NIST Measurement Services:

NEU NIST PUBLICATION

April 20, 1989

U.S. Department of Commerce

National Institute of Standards and Technology
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-tool metrology, precision 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 manufacturing 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 programming 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 cells; 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.
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
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, Wasliington, DC 20402-9325
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
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
Contents

Page

1. Description of Service 1

2. The International System of Units 2

3. Mass Standards in Practice 3

3.1 Kilograms 3

3.2 Other Denominations 6

4. Density Determination of Single-Piece Kilograms

Using Submersible Balance 7

4 . 1 Apparatus 8

4.2 Principles of Use 10

5. Cleaning of Weights 11

5.1 Categories of Weights 11

5.2 Cleaning Procedures 12

5.2.1 One-Piece Weights 12

5.2.2 Screw-Knob Weights 12

5.2.3 Sheet-Metal Weights 13

5.3 Temperature Equilibrium 13

5.4 Storage 13

5.5 Brushes 14

6. Method of Calibrating Dead Weights 14

6.1 Measurement Algorithm 14

6.2 Uncertainty of Value Assigned to Piston Weights 15

7. Method of Calibrating Standard Weights 15

V
7.1 Measurement Algorithm 15

7.2 Uncertainty of Value of Standard Weights 16

8. Quality Control 16

8.1 F-Test 19

8.2 t-Test 19

8.3 Between-Times Components 23

9. Future Plans 23

10. References 25

Appendices

A. Least Squares Analysis Al

B. Sample Calibration Report Bl

C. Sample Surveillance Test Report CI

D. Sample Dead-Weight Calibration Report Dl

vi
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

1
established for NBS Classes A, B, M, or S-1 prior to submission [ 1 ]

. 1 No rmally

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 lb to

1 filh 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 lb)

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/crn^ 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

'^New 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 El, E2

Fl, and F2 . (See ASTM E617.)

^We will also accept ANSI/ASTM Grades S and 0 as well as OIML classes El,

E2, Fl, or F2.

2
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 Btareau of

Weights and Measures (BIPM) on land provided by the French government in

S6vres, 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 1x10 ^) . 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.

3
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

a mass 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 vacuiom 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
B.

Figure 1. A. A stainless-steel kilogram (density 8000 kg/m-^) balances a platinum- iriditun 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 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/cvsr' at 20 °C in air of density 1.2

g/cm3 [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, Nl 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 Nl 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 Nl 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 Nl and N2 to standards of

stainless steel density of 8.0 g/cxar . 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 Sevres 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
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 2 1 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. However, 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
4 . 1 Apparatus

The balance modified for this work is a Mettler PL1200, 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.

^ Certain trade «HMes 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.

8
Figure 2. Cross -sectional view of the balance Immersed In Its

thermostated bath. A conventionally- shaped standard weight is

shown on the pan. Unconventional loads may also be

accommodated by the pan as suggested by the sphere (drawn with

dashed lines)

9
Table 1. Comparison of Properties of FC-75 and Water

Property (at 25 "C) FC - 75 Water

Density (kg/m-^) loUU 1 AAA lUUO

Coefficient of expansion ("C ^) 1 . 6x10 32 . 5x10 4

Kinematic viscosity (cm /s) 0 . oZXlO 2 0 . 89x10 2

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/cm-°C) 1.4x10' 3 6.1x10"3

^Values for FC-75 supplied by the manufacturer.

4.2 Principles of Use

We illustrate the use of the submersible balance by finding the volume, V^, of an object, A, when its mass, M^, is known. Placing the object on the balance

produces a reading, 0^, which is related to the other parameters through the

equation

Oa = K [ Ma - ^(t)VA(t)] (1)

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 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"-^g/cm-^, 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,

M - 0

A A

(2)

10
The problem with using eq (2) is that the precision with which 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 SI. Then

^si- Qsi

p = —V

si

and

M - 0

A A V = — V (3) ^ «sr °si

In practice, SI is a stainless-steel kilogram whose volume has been determined

to better than 1 x 10"^ by classical hydrostatic weighing. We also include a check standard, S2 in the measurements. The check standard is similar to SI

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
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.'^ 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.

^ Some solvents are health hazards and should be used in an approved safe

manner
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
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: Si

2) Read the balance with unknown on the pan: D]^ + S2

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

4) Read the balance with no load: S4

Here represents a reading of the angle of tilt of the balance relative to an arbitrary zero and Di 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
The mass of the unknown is computed to be:

Di - pV^ + A - pV^ - + S3 - S^)

S3-S2

M = ; 7z X 1 - p/DX

Where = the calibrated mass of I>i Ml = the volume of

A = the mass of the sensitivity weight

= the volume of the sensitivity weight

Dx = the density of the unknown (supplied by the customer)

p = 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, a, where a is the standard deviation of the

process. Therefore:

Uncertainty of value = 3a + 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
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
Table 2 . Capacities and standard deviations of balances us

Balance Capacity Standard Deviation

3 a6 0. 0005 "'6 20 0..0024

40 0

, 0039

1 60 0 014

1 kg 0,,032

10 2,,5 mg

30 8,.2

1 lb 0,,031 /ilb

6 0,,46

50 5,,5 mg

2500 0.,002 lb

30000 0,,017 lb

17
Table 3. Typical random components of calibration uncertainties

Nom. Val Uncertainty

1000 g

500

300

200

100

50

30

20

10

5

3

2

1

0.072 mg

0.059

0.057

0.050

0.058

0.035

0.029

0.024

0.026

0.013

0.0082

0.0061

0.0049

500 mg

300

200

100

50

30

20

10

5

3

2

1

0.0026 mg

0.0017

0.0012

0.0010

0.00089

0.00087

0.00080

0.00090

0.00083

0.00085

0.00079

0.00090

Nom. Value Uncertainty

1000 g

2 kg

3

5 10

20

30

0.072 mg

6.6

7.8

10.0

15.5

34

55

1 lb

50

500

2500

10000

30000

0.11 filh

22.

0.0028 lb

0.0073

0.054

0.11

18
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 Nl and N2.

We actually use the total mass of Nl 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
BALANCL 12 OUTLIER CODE: CHK STD=C. STD DEV=S. BOTH=0

H 1 1 1 1 1 1 1 1 1

. 1 147E+0e+

.8557E-ei+

• 2

.5641E-ei+

• 2 . • » 2

• 2. 2 . 2 22 . 2 2. ••222. 2».»

2 22. 2 5. ». ••2. 22 . 2. • 2* • .• • ••4 2. • • 22

* 3 6 24 •3 .*• ••«• 2 .

• • • • • 2. . »• 2 . • •3.4 • -01+ • • • 22 2 .» 3 • . . 22. ••2 • +

• • • 4* • •2 • • . 2 . 3«... 3 • 2 7 »2 • * • 2..>. . 3 • • •

• • 32 • 3. • • . . ..2 2 •

• • • 2 • . .4 2. • • • • • * • 2 . 3 • * • 2 . • • • • * •

-.1899E-e2+

-.3106E-ai+

.67ee0E+02 .71000E+02 .75000E+02 .79e00E+02 .B3000E+02 .87e00E+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.
CHECK s.aNDARO 41 BALANCE 12

I 1 1 -.1932E+02+

. 1938E+02+

. 1943E+02+

-.1949E+e2+

• • 22 • _ 2« • •

• 2 • •

• 2 • • 2 •

• • •

• • • 3 •

• • 2

• •

• 2*2 3 • • • 2 •

• • • • • • • « « 2

• • • • • • • • • •

• • • 2

• • • • 2 2

• • • • 2

3 • • • • •••

• 4 2 •2 • (2 • •

• 3

2

*

2»

3 • •

-.1954E+02+

-.196eE+e2+

.7400eE+02 .77000E+02 .80000E+O2 .830e0E+02 .B6000E+02 .89000E+02 CORRECTIONS TO CHECK STANDARD VS TIME

Figure 4. Control chart for the measured difference in mass between

kilograms Nl 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
CHECK ..^fiD

-.4752E-01+

OUTLIEK —I jE: CHK STO -C. STO DEV=S, BOTH .=0

-.5*07E-ei+

-.6063E-01+

-.6718E-01+

2.22

3 2. . 2.222. . .6345322

.5533. 23 5 .22 2559223.

.462224. 2543 23. 333. 32

2 2 . 2 . .

2 .2 . 4.33

.2

5.2.

2 . . 2 22. ...422. .32

2. . .4.2 . 2. .2.3. 224252.3.

..3.. 352

.2 . .

. .2

322!

2.

• • • 2 3«« 42»

2 4.222 2

2 4. .3 .• •3» • ••3«2

.2. 44..32.« 23. 2

.2

.2. 3»34..

2 .2

2

2 2 • ••

• 3 * * •4 •2 2»«» 2

• 3332.3

22 •••2 ••

• 25 . •

» 2»

2» •••23«3 • 2

•• 243 • •

• • 2**«3 •2.««225»2342«

2 32.2333 2

•• 323. »2«

• *• 2 • 2 •

• • • • • 2

22»

«2

• 22 -

.2.

.7374E-01+

.B030E-01+ +

i 1 1 1 I

1 1 1 H 1 h .62000E+02 .67000E+02 .72000E+02 .77000E+02 .82000E+02 .87000E+02

••NOTE. 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
processes which change Nl 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 Nl and N2

which nevertheless preserved the value of Nl - 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 Nl and N2 is

not well-enough determined. Second, the use of the difference in mass of Nl

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 Nl 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 cm"-^.

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 cm have been

purchased. Their densities have been determined to 10 parts per million by

hydrostatic weighing.

23
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 platinumiridium 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 Nl 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 stainlesssteel 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
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] Aimer, H. E. , Weight Cleaning Procedures, NBSIR 74-443 (1973 November).

[12] Aimer, 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

Appendix A

LEAST SQUARES ANALYSIS [8]

We begin then with a set of n observations, yi, y2i • • • Yn involving k

objects where values, /S^ > ^^2 > • • • ^° ^® determined. The set of

observations can be represented by the equations for their expected values,

E(yi).

E(yi) = xli^i + xi2^2 • • • xik^k (D

E(y2) = X2i;3i + t^22^2 • • • ^2VP\i

E(yn) = Xnl^l + Xn2^2 • • • ^nk^k

or in matrix form E(y) = X/S where the element, Xj^j , 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.

^1 Pi ^3 Pk

+ X = ' 1 -1 0 0

+ 1 0 -1 0

+ 1 0 0 -1

+ 0 0 1 -1

+ 0 1 0 -1

+ . 0 0 1 -1

In the least squares analysis one forms the normal equations

X'X^ = X'y

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
3

-1

-1

-1

1 -1

3 -1

1 3

1 -1

-1 1

-1

-1

3

|8 =

yi + 72 + 73

-yi + y4 + ys

-72 + y4 + ys

L -y3 + y4 + ye

A A * A A A where P is the column vector with elements , pi, ^93, ^84, the caret being

used to denote the fact that the values are functions of the observations , and

not the sought-after values, /3.

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

m (2)

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

the function

$ = X(deviations)2 + 2S(ri)9i + (3)

The normal equations now contain an additional "unknown," namely A and written

out in full are as follows:

2-

^^2^1^1 ^^2^2 ^^2Vk ^2^ ^ ^^2^

(4)

K^k ^ ^k^ =

^1^1 Vk m

A2
where

or in matrix notation

n

n

'X'X r X'y

r' 0 A.

The solution may be written out formally as follows:

CX' h

h'X' 0

' C h

^

' X'y

^ f

. h' 0 , V

y

(5)

(6)

To facilitate computation it is convenient t9 have the values, written out

as linear functions of the y's and m, i.e., ^ = [CX' , h] y. This leads to a set of multipliers of the observations of the form m

h = ^11^1 ^ Hi^i g, y + h,m^In-'n 1 (7)

These multipliers, g. . and hj^, 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 (i8i)=C^^a^, Covariance C^^, j

) = C^ja^ (8)

The quantity, , 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+l degrees of freedom for a standard deviation, s, formed by

A3

-A
2 2 s = ; r y (deviations). (9)

(deviation). = y. " (x.^J^ + ^^^^^. . . x.^^^)

One can write these deviations a§ a function of the observations by noting that

the predicted values are just X/9 and the deviations are thus

dev = y - = y - X[CX' ,h] (m] = y - [XCX',0] [m] (10) = [I-XCX']y

which can be written as dev^= ^11^1 ^12^2 •

• • ^in^n ^^^^

dev = d .y. + d _y_ . . . d y n nl"^ 1 n2"^2 nn"^n

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 kn9w the gtandard

deviation for the various sums. For a sum of two items, jS^ and )9j , one has

Var(^i + /9j) = Var(^i) + Var(^j) = 2Cov()8i, ^j

)

and for a linear combination

L = iJi + i2/82 • • • Ji]^k (12)

Variance (L) = i'C^a^

where £' = (ii . . . i^^) , 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 C^j^

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.

A4
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).

A5

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
U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NATIONAL MEASUREMENT LABORATORY

GAITHERSBURG, MD . 20899

' REPORT

0 F MASS VALUES

COMPANY X LOCUS, U.S.A.

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

MANUFACTURER : COMPANY Y SEPTEMBER 1, 1986

TEST NUMBER DEMOl

FOR THE DIRECTOR,

NATIONAL MEASUREMENT LABORATORY

JOE D. SIMMONS, CHIEF

LENGTH AND MASS DIVISION

CENTER FOR BASIC STANDARDS

B2

,4
COMPANY X PAGE 1 LOCUS, U.S.A.

SET OF MASS STANDARDS : 500 MG - IMG TEST NUMBER DEMOl

INTRODUCTION

THIS DOCUMENT IS A COMPREHENSIVE REPORT COVERING THE SEQUENCE

OF OPERATIONS USED TO ASSIGN MASS

VALUES TO 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 COLLECTIONS 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

WHICH RELY, DIRECTLY OR INDIRECTLY, ON MASS MEASUREMENTS TO 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 APPROPRIATE 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 MEASUREMENT 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
COMPANY X PAGE 2 LOCUS, U.S.A.

SET OF MASS STANDARDS : 500 MG - IMG TEST NUMBER DEMOl

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 WEIGHINGS. 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 THE OBSERVED DATA. IN THE COMPUTATIONS, 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 OBSERVATIONAL 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

STANDARD IS MEASURED WITH EACH

TEST OF UNKNOWNS AND THE COLLECTION OF VALUES OVER TIME IS USED

TO EVALUATE THE PERFORMANCE OF THE MEASUREMENT PROCESS.

IN THE CASE OF THE SERIES

WHICH INCLUDES THE KNOWN STANDARDS, 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

B4
COMPANY X PAGE 3 LOCUS, U.S.A.

SET OF MASS STANDARDS : 500 MG - IMG TEST NUMBER DEMOl

POSSESS THE PROPERTIES OF RANDOMNESS 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 TO 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. CORRELATION STUDIES, AS WELL AS SUPPLE- MENTAL EXPERIMENTS, ARE USED TO 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.

SERIES OF MEASUREMENTS JUDGED

AS OUT OF CONTROL RELATIVE TO 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 STANDARDS AT THE 1 KILOGRAM LEVEL,

DESIGNATED Nl 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 KA , 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

Nl 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.

B5
COMPANY X PAGE A LOCUS, U.S.A.

SET OF MASS STANDARDS : 500 MG - IMG TEST NUMBER DEMOl

A BALANCE UNDER STABLE OPERATING 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 THE 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 TO 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

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., ABRASIONS, 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
COMPANY X PAGE 5 LOCUS, U.S.A. SET OF MASS STANDARDS : 500 MG - IMG TEST NUMBER DEMOl

REFERENCES

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

1. 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)

A.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. 197A)

7. 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)

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

BALANCE 2 OPERATOR 3 9 ACCEPTED WITHIN STANDARD DEVIATION OF THE PROCESS 0.002A0 MG

ACCEPTED BETWEEN STANDARD DEVIATION OF THE PROCESS 0.00000 MG

CALIBRATION DESIGN 41 RESTRAINT VECTOR 10 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 10 0 ACCEPTED MASS CORRECTION OF CHECK STANDARD -0.00740 MG

REPORT VECTOR 0 0 0 0

TEST CONDITIONS BEFORE AFTER AVERAGE

CORRECTED TEMPERATURE IN DEGREES C 22., 85 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., 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

WEIGHTS BEING NOMINAL DENSITY COEFFICIENT ACCEPTED

TESTED VALUE G G/CM3 AT 20C OF EXPANSION CORRECTION MG

NB 1 G 1..0000 8., 3406 . 000040 -0 ,.06971 AA 1 G 1.,0000 7 ., 8704 . 000045 -0..00740

1 G 1..0000 8.,4000 .000054

SUM 1 G 1.,0000 16,, 6000 . 000020

B8
COMPANY X PAGE 7 LOCUS, U.S.A. SERIES 1 SET OF MASS STANDARDS : 500 MG - IMG 8/29/ 86 TEST NUMBER DEMOl

BALANCE 2 OPERATOR 39

CALIBRATION DESIGN 41

A 1

GRAMS

+111

A 2 + A3 + A 4 + - A 5 + A 6 + R + "

OBSERVATIONS IN DIVISIONS

DOUBLE SUBSTITUTION ONE PAN BALANCE

A 1 8.1660 8.2200 13.2310 13.1810

A 2 8.1680 8.2030 13.2160 13.18A0

A 3 8.1690 8.1500 13.1650 13.18A0

A A 8.2160 8.2060 13.2150 13.2340

A 5 8.2200 8.1500 13.1620 13.2350

A 6 8.2010 8.1460 13.1630 13.2100

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

BALANCE 2 OPERATOR 39

CALIBRATION DESIGN «1

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 OBSERVED

A(I) DELTA(I) SENSITIVITY DRIFT(I) SENSITIVITY

(MG) (MG) (MG/DIV) (MG) (MG/DIV)

A 1 -0.05177 -0.00087

A 2 -0.03335 0.00062

A 3 0.01892 0.00025

A h 0.01444 -0.00249

A 5 0.07118 0.00162 A 6 0.05077 -0.00187

0 ,. 99558 0 ,, 00199 0 ,. 99616

0 ,. 99558 0 ,, 00149 0 ,. 99567

0 ,. 99558 0 .. 00000 0 ,. 99497

0 ,. 99558 0 .. 00448 0 ,. 99706

0 ,. 99558 0., 00149 0 ,. 99587

0 ,, 99558 -0 ,, 00398 0 .. 99378

VOLUME SYSTEMATIC 3 S.D. UNCERTAINTY

ITEM CORRECTION (AT T) ERROR LIMIT LIMIT

(G) (MG) (CM3) (MG) (MG) (MG)

1.0000

1.0000

1 . 0000

1.0000

-0.06971

-0.01029

-0 . 03673

-0 . 15925

0 .11990

0 . 12707

0. 11906

0 . 06023

0 . 00087

0 . 00087

0 . 00087

0 . 00087

0 . 00000

0 . 00509

0 . 00509

0 . 00509

0 . 00087

0 . 00596

0 . 00596

0 . 00596

TEMPERATURE T= 22.92 C

RESTRAINT FOR FOLLOWING SERIES

RESTRAINT VECTOR 0 0 0 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
COMPANY X PAGE 9 LOCUS, U.S.A. SERIES 1 SET OF MASS STANDARDS : 500 MG - IMG 8/29/ 86 TEST NUMBER DEMOl

BALANCE 2 OPERATOR 39 MAXIMUM LOAD 1.0000 G

STARTING RESTRAINT NUMBER 4

CALIBRATION DESIGN «1

PRECISION CONTROL

OBSERVED STANDARD DEVIATION OF THE PROCESS 0.00212 MG

ACCEPTED STANDARD DEVIATION OF THE PROCESS 0.002A0 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 10 0 CHECK STANDARD USED 10 ACCEPTED MASS CORRECTION OF CHECK STANDARD -0.007A0 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

CORRECTED TEMPERATURE IN DEGREES C CORRECTED PRESSURE IN MM HG

CORRECTED HUMIDITY IN PERCENT

COMPUTED AIR DENSITY IN MG/CM3

TEMPERATURE CORRECTION

PRESSURE CORRECTION

HUMIDITY CORRECTION

OBSERVED TEMPERATURE IN DEGREES C OBSERVED PRESSURE IN MM HG OBSERVED HUMIDITY IN PERCENT

BEFORE AFTER AVERAGE

22,. 85 23 ,. 00 22,, 92

759,.028 758., 828 758,, 928

27 ,. 50 27 ,. 30 27 ,,40

1,. 1883 1,. 1874 1,, 1879

0 ,.00 0 ,.00 -0 ,. 172 -0 ,. 172

0,.00 0 ,. 00

22,. 85 23 ,. 00

759,.200 759,. 000

27..50 27 ,.30

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

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 1110 0 0 MASS CORRECTION OF RESTRAINT -0.15925 MG

VOLUME OF WEIGHTS BEING USED IN RESTRAINT AT 23.28 0.0602A CM3

SYSTEMATIC ERROR IN THE RESTRAINT 0.00087 MG

3 STANDARD DEVIATION LIMIT FOR RANDOM ERROR AFFECTING RESTRAINT 0.00509 MG

CHECK STANDARD USED 12 CHECK STANDARD VECTOR 0 0 0 0 10

ACCEPTED MASS CORRECTION OF CHECK STANDARD -0.0085/. MG

REPORT VECTOR 11110 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,, A29 758,, 629

CORRECTED HUMIDITY IN PERCENT 27 ,. 30 Zk ., 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 -0., 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 DE TESTED VALUE G G/CM3

500MG 0 ,. 5000 16 300MG 0 ,.3000 16 200MG 0 ,.2000 16 lOOMG 0 ,. 1000 16 AN/ lOOMG 0 ,. 1000 8 SUM lOOMG 0 ,. 1000 8

(JSITY COEFFICIENT ACCEPTED

AT 20C OF EXPANSION CORRECTION MG

.6000 .000020

.6000 .000020

.6000 .000020

.6000 .000020

.4100 .000039 -0.00854

.1788 .000049

B12
COMPANY X PAGE

LOCUS, U.S.A. SERIES

SET OF MASS STANDARDS : 500 MG - IMG 8/29/

TEST NUMBER DEMOl

BALANCE 13 OPERATOR 3 9

CALIBRATION DESIGN 62 MG

500 300 200 100 100 100 A 1 + + A 2 + + A 3 + + A It + A 5 + A 6 + + A 7 - + + A 8 + + A 9 + A 10 + A 11 + R + + +

OBSERVATIONS IN DIVISIONS

DIRECT READING

A 1 20.A000 10020. AOOA A 2 -16.5000

A 3 6.8500

A A A. 1000 A 5 -28.8500

A 6 8.8000

A 7 -26.7000

A 8 1A.2500

A 9 -25.3000

A 10 -45.2000

A 11 -28.3000 9971.7002

B13
COMPANY X PAGE 12 LOCUS, U.S.A. SERIES 2 SET OF MASS STANDARDS : 500 MG - IMG 8/29/ 86 TEST NUMBER DEMOl

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

Ad)

(MG)

DELTAd ) (MG)

OBSERVED

SENSITIVITY

(MG/DIV)

A 1 0., 02040 -0 ,. 00081

A 2 -0 ..01650 -0.. 00016

A 3 0 ,. 00685 -0..00003 A 0 .. 00410 0.. 00018

A 5 -0 ,,02885 0 .. 00083 A 6 0 ..00880 0 .. 00019

A 7 -0.. 02670 -0.. 00073 A 8 0 ..01425 -0 ,. 00029 A 9 -0 .. 02530 -0 .. 00038

A 10 -0 .. 04520 -0 .. 00003 A 11 -0 ,. 02830 -0,. 00042

0 . 00100

0.00100

VOLUME SYSTEMATIC 3 S.D.

TEMPERATURE T= 23.28

UNCERTAINTY

ITEM CORRECTION (AT T) ERROR LIMIT LIMIT

(G) (MG) (CM3) (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

RESTRAINT FOR FOLLOWING SERIES

RESTRAINT VECTOR 0 0 MASS CORRECTION

VOLUME AT 20 C SYSTEMATIC ERROR

3 STANDARD DEVIATION LIMIT

0 0 1 0.01204 MG

0.01223 CM3

0.00009 MG

0.00074 MG

B14
COMPANY X PAGE 13 LOCUS, U.S.A. SERIES 2 SET OF MASS STANDARDS : 500 MG - IMG 8/29/ 85 TEST NUMBER DEMOl

BALANCE 13 OPERATOR 39

CALIBRATION DESIGN 62

SUM WEIGHTS USED FOR THE LINEAR COMBINATIONS

(MG) MG

500 300 200 100 1000 + + + 900 + + + 800 + + 700 + + 600 + + 500 + + AOO + +

300 + 200 + 100 +

VALUES AND UNCERTAINTIES FOR COMBINATIONS OF WEIGHTS

(UNCERTAINTY IS 3 STANDARD DEVIATION LIMIT PLUS ALLOWANCE FOR

SYSTEMATIC ERROR.

)

SUM

(MG)

CORR

(MG)

SYSTEMATIC

(MG)

3 S.D. ERROR

(MG)

UNCERTAINTY

LIMIT

(MG)

1000

900

800

700

600

500 AOO

300

200

100

-0. 15925

-0 . 11875

-0 . 12046

0 . 11646

-0.07595

-0 . 08159

-0 . 04108

-0 . 04280

0.03879

0.00171

0.00087

0.00078

0.00070

0.00061

.00052

, 00043

, 00035

, 00026

. 00017

. 00009

0.00509

0 . 00463

0 . 00409

0.00359

0.00312

, 00257

.00216

, 00159

, 00109

. 00074

0 . 00596

0 . 00542

0 . 00479

0 . 00420

0 . 00364

0 . 00300

0 . 00251

0 . 00185

0 . 00127

0 . 00082

B15
COMPANY X . PAGE lA LOCUS, U.S.A. SERIES 2 SET OF MASS STANDARDS : 500 MG - IMG 8/29/ 86 TEST NUMBER DEMOl

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

CALIBRATION DESIGN 62

PRECISION CONTROL

OBSERVED STANDARD DEVIATION OF THE PROCESS 0.00063 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 0 0 0 0 10

CHECK STANDARD USED 12 ACCEPTED MASS CORRECTION OF CHECK STANDARD -0.0085A 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

CORRECTED TEMPERATURE IN DEGREES

CORRECTED PRESSURE IN MM HG

CORRECTED HUMIDITY IN PERCENT

COMPUTED AIR DENSITY IN MG/CM3

TEMPERATURE CORRECTION

PRESSURE CORRECTION

HUMIDITY CORRECTION

OBSERVED TEMPERATURE IN DEGREES C OBSERVED PRESSURE IN MM HG OBSERVED HUMIDITY IN PERCENT

BEFORE

23.25

758.828

27 . 30

1. 1863

0.00

-0 . 172 0.00

23.25

759.000

27.30

AFTER

23 . 30 758.429

24 . 10

1. 1859

0.00

-0. 171 0.00

23 . 30 758.600

24 . 10

AVERAGE

23.28

758.629

25. 70

1. 1861

B16
COMPANY X PAGE 15 LOCUS, U.S.A. SERIES 3 SET OF MASS STANDARDS : 500 MG - IMG 8/30/ 86 TEST NUMBER DEMOl

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 1110 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

CHECK STANDARD USED lA CHECK STANDARD VECTOR 0 0 0 0 10

ACCEPTED MASS CORRECTION OF CHECK STANDARD -0.00046 MG

REPORT VECTOR 11110 0

TEST CONDITIONS

CORRECTED TEMPERATURE IN DEGREES C CORRECTED PRESSURE IN MM HG

CORRECTED HUMIDITY IN PERCENT

COMPUTED AIR DENSITY IN MG/CM3

TEMPERATURE CORRECTION

PRESSURE CORRECTION

HUMIDITY CORRECTION

OBSERVED TEMPERATURE IN DEGREES C OBSERVED PRESSURE IN MM HG

OBSERVED HUMIDITY IN PERCENT

BEFORE AFTER AVERAGE

22 . 95 23 .05 23 .. 00 760 ,. 227 760 .. 027 760 .. 127

30 ,. 00 30 ..70 30 ..35

1

. 1895 1. 1886 1

. 1891

0 ,. 00 0 .. 00

-0 ,. 173 -0 .. 173

0 ,. 00 0 .. 00

22.. 95 23 ..05 760 .400 760 ..200

30 ,. 00 30 .. 70

WEIGHTS BEING NOMINAL DENSITY COEFFICIENT ACCEPTED

TESTED VALUE G G/CM3 AT 20C OF EXPANSION CORRECTION MG

NEW 50MG 0.0500 16.6000 .000020

30MG 0.0300 16.6000 .000020

20MG 0.0200 2.7000 .000069

lOMG 0.0100 2.7000 .000069

AN/ lOMG 0.0100 8.4100 .000039 -0.00046

SUM lOMG 0.0100 2.7000 .000069

B17
COMPANY X PAGE 1 LOCUS, U.S.A. SERIES

SET OF MASS STANDARDS : 500 MG - IMG 8/30/

TEST NUMBER DEMOl

BALANCE 13 OPERATOR 39

CALIBRATION DESIGN 62 MG

50 30 20 10 10 10 A 1 + + A 2 + + A 3 + + A A + A 5 + A 6 + + A 7 + + A 8 + + A 9 + A 10 + A 11 + R + + +

OBSERVATIONS IN DIVISIONS

DIRECT READING

A 1 9.1000 10009.1006

A 2 -A3. 2000

A 3 -0.1000

A A -ll.AOOO

A 5 -59.6000

A 6 -13.8000

A 7 -55.7000

A 8 8.A000

A 9 -11.8000 A 10 -A3. 8000 A 11 -2A.OOO0 9976.0000

B18
COMPANY X PAGE 17 LOCUS, U.S.A. SERIES 3 SET OF MASS STANDARDS : 500 MG - IMG 8/30/ 86 TEST NUMBER DEMOl

BALANCE 13 OPERATOR 39

CALIBRATION DESIGN 62

SENSITIVITY WEIGHT

MASS 10.00000 MG

VOLUME 0.00000 CMS 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

A(I)

(MG)

DELTA(I)

(MG)

OBSERVED

SENSITIVITY

(MG/DIV)

A 1 0 ,. 00910 0.. 00003 A 2 -0.. 0^1320 0 ., 00032

A 3 -0 ,. 00010 0,. 00016

A 4 -0.. OllAO 0 ,.00017 A 5 -0.. 05960 -0.. 00068

A 6 -0..01380 0..00058

A 7 -0..05570 -0 .. 00005

A 8 0.. 008A0 0,. 00015 A 9 -0..01180 0.. 00054

A 10 -0 ,. 04380 0..00049 A 11 -0.. 02400 -0..00035

0.00100

0 . 00100

ITEM

(G)

CORRECTION

(MG)

VOLUME

(AT T)

(CM3)

SYSTEMATIC

ERROR

(MG)

3 S.D. LIMIT

(MG)

UNCERTAINTY

LIMIT

(MG)

0500

0300

0200

0100

0100

0100

00346

00198

01351

02325

00039

03457

00301

00181

00741

00371

00119

00372

0 . 00004

0 . 00003

0 . 00002

0.00001

0 . 00001

0.00001

0 . 00051

0.00050

0.00042

0.00054

0.00054

0 . 00054

0 . 00055

0 . 00053

0 . 00044

0.00055

0 . 00055

0 . 00055

TEMPERATURE T= 23.00

RESTRAINT FOR FOLLOWING SERIES

RESTRAINT VECTOR 0 0 0 0 0 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 18 LOCUS, U.S.A. SERIES 3 SET OF MASS STANDARDS : 500 MG - IMG 8/30/ 86 TEST NUMBER DEMOl

BALANCE 13 OPERATOR 39

CALIBRATION DESIGN 62

SUM WEIGHTS USED FOR THE LINEAR COMBINATIONS

(MG) MG

50 30 20 10 10 10 100 ++ + 90 + + +

80 + +

70 + + 60 + +

50 + +

AO + +

30 + 20 +

10 +

VALUES AND UNCERTAINTIES FOR COMBINATIONS OF WEIGHTS

(UNCERTAINTY IS 3 STANDARD DEVIATION LIMIT PLUS ALLOWANCE FOR

SYSTEMATIC ERROR.

)

SUM

(MG)

CORR

(MG)

SYSTEMATIC

(MG)

3 S.D. ERROR

(MG)

UNCERTAINTY

LIMIT

(MG)

100

90

80

70

60

50

«0

3020

10

0 . 0120A

0 . 02178

0.00147

0 .01006

0.01980

.01550

. 02523

.00198

,01351

.02325

0 . 00009

0 . 00008

0.00007

0.00006

0.00005

0000^1 00003

00003

00002

00001

0.0007A

0.00096

0 . 00071

0 . 00068

0 . 00078

0 . 00051

0.00077

0 . 00050

0.00042

0.0005A

, 00082

, OOlOA

, 00078

, 00074

, 00083

, 00055

, 00081

0.00053

0.000A4

0 . 00055

B20

4
COMPANY X PAGE 19 LOCUS, U.S.A. SERIES 3 SET OF MASS STANDARDS : 500 MG - IMG 8/30/ 86 TEST NUMBER DEMOl

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 0 0 0 0 10

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 CORRECTED PRESSURE IN MM HG 760 ,.227 760., 027 760

CORRECTED HUMIDITY IN PERCENT 30 ,.00 30.. 70 30 COMPUTED AIR DENSITY IN MG/CM3 1,. 1895 1.. 1886 1 TEMPERATURE CORRECTION 0,.00 0 ..00 PRESSURE CORRECTION -0 ,. 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

B21
COMPANY X PAGE 20 LOCUS, U.S.A. SERIES 4 SET OF MASS STANDARDS : 500 MG - IMG 8/30/ 86 TEST NUMBER DEMOl

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 1110 0 0 MASS CORRECTION OF RESTRAINT 0.03A57 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 0.0005A MG

CHECK STANDARD USED 139

CHECK STANDARD VECTOR 0 0 0 0 10

ACCEPTED MASS CORRECTION OF CHECK STANDARD -0.00216 MG

REPORT VECTOR 11110 0

TEST CONDITIONS

CORRECTED TEMPERATURE IN DEGREES C CORRECTED PRESSURE IN MM HG

CORRECTED HUMIDITY IN PERCENT

COMPUTED AIR DENSITY IN MG/CM3

TEMPERATURE CORRECTION

PRESSURE CORRECTION

HUMIDITY CORRECTION

OBSERVED TEMPERATURE IN DEGREES C OBSERVED PRESSURE IN MM HG OBSERVED HUMIDITY IN PERCENT

BEFORE AFTER AVERAGE

22,. 90 23 ..00 22., 95

759,. 527 759., 327 759., A27

31,. 60 32..60 32., 10

1. 188« 1.. 1875 1., 1879

0 ,, 00 0 ..00 -0 ,. 173 -0 .. 173

0., 00 0 .. 00

22.. 90 23 ., 00

759., 700 759., 500

31..60 32., 60

WEIGHTS BEING NOMINAL DENSITY COEFFICIENT ACCEPTED

TESTED VALUE G G/CM3 AT 20C OF EXPANSION CORRECTION MG

5MG 0.0050 2.7000 .000069

3MG 0.0030 2.7000 .000069

2MG 0.0020 2.7000 .000069

IMG 0.0010 2.7000 .000069

T IMG 0.0010 8.5000 .000039 -0.00216

SUM IMG 0.0010 2.7000 .000069

B22
COMPANY X PAGE 2 LOCUS, U.S.A. SERIES

SET OF MASS STANDARDS : 50 0 MG - IMG 8/30/

TEST NUMBER DEMOl

BALANCE 13 OPERATOR 39

CALIBRATION DESIGN 62 MG

5 3 2 1 A 1 + - - + A 2 + A3 + - - - A 4 + -

- A 5 + - - A 6 + - + A 7

' + - - A 8 + -

- A 9 + - A 10 + - A 11 + R + + +

OBSERVATIONS IN DIVISIONS

DIRECT READING

A 1 8.4000 10008.4004

A 2 2.4000

A 3 -8.8000

A 4 1.1000

A 5 7.2000

A 6 6.0000

A 7 -9.1000 A 8 -11.2000 A 9 7.6000 A 10 8.0000 A 11 17.8000 10017.7998

B23
COMPANY X PAGE 22 LOCUS, U.S.A. SERIES A SET OF MASS STANDARDS : 500 MG - IMG 8/30/ 86 TEST NUMBER DEMOl

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

A(I) DELTA(I) SENSITIVITY

(MG) (MG) (MG/DIV)

A 10 A 11

0 . 008A0

0 . 00240

-0 . 00880

0 . 00110

0 .00720

0 . 00600

-0 . 00910

-0 .01120

0.00760

0.00800

0.01780

0 . 00028

0 . 00039

0 . 000A6

0 . 00032

00003

00059

00011

00046

00009

00092

00098

0 . 00100

0 . 00100

VOLUME SYSTEMATIC 3 S.D. UNCERTAINTY

ITEM CORRECTION (AT T) ERROR LIMIT LIMIT

(G) (MG) (CM3) (MG) (MG) (MG)

0 . 0050

0 . 0030

0 . 0020

0.0010

0.0010

0.0010

0.01768

0 . 00600

0 .01089

0 . 00555

-0 . 00265

-0 . 00358

0 . 00186

0 . 00111

0 . 00074

0 .00037

0 .00012

0.00037

0 . 00000

0 . 00000

0 . 00000

0 . 00000

0 . 00000

0 . 00000

0 . 00044

0 . 00048

0 . 00041

0 . 00054

0.00054

0 . 00054

0 . 00045

0 . 00048

0 . 00041

0 . 00054

0 . 00054

0 . 00054

TEMPERATURE T= 22.95 C

B24
COMPANY X LOCUS, U.S.A.

SET OF MASS STANDARDS

TEST NUMBER DEMOl

500 MG - IMG

PAGE 23 SERIES A 8/30/ 86

BALANCE

OPERATOR

1339

CALIBRATION DESIGN 62

SUM

(MG)

10

9

8

76

5

432

1

WEIGHTS USED FOR THE LINEAR COMBINATIONS

MG

VALUES AND UNCERTAINTIES FOR COMBINATIONS OF WEIGHTS

(UNCERTAINTY IS 3 STANDARD DEVIATION LIMIT PLUS ALLOWANCE FOR

SYSTEMATIC ERROR.

)

SUM

(MG)

CORR

(MG)

SYSTEMATIC

(MG)

3 S.D. ERROR

(MG)

UNCERTAINTY

LIMIT

(MG)

10

9

a

76

5

432

1

03457

02923

02368

02857

02322

01689

01155

00600

01089

00555

.00001

.00001

.00001

. 00001

. 00001

. 00000

, 00000

0.00000

0.00000

0.00000

0 . 00054

0.00084

0.00058

0.00058

0 . 00072

0.00044

0.00075

0 . 00048

0 . 00041

0 . 00054

0 . 00055

0 . 00085

0 . 00059

0 . 00059

0 . 00073

0 . 00045

0.00075

0 . 00048

0.00041

0.00054

B25
COMPANY X PAGE 2

LOCUS, U.S.A. SERIES A SET OF MASS STANDARDS : 500 MG - IMG 8/30/ 86 TEST NUMBER DEMOl

BALANCE 13 OPERATOR 39 MAXIMUM LOAD 0.0060 G STARTING RESTRAINT NUMBER «

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 0 0 0 0 10

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

CORRECTED TEMPERATURE IN DEGREES C CORRECTED PRESSURE IN MM HG

CORRECTED HUMIDITY IN PERCENT

COMPUTED AIR DENSITY IN MG/CM3

TEMPERATURE CORRECTION

PRESSURE CORRECTION

HUMIDITY CORRECTION

OBSERVED TEMPERATURE IN DEGREES C OBSERVED PRESSURE IN MM HG

OBSERVED HUMIDITY IN PERCENT

BEFORE AFTER AVERAGE

22.. 90 23 .. 00 22.. 95

759.. 527 759.. 327 759.. 427

31..60 32.. 60 32.. 10

1.. 1884 1.. 1875 1.. 1879

0 ., 00 0., 00

-0 .. 173 -0.. 173

0 ..00 0 .. 00

22.. 90 23 .. 00

759.. 700 759.. 500

31., 60 32.. 60

B26
COMPANY X PAGE 2 5 LOCUS, U.S.A. 8/30/ 66 SET OF MASS STANDARDS : 500 MG - IMG TEST NUMBER DEMOl

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 MAGNITUDE 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 TO 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 CONSISTENT MASS VALUES FOR OBJECTS WHICH

DIFFER SIGNIFICANTLY IN DENSITY

AND/OR FOR MEASUREMENTS WHICH MUST

BE MADE IN DIFFERING ENVIRONMENTS.

THE RELATION ILB AVDP= . A5359237KG

IS USED AS REQUIRED.

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 DISPLACEMENT 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 NOMINAL 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. A G/CM3 AT 0 CELSIUS

WHOSE COEFFICIENT OF VOLUMETRIC

EXPANSION IS 0.000 05A PER DEGREE

CELSIUS, AND WHOSE VALUE IS BASED

B27
COMPANY X PAGE 2 LOCUS, U.S.A. 8/30/ SET OF MASS STANDARDS : 500 MG - IMG TEST NUMBER S

ON ITS TRUE MASS OR WEIGHT IN VACUO

CORRECTION B - 'APPARENT MASS

VERSUS DENSITY 8.0' IS DETERMINED

BY A HYPOTHETICAL WEIGHING OF THE

WEIGHT, IN AIR HAVING A DENSITY OF

1.2 MG/CM3, WITH A STANDARD HAVING

A DENSITY OF 8.0 G/CM3 AT 20 CELSIUS, AND WHOSE VALUE IS BASED

ON ITS TRUE MASS OR WEIGHT IN VACUO.

B28
COMPANY X PAGE

LOCUS, U.S.A. 8/30/

SET OF MASS STANDARDS : 50 0 MG - IMG TEST NUMBER DEMOl

TABLE I

MASS UNCERTAINTY VOL AT 20 COEF OF ITEM (G) (G) (CM3)

500MG . «9992233 0 .. 00000300 0 ,. 03012 0 . 000020

300MG .29995722 0 ,. 00000185 0 ,.01807 0 . 000020

200MG . 19996121 0 ,. 00000127 0 ,.01205 0 . 000020

lOOMG . 10000171 0 .00000082 0 ,. 00602 0 . 000020

50MG .0499965A 0 .,00000055 0 ,.00301 0 . 000020

3 0MG .03000198 0 ,. 00000053 0 ,.00181 0 . 000020

20MG .02001351 0 .. OOOOOOAA 0 ,. 007A1 0 .000069

lOMG .01002325 0 .. 00000055 0 ,. 00371 0 . 000069

5MG .00501768 0 .. 00000045 0 ,. 00186 0 .000069

3MG .00300600 0 .. 000000A8 0 ,. 00111 0 . 000069

2MG .00201089 0 ., OOOOOOAl 0 ,. 0007A 0 . 000069

IMG .00100555 0.. 0000005A 0,. 00037 0 . 000069

B29
COMPANY X PAGE 28 LOCUS, U.S.A. 8/30/ 86 SET OF MASS STANDARDS : 500 MG - IMG TEST NUMBER DEMOl

TABLE II

ITEM COR. A (MG) COR.B (MG)

NEW

500MG

300MG

200MG

lOOMG

50MG

30MG

20MG

lOMG

5MG

3MG

2MG

IMG

- . 04231

- . 02158

- . 02465

. 00879

. 00008

. 00410

. 00748

. 02023

.01616

. 00510

.01028

. 00525

. 03881

.01948

.02325

.00948

.00043

.00431

.00762

. 02030

.01620

.00512

.01030

. 00525

B30
Appendix C

Surveillance Test

The following is the report of a surveillance test [7]. Subsequent 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

CI
UNITED STATES DEPARTMENT OF COMMERCE National Bureau of Standards

Gaithersburg. Maryland 20099

September 18, 1986

In reply refer to:

Subject:

Items:

The above items have been inter compared in sums. The differences as measured

have been compared with the differences computed from the values under

22571 6-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 22571 6-B.

Sincerely,

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

Dl
(i*cv. txm)

U.S. DEPARMENT OF COMMERCE

NATIONAL BUREAU Of STANDARDS

OAlTHiRSBURG. MARYLAND 20e*t

REPORT OF CALIBRATION

NBS Test Number:

For:

Items:

The above

of mass.

items have the mass values shown with reference to the NBS

Item

Mass

(g)

Uncertainty

(g)

Density

(g/cm3)

lkg-1 999.9968 0.0033 7.92

1kg-2 999.9985 0.0033 7.92

1kg-3 1000.0007 0.0033 7.92

Ikg-^ 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 ^%. Test

conditions: mass computed using air density 1.175rag/cm3 for all items.

D2
The National Bureau of Standards uses the following relationship between the

metric unit of mass and the U.S. customary unit of mass: one pound

(avoirdupois) equals 0.'i^5359237 kilogram.

For the Director,

National Measurement Laboratory

Joe D. Simmons, Chief

Length and Mass Division

Center for Basic Standards

loSv, completed: September 3, 1985

Note: Mass and associated density values listed above are appropriate

for Mjjj and pjjj in Equation (2^) from NBS Monograph 65,

"Reduction of Data for Piston Gage Pressure Measurements."

D3

NBS-n4A IREV. 2-BC) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. NIST/SP-250/31

2. Performing Organ. Report No, 3. Publication Date January 1989

4. TITLE AND SUBTITLE

NISI Measurement Services: Mass Calibrations

5. AUTHOR(S)

Richard S. Davis

6. PERFORMING ORGANIZATION (If joint or other than NBS. see in struct/on s) 7. Contract/Grant No.

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

8. Type of Report & Period Covered (formerly NATIONAL BUREAU OF STANDARDS)

U.S. DEPARTMENT OF COMMERCE Final

GAITHERSBURG, MD 20699

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

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

11. ABSTRACT (A 200-word or less factual summory of most significant information. If document includes a si gnificant

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

Unlimited

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20402.

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Description and Operation

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