PREFACE

This handbook is the third of a series developed by the National Bureau of
Standards for use in the management of the national weights and measures
measurement system. The other two publications are:

NBS Handbook 143, "State Weights and Measures Laboratories,
Program Handbook," and :

NBS Special Publication 686, "State Weights and Measures
Laboratories, Program Description and Directory."

State weights and measures laboratories are in the forefront in assuring
equity in the marketplace. A key to their success in that role is their
ability to provide high accuracy calibrations and measurements. Those calibra-
tions and measurements must be traceable to the national standards and must be
in statistical control. Statistical control depends on a quality measurement
assurance program which, in turn, depends on a competent staff, and adequate
facilities and equipment.

This handbook provides the basis for the quality measurement assurance
program by documenting good laboratory practices (GLPs), good measurement
practices (GMPs), and standard operations procedures (SOPs). Those following
the guidance in this handbook will be assured that their measurement data are
properly evaluated and limits of random and systematic error assigned.

State laboratories are expected to study and use the material in this
handbook, tailoring the material to fit their unique requirements. Although
the handbook was written with the specific needs of the state laboratories in
mind, it should be useful to the wider audience of laboratories engaged in high
accuracy metrological measurements.

The authors encourage the users to comment on their experience in the use
of this material so that it can be improved.

Albert D. Tholen
Office of Weights and Measures
National Bureau of Standards

dit


8.

Statistical Techniques

8.1

8.2

8.3

8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11
8.12

Estimation of Standard Deviation from a
Series of Measurements on a given Object

Estimation of Standard Deviation from Differences
of k Sets of Duplicate Measurements

Estimation of Standard Deviation from the Average
Range of Several Sets of Measurements

Pooling Estimates of Standard Deviation

"Within" and "Between" Standard Deviation
Confidence Interval for the Mean

Confidence Interval for Sigma

Statistical Tolerance Intervals

Comparing Estimates of Standard Deviations
Comparing a Set of Measurements with a given Value
Comparing Two Sets with Regard to their Means

Use of Random Numbers

Tables

Table
Table
Table
Table
Table
Table

Table

Table
Table
Table

9.1. Use of Ranges to Estimate Standard Deviation
9.2, Z-factors for Two-sided Confidence Intervals
9.3. Student t-Variate

9.4. Critical Values for the F-Test, Fo 975

9.5. Critical Values for the F-Test, Fo. ee

9.6. Two-sided Tolerance Interval Factors

9.7. Factors for Computing Two-Sided Confidence
Intervals for o.

9.8. Density of Air-Free Water

9.9, Density of Air

9.10. Coefficients of Linear and Cubical Expansion for
Materials Commonly Used in Laboratory Apparatus

and Standards

viii

8.1

8.1

8.2

8.2
8.2
8.3
8.4
8.5
8.6
8.6
8.7
8.7
8.9
9.1
9.3
9.4
9.5
9.6
9.7
9.8

9.9
9.10
9.11

9.12


5.

TABLE OF CONTENTS

Introduction

Concepts of Accuracy, Precision, and Statistical Control
Quality Assurance in a Metrology Laboratory

Good Laboratory Practices (GLPs)

GLP No. 1 Measurement Control for Mass Calibration

GLP No. 2 Minimum Requirements for the Physical
Facilities for Weights and Measures Laboratory

GLP No. 3 Care of State Standards
GLP No. 4 Periodic Recalibration of State Standards
GLP No. 5 Laboratory Administration

GLP No. 6 Prerequisites for Testing Measurement
Standards and Equipment

GLP No. 7 Calibration Systems Requirements-Military
Standard 45662

GLP No. 8 Sealing of Equipment

GLP No. 9 Reporting Mass Values and Uncertainties
GLP No. 10 Purity of Water

GLP No. 11 Painting Weights

GLP No. 12 Laboratory Records

GLP No. 13 Drying Containers
Good Measurement Practices (GMPs)

GMP No. 1 Reading Turning Points on an Equal
Arm Balance

GMP No. 2 Reading the Center of Graduations When
Using a Microscope

GMP No. 3 Method of Reading a Meniscus

GMP No. 4 Adjusting the Optical Scale on a Single
, Pan Mechanical Balance

1.1
2.1
3.1
4.1

GLP 1-1

GLP 2-1
GLP 3-1
GLP 4-1

GLP 5-1
GLP 6-1

GLP 7-1
GLP 8-1
GLP 9-1
GLP 10-1
GLP 11-1
GLP 12-1
GLP 13-1
5.1

GMP 1-1

GMP 2-1

GMP 3-1

GMP 4-1




7.

soP

SOP

SOP

SOP

SOP

SOP

soP

SOP

SOP

SOP

SOP

No.

No.

No.

No.

No.

No.

No.

No.

No.

No.

No.

11

12

13

14

15

16

17

18

19

20

21

Recommended
Calibration

Recommended
Calibration

Recommended
Calibration
Method

Recommended

Gravimetric Calibration of Volumetric Ware Using

Standard Operations Procedure for
of Metal Tapes, Bench Method

Standard Operations Procedure for
of Steel Tapes, Tape-to-Tape Method

Standard Operations Procedure for
of Volumetric Ware, Gravimetric

Standard Operations Procedure for

an Electronic Balance

Recommended
Calibration

Standard Operations Procedure for
of Intermediate and Large Volume

Standards, Gravimetric Method

Recommended

Calibration of Measuring Flasks, Volume Transfer

Method

Recommended

Standard Operations Procedure for

Standard Operations Procedure for

Control Charts for Calibration of Measuring
Flasks, Volume Transfer Method

Recommended
Calibration

Standard Operations Procedure for
of Graduated Neck Volumetric Field

Standards, Volumetric Transfer Method

Recommended
Calibration
Method

Recommended

Standard Operations Procedure for
of Large Metal Provers, Volumetric

Standard Operations Procedure for

Control Charts for Calibration of Neck-Type
Provers, Volumetric Method

Recommended
Calibration

Miscellaneous Subjects

7.1
7.2
7.3
7.4

Standard Operations Procedure for
of LPG Provers

NBS Support for the Measurement System

Tolerances

Distinction Between Mass and Apparent Mass

Control Charts

vii

soP

SOP

SOP

SOP

SOP

SOP

SOP

SOP

SOP

SOP

SOP

11-1

12-1

13-1

146-1

15-1

16-1

17-1

18-1

19-1

20-1

21-1

+12

16


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“Uncay OF

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

NBS HANDBOOK 145
£

a
é

Handbook for the Quality

Assurance of
_Metrological Measurements

John K. Taylor and Henry V. Oppermann



Acknowledgment.

The authors are grateful to a number of their colleagues arid associates at
the National Bureau of Standards who have encouraged and aided them during the
preparation of this handbook. The basic concept for it arose from early
discussions with Dr. Arthur 0. McCoubrey, formerly Director of Measurement
Services at NBS. Mr. Albert D. Tholen, Manager of the NBS Office of Weights
and Measures, saw this handbook as an integral part of the quality assurance
Program for State laboratories. He vigorously supported its development and
provided the funding that made possible its publication.

The practices and procedures presented in the handbook are based largely on
the research and experience of numerous scientists at NBS, both named and
unnamed, whose individual and collective goals have been to develop and utilize
metrological procedures of the highest quality to serve the ever demanding
needs of modern technology.

We are especially grateful to Mrs. Carroll Croarkin and Dr. Keith Eberhardt
who critically reviewed the statistical aspects of the manuscript and made many
helpful suggestions for the development of the uncertainty statements in the
procedures.

Finally, but certainly not the least, we wish to express our thanks to Mrs.
Janiel Reed and Ms. Ulesia Gray of the Text Editing Facility of the NBS Center
for Analytical Chemistry for their cheerful cooperation and assiduity in the
preparation of the manuscript for publication.


Table 9.11. A Short Table of Random Numbers 9.13
10. Glossary 10.1

11. Bibliography 11.1


GMP No.
GMP No.
GMP No.
GMP No.
GMP No.
GMP No.
6. Standard

SOP No.

SOP No.

SOP No.

SOP No.

SOP No.

SOP No.

SOP No.

SOP No.

SOP No.

SOP No.

9
10

Weight Cleaning Procedures

Cleaning Metal Volumetric Measures

Cleaning Precision Glassware

Recommended Form of Reporting Tape Calibrations
Equations for Metallic Tapes

Weighing Operations

Operations Procedures (SOPs)

1

10

Recommended Standard Operations Procedure
for Preparation of Calibration/Test Reports

Applying Air Buoyancy Correction

Recommended Standard Operations Procedure for
Weighing by Double Substitution Using an
Equal-Arm Balance

Recommended Standard Operations Procedure for
Weighing by Double Substitution Using a Single -
Pan Mechanical Balance, Full Electronic Balance,
or a Balance with Digital Indications and
Built-in Weights

Recommended Standard Operations Procedure for
Using a 3-1 Weighing Design (Double
Substitution)

Recommended Standard Operations Procedure for
Weighing by Transposition

Recommended Standard Operations Procedure for
Weighing by Single Substitution Using a Single
Pan Mechanical Balance, a Full Electronic
Balance, or a Balance with Digital Indications
and Built-in Weights

Recommended Standard Operations Procedure for
Tolerance Testing of Mass Standards by Modified
Substitution

Recommended Standard Operations Procedure for
for Control Charts for Calibration of Mass
Standards

Recommended Standard Operations Procedure
for Calibration of Rigid Rules

vi

GMP

GMP

SOP

SOP

soP

SOP

SOP

SOP

SOP

SOP

SOP

5-1
6-1
7-1
8-1

9-1

3-1

6-1

7-1

8-1

SOP 9-1

10-1


Library of Congress Catalog Card Number: 86-600583
National Bureau of Standards Handbook 145

Natl. Bur. Stand. (U.S.), Handb. 145, 288 pages (Nov. 1986)
CODEN:NBSHAP

U.S. Government Printing Office
Washington: 1986

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



Handbook for the Quality Assurance of
Metrological Measurements

John K. Taylor and Henry V. Oppermann
National Bureau of Standards
Gaithersburg, MD 20899

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary
NATIONAL BUREAU OF STANDARDS, Emest Ambler, Director

Issued November 1986


he Nationa, ureau of Standards’

Bureau's overall goal is to st
their effective application for public benefit. To this end,
basis for the nation's physical measurement system, i
government, (3) a technical basis for equity in trade, and (4) technical

services to promote public safety.

‘The Bureau’s technical work is performed by the National Measurement Laboratory, the National

Engineering Laboratory, the Institute for Computer Sciences and
Science and Engineering.

The National Measurement Laboratory’

Technology, and the Institute for Materials

Provides the national system of physical and chemical Measurement;
Coordinates the system with measurement systems. of other nations and
furnishes essential services leading to accurate and uniform physical and
chemical measurement throughout the Nation's scientific community, in-
dustry, and commerce; provides advisory and research services to other
Government agencies; conducts physical and chemical research; de
Produces, and dis tes Standard Reference Materials; and provides
calibration services. The Laboratory consists of the following centers:

The National Engineering Laboratory

© Basic Standards*

© Radiation Research

© Chemical Physics
Analytical i

Provides technology and technical services to the public and private sectors to
address national needs and to solve national problems; conducts research in
engineering and applied science in support of these efforts; builds and main-

and proposes new engi
mechanisms to transfer results of its research to the ultimate user. The
Laboratory consists of the following centers:

The Institute for Computer Sciences and Technology

© Applied Mathematics

© Electronics and Electrical
Engineering*

> Building Tectoig

e it a

© Fire Research .

© Chemical Engineering”

Conducts research and provides scientific and technical services to aid
Federal agencies in the selection, acquisition, application, and use of com-
puter technology to improve effectiveness and economy in Government
accordance with Public Law 89-306 (40 U.S.C. 759), relevant

© Programming Science and
Technology
© Computer Systems

‘Operations in ineerin;

Executive » and other directives; carries out this mission by managing Engi .

the Federal Information i Program, developing Federal

ADP standards guidelines, and managing Federal participation in ADP

voluntary standardization activities; provides scientific and technological ad-

wisory services and assistance to Federal agencies; and provides the technical

foundation for computer-related policies of the Federal Government. The in-

Suitute consists of the following centers:

The Institute for Materials Science and Engineering

Conducts research and provides measurements, data, standards, reference © Ceramics

materials, quantitative understanding and other technical information funda- ¢ Fracture and Deformation 3

mental to the roces + Structure, properties and performance of materials: * Polymers

addresses the scientific basis for new advanced materials technologies; plans * Metallurgy
around cross-country scientific themes such as nondestructive © Reactor Radiation

evaluation and Phase diagram development; oversees Bureau-wide technical
Tesearch and nondestructive evalua-
technical information resulting from
the following Divisions:

"Headquarters and Laboratories ar ‘Gaithersburg. MD. uniess otherwise Noted: mailing address

Gaithersburg, MD 20899.
“Some divisions within the center are located at Boulder, CO 80303.
Located at Boulder. CO, with some elements at Gaithersbure. MD


—*
“ws
: UNITED STATES DEPARTMENT OF Commerce
5 | National inatitute of Standerde and Technology
% va (formerly National Bureau of Standerda)
Mares ot Geithersburg. Meryiend 20883

June 2, 1989

MEMORANDUM FOR: Users of NBS Handbook 145

From: Henry Oppermann
Subject: Errata Sheets/Rep! ent Pages

Attached are replacement pages for NBS Handbook 145, “Handbook for the Quality Assurance of
Metrological Measurements.” These pages are to replace pages that contained errors in the original
Publication. The page numbers and the errors that have been corrected are summarized below.

Page SOP 2-6 The words “at 0 °C* were added to the second sentence on the last paragraph to
complete the density statement for 8.4 g/cm’,

Page SOP 2-9 The subscript in the numerator of the numerator of equation 5 for the density
of air at the time of balance calibration and the subscript in the definition of the
symbols under the equation has been changed from a “c" to an “A‘.

Page SOP 2-11 Another set of brackets were added to equation 7.
Page SOP 15-5 The plus and minus signs associated with the air density times the volumes of the

standards equation in 3.2 were reversed and has a significant effect on the value
computed for the volume of the standard.

Page 8.3 The square root sign in the formula at the top of the page was omitted in the
original publication and has been added.
Page 9.10 The water density for 29 °C was changed to correct a typographical error.

Dieser tem to te aeeebSien mana. who have nat recived thee replacement pages,
please them to the availability of these pages. ies obtained ling the Office
of Weights and Measures at (301) 975-4004. my cating

SOP II-F
N- 0 Havch 29, (1970
uel -
Neie