard deviation. The design

solution gives values for the difference between the

"knowns," ((.) — (. •)), and the "unknowns," (x) and

(y). These values are hnear combinations of "single"

measurements so that:

s.d. (( . ) — (• •)) = A(Tw = (Tt

s.d. (x) = s.d. (y) = B<Jw

where A, B, reflect the redundancy of the design.

For the designs used, A ~ 0.58, so that one would

expect (Tt<o-w Table 32 showed clearly that

this is not the case thus indicating that there is a long term source of variability which, as yet, has

not been characterized. For Process II, the random

component of the uncertainty must reflect this

variability.

Process I is hke the process described by figure

23. There are at least four independent parameters

associated with known sources of variabiUty, the

atmospheric pressure, temperature and relative

humidity, and the temperature of the block. As an example of correlation, figure 25 shows clearly

that the initial variability associated with the

values obtained for the 10 in cervit control block,

in figure 9, is related to relative humidity. The

corrective action taken, described in reference

[14], resulted in a smaller standard deviation. As

coUections of data increase, additional correlation

studies provide insight as to process behavior, and

provide a means to identify and reduce the magnitude of systematic variability.

The values established in Process I are used as "constants" in the restraint for Process II, thus

the uncertainty of the restraint, (.) + (. .), is in part

the systematic error associated with Process II results. The uncertainty of the restraint. Process I being free from known sources of systematic

error, is three times the combined standard deviations associated with the (.) and (. .) predicted

values such as shown in table 32. A proportion

part, NjR, where N is the nominal value of the

restraint and R is the nominal value of the "unknown," becomes the systematic error term for

the result from Process II. For the restraint used

in the current designs, the S.E. component of the

uncertainty of the announced value for the "unknowns" is (V2)(Unc.(.)+(. .)). The (Unc.(.)+(. .)) is based on Process I performance parameters.

For the design in current use, the random comWith the exception of environment temperature, there are no independent parameters at the present time which can be used to identify the source or sources of this systematic variability in Process II. The metrologist is interested in determining the source and magnitude of the between-time components of variability. Understanding

the nature of this variabihty generally leads to improved equipment and measurement

procedures. On the other hand, one may not be able to reduce the magnitude of the

variability without severely limiting the practicality of the measurement process.

46
<

>

5 6 7 VAPOR PRESSURE

Figure 25. Value versus vapor pressure.

ponent of the uncertainty of the announced values

is computed by the relation:

3(t{x) = 3a (y) = 3

48

as given in section 10 of reference [6]. The total

s.d., (Tt, and the within s.d., (Tw, are Process 11 performance parameters.

7.2. Verifying the Uncertainty

Having established the appropriate quantitative

process performance parameter and constructed a suitable uncertainty statement, it is of interest to verify that the statement is in fact descriptive of

the expected closure. For one such test, a set of

reference blocks designated NBS (. . .) was con- sidered as a typical set of long blocks. The results of

measurements on these blocks are shown in table

34. The first sequence of measurements, labeled

"typical," established values for these blocks relative to the values of the NBS (.) and (. .) reference

blocks by means of Process II. The (. . .) blocks were

also included in many sequences of measurements

in the course of evaluating Process II. The average

of the collection of values is also shown. Finally,

values were assigned to the {. . .) blocks by Process I measurements. The uncertainties shown for each

of the three values are based on the latest process

information. In all cases, the values agree within

. the expected limits.

As a second test, in another facility the values

assigned to reference block set No. 496 were compared to reference block set S-183873 [22]. The

values for blocks of set No. 496 were assigned by

a normal Process II measurement. (The Process II measurements have been used for some time in the

normal NBS gage block calibration service.) The

values for the blocks of Set No. S-183873 had been

assigned by the old multiple wavelength NBS

interferometric process. Under the assumption

that the initial uncertainties of the S-183873 values were reasonably correct, the closure, as shown in

table 35, was within limits established by the uncertainty of the Process II measurements and the

uncertainty of the values assigned to Set No.

S-183873.

7.3. Other Measurement Processes

Measurement processes in many different en- vironments comprise a measurement system. Consistency within the system is assured if closure,

within the capabilities of the various processes, can be demonstrated. Early in the program, a co- operative effort was made to verify closure between

two different measurement processes. Blocks of

nominal size 5 in and 16 in were chosen for this work.

The comparison designs used required a comparison

of all pairs in a group of four, (six observed differences). One block was considered as a "known."

The second block was considered as a "check

standard," and the other two blocks were considered

to be "unknowns." In each case, two blocks went

47
Table 34

Suninajcy Data for (...) Reference Blocks

PROCESS II PROCESS I

(...)

T^/pical Summary

Date

Y

Ave No S.D.* S.E. UNC** Ave No UNC

1117- R 2/22/72 17.70 17.5 40 .54 .47 .73 xD . y

o .47

XJZ'i D 2/24/72 -6.37 -7.3 83 .59 .57 .76 -8.7 2 .79

1136- 7 2/25/72 12.03 12.0 40 .63 .69 .98 12.7 2 .81

1140- 8 2/28/72 8.80 8.3 98 .67 .77 .97 9.1 3 .75

1103-10 2/29/72 22.20 21.8 36 .76 .98 1.37 21.2 2 1.15

1132-12 3/1/72 9.13 9.6 40 .85 1.18 1.60 10.6 2 1.38

1134-16 3/3/72 10.00 9.3 17 1.02 1.63 2.37 10.2 2 1.82

1123-20 3/6/72 43.00 42.8 25 1.20 2.10 2.82 46.2 3 1.87

* Process total S.D. from Table 32

** UNC = 3 (total

of the siam in

S.D.)/ /n + S

Table 23.

. E. (S.E. is one-half of the uncertainty

Table 35 Closure cn Set No. 496

Table 36

"Echelon" Closure, Process II

NonLnal

Size

NBS Prooess II Lab "A" &

S.D. n S.E. UNC ^II" S.E.

5 0.8 .54 1 .48 2.10 0.4 3 0.4

6 9.0 .59 1 .57 2.34 13.5 3 -4.5

7 18.5 .63 1 .68 2.57 19.1 3 -0.6

8 13.0 .67 1 .77 2.78 11.4 3 1.6

10 15.4 .76 1 .99 3.27 16.8 3 -1.4

12 19.6 .85 1 1.18 3.73 21.8 5 -2.2

16 19.2 1.02 2 1.63 2.35 19.3 5 -0.1

20 12.7 1.20 1 2.10 5.60 19.6 5 -6.9

* Average of n values with respect to NBS ( . ) and ( . . ) blocks

** with reference to a set S-183873 (values previously established

by multiple wavelength interferometry with estimated uncertainty,

S.E. , as shown)

to the next measurement process, assuming the

same roles. The results of the work on the 16 in

blocks are discussed in section 5.5, because of

thermal problems encountered. The results of the

work with the 5 in blocks are shown in table 36.

Referring to table 36, five independent sequences

of measurements were made at NBS on the blocks

designated M136, H178, 4114, and (X616A + X368A).

Block Serial No.

location M136 H178

NBS 28.0

n=6

Lab "A" n=3

3.0

(.62) C

X616A

+

4114 X368A A138

3.4 8.3

(.62) (.62)

1290 1162

3.0

R

3.1

(1.62) C

-22.5 -12.3

(1.62) (1.62)

Lab "B" -22 5 -10 2 3.0 8 n=3 (2.62) (2 62) (2.62) R C

NBS / J/ NBS 28.0 2.0 -22 1 -11 a n=l (1.4) (1.4) (1. «) R C \ ' > '

28.0 2.8 1 6 7

(1.4) (1 4) (1. 4) R C

( ) Uncertainty

R Restraint Value C "Qiedc Standard"

M136 was assumed known and without error, so

that the value assigned was the restraint on the solution for values for the remaining blocks. The values

shown for the other blocks is the average of 5

independent measurements. The uncertainties

48
shown are those thought to be appropriate at the

time. Two blocks, H178 and 4114, were forwarded

to "Lab A."i9

Three independent sequences of measurements

were made at "Lab A," using the assigned value

for H178 as the restraint, and 4114 as a "check

standard." Blocks A138 and A142 were the "unknowns." The agreement between the value obtained for 4114 relative to H178, and the "known"

value of 4114 relative to M136 is one measure of

the agreement between the two measurement processes. Blocks A138 and A142 were passed on to a simulated "Lab B." The initial uncertainty of the

value for H178, unc. — 0.62 microinches, was the

systematic component of the "Lab A" uncertainty.

Again, three independent sequences of measure- ments were made in "Lab B," using the value as- signed to A136 by "Lab A" as the restraint. The

agreement between the value assigned to A142

relative to A138, and the "known" value for A142

is a measure of the agreement between "Lab A"

and "Lab B." In normal procedures, blocks 1290

and 1162 would pass on to other labs. In order to close out the test, blocks H178, A138, A142, 1290

and 1162 were returned to NBS. Using the same

sequence of comparisons, the pairs of blocks,

A138 and A142, and 1290 and 1162, were each compared once with the pair M136 and H178. Again,

the values obtained for H178 relative to M136

verified the consistency of the NBS Process. The

values obtained for the other blocks demonstrated

closure through one and two transfer processes.

In all cases the agreement was within the expected

limits.

The U.S. Navy Eastern Standards Laboratory assumed the role of both "Lab A"

and "Lab B" in this study.

In most metrology laboratories, Icng gage block

comparisons are made using equipment designed

specifically for the purpose. In use, however, a wide variety of equipment could be used to make the

necessary comparisons. In order to simulate a

situation in which one has to construct a comparator,

the arrangement shown in figure 26 was used to compare 5 in and 12 in blocks. Six independent

measurements were made, following an intercomparison design. The results are compared with both

previous work and an average of two direct comparisons in table 37. With the particular equipment

used, the standard deviation of the simplified

"comparator" was 2 microinches. Assuming the

uncertainty of the ((.)+USN) restraint is about

the same as the uncertainty of the ((.)+(..))

restraint, the closure obtained was within the

expected limits.

Figure 26. Schematic diagram, simplified comparator.

Comparison, Process II Results with Results from Simplified Comparison Process

Date Type of Measurement

Nominal

Size Restraint Block Unknowns Estimated Uncertainty

Block Value Block Value Standard

Deviation S.E.* Total

2/73 6 Series with

process as shewn in figure 26

5 (.) + (..) 4114 - .9 1628 57.13 2.0 .95 3.4

12/70 Average of two direct ccmparisons

5 (.) 1628 57 .5 .67 1.72

11/71 6 Series with

regular proosss

5 (.)+USN 4114 -1.6 .5 .95 2.45

12/70 Average of two direct corparisons

12 (.) 118 .8 1.69 3.1

9/71 6 Series with

regular process

12 ( .

) +USN 3507 16 .8 2.36 2.69

2/73 6 Series with

process as shewn in figure 26

12 (.) + (..) 3507 22 120 2.0 2.36 4.81

* The systematic error, or uncertainty, associated with the restraint block values.

49
7.4. Operational "Addition"

A recurring question in the use of all gage blocks

is associated with "additivity." Gage blocks of vari- ous selected nominal sizes are "wrung" together to construct lengths which are not normally assigned to single blocks. The "wringing" is in effect an

"operational" definition of length addition. One is concerned as to the agreement between the length

of the combination, and the sum of the lengths

assigned to each block in the combination. The element of interest is the variability of the thickness

of the film in the interfaces between the blocks.

The mechanism of "wringing" is not well understood. One can, however, postulate the thickness

of the film as being somewhere between "zero"

for bare metal contact, such as discussed in section

5.6, and a "max" associated with the "feel" of the

"wring." Each Process I measurement includes a

finite film thickness, that between the block and the

platen to which it is "wrung." The average of a

collection of repeated Process I measurements

includes an average film thickness. The variability

of the collection includes the variability of the film

thickness about that average. A comparison between

the total process s.d., err, and the s.d. associated

with the collection of values for the control blocks,

which are "permanently wrung" to their respective

platens, should provide a measure of the "wringing

film" variability associated with the NBS artifacts

and procedures.

For Process I measurements at the 10 in level,

or T- — 0.54, from table 32 in section 6.5. For the collection of Process I values for the 10 in control block,

part of which are shown in figure 9 in section 5.1,

s.d. = 0.33. One can think of the "wringing" film

variability as being a between-time component of

variance which is step-like in nature. For each

"wring," there is a reasonably stable film of some

finite thickness, the thickness varying about some

average thickness. Under these conditions, the variability of the film, o-/, is {(0.54)2-(0.33)2)i/2 or af=

0.43. Thus, on the average, one would expect the

"wringing" film thickness to be on the order of 2 or

3cr/. The expected Process I total s.d. for a "wrung"

combination of blocks would be err =((0.33)^

+ n(.43)'^)'/-, or for a combination of two blocks,

o-r=0.69.

In the first series of measurements reported in

table 36, one 5 in "block" was a summation of a 2

in block and a 3 in block. Between each of the six

series of intercomparisons, the summation was

disassembled, cleaned, and reassembled. A comparison of the values obtained for the summation,

and the two single blocks, is shown in figure 27.

While all of the values were well within the expected

hmits based on the total standard deviation of

Process II, the values associated with the summation appear to show more variability.

From estimates of the s.d. of the points shown,

the variability of the collection of values for the

summation has an additional random component of

s.d. 0.5 microinches over and above the s.d. of the

values for the single blocks. This is in reasonable

agreement with cr/ as determined above. The

accepted values for the individual blocks were

7.3 and 0.3, thus the sum of the individual values

agrees very well with the value assigned to the

summation.

BLOCK

MI36 HI78 4114 X6I6A + X368A

(RESTRAINT) (AVE.) (AVE.) (AVE ) 5.000,028,0 5.000,003,0 5.000,003,4 5.000,008,3

UJ

EXPECTED LIMITS = 3o-, = 3x0,46 = 1.4

Figure 27. Variability of 5 in combination.

Process I measurements were made on summations of nominal size 10, 14, 16 and 20 in. The re- sults are summarized in table 38. Again, the values

obtained for the summations are in good agreement

with the sums of the accepted values of the in- dividual blocks. The accepted values are from

table 13. There is some evidence that the correction for the compression of the bottom block of the

stack due to the weight of the top block is smaller

than the "wringing" variability.

One might conclude from the above data that,

with careful "wringing," the variability associated

with the "wringing" process is not large. Certainly,

all of the evidence seems to support such a conclusion. However, "wringing" is a complex phenomenon. AU of the factors which might influence

variability from this source have not been identified.

The above data merely indicates that the procedures used with long blocks at the NBS do not cause a large variability in the results. "Wringing"

to establish stacks of desired length is a common

practice with short blocks. Extensions of the above

studies are in process in order to establish a

quantitative estimate of the limits of variability

expected in stacks of 2, 3, and 4 short gage blocks

[23].

The introduction to the appendix, as shown in

figure 29, states the criteria used to define the state

of operation "in control." The body of the appendix, as shown in figure 30, lists the seriid numbers of the NBS reference blocks which were

used. Four blocks of the same nominal size are used

50
Table 38 Value of SiJtrrBticn vs Sunmaticn of Values

Size Block Summation (^feas.) n S.D. UNC

10 H178 + m.36 30.3 3 .54 .94 30.1 .3 14 W202A + H105 9.0 3 (.76) (1.32) 9.9 .5 16 H143 + M103A 57.9 3 .86 1.49 57.1 .6 20 H148 + m09 54.9 3 1.08 1.87 56.4 .9

* Computed from values shovm in table 13, Including the compression correction, "C", shown in the next column.

in each comparison sequence. The NBS (.) and (. .) blocks are the reference blocks, blocks Irom the

set for which this report appUes were grouped

with the set of blocks mentioned to establish the

group of four. The check standard accepted value

is the Process II long term average difference between the reference blocks, ((.)—(. .))II. The observed value is that obtained in the sequence of

measurements used to establish the value in the

report. The t test is based on the accepted total

standard deviation for Process II, as shown. The

within standard deviation is that associated with

the sequence of measurements used to establish

the reported values. The accepted standard deviation is the long term average within standard

deviation for Process II. Eight sequences of meas- ments were required to establish the reported

values and no repeats were necessary by virtue of

the process being "out of control."

8. Summary

The Measurement Assurance Programs emphasize the establishment of confidence in measure- ment results by operational demonstration. One

is concerned with the variability of his own process

and the relationship between his results and the

task he is trying to accomplish. Process variability over time included effects from all sources, some

of which are known or can be deduced, some of

which are suspected or imagined, and some of which

are not as yet or may never be detected. Realistic error limits, or bounds for the effects of systematic

errors, provide both a means to assess the re- sults and a basis for monitoring the process

performance. The work described is concerned

with relating the generally unaccessible defined length unit, in terms of wavelength, to accessible artifacts such as gage blocks. The basic

techniques which have been utilized are precise

process definition, redundancy of measurement over time and location, and closure both between the

results from different processes and between predicted and observed values. In essence, one

searches for a measurement algorithm which

adequately describes the observed results.

In detail this paper documents the transition

from multiple wavelength interferometry to single

wavelength interferometry in the assignment of

length values to long gage blocks, and the development of a suitable transfer process to provide access to the unit. Two aspects of this work emerge

with clarity: the benefits of the "one shot" as- signment of values to large numbers of gage blocks

by interferometry as used in the past were largely

esthetic, in addition to being costly and time

consuming; and NBS must devote its interferometric

measurement capability to the maintenance of

suitable reference artifacts, techniques for closure

between various interferometric measurement processes, and to the development of large "on-scale"

range comparators.

This paper documents in part a measurement

process analysis; "in part" because a process

study is a continuing effort to understand the

measurement process itself. Heretofore, in pursuit

of a minimum uncertainty, major efforts were made

to severely restrict the previous measurement

processes. Meaningful measurements are made in a real world subject to all sorts of perturbations.

Realistic uncertainties in this real world direct the

efforts toward process definition and process re- sponse to these perturbations.

In the work described, the main effort has been to establish realistic uncertainty statements. The

present task has been merely to identify, and "correct" if possible, the largest sources of error in

the restricted environmental conditions of the NBS

facilities. Further efforts are needed to identify

other sources of systematic errors which are present,

as evidenced by the magnitude of the total standard

deviation. Measurements must be made over a wider

range of environmental conditions. One should be

able to predict a realistic uncertainty for any set of

conditions and objects, and then verify the validity of

the uncertainty by actual measurement.

51
DIMFNSIONAL TECHNOLOGY

NATIONAL BUREAU OF STANDARDS

WASHINGTON O.C. 20234

TEST NO. 210448

OPERATOR CT COMPARATOR G3

DOALL GRADE AA

4/ 2/74

SERIAL LENGTH = NOMINAL * NUMBER AT 20 C

( INCHES)

4521 5.00000039 5.000000

4703 6.00000838 6.000000

3316 7.00000808 7.000000

4002 8. 00000Q62 8.000000

4014 10.00000412 10.000000

4012 12.00001455 12.000000

3505 16.00002761 16.000000

3620 20.00002004 20.000000

PAGE 6

GROUP 7 5. 000000 TO 20. 000000

CORR . UNC • = SYS

3 S.D. COEFF

f R R n R OF FXP

( V A L U E S I N M I C R 0 -INCH E S 1

.394 2.001 .4 73 1. 528 11.5

8 .384 2.255 . 5 68 1.686 11.5

8.075 2. 498 . 6 86 1.812 11.5

9.625 2.709 .7 72 1.937 11.5

4. 124 3.199 .983 2.216 11.5

14.553. 674 1. 1 82 2. 493 11.5

27.606 4.618 1.6 28 2.990 11.5

20.040 5. 605 2. 1 00 3. 504 11.5

Figure 28. Report of calibration.

APPENOI

THIS APPENDIX PRESENTS DATA ON THE MEASUREMENT

PROCESS BY WHICH THE VALUES WERE ASSIGNED TO THE

BLOCKS, THE PROCESS FOR EACH NOMINAL SUE IS

VERIFIED AS BEING IN A STATE OF STATISTICAL

CONTROL BY USING BOTH THE VALUE OBTAINED FOR THE

CHECK STANDARD AND THAT OBTAINED FOR THE STANDARD

DEVIATION.

THE STANDARD DEVIATION (BASED ON 4 DEGREES OF

FREEDOM) COMPUTED FROM THE DEVIATIONS BETWEEN

OBSFRVED AND PREDICTED VALUES IS COMPARED BY

TAKING ITS RATIO TO THE LONG RUN VALUE FOR THE

WITHIN RUN STANDARD DEVIATION. IF THF SQUARE OF

THE RATIO DOES NOT EXCEED THE CRITICAL VALUE,

4.62, FOR THE .01 PROBABILITY POINT OF THE F

DISTRIBUTION. THE PROCESS IS REGARDED AS BEING IN

CONTROL FOR PRECISION. IN ADDITION, THE VALUE FOR

THE CHECK STANDARD SHOULD NOT DEVIATE FROM ITS

ACCEPTED VALUE BY MORE THAN 3.29 TIMES THE 'TOTAL*

STANDARD DEVIATION FOR THE PROCESS TO BE REGARDED

AS BEING IN CONTROL WITH RESPECT TO POSSIBLE

SYSTEMATIC SHIFTS IN PERFORMANCE. (THE CRITICAL

VALUE 3-29 CORRESPONDS TO THE O.OOl PROBABILITY

POINT FOR THE STANDARDIZED NORMAL DISTRIBUTION.)

IF EITHER OF THFSE TESTS ARE 'FAILED,* THE

COMPLETE SET OF MEASUREMENTS FOR THAT NOMINAL

LENGTH ARE REPEATED AND THESE INDEPENDENT NEW

VALUES ARE USED IN THIS REPORT.

Figure 29. Introduction to report of calibration appendix.

52
)IMENSIONAL TFCHNOLOGY

MATIONAL BUREAU OF STAiMOAROS

WASHINGTON O.C. 20234

TEST NO. 210448

IPERATOR CT

30ALL

4/ 2/74

PAGE A- 6

GROUP 7

5.000000 TO 20. 000000

COMPARATOR G3

GRADE AA

THESE ARTIFACTS WERE GROUPED WITH SIMILAR ARTIFACTS FROM

TEST NO. 210249 IN THE FOLLOW ING SERIES OF MEASUREMENTS

.

SER lAL NO. CHECK STD. STANDARD DEVIATION

NOMINAL ( . ) ( .. ) ACC. OBS. T THI S RUN ACC. F (0,F.=4

J

VALUE

5. 000000 M136 H178 28.460 29.125 1.231 .185 .470 . 155

6. 000000 Ml 15A H312 33.476 33.583 . 182 .190 .470 . 164

7.000000 W202A H105 23.562 23.692 .2 06 .330 .470 .493

8. 000000 M103A H143 44.212 44.875 .990 .541 .470 1.324

10.000000 M 109A H148 61. 373 62. 633 1.658 .371 .470 .622

12.000000 M135A H249 56.908 57.533 .736 .170 .470 .130

16.000000 M109A H155 57.282 57.058 -.219 .490 .570 . 738

20. 000000 A157 H146 -16.484 - 16.042 . 369 .848 .720 1 . 386

NO, OF REPEATED SERIES

THE RATIO OF THE OBSERVED S.O. TO THE ACCEPTED S.D.

F VALUE AND THEREFORE THE PROCESS IS TAKEN TO BE IN

IS LESS THAN THE CRITICAL

STATISTICAL CONTROL.

THE T VALUE t THE RATIO OF THE DIFFERENCE BETWEEN THE OBSERVED VALUES AND THE

ACCEPTED VALUES FOR THE CHECK STANDARD TO THEIR CORRESPONDING STANDARD DEVIATIONS) DOES NOT EXCEED THE CRITICAL VALUE OF 3. THEREFORE THE PROCESS IS

REGARD AS BEING IN STATISTICAL CONTROL. THE STANDARD DEVIATIONS USED TO COMPUTE THE T VALUES WERE AS FOLLOWS: .540 .590 .630 .670 .760 .850 1.020

Figure 30. Report of calibration.

The results of measurements made at NBS on

both long blocks; from 5 in to 20 in, and short blocks,

0.1 in to 4 in are presented in a "laboratory notebook" type of report. The report consists of three

sections: an introduction which is reprinted in appendix 5; the statement of values and uncertainties

which, for a typical long block set, is shown in figure

28; and an appendix which reports the state of the

NBS measurement performance at the time the

reported values were established, as shown in

figures 29 and 30.

Referring to figure 28, the blocks for which the

report applies are identified by owner and by serial

number. The operator and the instrument used in

making the comparisons are identified. The values,

at 20 °C, are reported as block length, and as nominal

block length and a correction. The uncertainty,

which is plus or minus, is an expression of the limits

within which values from repeated measurements

are expected to fall. The systematic error component

of the uncertainty relates to the uncertainty of the

values assigned to the reference blocks used in the

comparisons as previously discussed. The magnitude of the systematic error reflects the Process I ("new" interferometric) measurements made by

NBS on the complement of reference standards.

The random component of the uncertainty, 3 s.d.,

is based on the Process II (comparison process)

performance parameters. The coefficient of ex- pansion, in microinches per inch per °C, has been

used to correct for small differences in temperature

between the measurement environment and 20 °C.

Since practically all long gage blocks are made from

the same type of material, which is processed to obtain very nearly the same physical properties, no differential penetration corrections have been

made.

53
This paper represents the efforts of many people

over a span of several years. The cooperation and

comments of Elmo Johnson and Dave Spangenberg

of the Navy Eastern Standards Laboratory, and of

J. C. Moody of Sandia Corporation, were most helpful. Geraldine Hailes, in addition to working with

Joe Cameron on reference [6], prepared the initial

computer programs for interfacing the measure- ment processes with the time-sharing computer.

The statistical aspects of this paper are due primarily to Joe Cameron. Ruth Varner constructed

programs to manage the very large amounts of data,

and prepared the Report format. John Beers, Clyde

Tucker, Grace Chaconas, Herb Badger, Ron Hartsock and Ruth Davenport were responsible for

developing and operating the measurement proc- esses as well as initially keeping track of all data.

Horace Bowman's work on surface penetration of

contacting probes was helpful. This work, still in

progress, is essential for work with "short" blocks

made from different materials. Those responsible

for the execution were: Gertrude Tesler who

patiently prepared the many typed drafts; Joanne

Mobley who punched a very large number of data

cards; and Hank Zoranski who prepared the art work. Finally, the comments of Karl Kessler, John

Simpson and Jimmie Suddeth, who acted as "unofficial" readers, were invaluable.

9. References

[1] Schweitzer, W. G. Jr., Kessler, E. G. Jr., Deslattes, R. D., Layer, H. P. and Whetstone, J. R., Description, performance, and

wavelengths of iodine stabilized lasers,

Appl. Opt. 12,2927 (Dec. 1973).

[2] Pontius, P. E. and Cameron, J. M., Realistic

uncertainties and the mass measurement

process, Nat. Bur. Stand. (U.S.), Monogr.

103, 17 pages (1967).

[3] Pontius, P. E., Measurement philosophy of

the Pilot Program for mass calibration,

Nat. Bur. Stand. (U.S.), Tech. Note 288,

39 pages (1968).

[4] Pontius, P. E., Mass and mass values, Nat.

Bur. Stand. (U.S.), Monogr. 133, 39 pages

(1974).

[5] Pontius, P. E., Simulating measurement

process variability, Nat. Bur. Stand. (U.S.),

in preparation.

[6] Cameron, J. M., Hailes, G., Designs for the

calibration of small groups of standards in

the presence of drift, Nat. Bur. Stand.

(U.S.), Tech. Note 844, 31 pages (Aug.

1974).

[7] Private communciation, Mr. D. Spangenberg.

[8] Refinement of values for the yard and the

pound. Federal Register, (F.R. Doc. 59-5442)

(July 1, 1959).

[9] Riddle, J. L., Furukawa, G. T. and Plumb,

H. H., Platinum resistance thermometry,

Nat. Bur. Stand. (U.S.), Monogr. 126 (April

1973).

[10] Summary Report of Length CaUbrations, Nat.

Bur. Stand. (U.S.), Test Report No.

232.09/G41865, (U.S. Navy).

[11] NatreUa, M. G., Experimental statistics, Nat.

Bur. Stand. (U.S.), Handbook 91, (1963).

[12] Unpubhshed work of Mr. B. Page, Length

Section, Nat. Bur. Stand. (U.S.) over the

period 1956 to 1958. This work is now in

the possession of Mr. J. S. Beers, Dimensional Technology Section, Optical Physics

Division, Nat. Bur. Stand. (U.S.).

[13] Beers, J. S. and Tucker, C. D., Gage block

flatness and paraUehsm measurement, Nat.

Bur. Stand. (U.S.), unpublished report.

[14] Beers, J. S., A gage block measurement proc- ess using single wavelength interferometry,

Nat. Bur. Stand. (U.S.), in preparation.

[15] Tucker, C. D., Preparations for gage block

comparison measurements, NBSIR 74-523,

(July 1974)

[16] Beers, J. S., Tucker, C. D., Intercomparison

procedures for gage blocks using electromechanical comparators, Nat. Bur. Stand.

(U.S.), in preparation.

[17] SiddaU, G. J. and Willey, P. C. T., Flat-surface

wringing and contact error variability, J. Phys. D, Appl. Phys., Printed in Great

Britain.

[18] Moody, J. C, Effect of visible thermal conditions during the treating of large gage

blocks. Metrology of gage blocks, Nat. Bur.

Stand. (U.S.), Circ. 581, pp. 67-70 (April

1955) (out of print).

[19] Pontius, P. E., Measurement Analysis Program and Gage blocks, A progress report.

Talk Presented at the 26th Annual Meeting

of the Standards and Metrology Division of

the American Ordnance Association,

Houston, Texas (April 14-15, 1971).

[20] Pontius, P. E., The Measurement Assurance

Program — A case: length measurements.

Part II Short Gage Blocks (0.1 in to 4 in),

Nat. Bur. Stand. (U.S.), Monogr., in

preparation.

[21] Meyerson, M. R., Giles, P. M. and Newfeld,

P. F., Dimensional stability of gage block

materials. Journal of Materials, JMLSA,

Vol. 3, No. 4, pp. 727-743 (Dec. 1968), published by the American Society for Testing

and Materials (1968).

[22] Private communication, J. C. Moody.

[23] Pontius, P. E., Cameron, J. M., Wringing

film variability studies, Nat. Bur. Stand.

(U.S.). Tech. Note in preparation.

54
10. Appendix 1. Definition and Use

of Length Value Assigned to a

Block or Artifact

Definition

Artifacts, with two opposite faces essentially

flat and parallel and generally in the form of rec- tangular parallelepipeds, are suitable length standards for a variety of uses. Ordered sets of such objects, available in several types and in lengths up to approximately 20 in, are usually called gage blocks.

Following a concept of the perpendicular distance

between a point and a plane as having a one-to-one

correspondence with a characteristic common to many objects, one length of a gage block is the perpendicular distance between a definite gaging point on one surface of a block and a base plane in close

proximity to the opposite surface, the distance being

expressed in appropriate measurement units. This

definition is used by the National Bureau of Standards and is also in general agreement with definitions used by other standards laboratories and

organizations.

Specifying both the gaging point and the attitude

of the block with reference to the base plane establishes a reasonably unique line interval to represent

a "defined length.""* The use of terminal points

other than the specified gaging point, and variations

in the method by which the base plane is brought

into close proximity to the bottom of the block, may

produce results which differ systematically from

the length according to the definition. Failure to achieve a reasonable perpendicular between the

defining line segment and the base plane, largely

a matter of adjustment of the comparator or interferometer being used, may introduce small systematic errors (cosine errors). Variations in block geometry which affect the attitude of the block with ref- erence to the base plane may introduce a variability

in the measurement. The significance of variabihty

from these sources must be judged relative to the

precision of the measurement process in which the

blocks are being used and relative to the functional

requirements which are to be satisfied by the

resulting measurement.

The dimensions of an artifact, one of which becomes the length by definition, are dependent on

both the temperature of the artifact at the time of

measurement and the historical age of the artifact.

All materials respond to temperature changes by

expanding or contracting in varying amounts. These

changes are temporary and occur continuously.

The relaxation and redistribution of stresses internal

to the block change the dimensions of the block.

These changes occur slowly and result in permanent

'' In this paper, length according to this definition is called the "defined length".

It is also frequently called the "ISO" length.

changes in block dimensions. Careful selection of

materials and control in the manufacturing process can reduce the magnitude of changes from these sources to some acceptable level. Regardless of

the minimizing techniques, however, changes from

both of these sources may be clearly observable in

many precise measurement processes.

A measurement consists of performing a prescribed sequence of operations which include cleaning and estabUshing the attitude of the block with

reference to the base plane as well as one or more

intercomparisons with other blocks or with wavelength scales. The entire measurement effort from

inspection to end result is called the measure- ment process. The result from the measurement

process is an estimate of the length according to a

particular definition and appropriate to the age of the

gage block and its temperature at the time of the

measurement. The practice used by the I^ational

Bureau of Standards to designate a "front," "top,"

"bottom," and a definite gaging point relative to the normal markings on a gage block is shown in

figure 1 of this appendix.

Assuming that the thermal coefficientof expansion

is reasonably linear in the neighborhood of 20 °C,

and that the age dependent changes in dimensions can be adequately expressed by a linear function, an estimate of a defined length appropriate to any

time and temperature can be predicted by the

following relation:

Lm{t,T)={N+Y,n{to,To) +Kiit-to))

il + K2iT-To)±{3(Ty+ {NIR)Sr))

3/8" X I 3/8"

Square Style Gage Blocks

NOTES:

N- S. represents the nominal size marking on the block. Front of the block is the ride with the nominal size marking or the side to the

right of the nominal size marking when it is marked on the gaging face. Top of the block is the upper gaging face. Bottom of the block is the lower gaging face. Gaging Point is ind'cated bv an X on the upper gacjino face and is located at the center on rectangular blocks and is located midway between the hole

and the front on hoke style blocks.

Figure 1. ^^Gaging point" definition.

55
where to. To refer to a specific time and temperature,

and the subscript m, expressed in Roman numerals,

designates the type of measurement used to establish Y. Having initially established estimates of

the parameters in this relation appropriate to a given block, further measurement efforts can be

used to (a) make minor adjustments of the parameters or (b) verify the continued use of the relation

to predict defined lengths for any time or temperature.

The right side of the above relation consists of

two bracketed terms, the first estabUshes a nu- merical value in some set of consistent measure- ment units, and the second establishes an uncertainty for the numerical value. Considering each

term in detail:

(1) Lm{t, T) is the predicted value to be as- signed as the defined length of a block at any time, t, and at any temperature, T. The

subscript, m, expressed in Roman numerals,

identifies the type of measurement process

used to assign the basic numerical values.

Where several types of measurements are involved, each must be clearly identified with an appropriate designator.

(2) is an arbitrarily assigned numerical value

exact to any required number of decimal

places. The use of an arbitrary reduces

the magnitude of the numbers in some of the

calculations, a convenience in hand computation but of httle concern when data are processed by digital computers. A'^ is usually

chosen so that |A^ — Z,| < the on-scale range

of the available instrumentation.

(3) Ymito, To) is a numerical term which can be

computed from current measurement data,

or which can be established by a review of

previous measurement data covering a long

time span. Ym{to, To) in combination with the

arbitrary number N determines Lm{to, To),

the predicted length value assigned as the

length of the defined interval at time, to, and

temperature. To-

(4) Ki is the first coefficient in the linear relation

describing the dimensional changes of the

gage block over a long time span. Since

each block changes at a different rate, Ki

must be determined from a collection of F's

taken over a sufficiently long time span to estabhsh the direction and amount of change

for each block. If, relative to the precision

of the measurement process, no long term

change is taking place, Ki — 0.

(5) {t — to) is the time lapse, expressed in

suitable units, since the establishment of an accepted Ym{to, To)-

(6) Ki is the thermal coefficient of linear expansion

of the gage block material in the direction

of F, or L. At the present time a handbook

value for the material from which the gage

block is constructed is normally used. Again,

since each long block has a unique characteristic coefficient of expansion, it may be

necessary to determine experimentally the

appropriate value if the available process

precision is to be utilized.

(7) {T — To) is the expected, or actual, temperature difference between the gage block at the

time for which the prediction is appropriate,

and the temperature associated with the

accepted Ym{to, To).

The last terms in the relation are. concerned with

establishing the uncertainty with Ym{to, T„). The

use of statistical methods to establish an uncertainty

for the resulting value presumes that the measure- ment process is operating under some sort of rea- sonable statistical control. That is, in continuous

operations, the results do not show grouping, bias

or trends. As stated before, the measurement is the

performance of a sequence of operations, some of

which are comparisons, with the intent of establishing a quantitative value for the defined length of the

block. Intercomparisons within a defined measure- ment permit the calculation of a standard deviation, (Tw, which is related to the measurement

process.

Repeating a defined measurement procedure

a number of times produces a sequence of numbers

representing the characteristic of some object,

in this case a sequence of F's. One can compute

another standard deviation, (Tt, for the collection

of these results. One can also compute the standard

deviation of the mean, or average (rg, which is representative of the confidence one can place on the average, or accepted, value for F. With

this brief background, we can proceed with the

description of the terms in the formula.

(1) The first term in the uncertainty brackets is the random component of the uncertainty.

The computation of CTy depends upon how

Ymito, To) has been determined.. For ex- ample, if the current estimate of Ymito, To)

is the result of a repeated sequence of defined

measurements over a relatively short time

span, the formula would be:

kcru) (T t , . , . , (Ty =——or , whichever is larger.

Vn Vn

A: is a factor that depends on the degree of re- dundancy in the defined measurement, aw is the

within-group standard deviation, as described

above, antf ra is the number of times the defined

56
measurement has been repeated. If it is known

that (Tt > kcTu), as described above, then at should

be used. On the other hand, from a collection of

YrnUo, To) covering a long time span, one may

want to determine a predicted value for some

particular time by fitting a curve to the collection

of points and using the extrapolated value for the

time of interest as the best current estimate of

Y. In this case, the calculation of the random

component of the uncertainty of Y is obviously a

different formula.

(2) The last term is the systematic component

of the uncertainty statement. This term is associated with the restraint on the defined

measurement which permits number assignments to characteristics of unknown objects.

The measurement procedures can only

quantify differences, thus one or more of

the objects must have assigned values,

called restraints on the measurement process. Sr is the uncertainty of the numbers

assigned to one or more objects used as

restraints and is a measure of some prior

measurement process performance. R is the total nominal length of the restraint

blocks. The fraction N/R prorates the systematic error to the unknown blocks which

are included in the current measurement.

The manner in which the uncertainty is treated as one moves from one laboratory

to another is explained in figure 2, an excerpt

from NBS Monograph 103.

s,Sa and Sb can be nearly equal, if so, then lab a and

LAB B CAN calibrate THIER OWN SET FROM SELECTED

STANDARD WEIGHTS

Figure 2. Uncertainty in a calibration sequence

{excerpt from Monograph 103).

Use

Stating the defined length of a block or artifact

in terms of (A^ + Y) suggests two different interpretations. Since A'^ is exact (the nominal length),

(N+Y) carries the uncertainty of F, thus when disseminating a length unit, one is concerned with

the uncertainty of Y. On the other hand, in many

instances the interest is in the |F| relative to some

particular requirement. That is, if |F| is less than

some hmiting value, the block is used as if the length

was N. Unfortunately, these two methods of interpretation are not well understood. In the first interpretation, the uncertainty of Y reflects all of

the terms in the above relation. In the second

interpretation, compliance with specification limits

is usually announced on the basis of a simple un- characterized measurement procedure.

There are several courses of action dependent

upon the intended usage. When the uncertainty of

Y is smaUer than the tolerance limits, one can ac- cept the Y and its uncertainty in Ueu of the specified

limits. For example, a length 4.000 028 ± .000 002

in as determined by measurement is a more precise basis for adjusting instruments, etc., than a statement that the length of the block does not

deviate from a nominal 4 in excess of 0.000 005

in. Such action, however, carries the implication

that all of the terms considered in establishing the

uncertainty of Fmust also be considered in the local

measurement process in which the block is to be

used.

In certain circumstances, one can use simplified

procedures to establish tolerance compliance. If the measurement process used is free from significant systematic errors (the magnitude of known

systematic effects is less than one s.d.) and if the

process standard deviation is less than approximately one-tenth the tolerance limit, a simple sorting

procedure should identify blocks which are significantly "out of tolerance." Reasonable tolerance

limits should encompass the combined uncertainty

of the production and inspection measurement

process.

Finally, one can evaluate the situation relative to a particular end use and accept those items which

are adequate. Generally speaking, one cannot compare the results for the same measurement performed by two different processes unless both proc- esses are well characterized. One cannot judge the

difference between the results without a detailed

knowledge of both processes and the methods of

computation (round off rules, etc.). This is particularly true when one measurement is in essence a sorting operation according to a locally determined

procedure. In many instances, the use of precise

measurement processes to estabhsh an "in tolerance

by actuality" will not confirm an "in tolerance by

local definition."

11. Appendix 2. Gage Block Intercomparison Designs

With the sequence of operations required to make

a "single measurement" precisely defined, the

schedule of "single measurements" to be made

57
between one or more "knowns" and a group of

"unknowns" is called an intercomparison design.

In general, the intercomparison design provides a means to obtain the most information from the fewest measurements. While many features can be

incorporated, the formulation of efficient designs is not a trivial task. Discussion of design formulation

is beyond the scope of this paper.

The sequence of operations required for a "single

measurement" can be shown symbohcally as:

Yi — W\ — + random error

where i,£^2are the unknown magnitudes of the

property of interest embodied in each of two objects; and Y\ is the observed difference in magnitude

expressed in appropriate measurement unit. A

design which requires difference measurements

between aU pairs in group of four objects would re- quire the following measurements:

Property Observations

y,

<x \ aC z

a? Ok? Yz

tSC 2 <iC 3 Y,

iX 2 aC ^

In matrix notation, this group of equations can be expressed as: + random errors

1 -

0 0

1 0 -0

1 0 0 -

0 1 -0

0 1 0 -

0 0 1 -

as" (X 2

a*" aC 1 Y^

a: 3 Yz

M>

(X 4 Y,

is:

or A^ = Y

The solution for

^

by the method of least squares

^ = {A'AY^A'Y

However, since only the differences have been

measured, {A'A) is singular. One or more of the

objects being compared can be grouped as a

restraint and the sum of the values, R, used to represent the magnitude of the property of interest

embodied in each of the objects, relative to the

be used to augment the above relation. The es- timate of the magnitude of the property of interest

embodied in each of the objects, relative to the

magnitude assigned to the "known" objects or

objects, that is, the restraint, becomes:

~A'A - 1 ~A'Y~

0 R

where ^' = (^i, ^2 • • • ^fc)

coefficients in the restraint

IS

^l^l-^^2^2+ ^hj

a vector of the

R.

Note that in the above, the script letters refer

to the magnitude of the property acting on the

comparison instrument, and the itahc letters are the numbers assigned as estimates of the magnitude of the property relative to a particular

restraint value R.

The standard deviation of the group of comparisons can be obtained by defining A to be the differ- ence between the observed value, Y, and the

expected value based on the estimated values:

n-k+1

for a design with n observations on k objects.

Since all of the comparisons required by a given

design can usually be made on one instrument in a

short time interval, the standard deviation computed

from the residual from one sequence of comparisons is called the estimated within group precision,

Sw, for a particular instrument. This standard deviation applies to the defined "single measurement."

For a given instrument, each defined "single

measurement" procedure will have a distinctive

standard deviation. Collections of Sw can be combined to obtain a long term or accepted within

group standard deviation, (Tw, one of the important

process performance parameters.

The flexibihty of intercomparison designs provides a means for the metrologist to obtain long se- quences of repeated measurements on the same

objects with httle additional measurement effort. If one is to beheve that the values assigned to the "unknowns" are vtdid over time, the fact must be

demonstrated. The idea of a "check standard"

refers to a difference between two objects, or the

58
value assignment to an object, the objects being

similar in all respects to the "unknown" and always

used in a particular measurement. For example,

in the design shown, an object with known value

could be designated This object would be called

the "starting standard" since its assigned value,

i^i, would be the restraint, ^-i could be the "check

standard," assumed unknown and always used with

^X. The sequence of measurements called for by the

design would assign values \o ^<i, Sf^-, and

^4 relative to ^x. While the objects and ^4 together

with their assigned values are passed on to others,

^2 remains with the process. The collection of

values for ^2 reflects not only the variation of both

and ^1 but also the variability of the process over time. The standard deviation of this collection

of values is called the "total standard deviation of

the process," err- The appropriate choice of location within the

design for the "starting standard(s)" and the

"check standard" is part of the design formulation.

Where possible, for the type of design shown,

both ^X and ^1 are used for "starting standards."

The restraint is taken as the sum of the assigned

values, {Sfx + ^2) and the difference between

Sfx and ^2 as determined from the measurements

serves as a "check standard." This procedure can sometimes reduce the systematic component of

the uncertainty of the values assigned to the un- knowns. (The systematic error of the restraint is prorated between the unknowns in proportion to the ratio of the value of the unknown to the value

of the restraint. This will be discussed in detail

elsewhere.)

The design shown is usually called a "four

one's" design, four being the number of objects

involved and the one being associated with the

limitations of the "on scale" range of the various

measurement instruments. For the most part,

available precise instruments have a limited on

scale range so that the objects being compared

must be nominally equal. It should be noted that

this is not a limitation imposed by the statistical

design.

The normal procedure for describing a design

is to show the A matrix, in terms of -f and — signs

(omitting the ones and zeros). The columns are labeled with the nominal values of the objects

being intercompared, and the rows are labeled with an identification for the results of the prescribed

comparison. The restraint vector is shown, and

in some cases, the location of the "check standard."

The design previously described could be shown

as:

1 - 1 1-2 1-3 1 -

1^(1) + —

F(2) + —

F(3) + —

F(4) + -

^(5) + -

F(6) + -

J? i\ -1-

1

C +

This would be interpreted as meaning the dif- ference, as measured by the prescribed procedure,

between object 1-1 and object 1-2 is called /4(1),

and so on. The restraint, i?,is the sum of the values

currently assigned to 1-1 and 1-2. The check

standard, C, is the difference between the values

determined in the process for 1-1 and 1-2. The

position of the restraint would be shown in vector

form, /? (1,1,0,0), and the check standard location

would be shown as C(l,-1,0,0). If only the first object, 1-1 had an assigned value, the restraint

vector would be /? (1,0,0,0), and the check standard would most likely be the second object, 1-2,

designated by the vector C (0,1, 0,0). For a fuller

treatment of this subject see reference [6].

12. Appendix 3. Gage Block

Interferometry

A typical gage block interferometer is shown

schematically in figure 1. A beam of coUimated

monochromatic light impinges on a beam splitter

part of which passes through to reference mirror

Ml, and part of which is reflected to the platen or reference mirror PI. The reflected beam from PI

passes through the beam splitter into the viewing

system. For the purpose of this discussion, the

reflected light from Ml can be thought of as coming

from the Virtual Image Ml, hence also passing

through the beam splitter into the viewing system.

The beams are recombined in the viewing system

to produce the observed interference fringe patterns.

It should be noted that in such a schematic diagram,

all angles m^st be shown very large. In the real

59
LASER LIGHT

SOURCE

WAVELENGTH = X COLLIMATING

LENS

(I) (2)

TUAL " VIR

IMAGE

Ml

FOCAL

PLANE

REF. MIRROR

Ml OBSERVED

FRINGE PATTERN

Figure 1. Schematic gage block interferometer.

instrument, all angles are very small so that cosine

length errors are practically negligible.

In detail, an arbitrary ray (1) divides at the beam

splitter, one part being reflected from PI along path

(PI) to the focal plane, and one part being reflected

from Virtual Ml along path (Ml). The diff'erence

in path length, starting at the beam sphtter and ending at the focal plane is of interest. For some position across the face of the platen, this difference in

path length wiU be an odd multiple of the half

wavelength of the Ught. Under this condition, the

two ray components will interfere destructively at the focal plane, and at that point in the observed

field would be the dark center of an interference

fringe. Because of the included angle (a + j8), between PI and Virtual Ml, the diff^erence in path

length for the two ray incident components continually changes as one moves across the viewing field. For ray (2) the difference wiU again be an odd multiple of the half wavelength, indicating the center of

the second fringe. Midway between ray (1) and ray

(2), the diff'erence in path length is an even multiple

of the half wavelength, therefore in this region there

is no destructive interference, thus the color of the

fight is seen. In the field of view the resulting fringe

pattern appears as alternate rows of dark and

colored bands.

The fringe pattern can be interpreted as shown in

figure 2. Starting with Virtual Ml, one can construct

a series of parallel planes representing the differ- ence in path length in odd multiples of the half

wavelength. Except for the first plane, these planes

represent incremental changes in elevation above

Virtual Ml of one wavelength. The intersection of

surface PI with these elevation planes, at points a

P+3 P + 2 P+ I

N + 4

N +3

N + 2

N + I

• 1 i i i

P + 4 PH-3 P-l-2 P + 1 F

d i

c ^

b

a

VIRTUAL IMAGE

M,

Figure 2. Adjusting interference fringe pattern.

through e, designates the centers of the observed

interference fringes when the angle of intersection

is (a + fi). While the order of the observed fringes

is not known, starting at point a, the center of Fringe

P, point b, the center of fringe P + 1, is one wavelength higher in elevation, and so on. If the intersection angle, y, is decreased by changing either a

or )8, or both, the fringes appear to broaden and

60
spread out, as shown in the top part of the figure 2. If the operation is done slowly, one can observe

fringe P + 1 move to a new location. Fringe P + 4

would move completely out of view.

With a gage block on the platen, as shown in

figure 3, the top surface of the block intersects

another set of parallel elevation planes in a similar manner. If the block length L, was shortened by the

amount dL, as shown, fringe B + 1 would be coincident with fringe P + 2. In like manner, if L was in- creased an appropriate amount, fringe B + I would

become coincident with fringe P -+ 3. From this, it follows that the difference in optical path length

associated with fringes B + 1 and P + 2 is:

iiB+l)-iP + 2) + {alb))k

where (fi + 1) — (P + 2) is a large integer (Int. F),

which must be determined by other means and (a/b)

is the observed fractional fringe. This path length

difference is equivalent to 2L, so that:

L = (Int.F+ (alb)) (\/2).

G +1

P +4

1 P + 3

1 P+2 P + l P

1

'

1 1

and the platen have the effect of changing the path

length differences in a manner not related to L. For

long blocks, small platens are used which are of

similar material and surface finish as the blocks in

order to obtain nearly the same optical properties on both surfaces. For a given setup, one must

determine experimentally the direction of increasing fringe order.

For a particular measurement, a "tentative"

assigned length, L(t, T) is expressed in "fringe" by:

F= 2(L(?, D)/\r.p,/=(Int. F + 0)

where Xr,p,/ is the wavelength of the laser radiation at the time of the measurement; T, p and /

being the air temperature, pressure and relative

humidity at the time the fringe photograph is taken,

and 0 is the computed fraction. In practice for

well known reference blocks such as the NBS (.) blocks considered in section 5.0, the accepted value,

Li{t, 20), is normalized to temperature T for

L{t, T). For other blocks, such as the NBS(. .) group considered in section 6.2, L{t, 20) is determined by mechanical comparison with suitable reference blocks.

(P + l)

2L = ((G-H)-{P-l-2)-i- (-^) X

L(i) {t,T)= I (P-G+ f )

Figure 4. Observed fringe pattern and interpretation.

To interpret the fringe photograph, figure 4,

fringes of increasing order P, P + l, etc. are associated with the platen, and fringes of order

B, fi+1, etc. are associated with the gaging

surface of the block. Thus:

Figure 3. Block length in terms offringe order.

In practice, the angle of inclination of PI with

respect to Ml is adjusted to obtain several fringes across the top of the block, with one fringe centered

very nearly over the defined gaging point. Differences, if any, in the optical properties of the block

F={P-B + alb)

where the ratio, a/6, is the "observed" fringe fraction,

00. Generally 0o is simply substituted for the

fractional part of F so that:

and

F' = (Int.P)+0o

61
Li{t, r)=F'(Xr,p,/)(|)+s

where s, the interferometer aperture correction,

is added.

There are cases in which the last digit in (Int.F)

must be raised or lowered by one. For example, if the fractional part of F is 0.98 and 0o is 0.03,

obviously the last whole number in F must be raised

by one before adding Oq. Finally, the value is normalized to 7"= 20° C:

L,it,20)=L,it,T){l + K2i20-T))

It should be noted that the above relation determines a total length value, not a deviation from

a nominal value. When the assigned value is ex- pressed in corrections to a nominal length, A^,

the correction Fi(t, 20°) is computed as follows:

L,{t,20)=N+Yi{t,20).

With the availability of "fringe counting" in- terferometers, the task of estabUshing an initial

estimate of the length of a block suitable for use in

single wavelength interferometry is greatly simplified. Such an instrument, shown schematically

in figure 5, uses a divergent light source. As before, the central ray impinges on the beam splitter,

with one component being reflected from mirror

Ml. In the position shown, the path difference between the two components is an odd multiple of

the half wavelength, so that the observed pattern

reflects destructive interference. The components

of the divergent rays R2 follow longer path lengths

(R2) and (M2), which again differ by an odd multiple

of the half wavelength. The result is a "bull's

eye" pattern. As the moving mirror Ml moves by

the amount dL, with the path (Rl) fixed, the dif- ference in path length for the central ray components relates dL directly to the half wavelength

of the light source. If Ml moved by the amount

dL is equivalent to a path length change of one

half-wavelength, the conditions for destructive in- terference do not exist for the central ray, and the

center fringe disappears. Adding additional move- ment of the amount dL will again cause the center

fringe to appear. A light sensitive detector focused on the center of the observed pattern will not only

"count" the fringes as mirror Ml is moved, but also

will estimate the fractional fringe change. While

this instrument is in essence making a displacement

measurement, when coupled with a suitable sur- face detector and mounted in a suitable frame,

estimates of length can be established by a procedure such as illustrated in figure 6.

DIVIRGENT LIGHT

SOURCE X

"Pi- - *i

Figure 5. Schematic "fringe counting" interferometer.

62

»
(I) (2)

(I) "NULL" SURFACE DETECTOR ON REFERENCE

SURFACE; "FRINGE COUNT", N,, OVER

DISPLACEMENT a.

(2) INSERT BLOCK; "FRINGE COUNT", Ng, OVER

DISPLACEMENT b, TO "NULL" ON BLOCK

GAGING POINT.

(3) L--|-(N,-Ne)

Figure 6. Arrangement to determine integral fringe order.

13. Appendix 4. The Gage Block

Comparator

Generally gage block comparators which utilize

contacting probes to detect the block surface are

called mechanical comparators. Several types are shown schematically in figure 1. In principle, the

separation, s, between two reference planes,

"A" - "A" and "B" - "B", is adjusted so that for

some y, an "on scale" condition exists for both

objects to be compared. At the microinch level,

the "on scale" range is usually limited so that the

two objects being compared must be very nearly

identical in size. Instruments differ in the way the

reference planes are defined, and in the way in

which the movement of the contacting probe, that

is a change in y, is detected and quantized.

For instruments of the type illustrated by figure 1,

(1), the bottom reference plane, "B" — "B", is the interface between the surface of comparator

anvil and the bottom gaging face of the block. The

anvil surface must be reasonably flat with a surface

finish such that the block will not "wring" to the

anvil. The top reference plane is established by

some "zero" electrical plane associated with the

top transducer. In most cases, the transducer is a sophisticated linear variable differential transformer (LVDT). Displacement of the moving

element from the electrical "zero" produces a signal

which is proportional to the change in y. Scale

shift such as adjusting to obtain a particular instrument indication for a given block, and scale span

(microinches per reading scale division), can be

accomplished by adjusting the electrical circuitry.

The tip of the probe is often a diamond ground to a spherical shape with a particular radius. The force,

F, acting on the probe under contacting conditions can be adjusted. In use, both the contact pressure

and the span should be checked periodically.

In use, block 1, standing vertically on plane

"B" — "B", is moved into the measuring position

by shding it gently under the probe until the point

of contact is very nearly identical with the defined

gaging point, such as shown in figure 2. The coordinate y(l), from the reference plane to the interface

between the probe and the block surface, relates to the instrument indication. Noting the indication,

Oi, block 1 is removed and block 2 inserted in

F(t) F(t)

(I) (2) (3)

Figure , L Schematic gage block comparator.

63
yd)

y(2)

P(i)

i

T

BLOCK

L(l)

L(2)

P(2)

I

BLOCK

2.

A

B

S= L(l)-P(l) + y(l) = L(2)-P{2) +y(2)

L(l)-L(2) = y{2)-y(l) + P(l) - P(2)

= y(2)-y(l) 4 ;8

but

yd) = -K(0, +h)

y(2)=-K(02+h)

so that

L(l)-L(2) = K(0(l)-0{2)) +;S + e

Figure 2. Differential penetration, j8.

the same manner. With O2, the indication obtained

for block 2, the difference in length can be determined from the relation:

L(l) -L(2) = /<:(0 , - O2) + /3 + e

where K relates the instrument observations to measurement units, (microinches per reading

scale division); /3 accounts for the difference in

penetration, (P(l) — P{2)), and e accounts for the

error of measurement. In most cases, the instrument is adjusted so that K=\.

The penetration, P, is a function of the force on

the probe, the radius of the tip and the physical

properties of the tip, as well as the surface and

physical characteristics of the gaging face of the

block. For a given probe and contact force, as long as the characteristics of the blocks being compared are nearly the same, j8 is essentially zero. If the characteristics of the blocks is such that /3 is large relative to the precision of the comparator,

two courses of action can be taken. One can adjust

F for each block in order to maintain /3 = 0, or one

can correct the observed data to account for

13 9^ 0. For most commercial comparators, the

latter course of action must be taken. In both

cases, the magnitude of the force, or the magnitude of the correction, must be determined by

independent experiments.

For instruments of the type shown in figure 1(b),

two contacting probes and two transducers are used. In this case the reference planes are the electrical "zeros" of the two transducers. The bottom

anvil is merely a support plane to hold the block in a reasonably reproducible attitude at the time of

measurement. Such instruments are used in the

same manner as the instruments of type 1(a).

Normally one can "read" the individual outputs of

both transducers, or the difference between the

outputs. When blocks of different materials are being compared, /8 must be determined for both

the top and bottom contact probes.

In the arrangement shown in figure 1(c), the

fixed top contact established a "point" reference in

the top reference plane which is through the

interface between the tip of the probe and the top

of the block. The bottom reference plane is again

the electrical "zero" of the transducer. In use, the

yoke is raised to permit inserting the block into

the measuring position. The yoke is lowered into

the reading position shown. The top contact

pressure is adjusted by means of springs and

counterweights acting on the yoke, and the bottom

contact pressure is adjusted at the transducer.

Again, if the blocks being compared have dif- ferent physical properties, y8 must be determined

for both contacts.

64
Appendix 5.

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

INSTITUTE OF BASIC STANDARDS

WASHINGTON, O.C. 20234

REPORT

0 F LENGTH VALUES

DIMENSIONAL TECHNOLOGY

NATIONAL BUREAU OF STANDARDS

WASHINGTON O.C. 20234

DOALL

GRADE AA

APRIL 02-04 1974

TEST NUMBER 210448

FOR ADDITIONAL

INFORMATION CONTACT

J. A. SIMPSON

CHIEF, DIMENSIONAL

TECHNOLOGY SECTION

65
BENOIX CORPORATION PAGE I- 1 ELECTRICAL COMPONENTS DIVISION

SIDNEY NEW YORK 13838

TEST NO. 210495

INTRODUCTION

THIS DOCUMENT IS A COMPREHENSIVE

REPORT COVERING THE SEQUENCE OF

OPERATIONS USED TO ASSIGN LENGTH

VALUES TO THE ARTIFACTS IDENTIFIED

ABOVE. IT INCLUDES A DESCRIPTION

OF THE MEASUREMENT METHODS AND

PROCEDURES WHICH WERE USED, AND A SUMMARY OF THE ANALYSIS OF THE

MEASUREMENT DATA. THE ARTIFACTS

HAVE BFEN DIV IDED INTO GROUPS AS

FOLLOWS:

GROUP I LESS THAN . 1 IN GROUP II . 1 TO .107 IN GROUP I I I . 108 TO . 126 IN GROUP IV .127 TO . 164 IN GROUP V . 147 TO .500 IN GROUP VI .55 TO 4.0 IN

GROUP VII 5 .0 TO 20.0 IN

THE ASSIGNED LENGTH VALUES, THE

THERMAL COEFFICIFNTS OF EXPANSION

(ASSUMED OR MEASURED AS NOTED) AND

THE UNCERTAINTIES OF THE VALUES

ARE PRESENTED. IN THE APPENDIX THE

STATISTICAL INFORMATION SHOWN

BECOMES A PART OF THE COLLECTION

OF DATA USED TO CHARACTERIZE THE

N8S MEASUREMENT PROCESS. SUCH A COLLECTION HAS BEEN USED TO

ESTABLISH THE CONTROL LIMITS FOR

SURVEILLANCE OF THE MEASUREMENT

PROCESS AND TO GIVE ASSURANCE OF

VALIDITY OF STATEMENTS ABOUT THESE

MEASUREMENTS. THESE COLLECTIONS

ARE OPEN FOR INSPECTION AT OUR

FACILITY. IT IS PRESUMED THAT

THESE ARTIFACTS WILL BE USED IN A SIMILARLY WELL-CHARACTERIZED

MEASUREMENT PROCESS SO THAT THE

STATISTICAL PARAMETERS OF BOTH

PROCESSES CAN BE COMBINED TO

PROVIDE A REALISTIC ESTIMATE OF

THE UNCERTAINTY OF THE LENGTH UNIT

AS ACTUALLY REALIZED IN ANOTHER

FACILITY. A COMPREHENSIVE SERVICE

DIRECTED TOWARD SUCH AN EVALUATION

IS PART OF A LENGTH MEASUREMENT

ASSURANCE PROGRAM OF THE NATIONAL

BUREAU OF STANDARDS.

LENGTH MEASUREMENT

THE ARTIFACTS COVERED BY THIS

REPORT WERE CLEANED AND TREATED

(LIGHTLY 'STOMED') TO REMOVE

SURFACE IMPERFECTIONS WHICH MIGHT

INTERFERE WITH THE MEASUREMENT.

ALL. OR SAMPLES, HAD BEEN TESTED

FOR THE ABILITY TO ADHERE CLOSELY

(•WRING*) TO SUITABLE FLAT

SURFACES AND TO EACH OTHER. NO

TESTS HAVE BEEN MADE TO ASCERTAIN

THE DEGREE OF "FLATNESS* OF THE

•GAGING* SURFACES OR THE DEGREE OF

'PARALLELISM* OF THE TWO 'GAGING*

SURFACES. SINCE NO "GAGING*

SURFACES ARE EITHER FLAT OR

PARALLEL, IT IS FELT THAT THE MOST

IMPORTANT ATTRIBUTE OF THE

ARTIFACT IS THE ABILITY TO BE MADE

TO ADHERE CLOSFLY TO APPROPRIATE

SURFACES (I.E., WRING). WHERE IT

IS FELT THAT QUANTITATIVE

ESTIMATES OF THE DEGREE OF

•FLATNESS AND PARALLELISM* ARE

REQUIRED, IT IS SUGGESTED THAT

ACCEPTED TESTS BE PERFORMED AT THE

POINT OF USAGE.

THE LENGTH VALUES ASSIGNED TO THE

ARTIFACTS IN THIS REPORT ARE WITH

REFERENCE TO THE VALUES ASSIGNED

TO SELECTED ARTIFACTS OF NB S. THE

REFERENCE VALUES HAVE BEEN

ESTABLISHED BY AN I NTE RF ER OM ET R I

66
BENOIX CORPORATION

ELECTRICAL COMPONENTS DIVISION

SIDNEY NEW YORK 13838

TEST NO. 210495

MEASUREMENT PROCESS AND ARE THE

LENGTHS OF A LINE FROM A DEFINED

•GAGING* POINT 'X* ON ONE SURFACE

TO AN AUXILIARY PLANE IN CLOSE

PROXIMITY TO THE OPPOSITE SURFACE.

PAGE I- 2

FOR LOCATION OF THE POINT, X» RELATIVE TO THE N!1MINAL SIZE

MARKING DENOTED BY 'SIZE' SEE THE

ACCOMPANYING FIGURE.

INTERCOMPARISON DESIGN

GROUPS OF FOUR ARTIFACTS OF THE

SAME NOMINAL SIZE. TWO REFERENCE

AND TWO 'UNKNOWN,' ARE

INTERCOMPAREO ACCORDING TO THE

FOLLOWING design:

OBSERVATION DIFFERENCE MEASURED

YI I) S. - s.. Y(2) Y ^ s.

Y( 3) X - Y

Y( 41 s.

.

- X Y( 5) s.. - Y

Y( 6) Y - S.

Y(7» s. - X Y«8) X - s..

THE SYMBOLS (.> AND (..» INDICATE

RFFERENCE ARTIFACTS, LISTED BY

SERIAL NUMBER IN THE BODY OF THE

REPORT. (X» AND lY) DESIGNATE

•UNKNOWN' ARTIFACTS, ONE SET OF

WHICH IS COVERED BY THIS REPORT,

AND THE OTHER COVERED BY TEST

NUMBERS STATED IN THE APPENDIX

THE REPORT.

TO

IN SUCH AN INTERCOMPARISON, ONLY

DIFFERENCES IN LENGTH CAN BE

MEASURED. BECAUSE OF THE LIMITED

RANGE OF PRESENT COMPARATORS, ALL

ARTIFACTS IN A GIVEN COMPARISON

ARE OF THE SAME NOMINAL VALUE. A REDUNDANCY IN THE NUMBER OF

MEASUREMENTS (EIGHT MEASUREMENTS

TO DETERMINE FOUR VALUES) PROVIDES

A MEANS FOR CHECKING ON THE

PRECISION OF THE PROCESS BY THE

METHOD OF LEAST SQUARES USING THE

SUM OF THE LENGTHS OF THE TWO

REFERENCE ARTIFACTS, (I.) « U.l),

AS THE RESTRAINT. THE COMPUTED

DIFFERENCE BETWEEN THE REFERENCE

ARTIFACTS ((.» - (..)) IS AN

INDEPENDENT ESTIMATE OF THE

DIFFERENCE, AND SERVES AS A •CHECK

STANDARD'

.

PROCESS CONTROL

THE STANDARD DEVIATION, AS

COMPUTED FROM THE LEAST SQUARES

SOLUTION, PROVIDES A CHECK ON THE

SHORT TERM, OR 'WITHIN-RUN^

PROCESS PRECISION. THIS VALUE IS

COMPARED WITH THE LONG RUN AVERAGE

OF THESE STANDARD DEVIATIONS

DESIGNATED THE ACCEPTED WITHIN-RUN

STANDARD DEVIATION OF THE PROCESS

FOR THE GROUP.

THE VALUES OBTAINED FOR THE

DIFFERENCE IN LENGTH BETWEEN THE

TWO •KNOWN' REFERENCE ARTIFACTS

PROVIDE, AS TIME GOES ON, A SEQUENCE OF VALUES THAT

REALISTICALLY REFLECT THE TOTALITY

OF VARIATIONS WHICH BESET

MEASUREMENTS OF TEST ITEMS. THE

STANDARD DEVIATION OF THIS

COLLECTION OF VALUES IS THE TOTAL

67
BENOIX CORPORATION PAGE I- 3 ELECTRrCAL COMPONENTS DIVISION

SIDNEY NEW YORK 13838

TEST NO. 210495

PROCESS STANDARD DEVIATION. TESTS OF THE VALUES FROM THE

CURRENT RUN CONFORM TO THEIR

RESPECTIVE DISTRIBUTIONS THEN ONE

IF THE 'WITHIN-RUN' STANDARD TAKES THIS AS EVIDENCE THAT THE

DEVIATION AND THE VALUES FOR THE PROCESS IS IN CONTROL. AND THAT

CHECK STANDARD CAN BE REGARDED AS PREDICTIVE STATEMENTS REGARDING

MEASUREMENTS FROM STABLE UNCERTAINTY ARE VALID.

PROBABILITY DISTRIBUTIONS AND THE

SYSTEMATIC ERRORS IN USE OF BLOCK

IN THE USE OF THESE BLOCKS IN PRACTICAL MEASUREMENT, TWO FACTORS

MAY INTRODUCE SYSTEMATIC ERRORS

INTO THE RESULTS: DISSIMILARITY

OF MATERIAL AND DEVIATION OF

TEMPERATURE FROM 20 C.

LENGTH VALUES CAN BE ASSIGNED TO

OTHER LIKE BLOCKS BY DETERMINING

THE DIFFERENCE IN LENGTH WITH A CONTACTING COMPARATOR. IF THE

BLOCKS ARE NOT SIMILAR. THE

INDICATED DIFFERENCE IS A FUNCTION

OF THF FORCE EXERTED BY THE

COMPARATOR PROBE ON THE ARTIFACTS

UNDER COMPARISON AS WELL AS THE

ELASTIC PROPERTIES AND SURFACE

GEOMETRY OF BOTH THE PROBE AND

ARTIFACTS IN THE IMMEDIATE

VICINITY OF THE POINT OF CONTACT.

DATA ADJUSTMENT TO COMPENSATE FOR

THESE DIFFERENCES MAY BE

NECESSARY. IF THE COMPARATOR

BEING USED HAS BOTH A TOP AND

BOTTOM CONTACT. THE DIFFERENTIAL

PENETRATION FOR BOTH CONTACTS MUST

BE CONSIDERED. THE UNCERTAINTY

FOR THE REPORTED VALUES SHOULD

INCLUDE AN ALLOWANCE FOR THE

UNCERTAINTY OF THE DIFFERENTIAL

PENETRATION CORRECTIONS. WHEN THE

TWO ARTIFACTS ARE MADE OF THE SAME

MATERIAL AND TESTED BY THE SAME

PROBEISI AT THE SAME CONTACT

FORCE, NO CORRECTION IS APPLIED.

ALL MEASUREMENTS FOR THIS REPORT

WERE MADE IN A TEMPERATURE

ENVIRONMENT IN THE NEIGHBORHOOD OF

20 C. ASSIGNED VALUES HAVE BEEN

ADJUSTED TO THAT APPROPRIATE FOR

USE IN AN ENVIRONMENT OF 20 C (1968 INTERNATIONAL PRACTICAL

TEMPERATURE SCALE) USING THE

STATED. OR HA NDBOOK . V AL UES FOR THE

TEMPERATURE COEFFICIENT OF LINEAR

EXPANSION. IN THE COMPARISON

PROCESS. ALL ARTIFACTS ARE AT VERY

NEARLY THE SAME TEMPERATURE.

CORRECTIONS BASED ON DIFFERENTIAL

COEFFICIENTS OF EXPANSION ARE

ASSUMED NEGLIGIBLE FOR ARTIFACTS

OF GROUPS I THROUGH VI. IN ORDER

TO EXTEND THE USEFULNESS OF THE

ASSIGNED VALUES OVER A TEMPERATURE

RANGE OF 20 C TO 25 C, IT MAY BE

NECESSARY TO DETERMINE A COEFFICIENT OF EXPANSION FOR EACH

ARTIFACT OF GROUPS VI AND VII. A PROCEDURE TO DO THIS IN THE NORMAL

COURSE OF MEASUREMENT IS NOW UNDER

DEVELOPMENT. MEASURED

COEFFICIENTS OF EXPANSION WILL BE

ASSIGNED TO EACH ARTIFACT WHEN

AVA ILABLE.

68
PAGE I- ^ ELECTRICAL COMPCNENTS DIVISION

SIDNEY NEW YORK 13838

TEST NO. 210495

UNCERTAINTY

THE PREDICTED, OR ACCEPTED, VALUES

OF THE REFERENCE ARTIFACTS ARE

ESTIMATES OF THE LENGTH AT 20 C.

THF SYSTEMATIC COMPONENT OF THE

UNCERTAINTY OF THE VALUES IN THIS

REPORT IS BASED ON THE UNCERTAINTY

OF THE VALUE FROM THE

INTERFEROMETRIC DETERMINATION.

THE BOUNDS FOR THE EFFECTS OF

RANDOM ERRORS IN THE

INTERCOMPARISONS ARE 3 TIMES THE

TOTAL STANDARD DEVIATION OF THE

PROCESS. WHEN THE BLOCKS ARE OF

DIFFERENT MATERIAL THAN THE

STANDARDS, A CORRECTION IS MADE

FOR DIFFERENTIAL PENETRATION AND

THE UNCERTAINTY VALUE IS INCREASED

BY ONE MICRO-INCH.

THE MAGNITUDE OF SYSTEMATIC ERRORS

FROM SOURCES OTHER THAN THAT OF

THE ACCEPTED VALUES FOR THE

REFERENCE ARTIFACTS IS CONSIDERED

NEGLIGIBLE AT TEMPERATURES VERY

NEARLY 20 C. IT SHOULD BE NOTED

THAT THE MAGNITUDE OF THE

UNCERTAINTY REFLECTS THE

PERFORMANCE OF THE MEASUREMENT

PROCESS USED TO ESTABLISH THESE

REFERENCE VALUES.

THE UNCERTAINTY IN ASSIGNED VALUE

CONTAINED IN THIS REPORT BECOMES A SYSTEMATIC ERROR FOR THE LENGTH

MEASUREMENTS OF THE USER. IN THE

ABSENCE OF OTHER SIGNIFICANT

SYSTEMATIC EFFECTS IN THE USER'S

MEASUREMENT PROCESS (A CONDITION

WHICH MUST BE DEMONSTRATED) THE

UNCERTAINTY OF THE VALUE ASSIGNED

BY THE USER IS AN APPROPRIATE

COMBINATION OF THE SYSTEMATIC

ERROR IN THE STANDARD AND THE

RANDOM COMPONENT ASSOCIATED WITH

HIS PROCESS. IF THE MEASUREMENT

PROCESSES ARE IN CONTROL AND

APPROPRIATE UNCERTAINTIES ARB

ASSIGNED, THE VALUES PRODUCED BY

DIFFERENT MEASUREMENT FACILITIES

WILL HAVE OVERLAPPING UNCERTAINTY

BANDS. ONE CANNOT DISCUSS

DIFFERENCES IN VALUES FOR THE SAME

OBJECT OBTAINED BY DIFFERENT

FACILITIES WITH ANY DEGREE OF

SERIOUSNESS UNLESS EACH VALUE IS

ACCOMPANIED BY A REALISTIC

UNCERTAINTY STATEMENT.

69
RENOIX CORPORATION PAGE I- 5 ELECTRICAL COMPONENTS DIVISION

SIDNEY NEW YORK 13838

TEST NO. 210^*95

FIGURE

TTTTTTTTTT

T TR.

T SIZE TR . T TR . T X TR . T TR . T TR . T TR . TTTTTTTTTTR .

TTTTTTTTTTTT

T SIZE TR

T ... TR

T . .X TR

T ... TR

T TR

TTTTTTTTTTTR

TTTTTTTTTT

r TP.

TR . TR . X TR E . TR Z . TR I . TR S . TTTTTTTTTT

TTTTTTTTTTTT

T T T ... T T . . T TXT T ... T

TTTTTTTTTTTT

RRRRRRRRRR

SIZE

THE 'T' REFERS TO TOP CONTACT SURFACE.

THE 'TR' REFERS TO THF REFERENCE EOGF.

THE GAGING POINT : X: IS LOCATED AT THE CENTER OF

RECTANGULAR BLOCKS AND MIDWAY BETWEEN THE HOLE

AND THE REFERENCE EDGE ON HOKE STYLE BLOCKS.

70
BENOIX CORPORATION PAGE I- 6

ELECTRICAL COMPONENTS DIVISION

SIDNEY NEW YORK 13838

TEST NO. 210495

REFERENCES

(1) SINGLE WAVELENGTH I NT ERF ER OM ETR Y FOR GAGE ftLOCK MEASUREMENT

PROCESS J- S. BEERS, NBS TECH NOTE , 1974

(2) GAGE BLOCK FLATNESS AND PARALLELISM MEASUREMENT, J. S. BEERS AND

C. D. TUCKER, N8SIR 72-239, AUGUST 1973

(3) THE APPLICATION OF CAPACITATIVE PROXIMITY SENSORS TO METROLOGY,

H. A. BOWMAN, NBS TECH NOTE (1974)

(4) DESIGNS FOR THE CALIBRATION OF SMALL GROUPS OF STANDARDS IN THE

PRESENCE OF EXPERIMENTAL DRIFT, J. M. CAMERON AND G. E. H4ILES

NBS TECH NOTE . 1974

(5> THE MEASUREMENT ASSURANCE PROGRAM - A CASE STUDY IN LENGTH

MEASUREMENTS. P. E. PONTIUS, NBS MONOGRAPH (TO BE PUBLISHED IN

1974)

(6) ON THE EFFECTS OF PHASE SHIFT AND WRINGING FILM THICKNESS UN GAGE

BLOCK LENGTH MEASUREMENT, P. E. PONTIUS AND J. M. CAMERON NBS

TECH NOTE , 1975

(7) CALIBRATION OF GAGE BLOCKS BY COMPARISON MEASUREMENT PROCESS

C. D. TUCKER, NBS TECH NOTE . 1974

(8) PREPARATIONS FOR GAGE BLOCK COMPARISON MEASUREMENTS C. 0. TUCKER,

NBSIR , 1974

71
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBS Monograph 149

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

The Measurement Assurance Program -- A Case Study:

Length Measurements

Part I - Long Gage Blocks (5 in to 20 in)

5. Publication Date November 1975

6. Performing Organization Code

7. AUTHOR(S)

Paul h. Pontius

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 No.

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 Number: 74-31143

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.)

The differences between the methods of traditional metrology and the measurement

assurance programs are briefly discussed. The historical data relative to long

gage blocks (Sin to 20in) are analysed to provide a basis for comparison with

results from new measurement processes formulated in accordance with the

philosophies of the measurement assurance programs. The results from the new

processes are in agreement with the work of the past. The current length values

assigned and associated uncertainties are shown for selected long gage blocks

used in the dissemination of length by the National Bureau of Standards. These

long gage blocks are a part of a growing collection of similar well characterized artifact standards for use in comparative measurement processes. The

methods and techniques used in developing the new measurement process are discussed in some detail. It is the author's intent that, in addition to the

technical content, this paper be largely tutorial in the area of measurement

process analysis. This paper is, in essence, a report on the extension of the

techniques first suggested in NBS Monograph 103 "Realistic Uncertainties and

the Mass Measurement Process" to the area of length measurement.

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

)

Measurement algorithm; measurement assurance; measurement process;

measurement unit; process variability; uncertainty.

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