The problem with using eq (2) is that the precision with which Va can be
measured far exceeds the accuracy with which p is known. Thus, for best
results, one should also measure an object whose mass and volume are known.
Placing such an object on the balance essentially calibrates the density of the
fluorocarbon at the time of weighing. Let the known object be called S1. Then

M,,- 0,

p= $1 S1
Vs1
and
M, - O
A A
vy =e y Q)
A Mgi7 054 $1

In practice, Sl is a stainless-steel kilogram whose volume has been determined
to better than 1 x 107° by classical hydrostatic weighing. We also include a
check standard, $2 in the measurements. The check standard is similar to $1
and similarly calibrated.

5. Cleaning of Weights

It is essential that weights being calibrated, as well as the standards used,
be clean if the calibration is to be accurate and meaningful. Therefore, a
cleaning procedure should be a part of every calibration. [11]

5.1 Categories of Weights

For cleaning purposes, weights may be divided into four categories.

1. One-piece weights.

This category will include all one-piece weights except lacquered weights,
sheet metal weights and small wire weights.

2. Screw-knob weights.

This category will include all weights with adjusting cavities except
lacquered weights.

3. Lacquered weights.
This category includes all lacquered or painted weights.
4. Sheet metal weights and wire weights.

11


U. S. DEPARTMENT OF COMMERCE
NATIONAL BUREAU OF STANDARDS
NATIONAL MEASUREMENT LABORATORY

GAITHERSBURG, MD. 20899

REPORT
OF
MASS VALUES

COMPARY X

LOcUS, U.S.A.

SET OF MASS STANDARDS : 500 MG - 1MG
SERIAL NUMBER 00001

MANUFACTURER : COMPANY Y

SEPTEMBER 1, 1986

TEST RUMBER DEMO1

FOR THE DIRECTOR,
NATIONAL MEASUREMENT LABORATORY

JOE D. SIMMONS, CHIEF
LENGTH AND MASS DIVISION
CENTER FOR BASIC STANDARDS

B2


where n

n
Tay = 2k

or in matrix notation

KX x) (A) = >| (5)
xr’ 0. d, m
The solution may be written out formally as follows:

B) = [ch Xty) = ([ cx’ oh y (6)
a h’ 0 mn h’x’ oO m
To facilitate computation it is convenient tg have the values, B, written out

as linear functions of the y’s andm, i.e., B = [CX', h] y. This leads to a
set of multipliers of the observations of the form n

By = 81191 * 82% + + Sinn tm TM

Be = Bg. + Ba¥2 Benn te

These multipliers, 8; and hy, are given in Appendix B in transposed form for
some of the designs.”~The matrix C is important because the variances and
covariances of the estimates are given by

Variance (B;)=C, 07, Covariance (Bis By) = C450? (8)
The quantity, o, is the variance (square of the long run value of the standard

deviation) associated with the process. In a set of n observations on k items

and r = 1 restraints one has n - k+r=n- k +1 degrees of freedom for a
standard deviation, s, formed by

A3


COMPARY X PAGE
Locus, U.S.A.

SET OF MASS STANDARDS : 500 MG - 1MG

TEST NUMBER DEMO1

REFERENCES

THE FOLLOWING REFERENCES ARE SUGGESTED FOR DETAILED DESCRIPTION OF
PORTIONS OF THIS REPORT , AND FOR GENERAL INFORMATION CONCERNING THE
MASS MEASUREMENT PROCESS:

-PONTIUS, P. E., AND CAMERON, J. M.

REALISTIC UNCERTAINTIES AND THE MASS MEASUREMENT PROCESS
NAT, BUR. STAND. (U.S.), MONOGR. 103

(AUG. 15, 1967)

2,PONTIUS, P. E.
MEASUREMENT PHILOSOPHY OF THE PILOT PROGRAM FOR MASS CALIBRATION
NAT, BUR. STAND. (U.S.) TECH. NOTE 288
(MAY 6, 1966)

3.BOWMAN. H. A.. AND SCHOONOVER. R. M. WITH APPENDIX BY MILDRED JONES
PROCEDURE FOR HIGH PRECISION DENSITY DETERMINATIONS BY HYDROSTATIC
WEIGHING
J, RES. NAT. BUR. STAND. (U.S.) 71C. ENGINEERING AND INSTRUMENTATION
NO. 3, 179-198 (JULY-AUG. 1967)

4.NATRELLA, M. B.
EXPERIMENTAL STATISTICS
NAT. BUR. STAND. (U.S.) HANDBOOK 91
(AUGUST 1, 1963)

5.KU, H. H.
PRECISION MEASUREMENT AND CALIBRATION - SELECTED NBS PAPERS ON
STATISTICAL CONCEPTS AND PROCEDURES
NAT. BUR. STAND. (U.S.) SPEC. PUBL. 300
VOL. 1 (FEB. 1969)

6.PONTIUS, P. E.

MASS AND MASS VALUES
NAT. BUR. STAND. (U.S,) MONOGR. 133
(JAN. 1974)

-CAMERON, J. M., CROARKIN, M. C. AND RAYBOLD, R. C.
DESIGNS FOR THE CALIBRATION OF STANDARDS OF MASS
NAT. BUR. STAND, (U.S,) TECH. NOTE 952

(JUNE 1977)

-VARNER, R. N., AND RAYBOLD, R. C.
NATIONAL BUREAU OF STANDARDS MASS CALIBRATION COMPUTER SOFTWARE
NAT. BUR. STAND. (U.S.) TECH. NOTE 1127

(JULY 1980)

B7


Kha

A.

B.
Figure 1. A. A stainless-steel kilogram (density 8000 kg/m?) balances a
platinum-iridium kilogram (density 21500 kg/m?) at normal
atmospheric conditions. B. Under vacuum conditions one can
see that the mass of the stainless-steel kilogram actually
exceeds that of the platinum kilogram by about 0.1 g.

5


The National Bureau of Standards uses the following relationship between
metric unit of mass and the U.S. customary unit of mass: one pound
(avoirdupois) equals 0.45359237 kilogram.

For the Director,
National Measurement Laboratory

Joe D. Simmons, Chief
Length and Mass Division
Center for Basic Standards

‘vat completed: September 3, 1986
Note: Mass and associated density values listed above are appropriate

for My and pm in Equation (24) from NBS Monograph 65,
"Reduction of Data for Piston Gage Pressure Measurements."

D3

the


COMPANY X PAGE 15
LOCUS, U.S.A. SERIES 3
SET OF MASS STANDARDS : 500 MG - 1MG 8/30/ 86
TEST NUMBER DEMO1

BALANCE 13
OPERATOR 39
ACCEPTED WITHIN STANDARD DEVIATION OF THE PROCESS 0.00050 MG
ACCEPTED BETWEEN STANDARD DEVIATLON OF THE PRUCESS 0.00000 MG

CALIBRATION DESIGN 62

RESTRAINT VECTOR 1 1 12 0 0 0

MASS CORRECTION OF RESTRAINT 0.01204 MG
VOLUME OF WEIGHTS BEING USED IN RESTRAINT AT 23.00 0.01223 CM3
SYSTEMATIC ERROR IN THE RESTRAINT 0.00009 MG

3 STANDARD DEVIATION LIMIT FOR RANDOM ERROR AFFECTING RESTRAINT = 0.00074 MG

CRECK STANDARD USED 14

CHECK STANDARD VECTOR o oo o oOo 4 ©
ACCEPTED MASS CORRECTION OF CHECK STANDARD -0.00046 MG
REPORT VECTOR 21 2 2 2 0 0
TEST CONDITIONS BEFORE AFTER AVERAGE
CORRECTED TEMPERATURE IN DEGREES C 22.95 23.05 23,00
CORRECTED PRESSURE IN MM EG 760.227 760,027 760,127
CORRECTED HUMIDITY IN PERCENT 30.00 30.70 30.35
COMPUTED AIR DENSITY IN MG/CM3 1.1895 1.1886 1.1891
TEMPERATURE CORRECTION 0.00 0,00
PRESSURE CORRECTION 70.173 -0.173
HUMIDITY CORRECTION 0.00 0.00
OBSERVED TEMPERATURE IN DEGREES C 22.95 23.05
OBSERVED PRESSURE IN MM HG 760.400 760.200
OBSERVED HUMIDITY IN PERCENT 30.00 30.70
WEIGHTS BEING NOMINAL DENSITY COEFFICIENT ACCEPTED
TESTED VALUE G = G/CM3 AT 20C OF EXPANSION CORRECTION MG

NEW SOMG 0.0500 16.6000 000020

30MG 0.0300 16,6000 000020

20MG 0.0200 = 2. 7000 oonnso

10MG 0.0100 2.7000 000069
AN/ 10MG 0.0100 8.4100 -000039 -0.00046
SUM 10MG 0.0100 2.7000 000069

B17


COMPANY X
LOCUS, U.S.A.

SET OF MASS STANDARDS :

TEST NUMBER DEMO1

BALANCE

L

OPERATOR 3}

3
9

CALIBRATION DESIGN

SUM
(MG)

1000
900
800
700
600
500
400
300
200
100

‘SUM
(MG)

1000
900
800
700
600
500
400
300
200
100

62

500 MG - 1MG

WEIGHTS USED FOR THE LINEAR COMBINATIONS

MG

500 300 200
+ + +

+ +

+ +
+ +

+

+ +

+

+
+

100

+

100

100

VALUES AND UNCERTAINTIES FOR COMBINATIONS OF WEIGHTS
(UNCERTAINTY IS 3 STANDARD DEVIATION LIMIT PLUS ALLOWANCE FOR
SYSTEMATIC ERROR. )

0.
0.
0.
-0.

-0
-0

-0.
-0.
-0.

CORR
(MG)

15925
11875
12046
11646
07595
08159
04108
04280
03879
00171

SYSTEMATIC
(MG)

ecccoce000

00087
00078
00070
00061
00052
00043

00035

00026
00017
00008

3.8.D.
ERROR
(MG)

00509
00463
00408
00359
00312
00257
00216
00153
00109
00074

ecceacccce

B15

uN

eccecee000

(CERTAINTY
LIMIT
(MG)

00596
00542
00479
00420
00364
00300
00251
00185
00127
00082

PAGE 13
SERIES 2
8/29/

86


COMPANY X PAGE 19
LOCUS, U.S.A. SERIES 3
SET OF MASS STANDARDS : 500 MG - 1MG 8/30/ 86
TEST NUMBER DEMO1

BALANCE 13
OPERATOR 39
MAXIMUM LOAD 0.0600 G
STARTING RESTRAINT NUMBER 4

CALIBRATION DESIGN 62

PRECISION CONTROL

OBSERVED STANDARD DEVIATION OF THE PROCESS 0.00052 MG
ACCEPTED STANDARD DEVIATION OF THE PROCESS 0.00050 MG
DEGREES OF FREEDOM = 6

F RATIO 1,083

F RATIO IS LESS THAN 2.81 (CRITICAL VALUE FOR PROBABILITY = .01).
THEREFORE THE STANDARD DEVIATION IS IN CONTROL.

CHECK STANDARD VECTOR C) o 0 0 1 00

CHECK STANDARD USED 14

ACCEPTED MASS CORRECTION OF CHECK STANDARD -0.00046 MG
OBSERVED CORRECTION OF CHECK STANDARD -0.00039 MG

STANDARD DEVIATION OF THE OBSERVED CORRECTION 0.00018 MG
T VALUE 0.41

ABSOLUTE VALUE OF T IS LESS THAN 3.
THEREFORE CHECK STANDARD IS IN CONTROL.

TEST CONDITIONS BEFORE AFTER AVERAGE
CORRECTED TEMPERATURE IN DEGREES C 22.95 23.05 23.00
CORRECTED PRESSURE IN MM HG 760.227 760.027 760,127
CORRECTED HUMIDITY IN PERCENT 30.00 30.70 30.35
COMPUTED AIR DENSITY IN MG/CM3 1.1895 1.1886 1.1891
TEMPERATURE CORRECTION 0.00 0.00

PRESSURE CORRECTION -0.173 70.173

HUMIDITY CORRECTION 0.00 0.00

OBSERVED TEMPERATURE IN DEGREES C 22.95 23.05

OBSERVED PRESSURE IN MM HG 760.400 760.200

OBSERVED HUMIDITY IN PERCENT 30.00 30.70

B21


COMPANY X
LOCUS, U.S.A.

SET OF MASS STANDARDS :

TEST NUMBER DEMO1

BALANCE 13
OPERATOR 39

500 MG - 1MG

CALIBRATION DESIGN 62
SUM WEIGHTS USED FOR THE LINEAR COMBINATIONS
(MG) MG

5 3 1 1 1
10 + +
9 + + +
a8 + +
7 +
6 + +
5 +
4 + +
3 +
2
1 +

VALUES AND UNCERTAINTIES FOR COMBINATIONS OF WEIGHTS
(UNCERTAINTY IS 3 STANDARD DEVIATION LIMIT PLUS ALLOWANCE FOR

SYSTEMATIC ERROR.)

SUM CORR
(MG) (MG)

03457
02923
02368
02857
02322
01689
01155
00600
01089
00555

ecccceccce

SYSTEMATIC
(MG)

C)
0
)
0)
C)
C)
0
C)
C)
C)

00001
00001
00001
00001
00001
00000
00000
00000
00000
00000

3.8.D.
ERROR
(MG)

00054
00084
00058
00058
00072
00044
00075
00048
00041
00054

eocccoccce

B25

UNCERTAINTY

eececce000

LIMIT
(MG)

00055
00085
00059
00059
00073
00045
00075
00048
00041
00054

PAGE 23
SERIES 4
8/30/

86


COMPANY X PAGE 11
LOCUS, U.S.A. SERIES 2
SET OF MASS STANDARDS : 500 MG - 1MG 8/29/86
TEST NUMBER DEMO1

BALANCE 13
OPERATOR 39

CALIBRATION DESIGN 62

MG

500 300 200 100 100 © 100
Al + - - + -
A 2 + - - + -
A 3 + - - - +
A 4 + - -
AS + - - -
A 6 + + - -
AT + - - + -
A 8 + - - - +
Ag + - -
A 10 + - -
Alt + - -
R + + +

OBSERVATIONS IN DIVISIONS
DIRECT READING

20.4000 10020. 4004
-16.5000
6.8500
4.1000
-28,8500
8.8000
-26.7000
14,2500
-25.3000
-45.2000
-28.3000 9971. 7002

oe

PS eavausene

B13


The mass of the unknown is computed to be:

Dy - pV, + A= pV, (Sy - 8, +83 - S,)
S83-S2
Me 1- of,

Where Dy = the calibrated mass of Dy
the volume of Dy
= the mass of the sensitivity weight
= the volume of the sensitivity weight
the density of the unknown (supplied by the customer)
the computed density of air in the balance,

6.2 Uncertainty of Value Assigned to Piston Weights

It is presumed that the weighings are being carried out by means of a
measurement process whose parameters (precision, possible systematic errors,
etc.) are known and sufficient evidence is collected to insure that the process
is in a state of statistical control.[13] For each method of weighing there is
a standard deviation associated with a single measurement of mass difference.
This standard deviation is based on considerable history and is used in
preference to a standard deviation based on the results of say one day’s work.
Such a value if available provides the means for judging whether or not to
accept that day’s measurement as being in control.

The uncertainty of the mass value of the piston weights consists of two parts;
the uncertainty due to random errors of measurement and the systematic
uncertainty due to the uncertainty in the value of the standard. The limit of
the uncertainty due to random errors of measurement may be taken to be three
times the standard deviation, o, where o is the standard deviation of the
process. Therefore:

Uncertainty of value = 30 + uncertainty of standards.

7. Method of Calibrating Standard Weights
7.1 Measurement Algorithm

An unusual aspect of mass calibrations is that, although the standard is
defined at one value, one is typically asked to calibrate a set of weights
spanning several decades of mass and, often, not even encompassing the nominal
defining value (that is, 1 kilogram). We approach this problem in the
following way: 1. The weight in the set of unknowns which is closest in value
to 1 kg is calibrated against an NBS standard of the same nominal value. 2.

15


COMPANY X

LOCUS, U.S.A.

SET OF MASS STANDARDS :
TEST NUMBER DEMO1

500 MG - 1MG

INTRODUCTION

THIS DOCUMENT IS A COMPREHEN-
SIVE REPORT COVERING THE SEQUENCE
OF OPERATIONS USED TO ASSIGN MASS
VALUES 10 THE WEIGHTS IDENTIFIED
ABOVE. IT INCLUDES A COMPLETE
DESCRIPTION OF THE MEASUREMENT
METHODS AND PROCEDURES WHICH WERE
USED, ALL OF THE DATA, AND THE
ANALYSIS OF THIS DATA. THE
RESULTS ARE PRESENTED IN SEVERAL
FORMATS. ASSIGNED MASS VALUES,
DISPLACEMENT VOLUMES, COEFFICIENTS
OF EXPANSION, UNCERTAINTIES, TO-
GETHER WITH THE SUMMED VALUES FOR
LINEAR COMBINATIONS OF THE WEIGHTS
IN EACH DECADE ARE PRESENTED AT
THE END OF THE APPROPRIATE SERIES.
THIS INFORMATION SHOULD BE USEFUL
TO THOSE WHO MUST ASSIGN MASS
VALUES TO OBJECTS OTHER THAN
WEIGHTS. FOR CONVENIENCE, THE
VALUES AND UNCERTAINTIES, TOGETHER
WITH OTHER APPROPRIATE DATA AND
COMMENTS ARE ALSO SUMMARIZED IN
TABLES I AND II AT THE END OF THE
REPORT. CERTAIN INTERMEDIATE
PAGES ARE SUMMARIES OF STATISTICAL
DATA WHICH RELATE TO THE MASS
MEASUREMENT PROCESS USED TO
PERFORM THIS WORK. THESE PAGES
HAVE BEEN LEFT IN THE REPORT TO
RETAIN CONTINUITY. COPIES OF
THESE PAGES BECOME PART OF A
COLLECTION OF STATISTICAL DATA
WHICH REFLECTS THE MEASUREMENT
PROCESS PERFORMANCE OVER A PERIOD
OF TIME. SUCH A COLLECTION HAS
BEEN USED TO ESTABLISH THE CONTROL
LIMITS FOR ACCEPTING THE RESULTS
OF THIS MEASUREMENT. THESE COL-
LECTIONS ARE OPEN FOR INSPECTION
AT OUR FACILITY.

THE MASS MEASUREMENT SYSTEM
THE MASS MEASUREMENT SYSTEM

WITHIN THIS COUNTRY CONSISTS OF
ALL OF THE MEASUREMENT PROCESSES

PAGE

WHICH RELY, DIRECTLY OR INDIRECT-

LY, ON MASS MEASUREMENTS 10
ACCOMPLISH A WIDE VARIETY OF
ENDEAVORS. IN ORDER FOR THIS
SYSTEM TO FUNCTION PROPERLY,
EVERYONE WHO MAKES MEASUREMENTS
MUST BE ABLE TO VERIFY THAT HIS
MEASUREMENT = PROCESS — PRODUCES
CONSISTENT RESULTS WHICH ARE
COMPATIBLE WITH HIS PARTICULAR
REQUIREMENTS. THE WEIGHTS COVERED

BY THIS REPORT, TOGETHER WITH THE
ASSIGNED VALUES AND THE APPRO-
PRIATE UNCERTAINTIES FOR THESE
VALUES, PROVIDE IN PART A BASIS
FOR CONSISTENT MEASUREMENTS WITHIN

THIS SYSTEM OF RELATED MEASUREMENT
PROCESSES.

APPROPRIATE CHARACTERIZATION
OF ANY MEASUREMENT PROCESS. IS
FUNDAMENTAL TO VERIFYING THAT

RESULTS ARE CONSISTENT WITH THE
END REQUIREMENT WITH RESPECT TO
CORRECTNESS AND ECONOMY OF THE
MEASUREMENT EFFORT. WITHOUT THIS
INFORMATION, THE BENEFITS OF
OWNERSHIP OF THESE WEIGHTS MAY BE
COMPLETELY ILLUSORY. THE ASSIGNED
UNCERTAINTIES IN THIS REPORT ARE
DESCRIPTIVE OF OUR MASS MEASURE-
MENT PROCESS. EFFECTIVENESS OF
THE TRANSFER OF THE UNIT FROM ONE
FACILITY TO ANOTHER SHOULD BE
VERIFIED BY AN INDEPENDENT TEST.
IT IS PRESUMED THAT THESE WEIGHTS
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 MASS UNIT
AS ACTUALLY REALIZED IN ANOTHER
FACILITY. A COMPREHENSIVE SERVICE
DIRECTED TOWARD THE EVALUATION OF
A PARTICULAR MASS MEASUREMENT
PROCESS IS AVAILABLE THROUGH THE
MASS MEASUREMENT ASSURANCE PROGRAM
OF THE NATIONAL BUREAU OF
STANDARDS.

B3


U.S. DEPARMENT OF COMMERCE
NATIONAL BUREAU OF STANDARDS
GAITHERSBURG, MARYLAND 20099

REPORT OF CALIBRATION

NBS Test Number:

For:

Items:

The above items have the mass values shown with reference to the NBS standard
of mass.

Mass Uncertainty Density
Iten te) _—_@) (g/en3)
1kg-1 999.9968 0.0033 7.92
1kg-2 999.9985 0.0033 7.92
1kg-3 1000. 0007 0.0033 7.92
1kg-4 999.9969 0.0033 7.92
1kg-5 999.9960 0.0033 7.92
1kg-6 999.9952 0.0033 7.92

The uncertainty figure is an expression of the overall uncertainty using three
standard deviation as a limit to the effect of random errors of measurement
plus the systematic errors, assuming the density is correct within 1%. Test
conditions: mass computed using air density 1.175mg/cm3 for all items.

D2


NIST Spec. Publ. 250-31
Errata:
p. 16, first paragraph

delete the words "for nominal values 1 kg and below"

p- 22, caption for Figure 5

change 0.4 mg/yr to 0.4 pug/yr

Pp. A4 (Appendix A)

the first sentence after eq. (11) should read "The array of

coefficients, dij is given in Appendix B of ref. [8] for some of the
designs."


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BS-114A (REV. 2-80)

U.S. DEPT. OF COMM. 1, PUBLICATION OR 2. Performing Organ. Report Nod 3. Publication Date
REPORT NO.
ATA
SHEET Ge retro) NIST/SP-250/31 January 1989

4, TITLE AND SUBTITLE

NIST Measurement Services: Mass Calibrations

5. AUTHOR(S) .
Richard S. Davis

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7. Contract/Grant No.
NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY
(lormerty NATIONAL BUREAU OF STANDARDS) #. Type of Report & Period Covered
U.S. DEPARTMENT OF COMMERCE Final
GAITHERSBURG, MD 20899

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

Same as Item #6

10. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 88-600608

([)] Document describes a computer program; SF-185, FIPS Software Summary, is attached,

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant
bibliography or literature survey, mention it here)

The NIST calibration service for standard masses is described. Weights which
are accepted for calibration range in nominal values from 1 mg to 13,600 kg
(30,000 pounds). We also accept weights used to generate standard pressures in
piston gages. Cleaning procedures used on weights prior to calibration are
described. The measurement algorithms (including density determinations of
single-piece kilogram weights) and the uncertainties assigned to calibrated
weights are discussed. We also describe the system now in Place to monitor the
quality of calibrations. Finally, we assess the limitations of the present
controls on measurement quality and outline improvements which are underway.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)
calibration; density; kilogram; least squares; mass; piston weights; uncertainty

13. AVAILABILITY 14. NO. OF
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For Official Distribution, Do Not Release to NTIS 72

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USCOMM-DC 6043-P80


Appendix A

LEAST SQUARES ANALYSIS [8]

We begin then with a set of n observations, yj, y2, - - - Yn involving k
objects where values, 61, 62, . . . By are to be determined. The set of
observations can be represented by the equations for their expected values,

E(yi),

E(y1) = *1161 + 1282 - - - *1Kok (1)
E(y2) = *2181 + *2282 - - - X2Koq
E(yn) = ¥n161 + %n262 - + - ¥nkFk

or in matrix form E(y) = X6 where the element, xjj, of the X matrix is 0 if the
weight is absent, and 1 or -1 depending on the direction of the comparison. In
this note we shall adopt the convention of using just the signs so that, for
example, all possible comparisons (ignoring direction) of 4 nominally equal
objects will have the representation,

Bi 62 B3 Ba

+ - X= 1 -1 0 0
+ - 1 0 -1 0
+ - 1 0 o -1
+ - 0 O 1 -1

+ - o 1 o -1

+ - o Oo 1 -1

In the least squares analysis one forms the normal equations

X'XB = Ky

where the entries in X'X are merely the sums of squares and sums of cross
products of the columns of X. In the above case, one gets

Al


5.2 Cleaning Procedures
5.2.1 One-Piece Weights

One-piece weights, 1 gram and larger, are generally steam cleaned. The weights
are either held or placed in a jet of steam and manipulated so that the entire
surface of the weight is subjected to the cleaning action of the steam long
enough to clean it. A superficial steaming is not enough. The weight is then
dried, either by evaporation or careful wiping with a soft non-abrasive
material free from oil and other substances that will leave a residue on the
weights, such as high grade cheesecloth. Care must be exercised that no water
spots are left on the weights as they dry. Visible particles on the weights
should be brushed or wiped off before steam cleaning them. If a steam
generator is not available, one-piece weights may be cleaned either by
immersing them in a hot or boiling distilled water bath in a non-metallic
container or according to the procedures for screw-knob weights.

Occasionally, a weight will have foreign material adhering to it that requires
the use of solvents. Ethyl alcohol is a good general solvent.4 If alcohol
does not remove the material, other solvents may be used, such as benzene,
1,1,1- trichloroethane, etc. Alcohol is then used to remove any film left by
the other solvents. The weights are then steam cleaned as outlined above.
Cleaning and, in particular, steam cleaning, may adversely affect some alloys.
For these alloys, only solvent cleaning is used.

5.2.2 Screw-Knob Weights

Weights in this category are usually cleaned by wiping with a soft non-
abrasive material, free from oils or other substances that will leave a residue
of any kind on the weights, such as high grade cheesecloth. Occasionally, a
weight will have foreign matter adhering to it that requires the use of
solvents, applied with a cloth. Ethyl alcohol is a good general solvent. If
alcohol does not remove the foreign material, other solvents may be used.
Alcohol is then used to remove any film left by the other solvents.

To prevent spotting the weights when using solvents, the weights are wiped dry.
Care is taken that no liquid gets under the knobs or especially into the
adjusting cavity.

A modified steam cleaning procedure may be used on screw-knob weights. The
bottoms and sides are steam cleaned, care being taken that no liquid or vapor
gets under the knob or into the adjusting cavity.

4 some solvents are health hazards and should be used in an approved safe
manner.

12


Table 3. Typical random components of calibration uncertainties

Nom. Val. Uncertainty Nom. Value Uncertainty
1000 g 0.072 mg 1000 g 0.072 mg
500 0.059 2 kg 6.6
300 0.057 3 7.8
200 0.050 5 10.0
100 0.058 10 15.5
50 0.035 20 34
30 0.029 30 55
20 0.024
10 0.026
5 0.013
3 0.0082
2 0.0061
1 0.0049
500 mg 0.0026 mg
300 0.0017
200 0.0012
100 0.0010
50 0.00089
30 0.00087
20 0.00080 1 lb 0.11 plb
10 0.00090 50 22.
5 0.00083 500 0.0028 1b
3 0.00085 2500 0.0073
2 0.00079 10000 0.054
1 0.00090 30000 0.11

18


5.5 Brushes

Brushes require special attention because they are easily contaminated and
often are the last cleaning instrument used before the weights are calibrated.
Only soft brushes, such as camel hair brushes are used on weights.

The brushes are cleaned by washing with soap and water, then rinsing in ethyl
alcohol and allowed to dry in air. New brushes are cleaned before using to
remove any oil or other matter that might contaminate the weights. Used
brushes are cleaned as often as necessary to be sure that the brushes
themselves do not contaminate the weights.

6. Method of Calibrating Dead Weights
6,1 Measurement Algorithm

The following method of calibrating dead weights--including pressure gage
(piston gage) weights--is routinely used [12]. The method employs simple
weighing designs and includes corrections for the standards and the buoyant
effect of the atmosphere. Calibrations of dead weights are at a lower accuracy
than calibrations of mass standards.

The comparisons are made on several different balances whose precision is
adequate for the requirements of the weights being tested.

In general, the "Mass Value" of the standard means its True Mass value and its
correction means its True Mass Correction unless otherwise indicated.
Measurements are often made on by double-substitution weighing, against the
built-in weights of an appropriate single-pan balance. These weights have, in
turn, been calibrated against NBS standards. The weighing algorithm is:

1) Read the balance with no load: 84

2) Read the balance with unknown on the pan: Dy + So

3) Read the balance with unknown & sensitivity weight: Dy + S3

4) Read the balance with no load: S,
Here Sj represents a reading of the angle of tilt of the balance relative to an
arbitrary zero and Dj represents the nominal values of the summation of dial
weights which was used when the balance is loaded. Tare weights are placed on

the balance pan as necessary to ensure that the same dial weights are used for
operations 2) and 3) (no dial weights are used if no load is on the balance).

14


3 -l -1 -1) B= yi + y2+ y3

-1 3 -1 -1 -yi + yg t+ y5
“1-1 3-1 -y2 + ya + y5
“Po -1 0-2 3 -y¥3 + ya + ¥6

where B is the column vector with elements Bi, 2, 83, By, the caret being
used to denote the fact that the values are functions of the observations, and
not the sought-after values, f.

It can easily be verified in this case that the system of equations is not of
full rank (e.g., the column totals are zero) and this is a property of all
designs where only differences are measured. In mass calibration, one has one
or more standards whose value can be taken as known and these provide the
restraint on the system needed to give a unique set of answers. Usually these
involve a starting kilogram or a unique summation such as 5 + 3 + 2 which has
been determined in a previous series or is the initial unit value for an
ascending series such as the 1, 2, 3, 5 series. One can write the restraint in
the form

rjB1 + 199... + 1S, =m (2)

and use the method of Lagrangian multipliers (with multipliers 2A) to minimize
the function

® = Y(deviations)? + 25(r181 +. . . thBke - m) (3)

The normal equations now contain an additional "unknown," namely \ and written
out in full are as follows:

7B, + Wxyxy8) Deb, + ra Iyy 4)
Wx, 8, + 1x58, te Ix,% by, + rd = Ixy

Wyby + Dygaby A A = Day

r4B, + r9Bo see nb, = m

A2


170 ELECTRONIC CABLE

(WERT FLUID LEVEL

AIR HEAD ADJUST

BALANCE PAR ——__|

STORAGE TRAY

(WERT FLUID

WATER LEVEL

THERMOSTAT OUTPUT

—

(a

THERMOSTATED WATER
| + Ky stanparo

|____— GLASS. CHAMBER

TOP LOADING ELECTRONIC BALANCE

12009 CAPACITY

THERMOSTAT INPUT

BALANCE LEVEL ADJUST

Figure 2. Cross-sectional view of the balance immersed in its

thermostated bath.
shown on the pan.

A conventionally-shaped standard weight is
Unconventional loads may also be

accommodated by the pan as suggested by the sphere (drawn with
dashed lines).


U.S. Department of Commerce

National Institute of Standards and Technology
(formerly National Bureau of Standards)
Gaithersburg, MD 20899

Official Business
Penalty for Private Use $300


COMPANY X PAGE 21
LOCUS, U.S.A. SERIES 4
SET OF MASS STANDARDS : 500 MG - 1MG 8/30/ 86
TEST NUMBER DEMO1

BALANCE 13
OPERATOR 39

CALIBRATION DESIGN 62

MG

5 3 2 1 1 1
Al + - - + -
A 2 + - - + -
A 3 + - - - +
A 4 + - -
AS + - - - -
A 6 + - + - -
a7 + - - + -
A 8 + - - - +
A 9 + - -
A 10 + - -
All + - -
R + + +

OBSERVATIONS IN DIVISIONS
DIRECT READING

8.4000 10008. 4004
2.4000
-8.8000
1.1000
7.2000
6.0000
-9,1000
-11.2000
7.6000
8.0000
17.8000 10017.7998

PPP >>> rer >>

Be
ESeavansone

B23


1. Description of Service

The National Bureau of Standards maintains the national standard for mass in
the form of the prototype kilogram K20 and its companion K4 and provides
services to support the segments of the national measurement system which rely
directly or indirectly on mass measurements. These services are offered only
to those customers whose requirements cannot be met by state laboratories. In
order to provide prompt and useful service, the acceptance of the items for
calibration or test is based on discussions with each user to determine details
necessary to meet measurement and delivery requirements, and on inspection of
the item at the Bureau to determine its suitability for the usage intended.

Services are available to enable a user to establish a measurement assurance
program for certain measurement processes. This may involve developing
procedures for establishing and maintaining a state of statistical control for
the measurements, the determination of the offset of the process from the
national system, and assisting in the determination of the uncertainty of
measurements made by the user's process.

Arrangements for calibration (or test) must be completed before shipping
apparatus to the Bureau. While all services are on an actual-cost basis,
subject to a $25 minimum charge, a mutual agreement on the work to be performed
generally results in substantial savings for the user. Detailed packing and
shipping instructions are available on request. Items not accepted for
calibration or test will be returned, the cost of inspection or the minimum
charge will be applicable.

The results of a calibration or test will be reported in a National Bureau of
Standards Report of Calibration Test or of Special Test (which in many cases is
prepared by a computer program), a continuation report, or a letter report. In
each of these, the values reported are accompanied by an appropriate estimate
of uncertainty (allowance for random and systematic errors) as determined by an
analysis of the specific measurement process. A continuation report is used
for those items submitted for recalibration on which preliminary tests indicate
that no significant changes have occurred since the last calibration. Usually
a letter report is used to report a test for compliance with a specification
which states limits for the departure of the actual value from nominal.

Charges for these services are listed in the NBS SP250 Appendix. Upon receipt
of a request for services, an estimated cost will be given along with a firm
date for completion. An effort will be made to discuss the measurement

requirement with the customer so as to give proper service at minimum cost and
delay.

The Bureau's calibration of reference standards of mass provides extensions of
the mass unit embodied in the NBS standard of mass. A normal calibration
consists of establishing a mass value and the appropriate uncertainty for that
value for each weight which has been designated to be a reference standard. It
is desirable, but not necessary, that a weight meet the adjustment tolerances


2. An existing kilogram comparator has been reconditioned and partially
automated so that its standard deviation is more than 15 times less than
that of the comparator used for routine calibrations. Thus, if there were
no between-times components, it would require 225 measurements on the less
precise balance to achieve the same uncertainty as one measurement on the
more precise balance.

3. The two platinum-iridium prototype kilograms of the United States have
recently been recalibrated by the International Bureau of Weights and
Measures (BIPM) along with two of our stainless-steel working standards.
Good internal consistency was obtained between measurements made at NBS and
at BIPM. The results show excellent long-term stability of our platinum-
iridium standards with respect to the SI unit as maintained by the BIPM.

4. An exhaustive series of measurements is underway using our best kilogram
comparator. These measurements will establish the long-term stability of
our new stainless-steel weights as well as determine how reproducibly they
can be cleaned. We have also made preliminary measurements of N1 and N2
which can be precisely tied to the SI unit as maintained by the BIPM.

5. When the measurements described in 4. are completed, four of the six
new stainless-steel kilograms will be used as working standards. The
remaining two will not be used but instead, along with the two stainless-
steel weights which have been calibrated at the BIPM, will serve to monitor
the constancy of the working standards thus prolonging the times between
calibrations against our platinum-iridium prototypes.

24


COMPANY X PAGE 28
LOCUS, U.S.A. 8/30/ 86
SET OF MASS STANDARDS : 500 MG - 1MG
TEST NUMBER DEMO1

TABLE II
ITEM COR.A (MG) COR.B (MG)
500MG - 04231, -,03881
300MG
200MG ~.02465 -.02325
100MG 00879 00948
NEW 5OMG 00008 00043
30MG 00410 00431
20MG 100748 00762
10MG 02023 02030
SMG +01616 01620
3MG 00510 00512
2MG 01028 01030
AMG 00525 00525

B30


UNITED STATES DEPARTMENT OF COMMERCE
National Bureau of Standards
Gaithersburg. Merylend 20893

ot

<a
wot

September 18, 1986

In reply refer to:

Subject:

Items:

The above items have been intercompared in sums. The differences as measured
have been compared with the differences computed from the values under
225716-B. One or more of the items have been checked against national
standards. The results of this test indicate that there is no significant
change since the last calibration. This test assures the continuing accuracy
of the values under 225716-B.

Sincerely,

<

IE D. SIMMONS, Deputy Director
Center for Basic Standards

Attachment

c2


Appendix D

Calibration of Dead Weights

The following is a typical report of calibration for a set of dead
weights.

D1


CHECK >+ANDARO 41 BALANCE 12

=. 193264024 +

~.19386+024 +
z 2 . . z
=. 194364028 2 ove ;
af - oe +
: eee * :
z e228 . 2 =
: zee :
: . : +3 z
: . +2 : z
z 3 z
=. 194964024 . . ;
* 33 . .
z : . 20 :
=. 195464024 +
=. 19688402 :
740085402 778085402 ~B0000r+e2 7e3000e+e2 "es000E+e2 ~390005+02

‘CORRECTIONS TO CHECK STANDARD VS TIME

Figure 4. Control chart for the measured difference in mass between
kilograms N1 and N2. The ordinate is the difference measured
in milligrams and the abscissa is the time of the measurement
in years since 1900. Control limits are not shown.

21


procedures utilized in connection with NIST Service Identification Numbers from
22010C to 22180M listed in the NBS Calibration Services Users Guide 1986-
88/Revised (pages 28-31). Inquiries concerning the contents of these documents
may be directed to the author(s) or to one of the technical contact persons
identified in the Users Guide.

Suggestions for improving the effectiveness and usefulness of the new series
would be very much appreciated at NIST. Likewise, suggestions concerning the
need for new calibration services, special tests and measurement assurance
programs are always welcome.

Joe D. Simmons, Acting Chief
Office of Physical Measurement Services

iv


PREFACE

Calibrations and related measurement services of the National Institute of
Standards and Technology provide the means for makers and users of measuring
tools to achieve levels of measurement accuracy that are necessary to attain
quality, productivity and competitiveness. These requirements include the
highest levels of accuracy that are possible on the basis of the most modern
advances in science and technology as well as the levels of accuracy that are
necessary in the routine production of goods and services. More than 450
different calibrations, measurement assurance services and special tests are
available from NIST to support the activities of public and private
organizations. These services enable users to link their measurements to

the reference standards maintained by NIST and, thereby, to the measurement
systems of other countries throughout the world. NIST Special Publication 250,
NIST Calibration Services Users Guide, describes the calibrations and related
services that are offered, provides essential information for placing orders

for these services, and identifies expert persons to be contacted for technical
assistance.

NIST Special Publication 250 has recently been expanded by the addition of
supplementary publications that provide detailed technical descriptions of
specific NIST calibration services and, together with the NIST Calibration
Services Users Guide, they constitute a topical series. Each technical
supplement on a particular calibration service includes:

specifications for the service

design philosophy and theory

description of the NIST measurement system
NIST operational procedures

measurement uncertainty assessment
error budget
systematic errors
random errors

NIST internal quality control procedures

The new publications will present more technical detail than the information
that can be included in NIST Reports of Calibration. In general they will also
provide more detail than past publications in the scientific and technical
literature; such publications, when they exist, tend to focus upon a particular
element of the topic and other elements may have been published in different
places at different times. The new series will integrate the description of
NIST calibration technologies in a form that is more readily accessible and
more useful to the technical user.

The present publication, SP 250-31, NIST Measurement Services: Mass Calibration
at the National Institute of Standards and Technology, by R. S. Davis, is one
of the documents in the new series. It describes calibration technology and

iii


Table 1. Comparison of Properties of FC-75 and Water

Property (at 25 °C) FC-754 Water
Density (kg/m?) 1800 1000
Coefficient of expansion (°c7!) 1.6x1073 2.5x1074
Kinematic viscosity (cm2/s) 0.82x1072 0.89x1072
Vapor pressure (Pa) 4000 3200
Surface tension (N/m) 0.015 0.072
Heat capacity (J/g-°C) 1.0 4.2
Thermal conductivity (W/em-°C) 1.4x1073 6.1x1073

Aavalues for FC-75 supplied by the manufacturer.

4.2 Principles of Use

We illustrate the use of the submersible balance by finding the volume, Va, of
an object, A, when its mass, Ma, is known. Placing the object on the balance
produces a reading, 0g, which is related to the other parameters through the
equation

O, = K [ Ma - (t)Va(t)] q)
where 0, is the difference in reading of the loaded and unloaded balance.

Here p is the density of the fluorocarbon and K is a constant scale-factor
which may be adjusted by turning a potentiometer controlling the calibration of
the balance. Both p and Vg are functions of the ambient temperature, t. In
succeeding equations the functional dependence on temperature is not shown
explicitly.

Normally K is adjusted by the balance manufacturer or user so that the balance
will read directly the mass of an object of density 8.0g/cm> in air of density
1.2 x 10-3g/em?, i.e. K = 1.000150. We found it convenient (though, of course,
not essential) to readjust K to exact unity. Thus we can ignore K in the
succeeding equations. Hence,

Vv. =— (2)

10


10.

7.1 Measurement Algorithm.

7.2 Uncertainty of Value of Standard Weights .

Quality Control .
8.1 F-Test .
8.2 t-Test .
8.3  Between-Times Components .
Future Plans.
References.
Appendices
A. Least Squares Analysis.
B. Sample Calibration Report .
C. Sample Surveillance Test Report .

D. Sample Dead-Weight Calibration Report .

vi

- 15

. 16

16

. 19
~ 19
. 23
. 23

. 25

AL
. Bl
. Cl

. D1


The rest of the weights in the set are calibrated in a self-consistent manner
using the weight calibrated in step 1 as the standard.

It is convenient to calibrate a set of weights a decade at a time, using as a
comparator the most sensitive balance available which will accommodate the
largest weight in the decade. Table 2 shows the set of balances which we use
for nominal values of 1 kg and below, along with their present standard
deviations. Note that we do not calibrate each individual weight in a weight
set against a corresponding NBS standard. This would be inefficient.
Instead, weights, or summations of weights within the decade are intercompared
at several nominal values. The recipe for choosing weights is referred to as a
"design". The designs are chosen so that if one of the weights within the
design has a known mass value, the mass values of the other weights can be
determined. We always pick designs in which we acquire redundant information
and calculate the "least squares" values as the calibration result. The least
squares solution minimizes the sum of squares of deviations of the predicted
minus observed values in much the same way as fitting a series of points on a
graph by the least-squares line minimizes the summation of the distances
squared of the points from the line. (See Appendix A.)

7.2 Uncertainty of Value of Standard Weights

The uncertainties which are assigned to weights which we calibrate result from
uncertainties in our starting standards and uncertainties in the comparison of
the unknown weights with our starting standards. Typically, random
uncertainties dominate the comparison operation. These are usually due to the
balance which is serving as the mass comparator.

The specific design which is used also enters into the assignment of
uncertainty. One can average a set of repeated measurements to find a better
estimated value than from one single measurement. So too, using a weight in
the set in more than one measurement results in a standard deviation of the
value assigned to the weight which is less than that of a single measurement.
How much less depends on the design. Table 3 shows typical calibration
uncertainties based on one commonly used metric weight set and a typical design
for that weight set. Note that large-valued masses are usually in avoirdupois
units (50 lb and above). The avoirdupois pound is defined as 0.45359237
kg.

One complication of using designs to assign mass values is that the
uncertainties assigned to the weights in a set are correlated. This means that
when weights are used in combination, the uncertainty of the combination cannot
be inferred directly from the uncertainties assigned to each weight
individually.

8. Quality Control

In the previous section we noted that the total uncertainty in the assignment
of mass values to unknown weights comes primarily from uncertainties in the
starting standards and random errors in the performance of balances used to

16


NIST Measurement Services:

_ Mass Calibrations
F

NIST
Special
Publication
250-31

RS. Davis

U.S. Department of Commerce
National Institute of Standards and Technology


COMPARY X

Locus, U.S.A.

SET OF MASS STANDARDS : 500
TEST NUMBER DEMO1

BALANCE 2
OPERATOR 39

CALIBRATION DESIGN 41

GRAMS
1 1 1

Al + -

A 2 + -

A 3 +

A 4 + -

A 5 +

A 6 +

R +

OBSERVATIONS IN DIVISIONS

MG - iMG

DOUBLE SUBSTITUTION ONE PAN BALANCE

Al 8.1660 8.2200
A 2 8.1680 8.2030
A 3 8.1690 8.1500
A 4 8.2160 8.2060
AS 8.2200 8.1500
A 6 8.2010 8.1460

13.

13

13

2310

+2160
13.

1650

+2150
13.
13.

1620
1630

Bg

13.
13.
13.
13.
13.
13.

1810
1840
1840
2340
2350
2100

PAGE 7
SERIES 1
8/29/

86


unit of mass, however, there has been no change in the definition for almost
100 years.

The unit of mass in the SI is the kilogram. Its value is defined with
reference to an object known as the International Prototype Kilogram (IPK).
The definition can be simply stated:

"A kilogram is equal to the mass of the International Prototype of the
kilogram."(4]

The IPK is kept and used under the supervision of the International Bureau of
Weights and Measures (BIPM) on land provided by the French government in
Sévres, near Paris.[5]

It is then necessary to establish a practical system of mass measurement based
on the simple definition.

3. Mass Standards in Practice
3.1 Kilograms

The first step is the easiest to achieve. Countries, such as the United
States, possess at least one replica of the IPK. These replicas are made of
the same material as the IPK (an alloy of 90 percent platinum/10 percent
iridium; density 21.5 g/cm), and have the same shape (a cylinder whose height
equals its diameter). The replicas are only within 1 milligram of the IPK but
differences between the replicas and the IPK can still be measured using the
best balances (such balances have the almost incredible precision of 1
microgram in 1 kilogram, or 1x1079), Thus each replica must be compared either
directly or indirectly with the IPK in order to establish its mass. The U.S.
bases its mass measurements on the value of replica no. 20 (sometimes referred
to as K20), which is kept at the National Bureau of Standards in Gaithersburg,
MD. The difference between the mass of the IPK and K20 was determined in 1890
and again in 1948. In 1984 K20 was compared indirectly with the IPK. A
detailed account of these latest measurements and a review of previous
measurements involving the replicas can be found in [6]. The mass of K20 is
thus known to be 1 kg -0.020 mg with an uncertainty of less than 0.010 mg.
Notice that, while the mass of the IPK is 1 kg by definition and thus has no
uncertainty, the mass value assigned to K20 is not exactly equal to its nominal
value and does have a finite uncertainty.

The IPK and its replicas, such as K20, are made of platinum/iridium for a
variety of reasons chief among which is resistance to chemical attack. The
expense of this alloy has precluded and still precludes the widespread use of
platinum/iridium weights. In the first half of this century, brass weights,
usually plated with nickel or rhodium, were the best quality weights
commercially available. More recently, stainless steel has supplanted plated
brass as the material with which the highest quality commercial weights are
fabricated.


established for NBS Classes A, B, M, or S-1 prior to submission[1] J Normally
weights are available from manufacturers, many of whom can furnish directly
documentation suitable for meeting quality assurance contracts and
requirements.

Individual weights or sets of weights in the range of 30 kg to 1 mg or 50 ib to
1 »lb in decimal subdivisions, which are designated as reference standards,
must be of design, material, and surface finish comparable to, but not
necessarily limited to, present NBS Classes A, B, M, S, or S-1.% Design,
material, and surface finish of large mass standards (from 50 to 50,000 1b)
must be compatible with the intended usage. For these large mass standards an
adjustment with reference to a nominal or desired value can be included as a
part of the calibration procedure.

The values of true mass (and an apparent mass correction) included in the
report will be determined by using computed volumes based on the manufacturer's
statement of density of the material, on the density computed from measured
volumes, or in the absence of this information, on estimated density values.
The apparent mass corrections are computed for 20 °C with reference to Normal
Brass (density 8.4 g/cm? at 0 °C, volume coefficient of expansion 0.000054/°C)
and to stainless steel (density 8.0 g/cm? at 20 °C) in an ideal air density of
1.2 mg/cm’. Apparent mass corrections to any other basis can be furnished if
requested,

For periodic recalibrations of reference mass standards, the user need measure
only differences between weights or groups of weights within a set and compare
them with computed differences. As long as the agreement is within allowable
limits, the values can be considered constant within the precision of the
comparison process. Mass standards which are submitted to the Bureau for
recalibration frequently are tested in this manner. If these tests indicate
that no significant changes have occurred, a continuation report so stating and
referring to the previous NBS Report of Calibration will be issued.

2. The International System of Units

Virtually all industrialized countries are signatories to a treaty which
establishes a consistent set of measurement units. The convention which has
been agreed to is called the International System of Units. It is frequently
abbreviated as SI (for Systeme International d’Unites, the treaty having been
written in French). An international committee, which was established through
a provision of the treaty, sees to it that the definitions of units in the SI
change to reflect improvements in measurement technology. In the case of the

JNew weights are more likely to be adjusted to ANSI/ASTM or OIML tolerance
[2,3]. We will accept ASTM Classes 1, 2, and 3 as well as OIML Classes E1, E2,
Fl, and F2. (See ASTM E617.)

2We will also accept ANSI/ASTM Grades S and O as well as OIML classes El,
E2, Fl, or F2.


COMPANY X PAGE 20
LOCUS, U.S.A. SERIES 4
SET OF MASS STANDARDS : 500 MG - 1MG 8/30/ 86
TEST NUMBER DEMO1

BALANCE 13
OPERATOR 39
ACCEPTED WITHIN STANDARD DEVIATION OF THE PROCESS 0.00050 MG
ACCEPTED BETWEEN STANDARD DEVIATION OF THE PROCESS 0.00000 MG

CALIBRATION DESIGN 62

RESTRAINT VECTOR 2 24 1 0 0 o

MASS CORRECTION OF RESTRAINT 0.03457 MG
VOLUME OF WEIGHTS BEING USED IN RESTRAINT AT 22.95 0.00372 CM3
SYSTEMATIC ERROR IN THE RESTRAINT 0.00001 MG

3 STANDARD DEVIATION LIMIT FOR RANDOM ERROR AFFECTING RESTRAINT 0.00054 MG

CHECK STANDARD USED 139

CHECK STANDARD VECTOR o o o o 1 0
ACCEPTED MASS CORRECTION OF CHECK STANDARD -0.00216 MG
REPORT VECTOR 1 2 42 2 0 C)
TEST CONDITIONS BEFORE AFTER AVERAGE
CORRECTED TEMPERATURE IN DEGREES C 22.90 23.00 22.95
CORRECTED PRESSURE IN MM HG 759.527 759.327 759.427
CORRECTED HUMIDITY IN PERCENT 31.60 32.60 32.10
COMPUTED AIR DENSITY IN MG/CM3 1.1884 1.1875 1.1879
TEMPERATURE CORRECTION 0.00 0.00
PRESSURE CORRECTION -0.173 70.173
HUMIDITY CORRECTION 0.00 0.00
OBSERVED TEMPERATURE IN DEGREES C 22.90 23.00
OBSERVED PRESSURE IN MM HG 759.700 759.500
OBSERVED HUMIDITY IN PERCENT 31.60 32.60
WEIGHTS BEING NOMINAL DENSITY COEFFICIENT ACCEPTED
TESTED VALUE G = G/CM3._ AT 20C OF EXPANSION CORRECTION MG
SMG 0.0050 2.7000 000069
3MG 0.0030 2.7000 000069
2MG 0.0020 2.7000 000069
1MG 0.0010 2.7000 000069
T 1MG 0.0010 8.5000 000039 -0.00216
SUM = 1MG 0.0010 2.7000 + 000069

B22


COMPANY X
LOCUS, U.S.A.

SET OF MASS STANDARDS :
TEST NUMBER DEMO1

500 MG - 1MG

POSSESS THE PROPERTIES OF RANDOM-
NESS ASSOCIATED WITH INDEPENDENT

MEASUREMENTS FROM A STABLE
PROBABILITY DISTRIBUTION. THE
REPORTED 'F RATIO‘ AND ‘T VALUE’

ARE TESTS OF THE VALUES FROM THE
CURRENT RUN FOR CONFORMITY 10
THEIR RESPECTIVE DISTRIBUTIONS AND
IF SATISFACTORY ARE TAKEN AS
EVIDENCE THAT THE PROCESS IS IN
CONTROL AND THAT PREDICTIVE
STATEMENTS REGARDING UNCERTAINTY
ARE VALID.

CONTROL CHARTS ON THE WITHIN-
RUN PROCESS PRECISION AND THE
VALUES OBTAINED FOR THE CHECK
STANDARD ARE KEY ELEMENTS IN
MONITORING THE STATE OF CONTROL OF
ANY PRECISE MASS MEASUREMENT
PROCESS. IN ADDITION TO PROVIDING
A BASIS FOR JUDGMENT AS TO THE
ADEQUACY OF A GIVEN PROCESS FOR A
PARTICULAR REQUIREMENT, THESE DATA
PROVIDE A MEANS TO JUDGE THE
IMPORTANCE OF LONG TERM, OR
‘BETWEEN-RUN’ VARIABILITY WHICH
CAN BE CHARACTERIZED BY THE
STANDARD DEVIATION OF THE VALUES
ABOUT THE MEAN. IF THERE IS AN
ADDITIONAL COMPONENT OF VARIANCE
ENTERING FROM RUN TO RUN, THIS
STANDARD DEVIATION WILL BE LARGER
THAN CAN BE ACCOUNTED FOR BY THE
WITHIN-RUN VARIABILITY. | CORRELA-
TION STUDIES, AS WELL AS SUPPLE-
MENTAL EXPERIMENTS, ARE USED 10
DETECT AND REDUCE THE MAGNITUDE OF
SIGNIFICANT SYSTEMATIC EFFECTS.
APPROPRIATE ACTION, E.G., ADDI-
TIONAL EMPIRICAL CORRECTIONS OR
CHANGES IN TECHNIQUE, CAN REDUCE
THE EFFECTS FROM KNOWN SOURCES OF

SYSTEMATIC VARIABILITY TO A
MAGNITUDE WHICH IS NO LONGER
IDENTIFIABLE IN THE DATA. IN THE

CASES WHERE A SIGNIFICANT LONG
TERM, OR BETWEEN-RUN, COMPONENT
REMAINS THE UNCERTAINTY HAS BEEN
APPROPRIATELY ADJUSTED.

PAGE 3

SERIES OF MEASUREMENTS JUDGED
AS OUT OF CONTROL RELATIVE 10 THE
APPROPRIATE PARAMETER ARE CARE-
FULLY EXAMINED, IF RERUNS WERE
NECESSARY IN THE COURSE OF THIS
WORK, THE ‘OUT OF CONTROL’ SERIES,
WITH REMARKS AS APPROPRIATE, ARE
ATTACHED AT THE END OF THE REPORT
FOR YOUR INFORMATION.

UNCERTAINTY

IT IS ASSUMED THAT THE PRESENT
‘ACCEPTED VALUES’ OF TWO NBS STAN-
DARDS AT THE 1 KILOGRAM LEVEL,
DESIGNATED Ni AND N2, ARE WITHOUT
ERROR. ESTIMATES OF THE UNCER-
TAINTY OF THE ACCEPTED VALUES OF
THE NBS STANDARDS RELATIVE TO THE
INTERNATIONAL PROTOTYPE KILOGRAM
CAN BE PROVIDED ON REQUEST.
HOWEVER, THESE ESTIMATES HAVE NO
REAL MEANING IN EITHER NATIONAL OR
INTERNATIONAL COMPARISON. THIS IS
BECAUSE OF THE LACK OF SUFFICIENT
DATA TO PROVIDE A REALISTIC
ESTIMATE OF THE UNCERTAINTY IN THE
VALUES ASSIGNED TO THE PROTOTYPE
KILOGRAMS K20 AND K4, PARTICULARLY
IN REGARD TO LONG TERM, OR
BETWEEN-RUN VARIABILITY. CHANGES
IN THE ACCEPTED VALUES FOR THE NBS
STANDARDS AT THE KILOGRAM LEVEL,
AS AND WHEN THEY OCCUR, WILL BE
REPORTED IN THE SCIENTIFIC PAPERS
OF THE BUREAU AND WILL BE GIVEN
WIDE DISTRIBUTION. IN CASES WHERE
SUCH CHANGES MAY BE OF IMPORTANCE,
OR WHERE CONTINUITY IS DESIRED,
INSTRUCTIONS WILL BE INCLUDED FOR
UP-DATING PREVIOUSLY REPORTED
VALUES. WHEN THE VALUES REPORTED
ARE BASED ON THE ACCEPTED VALUES
OF STANDARDS OTHER THAN STANDARDS
Ni AND N2 MENTIONED ABOVE, THE
UNCERTAINTY OF THE ACCEPTED VALUE
OF THE STANDARD BECOMES A
SYSTEMATIC ERROR IN THE ASSIGNMENT
OF VALUES TO OTHER STANDARDS AND
IS INCLUDED IN THE REPORT.

BS


processes which change Ni and N2 in nearly identical amounts. However, Nl and
N2 are used to calibrate weight sets which often include the decade from 1 kg
to 100 g. Every time weights in this decade are calibrated, the results are
checked with a 100-g check standard. If there were gross changes in N1 and N2
which nevertheless preserved the value of Ni - N2, they would eventually
produce failures of the t-test for the 100-g check standards. The problem,
then, is to devise a system which will check the constancy of the starting
kilogram standards with enough sensitivity to signal a change before its effect
is propagated to other masses.

8.3  Between-Times Components

There is a possibility that the standards we are using and measuring have a
variability which is a function of time. The shortest time of concern to us is
that needed to complete measurements for one design, approximately one hour.

We attribute the variability we see in this time scale to the balance (used as
comparator) and monitor its constancy by the F-test as described above. A much
longer period of interest would be the time between weight calibrations. This
is of the order of months or years. The difference between the short-term
variability and long-term variability of the measurement process is known as
the "between-times" component. We look for the existence of this component by
comparing the long-term and short-term standard deviations associated with the
check-standards. Ideally, the between-times component will be zero. However,
a significant component has been found to exist for calibrations involving the
highest relative precision.

For the cases in which we have detected a non-zero between-times component, we
have propagated its effect through the calibration process by assuming all
weights are subject to the same component as the check standards.

9. Future Plans

There are two major weaknesses in our quality controls at present. The first
is that the relationship between the SI unit of mass and the unit of mass as
embodied by the values assigned to our working kilogram standards N1 and N2 is
not well-enough determined. Second, the use of the difference in mass of N1
and N2 as the check standard at the 1-kilogram level is dangerously insensitive
to effects common to both kilograms. This is especially disturbing since Nl
and N2 are always stored together and receive identical use. A third but less
serious problem is that the alloy of which N1 and N2 are made is closer in
density to brass than to most commonly used stainless steels. This makes the
usual buoyancy corrections more important than they would need to be if the
working standards had a density closer to 8.0 g cmTM

To improve these three areas, we have completed or are near to completing the
following steps:

1. Six new kilograms weights of nominal density 8.0 g cmTM> have been
purchased. Their densities have been determined to 10 parts per million by
hydrostatic weighing.

23


COMPANY X PAGE 8
LOCUS, U.S.A. SERIES 1
SET OF MASS STANDARDS : 500 MG - 1MG 8/29/
TEST NUMBER DEMO1

BALANCE 2
OPERATOR 39

CALIBRATION DESIGN 41

SENSITIVITY WEIGHT

MASS 4.99198 MG
VOLUME 0.00185 CM3 AT 20 C
COEFFICIENT OF EXPANSION 0.000069
S*=S-PV(S)= 4.98978 MG
AVERAGE ODSERVED
ACI) DELTA(I) SENSITIVITY DRIFT(I) SENSITIVITY
(MG) (MG) (MG/DIV) (MG) (MG/DIV)
Al -0.05177 -0.00087 0.99558 0.00199 0.99616
A 2 -0,03335 0.00062 0.99558 0.00149 0.99567
A 3 0.01892 0.00025 0.99558 0.00000 0.99497
A 4 0.01444 -0.00249 0.99558 0.00448 0.99706
AS 0.07118 0.00162 0.99558 0.00149 0.99587
A 5 0.05077 -0.00187 0.99998 = -0.00398 0.99378
VOLUME SYSTEMATIC 3 S.D. | UNCERTAINT’
ITEM CORRECTION (AT T) ERROR LIMIT LIMIT
(6) (MG) ema) (MG) (MG) (MG)
1.0000 -0,06971 11990 0.00087 = 0.00000 0.00087

0
1.0000 -0.01029 0.12707 0.00087 0.00509 0.00596
1.0000 -0.03673 0.11906 0.00087 0.00509 0.00596
1.0000 -0.15925 0.06023 0.00087 0.00509 0.00596

TEMPERATURE T= 22.92 C

RESTRAINT FOR FOLLOWING SERIES

RESTRAINT VECTOR o 60 ° 1

MASS CORRECTION -0,15925 MG
VOLUME AT 20 C 0.06023 CM3
SYSTEMATIC ERROR 0.00087 MG
3 STANDARD DEVIATION LIMIT 0.00509 MG

Bio

86

Y


CHECK STA RD 4 OUTLIER JE: CHK STD =C, STD DEV=S, BOTH =0

~.4752E-01+ +
5407-014 +
= c =
=. 6063E-014. +
= o 20 =
- e23e3 0 20 -
~-6718E-21+ ee 2S ee 8 +
= ee Qeeed 2200 =
- 225923428 -
= 3202333 2 -
=. 73TAE-O14 +
=. 80306-014 +
-620006+02 + 67000E+02 + 72000E402 -77080E+02 -B2000E+02 -87000£+02

seNOTE, 9 POINTS FELL OUTSIDE THE LIMITS
CORRECTIONS TO CHECK STANDARD VS TIME

Figure 5. Control chart for the mass of a 1-g check standard. The
ordinate is the measured correction to nominal (in milligrams)
and the abscissa is the time of the measurement in years since
1900. The check standard is losing mass at the rate of about
0.4 mg/yr. Control limits are not shown.

22


COMPANY X- PAGE 27
LOCUS, U.S.A. 8/30/ 86
SET OF MASS STANDARDS : 500 MG - 1MG
TEST NUMBER DEMO1

TABLE I
MASS UNCERTAINTY VOL AT 20 COEF OF EXP

ITEM (G) (6) «M3 )
500MG 49992233 0,00000300 = 0.03012 0.000020
300MG 29995722 0.00000185 0.01807 0.000020
200MG -19996121 0.00000127 0.01205 0.000020
100MG 10000171 0.00000082 = 0.00602 0.000020
NEW 50MG 04999654 0.00000055 0.00301 0.000020
30MG -03000198 = 0.00000053 0.00181 0.000020
20MG +02001351 — 0.00000044 0.00741 0.000069
10MG +01002325 0.00000055 0.00371 0.000069
SMG -00501768  0.00000045 0.00186 0.000069
amc + 00300600 0.00000048 = 0.00111 0.000003
2MG +00201089  0.00000041 = 0.00074 0.000069
1MG +00100555 = 0.00000054 = 0.00037 0.000068

B29


Contents

Description of Service.

The International System of Units .
Mass Standards in Practice.

3.1 Kilograms.

3.2 Other Denominations.

Density Determination of Single-Piece Kilograms
Using Submersible Balance . see ee ee

4.1 Apparatus.

4.2 Principles of Use.

Cleaning of Weights .

5.1 Categories of Weights.

5.2 Cleaning Procedures.
5.2.1 One-Piece Weights .
5.2.2 Screw-Knob Weights.
5.2.3 Sheet-Metal Weights .

5.3 Temperature Equilibrium.

5.4 Storage.

5.5 Brushes.

Method of Calibrating Dead Weights.

6.1 Measurement Algorithm.

6.2 Uncertainty of Value Assigned to Piston Weights.

Method of Calibrating Standard Weights.

Page

10

Al

11

. 12

. 12

. 12

13

13

13

. 14

~ 14

. 14

. 15

15


5.2.3 Sheet-Metal Weights

First, the weights are placed in an acetone bath agitated to help loosen any
foreign material. A soft brush, such as a camel hair brush, may be used to
agitate the weights. The weights are removed from the acetone, allowed to dry
and then steam cleaned. For steam cleaning, the weights are held in front of a
jet of steam with forceps until the entire surface has been covered with steam.
(See Note on next page.) In order that the portion of the surface under the
forceps may be steamed, the weight is set down and picked up again with the
forceps holding the weight at a different spot than the first time; the weight
is again steamed. The weights are not allowed to touch the steam nozzle. Only
a low ash filter paper is used for drying the sheet metal weights. A circular
disk is folded unsymmetrically. The main body of the weight is placed between
the folds of the paper with the turned edge of the weight protruding. The main
body of the weight is dried by pressing lightly on the top of the paper. The
turned up edge is brushed lightly with a piece of filter paper. In some cases,
it may be necessary to brush the body of the weight with filter paper to remove
drops of water. Care must be exercised that no water spots are left on the
weights as they dry.

Note: The small fractional weights, say smaller than 5 mg, may be placed
in a hot or boiling distilled water bath for the final cleaning
instead of steam cleaning them. A hot or boiling distilled water
bath may also be used for the final cleaning of all sheet metal
weights when a steam generator is not available.

5.3 Temperature Equilibrium

Newly cleaned weights are allowed to come to temperature equilibrium before
they are calibrated. This may take several hours for the larger weights that
have been steam cleaned.

Generally, laboratory weights will come to temperature equilibrium over night.

5.4 Storage

Usually, weights are not placed in the balance immediately after cleaning, but
are stored for varying periods. The weights are stored under cover so that
they will stay clean. Weights 1 gram and larger may be stored on a tray lined
with filter paper and covered with an inverted glass dish. The smaller weights
may be stored in a small glass dish covered with a watch glass. In both cases,
the container is labeled with the weight identification.

When the weights are placed in the balance, they are carefully brushed to
remove any particles that may be on them. A small bulb type rubber syringe is
useful in removing lint and other small particles from weights. The particles
are blown off the weights. Therefore, neither the nozzle nor any other part of
the syringe need touch the weights.

13


COMPANY X

Locus, U.S.A.

SET OF MASS STANDARDS : 500 MG - 1G
TEST NUMBER DEMO1

BALANCE 13
OPERATOR 39

CALIBRATION DESIGN 62

SUM WEIGHTS USED FOR THE LINEAR COMBINATIONS

(MG) MG
50 30 20 10 10 10

1000 + + +

9 + + +

80 + +

7 + +

60 + +

50 + +

40 + +

30 +

20 +

10 +

VALUES AND UNCERTAINTIES FOR COMBINATIONS OF WEIGHTS
(UNCERTAINTY IS 3 STANDARD DEVIATION LIMIT PLUS ALLOWANCE FOR

SYSTEMATIC ERROR. )

SUM CORR = SYSTEMATIC

(MG) (MG) (MG)
100 0.01204 0.00009
90 0.02178 0.00008
80 -0.00147 0.00007
70 0.01006 0.00006
60 0.01980 0.00005
50 0.01550 0.00004
40 0.02523 0.00003
30 0.00198 0.00003
20 0.01351 0.00002
10 0.02325 0.00001

3.S.D.
ERROR
(MG)

00074
00096
00071
00068
-00078
00051
:00077
00050
00042
00054

ee00000000

B20

UNCERTAINTY

eocoeeccon

LIMIT
(MG)

00082
00104
00078
00074
00083
00055
00081
00053
00044
00055

PAGE 18
SERIES 3
8/30/

86


COMPANY ‘X
LOCUS, U.S.A.

SET OF MASS STANDARDS :
TEST NUMBER DEMO1

500 MG - 1MG

SUMMARY

FOR CONVENIENCE, THE RESULTS
OF THIS WORK ARE SUMMARIZED IN
TABLES I AND II. THE VALUES
ASSIGNED ARE WITH REFERENCE TO THE
STANDARDS IDENTIFIED ON THE DATA
SHEETS. THE UNCERTAINTY FIGURE IS
AN EXPRESSION OF THE OVERALL
UNCERTAINTY USING THREE STANDARD
DEVIATIONS AS A LIMIT TO THE
EFFECT OF RANDOM ERRORS OF THE
MEASUREMENT ASSOCIATED WITH THE
MEASUREMENT PROCESSES. THE MAGNI-
TUDE OF SYSTEMATIC ERRORS FROM
SOURCES OTHER THAN THE USE OF
ACCEPTED VALUES FOR _ CERTAIN
STARTING STANDARDS ARE CONSIDERED
NEGLIGIBLE, IT SHOULD BE NOTED
THAT THE MAGNITUDE OF THE UNCER-
TAINTY REFLECTS THE PERFORMANCE OF
THE MEASUREMENT PROCESS USED 10

ESTABLISH THESE VALUES. THE MASS
UNIT, AS REALIZABLE IN ANOTHER
MEASUREMENT PROCESS, WILL BE

UNCERTAIN BY AN AMOUNT WHICH IS A
COMBINATION OF THE UNCERTAINTY OF
THIS PROCESS AND THE PROCESS IN
WHICH THESE STANDARDS ARE USED.

THE ESTIMATED MASS VALUES
LISTED IN TABLE I ARE BASED ON AN
EXPLICIT TREATMENT OF DISPLACEMENT
VOLUMES, E.G., ‘TRUE MASS’, ‘MASS
IN VACUO’, MASS IN THE NEWTONIAN
SENSE. THE DISPLACEMENT VOLUME
ASSOCIATED WITH EACH VALUE IS
LISTED AS WELL AS THE VOLUMETRIC
COEFFICIENT OF EXPANSION. THESE
VALUES SHOULD BE USED, TOGETHER
WITH APPROPRIATE CORRECTION FOR
THE BUOYANT EFFECTS OF THE
ENVIRONMENT, TO ESTABLISH CONSIST-
ENT MASS VALUES FOR OBJECTS WHICE
DIFFER SIGNIFICANTLY IN DENSITY
AND/OR FOR MEASUREMENTS WHICH MUST
BE MADE IN DIFFERING ENVIRONMENTS.
THE RELATION 1LB AVDP=.45359237KG
IS USED AS REQUIRED.

PAGE 25
8/30/

THE ESTIMATED MASS VALUES
LISTED IN TABLE II ARE BASED ON AN
IMPLICIT TREATMENT OF DISPLACEMENT

VOLUMES, E.G., ‘APPARENT MASS’,
‘APPARENT MASS VERSUS BRASS’,
‘APPARENT MASS VERSUS DENSITY
8.0’. THE VALUES ARE LISTED AS

CORRECTIONS TO BE APPLIED TO THE
LISTED NOMINAL VALUE (A POSITIVE
CORRECTION INDICATES THAT THE MASS
IS LARGER THAN THE STATED NOMINAL
VALUE BY THE AMOUNT OF THE
CORRECTION). THESE VALUES ARE
COMPUTED FROM THE VALUES BASED ON
AN EXPLICIT TREATMENT OF DISPLACE-
MENT VOLUMES USING THE FOLLOWING
DEFINING RELATIONS AND ARE
UNCERTAIN BY THE AMOUNT SHOWN IN
TABLE I.

THE ADJUSTMENT OF WEIGHTS TO
MINIMIZE THE DEVIATION FROM NOMI-
NAL ON THE BASIS OF ‘NORMAL BRASS’
(IN ACCORDANCE WITH COR. A BELOW)
IS WIDESPREAD IN THIS COUNTRY AND
IN MANY PARTS OF THE WORLD.
VALUES STATED ON EITHER BASIS ARE
INTERNALLY CONSISTENT AND
DEFINITE. THERE IS, HOWEVER, A
SYSTEMATIC DIFFERENCE BETWEEN THE
VALUES ASSIGNED ON EACH BASIS, THE
VALUE ON THE BASIS OF ‘DENSITY
8.0’ BEING 7 MICROGRAMS/GRAM LAR-
GER THAN THE VALUE ON THE BASIS OF
NORMAL BRASS. THIS SYSTEMATIC
DIFFERENCE IS CLEARLY DETECTABLE
ON MANY DIRECT READING BALANCES.

CORRECTION A - ‘APPARENT MASS
VERSUS BRASS’ OR ‘WEIGHT IN AIR
AGAINST BRASS’ IS DETERMINED BY A
HYPOTHETICAL WEIGHING OF THE
WEIGHT AT 20 CELSIUS IN AIR HAVING
A DENSITY OF 1.2 MG/CM3, WITH A
(NORMAL BRASS) STANDARD HAVING A
DENSITY OF 8.4 G/CM3 AT 0 CELSIUS
WHOSE COEFFICIENT OF VOLUMETRIC
EXPANSION TS 0.000 054 PER DEGREE
CELSIUS, AND WHOSE VALUE IS BASED

B27


Further, the desirability of a design depends somewhat on the restraint being
used. In some cases, one’s judgment of a design changes depending on whether
one starts with a summation as known (e.g., 5 + 3 + 2) and works down, or with
a unit as known and works up (e.g., by use of a 1, 2, 3, 5 series).

AS


Appendix B

Sample Calibration Report

The following is a full calibration report for a set of weights with
denominations from 1 g to 1 mg.

Bl


COMPANY X PAGE 14
LOCUS, U.S.A. SERIES 2
SET OF MASS STANDARDS : 500 MG - 1MG 8/29/86
TEST NUMBER DEMO1

BALANCE 13
OPERATOR 39
MAXIMUM LOAD 0.6000 G
STARTING RESTRAINT NUMBER 4

CALIBRATION DESIGN 62

PRECISION CONTROL

OBSERVED STANDARD DEVIATION OF THE PROCESS 0.00069 MG
ACCEPTED STANDARD DEVIATION OF THE PROCESS 0.00050 MG
DEGREES OF FREEDOM 6

F RATIO 1.584

F RATIO IS LESS THAN 2.81 (CRITICAL VALUE FOR PROBABILITY = .01).
THEREFORE THE STANDARD DEVIATION IS IN CONTROL.

CHECK STANDARD VECTOR o o o 0 1 0

CHECK STANDARD USED 12

ACCEPTED MASS CORRECTION OF CHECK STANDARD -0.00854 MG
OBSERVED CORRECTION OF CHECK STANDARD -0.00862 MG

STANDARD DEVIATION OF THE’OBSERVED CORRECTION 0.00025 MG
T VALUE -0.34

ABSOLUTE VALUE OF T IS LESS THAN 3.
THEREFORE CHECK STANDARD IS IN CONTROL.

TEST CONDITIONS BEFORE AFTER AVERAGE
CORRECTED TEMPERATURE IN DEGREES C 23.25 23.30 23.28
CORRECTED PRESSURE IN MM HG 758.828 758.429 758.629
CORRECTED HUMIDITY IN PERCENT 27.30 24.10 25.70
COMPUTED AIR DENSITY IN MG/CM3 1.1863 1.1859 1.1861
TEMPERATURE CORRECTION 0.00 0.00

PRESSURE CORRECTION “0.172 -O.471

HUMIDITY CORRECTION 0.00 0.00

OBSERVED TEMPERATURE IN DEGREES C 23.25 23.30

OBSERVED PRESSURE IN MM HG 759,000 758.600

OBSERVED HUMIDITY IN PERCENT 27.30 24,10

B16


intercompare the unknowns with the standards. To control the quality of this
measurement system, we must insure that the mass of the starting standards does
not change and that the random error of the balances used has not deteriorated
from its accepted value. In addition, we must have a way to detect simple
blunders in data entry. We now describe the controls which are presently in
place [14] and outline improvements which are underway.

8.1 F-Test [7,13]

Every calibration includes a means of checking the balance performance. We
assume we know the balance performance based on a large accumulation of data
over a long period of time. Each new calibration provides us with another set
of data which can be compared with those previously collected. We check to see
whether the scatter in the most recent set of data is statistically consistent
with the accepted long-term standard deviation of the balance. Failure of this
test indicates either a blunder or a sudden degradation of the balance.

Figure 3 shows a control chart of the long-term standard deviation of a
kilogram balance used in the calibration service. Control limits vary
depending on the number of statistical degrees of freedom in a given design.
Similar charts are maintained for all the balances used.

8.2 t-Test [7,13]

Every calibration includes at least two standards along with the unknowns. One
standard is used to calibrate both the unknowns and the second standard, which
is well-known from many previous measurements. The second standard is called
the "check standard" for the following reason: As a result of a calibration,
the reference standard is used to assign mass values to the unknowns and the
check standard. This mass value of the check standard is then compared to the
long-term average of the check standard. A statistically significant
difference in the two values indicates a change in the standard, a change in
the check standard, or a blunder. Figure 4 is a control chart which shows the
long-term variability of the difference in measured mass of our two working
kilogram standards. Control charts are also maintained to look for unsuspected
variability as a function of ambient temperature, barometric pressure, relative
humidity, and air density.

Similar control charts are maintained for all the check standards in use.
Occasionally, a check-standard will show a significant change (usually a loss)
in mass with time. An example of such behavior is shown in figure 5. The
control limits in this case change slowly with time, and are not shown.

Check standards are included in every weighing design. This offers an
additional advantage which is best illustrated by an example. Routine
calibrations of mass at the 1-kg level begin with starting standards N1 and N2.
We actually use the total mass of N1 and N2 as the starting standard and use
the difference in mass between Nl and N2 as the check standard. This is a
mathematical convenience but is conceptually no different from using Nl as the
standard and N2 as the check. While the check standard is adequate for
detecting catastrophic changes in Nl or N2, it is obviously insensitive to any

19


86

COMPANY X PAGE 17
LOCUS, U.S.A. SERIES 3
SET OF MASS STANDARDS : 500 MG - 1MG 8/30/
TEST NUMBER DEMO1
BALANCE 13
OPERATOR 39
CALIBRATION DESIGN 62
SENSITIVITY WEIGHT
MASS 10.00000 MG
VOLUME 0.00000 CM3 AT 20 C
COEFFICIENT OF EXPANSION 0.000000
S*=S-PV(S)= 10.00000 MG
ACCEPTED SENSITIVITY = 0.00100 MG/DIV
OBSERVED SENSITIVITY = 0.00100 MG/DIV
I-TEST = 0,000
OBSERVED
ACI) DELTA(I) SENSITIVITY
(MG) (MG) (MG/DIV)
Al 0.00910 0.00003 0.00100
A 2 -0.04320 0.00032
A 3 -0.00010 0.00016
A 4 -0.01140 0.00017
AS -0.05960 -0.00068
A 6 -0.01380 0.00058
AT -0.05570 -0.00005
a8 0.00840 0.00015
ag -0,01180 0.00054
A 10 -0.04380 0.00049
All -0.02400 -0.00035 0.00100
VOLUME SYSTEMATIC 3S.D. UNCERTAINTY
ITEM CORRECTION (AT T) ERROR LIMIT LIMIT
(6) (Mg) (M3) (MG) (MG) (MG)
0.0500 -0.00346 0.00301 0.00004 0.00051 0.00055
0.0300 0.00198 0.00181 0.00003 0.00050 0.00053
0.0200 0.01351 0.00741 0.00002 0.00042 0.00044
0.0100 0.02325 0.00371 0.00001 0.00054 0.00055
0.0100 -0.00039 0.00119 0.00001 0.00054 0.00055
0.0100 0.03457 0.00372 0.00001 0.00054 0.00055
TEMPERATURE T= 23.00 C
RESTRAINT FOR FOLLOWING SERIES
RESTRAINT VECTOR ° o © o 1
MASS CORRECTION 0.03457 MG
VOLUME AT 20 C 0.00372 CM3
SYSTEMATIC ERROR 0.00001 MG
3 STANDARD DEVIATION LIMIT 0.00054 MG

B19


COMPANY X PAGE 26
LOCUS, U.S.A. 8/30/ 86
SET OF MASS STANDARDS : 500 MG - 1MG
TEST NUMBER S

ON ITS TRUE MASS OR WEIGHT IN WEIGHT, IN AIR HAVING A DENSITY OF

VACUO, 1.2 MG/CM3, WITH A STANDARD HAVING

A DENSITY OF 8.0 G/CM3 AT 20

CORRECTION B - ‘APPARENT MASS CELSIUS, AND WHOSE VALUE IS BASED

VERSUS DENSITY 8.0’ IS DETERMINED ON ITS TRUE MASS OR WEIGHT IN
BY A HYPOTHETICAL WEIGHING OF THE VACUO.

B28


Library of Congress Catalog Card Number: 88-600608

National Institute of Standards and Technology Special Publication 250-31
Natl. Inst. Stand. Technol., Spec. Publ. 250-31, 72 pages (Jan. 1989)
CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE
WASHINGTON: 1989

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325


COMPANY X PAGE 6
LOCUS, U.S.A. SERIES 1
SET OF MASS STANDARDS : 500 MG - 1MG 8/29/86
TEST NUMBER DEMO1

BALANCE 2

OPERATOR 39

ACCEPTED WITHIN STANDARD DEVIATION OF THE PROCESS 0.00240 MG
ACCEPTED BETWEEN STANDARD DEVIATION OF THE PROCESS 0.00000 MG

CALIBRATION DESIGN 41

RESTRAINT VECTOR 1 0 0 0

MASS CORRECTION OF RESTRAINT -0.06971 MG
VOLUME OF WEIGHTS BEING USED IN RESTRAINT AT 22.92 0.11990 CM3
SYSTEMATIC ERROR IN THE RESTRAINT 0.00087 MG

3 STANDARD DEVIATION LIMIT FOR RANDOM ERROR AFFECTING RESTRAINT 0.00000 MG

CHECK STANDARD USED 10
CHECK STANDARD VECTOR 0) 1 0 Cy)

ACCEPTED MASS CORRECTION OF CHECK STANDARD -0.00740 MG
REPORT VECTOR o 0 o 0
TEST CONDITIONS BEFORE AFTER AVERAGE
CORREGIED TEMPERATURE IN DEGREES C 22.65 23.00 22.92
CORRECTED PRESSURE IN MM HG 759.028 758.828 758.928
CORRECTED HUMIDITY IN PERCENT 27.50 27.30 27.40
COMPUTED AIR DENSITY IN MG/CM3 1.1883 1.1874 1.18679
TEMPERATURE CORRECTION 0.00 0.00
PRESSURE CORRECTION -0.172 -0.172
HUMIDITY CORRECTION 0.00 0.00
OBSERVED TEMPERATURE IN DEGREES C 22.85 23.00
OBSERVED PRESSURE IN MM HG 759.200 759.000
OBSERVED HUMIDITY IN PERCENT 27.50 27.30
WEIGHTS BEING NOMINAL DENSITY COEFFICIENT ACCEPTED
TESTED VALUE G = G/CM3_ AT 20C OF EXPANSION CORRECTION MG
NB 16 1.0000 8.3406 000040 -0.06971
AA 1G 1.0000 7.8704 000045 -0,00740
16 1.0000 8.4000 -000054
suM 1G 1.0000 16.6000 000020

B8


COMPANY X

LOCUS, U.S.A.

SET OF MASS STANDARDS :
TEST NUMBER DEMO1

500 MG - 1MG

‘A BALANCE UNDER STABLE OPERA-
TING CONDITIONS WILL EXHIBIT A
CERTAIN CHARACTERISTIC VARIABILITY
WHICH CAN BE DESCRIBED BY THE
STANDARD DEVIATION FOR SUCH
MEASUREMENTS. THE VALUE FOR A
PARTICULAR WEIGHT DETERMINED IN
REPEATED TESTS WITH THE SAME
WEIGHING DESIGN WILL HAVE ITS OWN
STANDARD DEVIATION WHICH WILL BE

SOME FUNCTION OF THE BALANCE
PRECISION AND (POSSIBLY) OF THE
BETWEEN-RUN COMPONENT. AS AN

OUTER LIMIT OF IHE DISTRIBUTION OF
RANDOM ERRORS, THREE TIMES THE
STANDARD DEVIATION IS USED.
SYSTEMATIC ERRORS DUE TO THE
PROCEDURES USED OR TO ENVIRON-
MENTAL EFFECTS ARE _ LARGELY
BALANCED OUT AND CAN USUALLY BE
REGARDED AS NEGLIGIBLE. WHEN A
NON-NEGLIGIBLE BOUND 10 THE
POSSIBLE EFFECT FROM KNOWN SOURCES
IS AVAILABLE, IT IS CALCULATED AND
REPORTED SEPARATELY, E.G., THE
UNCERTAINTY OF ACCEPTED VALUE AT
OTHER THAN THE 1 KILOGRAM LEVEL.
THE DISTRIBUTION IMPLIED BY THE
RANDOM ERRORS MAY THUS BE CENTERED
SOMEWHERE IN THE RANGE GIVEN BY
THE BOUNDS TO THE SYSTEMATIC
ERROR. THE TOTAL UNCERTAINTY IS
TAKEN AS THE SUM OF THESE TWO
COMPONENTS .

THE UNCERTAINTY ASSOCIATED
WITH THE ASSIGNED VALUE CAN BE
THOUGHT OF AS A BOUND TO THE
DEPARTURE OF THE ASSIGNED VALUE
FROM A HYPOTHETICAL AVERAGE VALUE
THAT WOULD BE OBTAINED IF IT WERE
POSSIBLE TO REPEAT THE MEASUREMENT
MANY TIMES OVER A WIDE VARIETY OF
CONDITIONS, E.G., SUBSTITUTE THE
WEIGHT FOR ONE OF THE CHECK
STANDARDS. THIS MEANS THAT THE
UNCERTAINTY BAND CENTERED ON THE
VALUES OBTAINED FROM EACH OF TWO
MEASUREMENTS OF THE SAME OBJECT
OVER SOME ARBITRARY TIME INTERVAL

PAGE 4

SHOULD ALMOST ALWAYS OVERLAP. IN
OTHER WORDS, WHILE A SECOND MEA-
SUREMENT WILL PRODUCE A DIFFERENT
VALUE, THIS VALUE WILL ONLY RARELY
DIFFER FROM THE FIRST VALUE BY
MORE THAN THE SUM OF THE TWO
UNCERTAINTIES. THE UNCERTAINTY
BANDS ARE NOT EXPECTED TO OVERLAP
IF SOME EVENT HAS OCCURRED IN THE
TIME INTERVAL BETWEEN THE TWO MEA-
SUREMENTS WHICH WILL CHANGE THE
MASS OF THE OBJECT, E.G., ABRA-
SIONS, ABUSE, CORROSION, IMPROPER
CLEANING AND THE LIKE.

THE UNCERTAINTY IN ASSIGNED
VALUE CONTAINED IN THIS REPORT
BECOMES A SYSTEMATIC EFFECT FOR
THE MEASUREMENT PROCESS IN WHICH
THESE WEIGHTS ARE TO BE USED. 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 ARE
ASSIGNED, THE VALUES PRODUCED BY
DIFFERENT MEASUREMENT FACILITIES
WILL HAVE OVERLAPPING UNCERTAINTY

BANDS AS DESCRIBED ABOVE. ONE
CANNOT DISCUSS DIFFERENCES IN
VALUES FOR THE SAME OBJECT

OBTAINED BY DIFFERENT FACILITIES
WITH ANY DEGREE OF SERIOUSNESS UN-
LESS EACH VALUE IS ACCOMPANIED BY
A REALISTIC UNCERTAINTY STATEMENT.

B6


Appendix C
Surveillance Test

The following is the report of a surveillance test [7]. Subscquent to a
calibration such as that shown in Appendix B, weights may be resubmitted
for periodic surveillance. Surveillance is a more rapid and less costly
procedure than calibration. The surveillance test can provide assurance
that the values of mass previously assigned to a set of weights are still

valid.

C1


The two conventions in widest use are: density 8.0 g/cm? at 20 °C in air of
density 1.2 g/cm; and density 8.39094 g/cm? at 20 °C in air of density 1.2

g/em> [7].

Mass in SI units is truly mass (or "vacuum" mass or "true" mass). When the
National Bureau of Standards (NBS) calibrates a stainless steel kilogram in
terms of its Pt/Ir national standard, a correction of order 0.1 grams must be
made to the raw data. This correction is large compared to the precision of
the mass comparison. Making the correction requires a great deal of effort.
Even doing the best one can, this buoyancy correction can be the major
contributor to the uncertainty in the calibration of the stainless steel
kilogram. If the steel kilogram is then used to calibrate other steel or brass
kilograms, the buoyancy corrections will be small and relatively easy to apply.
The use of stainless steel or other nickel-chrome alloys as "working standards"
also means that K20 can be used very infrequently, thereby minimizing wear and
the chance of accident.

The strategy of NBS was to put great effort into the calibration of two
standards, N1 and N2, having a density of 8.35 g/cm’. These two weights, made
of a nickel-chrome alloy, are then used to calibrate other weights of similar
density on a more routine basis. At the present time, errors in assigning
calibration value of N1 and N2 with respect to the IPK are not included in
error budgets. This practice is now in the process of being revised.

At the time N1 and N2 were fabricated, the majority of high-quality weights
were made of plated brass; hence the choice of alloy density. Now virtually
all high-quality weights are made of stainless steel. For this reason, NBS is
in the midst of changing its working standards from N1 and.N2 to standards of
stainless steel density of 8.0 g/cm’. This will be a relatively slow process
because the long-term stability of the new standards must first be established.
In addition, the tie to the SI unit is being carefully established so that a
meaningful uncertainty can be assigned.

3.2 Other Denominations

So far, we have described how the SI mass unit is transferred from the Pt/Ir
prototype in Sévres to a nickel-chrome or stainless steel working standard at
NBS. Obviously, it is essential to calibrate weights at other nominal values
above and below 1 kg.

The concept of .how this is accomplished is simple. Once one has a weight which
embodies an SI mass value, it is only necessary to find the ratio of the mass
of the known weight to the mass of the unknown weight. Since a ratio is
dimensionless, these measurements can, in principle, be accomplished by any
laboratory with sufficiently sensitive balances. For instance, if we have a
kilogram weight calibrated in SI units and we need to know the mass value of a
500-g weight, the following simple approach might be taken: The known 1-kg
weight could be used to calibrate a digital electronic balance of 1 kilogram
capacity. The unknown 500-g weight could then be placed on the balance and its
mass value read directly. (It would also be wise to check the balance
linearity and make the necessary corrections for air buoyancy.) Such

6


COMPANY X PAGE 16
LOCUS, U.S.A. SERIES 3
SET OF MASS STANDARDS : 500 MG - 1MG 8/30/ 86
TEST NUMBER DEMO1

BALANCE 13
OPERATOR 39

CALIBRATION DESIGN 62

MG

50 30 20 10 10 10
Al + - - + -
A 2 + - - + -
A 3 + - - - +
A 4 + - -
a5 + - - -
A 6 + - + - -
a7 + - - + -
A 8 + - - - +
A 9 + - 7
A 10 + - -
Alt + - -
R + + +

OBSERVATIONS IN DIVISIONS
DIRECT READING

9.1000 10009.1006
-43.2000
-0,1000
11.4000
-59.6000
-13.8000
-55.7000
8.4000
11.8000
43,8000
“24,0000 — 9976.0000

ee

He
EP Swoavaurene

B18


COMPANY X PAGE 22
LOCUS, U.S.A. SERIES 4
SET OF MASS STANDARDS : 500 MG - 1MG 8/30/ 86
TEST NUMBER DEMO1
BALANCE 13
OPERATOR 39
CALIBRATION DESIGN 62
SENSITIVITY WEIGHT
MASS 10.00000 MG
VOLUME 0.00000 CM3 AT 20 C
COEFFICIENT OF EXPANSION 0.000000

S*=S-PV(S)= 10.00000 MG

ACCEPTED SENSITIVITY = 0.00100 MG/DIV
OBSERVED SENSITIVITY = 0.00100 MG/DIV
T-TEST = 0.000

OBSERVED
ACI) DELTA(I) SENSITIVITY
(MG) (MG) (MG /DIV)

Al 0.00840 -0.00028 0.on100
A 2 0.00240 0.00039
A 3 -0.00880 -0.00046
A 4 0.00110 0.00032
AS 0.00720 0.00003
A 6 0.00600 -0.00059
A 7 -0.00910 0.00011
A 8 -0.01120 0.00046
ag 0.00760 -0.00009
A 10 0.00800 -0,00092
Alt 0.01780 0.00098 0.00100

VOLUME SYSTEMATIC 3 S.D. UNCERTAINTY
ITEM CORRECTION (AT T) ERROR LIMIT LIMIT
(6) (MG) cM3 ) (MG) (MG) (MG)
0.0050 0.01768 0.00186 0.00000 0.00044 0.00045
0.0030 0.00600 0.00111 0.00000 0.00048 0.00048
0.0020 0.01089 0.00074 0.00000 0.00041 0.00041
0.0010 0.00555 0.00037 0.00000 = 0.00054 0.00054
0.0010 -0.00265 0.00012 0.00000 0.00054 0.00054
0.0010 -0.00358 0.00037 0.00000 =o. nn054 0.00054

TEMPERATURE T= 22.95 C

B24


4.1 Apparatus

The balance modified for this work is a Mettler PL1200,3 the important
specifications of which are:

weighing range 0 - 1200 g
reproducibility <0.005 g
linearity <0.01 g

Significant mechanical and electronic modifications were introduced to the
balance and its enclosure. Specifically, the weighing cell of the balance was
separated from the supporting electronics and placed beneath the surface of an
inert liquid (see fig. 2).

Clearly, the fluid in which an electronic measuring cell is immersed must have
many special properties: it must be electrically insulating, it must be
chemically inert, it must be optically transparent (in order for the servo
optics to function properly), and it should not evaporate quickly. These
characteristics may be found, for example, in FC-75, a fluorinated fluid
manufactured by the 3M Company. A comparison of some of the properties of
FC-75 with those of water is given in table 1. An additionally noteworthy
property of FC-75 is its immense appetite for gases. For example, the fluid is
able to dissolve about 0.3 g of air per kilogram of fluid. This ability to
dissolve atmospheric gases, greatly inhibits bubble formation on immersed
objects--one of the most serious problems in conventional high-precision
hydrostatic weighing. Finally, the fluid is 77 percent more dense than water
at room temperature thereby increasing the signal to noise in comparison to a
normal hydrostatic weighing. The major disadvantages of this fluid as compared
to water are its large coefficient of thermal expansion and its cost. However,
use of FC-75 instead of water for conventional "hydrostatic" weighing has many
advantages.[10] The density of FC-75 is usually not known accurately enough
for the liquid to serve as a density standard. Instead, the fluid density is
calibrated at the time of use by including a solid object of known mass and
volume in the weighing scheme.

3 Certain trade names and company products are identified in order to
adequately specify the experimental procedure. In no case does such
identification imply recommendation or endorsement by the National Bureau of
Standards nor does it imply that the products are necessarily the best
available for the purpose.


NIST MEASUREMENT SERVICES:

Mass Calibrations

R. S. Davis

Precision Engineering Division

Center for Manufacturing Engineering

National Engineering Laboratory

National Institute of Standards and Technology
Gaithersburg, MD 20899

January 1989

NOTE: As of 23 August 1988, the National Bureau of
Standards (NBS) became the National Institute of
Standards and Technology (NIST) when President
Reagan signed into law the Omnibus Trade and
Competitiveness Act.

U.S. DEPARTMENT OF COMMERCE, C. William Verity, Secretary
Ernest Ambler, Acting Undersecretary for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY,

(formerly National Bureau of Standards)

Raymond G. Kammer, Acting Director


1
—_— ; 2
s = 71 z (deviations); (9)

3
'
com

(deviation) ; =Y 7 Oy By + X29 woe X51 A)

One can write these deviations ag a function of the observations by noting that
the predicted values are just Xf and the deviations are thus

dev = y - x8 = y - xtcx’,h) (8) = y - xcx’,o) (10)
= [1-KeX' ]y
which can be written as
dev= ay + 41 Yo se an (11)
dev = 4%4 * 92% se San

The array of coefficients, dj;, is given in Appendix B for some of the designs.
Weights are often used in combination and one needs to kngw the gtandard
deviation for the various sums. For a sum of two items, Aj and Bj, one has

Var (By + Bs) = var (A4) + var (B3) = 2Cov(Bi, Bs)
and for a linear combination
L= £461 + 2082... fab (12)
Variance (L) = 2'CRo2

where 2’ = (2; . . . 2%), C comes from the inverse of the matrix of normal
equations [see eq (6)].

DESIGNS FOR WEIGHING

The criteria for good weighing designs depend to some extent on the use
intended for the resulting values. For example, if the weights are to be used
independently of each other, then one would want the standard deviation [o Cjy
from formula (8)] for the value for each unknown weight to be the minimum
possible. If the weights are to be used in combination, then one wants the
variance of all appropriate linear functions to be as small as possible.

AG


Table 2.

Capacities and standard deviations of balances used

Balance Gapacit

3

20
40
160
1

10
30

1

6

50
2500
30000

&

kg

lb

17

SONUSD0MNDODOOCO

Standard Deviation

-0005 mg

0024
0039

.014
032
5 mg

2

031 lb
-46

5 omg
.002 lb
.017 1b


Center for Manufacturing Engineering

The Center for Manufacturing Engineering provides competence and develops technical data, findings, and
standards in manufacturing engineering, mechanical metrology, automation, robotics, control technology, and
precision mechanical engineering to support the discrete parts manufacturing industries; the Center also
controls/maintains the Automated Manufacturing Research Facility (AMRF) and consists of five Divisions.

Precision Engineering Division

Develops/maintains competence in metrology for length, mass, and angle, optics, machine-too! metrology, preci-
sion machining, and nanotechnology; incorporates metrology into precision manufacturing, including lithography
and metal working processes as well as the standards necessary for integration of equipment up to the manu-
facturing cell level.

Robot Systems Division

Develops/maintains competence in robotics, real-time sensory-interactive control technology, robot languages/
standards, and interface standards for computer-integrated manufacturing systems; conducts research into new
techniques of sensing and control, sensory data processing and communications, world models, robot program-
ming languages, interactive graphics for programming, and intelligent real-time control for industrial, military,
space and construction applications; develops experimental robot applications; performs technical activities
relating to standards for robots and computer-integrated manufacturing systems; performs research in robot
safety, robot assembly of parts, tools, and fixtures, and applications of intelligent control to military and industrial
systems.

Factory Automation Systems Division

Develops/maintains competence in computer science/software engineering, industrial engineering, control
systems engineering, and mechanical engineering including research into new techniques of intelligent machine
processes and machine-readable product data that merge technologies of artificial intelligence, information
systems, metrology, and industrial processes; performs technical analyses for feasibility of interface standards
and product data specifications for manufacturing systems; interfaces manufacturing data preparation systems
such as computer-aided design, process planning, and off-line equipment programming with the manufacturing
control systems; performs research/development on interfaces necessary to manage factory communication
network protocols and database management systems in a manufacturing environment; develops techniques for
the computer-assisted and automated generation of control code required for executing processes involved in
discrete-parts manufacturing industries.

Automated Production Technology Division

Develops/maintains competence in integration of machine tools and robots up to manufacturing cell level;
develops interfaces/networks necessary to combine robots and machines into workstations and workstations
into manufacturing celis; develops/maintains computer-assisted techniques for generation of computer code for
integration of machine tools and robots; maintains competence in engineering measurements and sensors, both
static and dynamic, of force and force related quantities, and other parameters required by discrete-parts
industry; conducts research on nature of the measurement process and transducers and the development,
characterization, and calibration of transducers used in discrete-parts manufacturing.

Fabrication Technology Division

Designs, fabricates, repairs, and modifies precision apparatus, instrumentation, components thereof, and speci-
mens necessary to the experimental research and development work of NIST; develops/maintains competence
in CAD/CAM, automated process planning, and shop management systems.



COMPANY X PAGE 9
LOCUS, U.S.A. SERIES 1
SET OF MASS STANDARDS : 500 MG - 1MG 8/29/86
TEST NUMBER DEMO1

BALANCE 2
OPERATOR 39
MAXIMUM LOAD 1.0000 G

STARTING RESTRAINT NUMBER 4

CALIBRATION DESIGN 41

PRECISION CONTROL

OBSERVED STANDARD DEVIATION OF THE PROCESS 0.00212 MG
ACCEPTED STANDARD DEVIATION OF THE PROCESS 0.00240 MG
DEGREES OF FREEDOM = 3.

F RATIO 0.782

F RATIO IS LESS THAN 3.79 (CRITICAL VALUE FOR PROBABILITY = .01).
THEREFORE THE STANDARD DEVIATION IS IN CONTROL.

CHECK STANDARD VECTOR 0 1 0 0

CHECK STANDARD USED 10

ACCEPTED MASS CORRECTION OF CHECK STANDARD -0.00740 MG
OBSERVED CORRECTION OF CHECK STANDARD -0.01029 MG

STANDARD DEVIATION OF THE OBSERVED CORRECTION 0.00170 MG
T VALUE -1.70

ABSOLUTE VALUE OF T IS LESS THAN 3.
THEREFORE CHECK STANDARD IS IN CONTROL.

TEST CONDITIONS BEFORE AFTER AVERAGE
CORRECTED TEMPERATURE IN DEGREES C 22.85 23.00 22.92
CORRECTED PRESSURE IN MM EG 759.028 758.828 758.928
CORRECTED HUMIDITY IN PERCENT 27.50 27.30 27.40
COMPUTED AIR DENSITY IN MG/CM3 1.1883 1.1874 1.1879
TEMPERATURE CORRECTION 0.00 0.00

PRESSURE CORRECTION -0.172 -0.172

HUMIDITY CORRECTION 0.00 0.00

OBSERVED TEMPERATURE IN DEGREES C 22.85 23.00

OBSERVED PRESSURE IN MM HG 759.200 759.000

OBSERVED HUMIDITY IN PERCENT 27.50 27.30

Bll


10. References

[1] Lashof, T. W. and Macurdy, L. B., Precision Laboratory Standards of
Mass and Laboratory Weights. NBS Circular 547, Section 1 (1954
August). Reprinted as NBSIR 78-1476 (1978 October).

[2] ASTM E617-81 Standard Specification for Laboratory Weights and
Precision Mass Standards, 1986 Annual Book of ASTM Standards, Vol.
14.02: 480-499.

[3] International Organization for Legal Metrology, OIML Recommendation
20.

[4] Goldman, D. T. and Bell, R. J., eds., The International System of
Units (SI): NBS Spec. Publ. 330 (1986 July).

[5] Page, C. H. and Vigoureux, P., eds., The International Bureau of
Weights and Measures 1875 - 1975: NBS Spec. Publ. 420 (1975 May).

[6] Davis, R. S., Recalibration of the U.S. National Prototype
Kilogram, J. Res. NBS 90 (4), July-August 1985: 263-283.

[7] Jaeger, K. B. and Davis, R. S., A Primer for Mass Metrology, NBS
Spec. Publ. 700-1 (1984 November).

[8] Cameron, J. M., Croarkin, M. C., and Raybold, R. C., Designs for
the Calibration of Standards of Mass, NBS Tech. Note 952, (1977
June).

[9] Schoonover, R. M. and Davis, R. S., Quick and Accurate Density
Determination of Laboratory Weights, Proc. 8th Conf. IMEKO
Technical Committee TC3, Krakow Poland, September 9-11, 1980.

[10] Bowman, H. A., Schoonover, R. M. and Carroll, C. L., A Density Scale
Based on Solid Objects, J. Res. NBS 78A (1), January-February 1974:
13-40.

[11] Almer, H. E., Weight Cleaning Procedures, NBSIR 74-443 (1973 November).

[12] Almer, H. E,, Method of Calibrating Weights for Piston Gages, NBS Tech.
Note 577 (1971 May).

[13] Croarkin, M. C., Measurement Assurance Programs Part II: Development and
Implementation, NBS Spec. Publ. 676 II; 1984.

{14] Varner, R. N. and Raybold, R. C., National Bureau of Standards Mass
Calibration Computer Software, NBS Tech. Note 1127 (1980 July).

25


COMPANY X

LOCUS, U.S.A.

SET OF MASS STANDARDS :
TEST NUMBER DEMO1

500 MG - 1MG

WEIGHING DESIGN

ONLY DIFFERENCES IN MASS CAN
BE MEASURED, THEREFORE THE MASS
VALUES FOR THE ‘UNKNOWN’ WEIGHTS
MUST BE DETERMINED BY COMPARISON

WITH OTHER WEIGHTS WHICH HAVE
ACCEPTED MASS VALUES. THE
‘UNKNOWN’ WEIGHTS TOGETHER WITH

‘CHECK STANDARDS’, ARE GROUPED AND
INTERCOMPARED ACCORDING TO THE
DESIGN SCHEDULE GIVEN AT THE BE-
GINNING OF EACH SERIES OF WEIGH-
INGS. THE FIRST SERIES CONTAINS
STANDARDS WHICH PROVIDE THE
STARTING VALUES FOR THE SERIES OF
WEIGHINGS AND PROVIDE THE TIE
POINT FOR CONSISTENCY THROUGHOUT
THE MEASUREMENT SYSTEM. THE
WEIGHING METHOD USED, I.E., DOUBLE
SUBSTITUTION, TRANSPOSITION, ETC.,
IS INDICATED ALONG WITH TH
OBSERVED DATA. IN THE COMPUTA-
TIONS, THE DISPLACEMENT VOLUMES
ARE TREATED EXPLICITLY, USING THE
DATA LISTED IN THE REPORT. IN ALL
CASES, A REDUNDANCY IN THE NUMBER
OF MEASUREMENTS PROVIDES A MEANS
FOR CHECKING ON THE PRECISION OF
THE PROCESS.

WHEN THERE ARE MORE EQUATIONS
THAN ‘UNKNOWNS’, NOT ALL OBSERVA-
TIONAL EQUATIONS CAN BE SATISFIED
EXACTLY AND THE METHOD OF LEAST
SQUARES IS USED TO PROVIDE
ESTIMATES OF THE ‘UNKNOWN’ VALUES.
THIS METHOD LEADS TO ESTIMATORS
WHICH ARE LINEAR FUNCTIONS OF THE
DATA AND WHICH HAVE STANDARD
DEVIATIONS READILY CALCULATED FROM
THE COEFFICIENTS OF THE LINEAR
FUNCTIONS AND THE STANDARD DEVIA-
TION OF AN INDIVIDUAL MEASUREMENT.
THE ‘CHECK STANDARD’ IS ALSO
TREATED AS AN UNKNOWN AND THE
AGREEMENT OF THE CURRENT RESULT
WITH THE ACCEPTED VALUE PROVIDES A
TEST OF THE ADEQUACY OF THE CUR-
RENT DATA. THIS SAME CHECK

PAGE 2

STANDARD IS MEASURED WITH EACH
TEST OF UNKNOWNS AND THE COLLEC-
TION OF VALUES OVER TIME IS USED
TO EVALUATE THE PERFORMANCE OF THE
MEASUREMENT PROCESS.

IN THE CASE OF THE SERIES
WHICH INCLUDES THE KNOWN STAND-
ARDS, THE ACCEPTED VALUES OF THESE
STANDARDS SERVE AS A RESTRAINT ON
THE SOLUTION OF THE EQUATIONS FOR
THE VALUES OF ALL OF THE WEIGHTS.
THE RESTRAINT FOR THE SOLUTION OF
SUBSEQUENT SERIES IS PROVIDED BY
THE VALUES ESTABLISHED FOR ONE OR
MORE WEIGHTS INCLUDED IN A
PREVIOUS SERIES.

ESTIMATED VALUES FOR WEIGHTS
WHICH HAVE BEEN GROUPED IN THE
SAME SERIES INVOLVE THE SAME
OBSERVATIONAL DATA AND ARE, IN
ALMOST ALL CASES, CORRELATED. FOR
EACH SERIES THERE IS A TABLE OF
COMBINATIONS TOGETHER WITH THE
APPROPRIATE UNCERTAINTY FOR EACH
COMBINATION .

PROCESS CONTROL

THE STANDARD DEVIATION, AS
COMPUTED FROM THE LEAST SQUARES
SOLUTION, PROVIDES A CHECK ON THE
SHORT TERM, OR ‘WITHIN-RUN’ PRO-
CESS PRECISION. AN AVERAGE OF A
NUMBER OF THESE STANDARD DEVIA-
TIONS IS TAKEN AS THE ACCEPTED
WITHIN-RUN STANDARD DEVIATION OF
THE PROCESS AND IS USED AS A
REFERENCE VALUE FOR SURVEILLANCE
OF THE PROCESS PRECISION. THE
VALUES OBTAINED FOR THE ‘CHECK
STANDARD’ PROVIDE, AS TIME GOES
ON, A SEQUENCE OF VALUES THAT
REALISTICALLY REFLECTS THE
VARIATIONS WHICH BESET PRECISE
MEASUREMENTS . COLLECTIONS OF
VALUES FOR BOTH THE WITHIN-RUN
PRECISION AND THE VALUE OBTAINED
FOR THE ‘CHECK STANDARD’ SHOULD


BALANCE 12 OUTLIER CODE: CHK STD=C, STD DEVS, BOTH=@

JMN47E+004 +
-BSS7E-O14 +
= 2 z
-S6S1E-O14 :
: eae . z
: + 2 : 2 2 or
: be 2'3e 2 est
z 220 2 ae =
z Pres ee TT TT
z 3 z
.2726E-014 . +
=. 1896-024 +
=.3106E-015 :
678005402 710085402 {75000602 ~79000E+02 "B300E+02 ~B7000E+02

STANDARD DEVIATIONS VS TIME,

Figure 3. Control chart for the standard deviation of the kilogram
balance used in routine mass calibrations. The ordinate gives
the measured standard deviation of the balance in milligrams
and the abscissa gives the time of the measurement in years
since 1900. Control limits are not shown.

20


Aside from the fact that plated brass or stainless steel are not as resistant
to chemical attack as is platinum/iridium, the major difference between
kilograms made of Pt/Ir and those of brass or steel is their size, more
specifically their volume. One kilogram of Pt/Ir has a volume of about 46.5
cm?; but a typical stainless steel kilogram has a volume of about 125 cm? and
one of brass has a volume of about 119 cm’. The difference in volume between a
Pt/Ir kilogram on the one hand and a brass or steel kilogram on the other is so
great that the buoyant effect of the air which surrounds the kilograms cannot
be neglected during weighing. If, for instance, one constructed a stainless
steel kilogram weight which exactly balanced the IPK when the two were compared
on the most precise balance available, the stainless weight would actually have
amass of about 1 kg + 94 mg. The "extra mass" came about because the
measurements were done in air. Air is a fluid which, like any fluid, produces
a buoyant effect on objects it surrounds. The effect can be as large and
dramatic as the Goodyear blimp. However, when it comes to mass standards and
weighing in general, the effect is small but extremely nettlesome. In the case
of the Pt/Ir and steel kilograms just mentioned, the buoyant force on the steel
exceeded that on the Pt/Ir so that almost 0.1 g extra steel was needed to
balance the two weights. Had the weighing been done in the absence of air,
i.e. in vacuum, there would have been no problems due to air buoyancy: the
mass of stainless steel which would exactly balance the IPK would have been
exactly 1 kilogram. The buoyancy effects are illustrated in figure 1.

Our concept of mass requires that the mass of an object be the same in vacuum
or air (or any other fluid) providing that the total amount of material
comprising the object has not changed (i.e, the weight does not dissolve,
evaporate, react chemically, etc. with the fluid which surrounds it). Thus a
correction must be applied to mass measurements made in air between standards
of different volumes. Let us return to the imaginary measurement in air which
showed that a stainless steel kilogram exactly balanced the IPK. The results
of this measurement can be stated in several different ways:

MASS: The mass of the stainless steel object is about 1 kg + 94 mg.

TRUE MASS: The true mass of the stainless steel object is about
1 kg + 94 mg (true mass = mass)

VACUUM MASS: The vacuum mass of the stainless steel object is about
1 kg + 94 mg. (vacuum mass = mass).

APPARENT MASS: The apparent mass of the stainless steel kilogram is about
1 kg + 0.0 mg when measured against Pt/Ir standards in air of
density 1.2 g/cm? at a temperature of 20 °C.

Note that when specifying apparent mass, one must define the specific weighing
conditions. Whereas the mass of an object is a fundamental attribute, its
apparent mass will depend on its density, the density of the standard to which
it was compared, and the density of air at the time the measurements were made.
(The temperature at which the measurements were made must be specified also
because the density of stainless steel, Pt/Ir, and other materials is a slight
function of temperature.) Because apparent mass is defined through a
particular convention, it is sometimes referred to as "conventional mass."

4


COMPANY X PAGE 24
LOCUS, U.S.A. SERIES 4
SET OF MASS STANDARDS : 500 MG - 1MG 8/30/ 86
TEST NUMBER DEMO1

BALANCE 13
OPERATOR 39

MAXIMUM LOAD 0.0060 G
STARTING RESTRAINT NUMBER 4

CALIBRATION DESIGN 62

PRECISION CONTROL

OBSERVED STANDARD DEVIATION OF THE PROCESS 0.00070 MG
ACCEPTED STANDARD DEVIATION OF THE PROCESS 0.00050 MG
DEGREES OF FREEDOM 6

F RATIO 1.955

F RATIO IS LESS THAN 2.81 (CRITICAL VALUE FOR PROBABILITY = .01).
THEREFORE THE STANDARD DEVIATION IS IN CONTROL.

CHECK STANDARD VECTOR o 0 o o 4 oO

CHECK STANDARD USED 139

ACCEPTED MASS CORRECTION OF CHECK STANDARD -0.00216 MG
OBSERVED CORRECTION OF CHECK STANDARD -0.00265 MG

STANDARD DEVIATION OF THE OBSERVED CORRECTION 0.00018 MG
T VALUE -2.77

ABSOLUTE VALUE OF T IS LESS THAN 3.
THEREFORE CHECK STANDARD IS IN CONTROL.

TEST CONDITIONS BEFORE AFTER AVERAGE
CORRECTED TEMPERATURE IN DEGREES C 22.90 23.00 22.95
CORRECTED PRESSURE IN MM HG 759.527 759,327 759.427
CORRECTED HUMIDITY IN PERCENT 31.60 32.60 32.10
COMPUTED AIR DENSITY IN MG/CM3 1.1884 1.1875 1.1879
TEMPERATURE CORRECTION 0.00 0.00

PRESSURE CORRECTION -0.173 -0.173

HUMIDITY CORRECTION 0.00 0.00

OBSERVED TEMPERATURE IN DEGREES C 22.90 23.00

OBSERVED PRESSURE IN MM HG 759.700 759.500

OBSERVED HUMIDITY IN PERCENT 31.60 32.60

B26


COMPANY X PAGE 10
LOCUS, U.S.A. SERIES 2
SET OF MASS STANDARDS : 500 MG - 1MG 8/29/86
TEST NUMBER DEMO1

BALANCE 13
OPERATOR 39
ACCEPTED WITHIN STANDARD DEVIATION OF THE PROCESS 0.00050 MG
ACCEPTED BETWEEN STANDARD DEVIATION OF THE PROCESS 0.00000 MG

CALIBRATION DESIGN 62

RESTRAINT VECTOR 1 01 1 0 0 °

MASS CORRECTION OF RESTRAINT -0.15925 MG
VOLUME OF WEIGHTS BEING USED IN RESTRAINT AT 23.28 0.06024 CM3
SYSTEMATIC ERROR IN THE RESTRAINT 0.00087 MG
3 STANDARD DEVIATION LIMIT FOR RANDOM FRROR AFFECTING RESTRAINT 0.00509 MG

CHECK STANDARD USED 12

CHECK STANDARD VECTOR 0 0 oOo oO 1 0
ACCEPTED MASS CORRECTION OF CHECK STANDARD -0.00854 MG
REPORT VECTOR 1 1 1 1 0 0
TEST CONDITIONS BEFORE AFTER AVERAGE
CORRECTED TEMPERATURE IN DEGREES C 23.25 23.30 23.28
CORRECTED PRESSURE IN MM HG 758.828 758.429 758.629
CORRECTED HUMIDITY IN PERCENT 27.30 24.10 25.70
COMPUTED AIR DENSITY IN MG/CM3 1,1863 1.1859 1.1861
TEMPERATURE CORRECTION 0.00 0.00
PRESSURE CORRECTION -0.172 70,171
HUMIDITY CORRECTION 0.00 0.00
OBSERVED TEMPERATURE IN DEGREES C 23.25 23.30
OBSERVED PRESSURE IN MM HG 759.000 758.600
OBSERVED HUMIDITY IN PERCENT 27.30 24,10
WEIGHTS BEING NOMINAL DENSITY, COEFFICIENT ACCEPTED
TESTED VALUE G = G/CM3 AT 20C OF EXPANSION CORRECTION MG
500MG 0.5000 16.6000 +000020
300MG 0.3000 16.6000 000020
200MG 0.2000 16.6000 +000020
100MG 0.1000 16.6000 000020
AN/ 100MG 0.1000 = 8.4100 000039 -0.00854
SUM 100MG 0.1000 © 8.1788 000049

B12


COMPANY X PAGE 12
Locus, U.S.A. SERIES 2
SET OF MASS STANDARDS : 500 MG - iMG 8/29/ 86
TEST NUMBER DEMO1
BALANCE 13
OPERATOR 39
CALIBRATION DESIGN 62
SENSITIVITY WEIGHT
MASS 10.00000 MG
VOLUME 0.00000 CM3 AT 20 C
COEFFICIENT OF EXPANSION 0.000000
S*=S-PV(S)= 10.00000 MG
ACCEPTED SENSITIVITY = 0.00100 MG/DTV
OBSERVED SENSITIVITY = 0.00100 MG/DIV
T-TEST = 0.000
OBSERVED
ACI) DELTA(I) SENSITIVITY
(MG) (MG) (MG/DIV)
a1 0.02040 -0,00081 0.00100
A 2 -0.01650 -0,00016
A 3 0.00685 -0,00003
A 4 0.00410 0.00018
AS -0.02885 0.00083
A 6 0.00880 0.00019
a7 -0.02670 -0,00073
A 8 0.01425 -0.00029
ag -0.02530 -0.00038
A 10 -0 04520 -0.00003
All -0,02830 -0.00042 0.00100
VOLUME SYSTEMATIC 3S.D, UNCERTAINTY
ITEM CORRECTION (AT T) ERROR LIMIT LIMIT
«G) (MG) (oM3) (MG) (MG) (MG)
0.5000 -0.07767 0.03012 0.00043 0.00257 0.00300
0.3000 -0.04280 0.01807 0.00026 0.00159 0.00185
0.2000 -0,03879 0.01205 0.00017 0.00109 = 0.00127
0.1000 0.00171 0.00602 0.00009 0.00074 0.00082
0.1000 -0,00862 0.01189  0,00009 0.00074 0.00082
0.1000 0.01204 0.01223 0,00009 0.00074 0.00082
TEMPERATURE T= 23.28 C
RESTRAINT FOR FOLLOWING SERIES
RESTRAINT VECTOR 0 o oO oO 1
MASS CORRECTION 0.01204 MG
VOLUME AT 20 C 0.01223 CM3
SYSTEMATIC ERROR 0.00009 MG
3 STANDARD DEVIATION LIMIT 0.00074 MG

B14


calibrations were, of course, done before the days of electronic balances.
Even today, higher precision can usually be obtained with mechanical balances
although with a great loss in convenience. Using an equal-arm balance, for
instance, one would need an additional 500-g weight. The mass difference
between the sum of both 500-g weights could be found with respect to the
calibrated 1-kg weight. This is enough information to assign mass values to
the two unknown weights. Similar, though more sophisticated, procedures are
used to calibrate weights of all denominations beginning with calibrated
kilogram standards.

Calibration of a set of weights consists of assigning values for the unknown
weights in terms of the known mass of one or more standards. For high
precision work, this involves the use of the balance as a comparator which
measures the difference between two objects (or two groups of objects) which
must have nominally the same mass because of the small "on-scale" range of the
comparator. In deriving units which are subdivisions of the basic unit or
multiples thereof, a variety of different weighing sets have been used because
of convenience or other practical considerations. A typical set is the 5 3 21
series which bridges the range from 10 to 1. In most cases, the calibration
algorithm provides for a check standard, treated as an additional unknown
weight, to be used for monitoring the performance of the measuring process. [8]

Precision weighing is usually done by some form of transposition weighing on a
two-pan balance or by substitution methods on a one-pan balance [7]. For
simplicity, it will be assumed that a well behaved comparator is available and
that measurements of differences in the mass of two objects or groups of
objects are corrected for air buoyancy effects and other environmental or
procedural factors [7]. It is further assumed that the measurements are
uncorrelated in the statistical sense and all are of equal precision. (These
latter two assumptions are non-trivial and special care has to be taken to
insure their validity so that the random error component of the uncertainty is
properly evaluated.)

The schedule of measurements for calibration should include provision for a
check standard and also for within-run redundancy. The decision as to which
one of a number of possible schedules or designs to use for intercomparison of
a set of weights depends on items such as the variance associated with
individual weights or combinations thereof. The least squares analysis from
which the values for the weights and their variances are calculated is
presented in Appendix A.

4, Density Determination of Single-Piece Kilograms Using a Submersible Balance

The buoyancy correction is important in precision weighing. For most cases, an
assumed density (supplied by the manufacturer) will suffice. Wowever, in the
case of 1-kg standards, it is desirable to measure the density of individual
weights. This measurement is now done routinely at NBS for single-piece
kilogram and pound weights sent for calibration. The density measurements we
use are a modification developed in our laboratory of the usual hydrostatic
weighings. A brief description of the technique which we use follows.[9]

7