Standard

Reference Materials:

HANDBOOK

FOR SRM

USERS

100

U57

260-100

1985

c 2 NBS Special

Publication

260-100

US. DEPARTMENT OF COMMERCE

National Bureau of Standards
TM he National Bureau of Standards' was established by an act of Congress on March 3, 1901. The M Bureau's overall goal is to strengthen and advance the nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a

basis for the nation's physical measurement system, (2) scientific and technological services for industry and

government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is performed by the National Measurement Laboratory, the National Engineering Laboratory, the Institute for Computer Sciences and Technology, and the Institute for Materials Science and Engineering

The National Measurement Laboratory

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

calibration services. The Laboratory consists of the following centers:

Basic Standards

Radiation Research Chemical Physics

Analytical Chemistry

The National Engineering Laboratory

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 maintains competence in the necessary disciplines required to carry out this research and technical service; develops engineering data and measurement

capabilities; provides engineering measurement traceability services; develops

test methods and proposes engineering standards and code changes; develops and proposes new engineering practices; and develops and improves mechanisms to transfer results of its research to the ultimate user. The

Laboratory consists of the following centers:

Applied Mathematics

Electronics and Electrical Engineering2 Manufacturing Engineering

Building Technology

Fire Research Chemical Engineering2

The Institute for Computer Sciences and Technology

Conducts research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and economy in Government

operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing

the Federal Information Processing Standards Program, developing Federal ADP standards guidelines, and managing Federal participation in ADP

voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and provides the technical foundation for computer-related policies of the Federal Government. The Institute consists of the following centers:

Programming Science and

Technology Computer Systems

Engineering

The Institute for Materials Science and Engineering

Conducts research and provides measurements, data, standards, reference

materials, quantitative understanding and other technical information funda- mental to the processing, structure, properties and performance of materials; addresses the scientific basis for new advanced materials technologies; plans

research around cross-country scientific themes such as nondestructive

evaluation and phase diagram development; oversees Bureau-wide technical programs in nuclear reactor radiation research and nondestructive evaluation; and broadly disseminates generic technical information resulting from

its programs. The Institute consists of the following Divisions:

Inorganic Materials Fracture and Deformation3 Polymers

Metallurgy Reactor Radiation

'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address

Gaithersburg, MD 20899.

2 Some divisions within the center are located at Boulder, CO 80303.

3 Located at Boulder, CO, with some elements at Gaithersburg, MD.
RATIONAL BUBEiMf

fiF STANDARDS Standard Reference Materials:

Handbook for SRM Users

John K. Taylor

Center for Analytical Chemistry

National Bureau of Standards

Gaithersburg, MD 20899

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director Issued September 1985
Library of Congress Catalog Card Number: 85-600576

National Bureau of Standards Special Publication 260-100

Natl. Bur. Stand. (U.S.), Spec. Publ. 260-100, 98 pages (Sept. 1985)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 1985

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402
PREFACE Standard Reference Materials (SRM's) as defined by the National Bureau of Standards (NBS)

are well-characterized materials produced in quantity and certified for one or more physical

or chemical properties. They are used to assure the accuracy and compatibility of measurements throughout the Nation. SRM's are widely used as primary standards in many diverse fields

in science, industry, and technology, both within the United States and throughout the world.

They are also used extensively in the fields of environmental and clincial analysis. In many aplications, traceability of quality control and measurement processes to the national mea- surement system are carried out through the mechanism and use of SRM's. For many of the Nation's scientists and technologists, it is therefore of more than passing interest to known

the details of the measurements made at NBS in arriving at the certified values of the SRM's

produced. An NBS series of papers, of which this publication is a member, called the NBS Special Publication - 260 Series, is reserved for this purpose.

This 260 Series is dedicated to the dissemination of information on different phases of the preparation, measurement, certification and use of NBS-SRM's. In general, much more detail will be found in these papers than is generally allowed, or desirable, in scientific

journal articles. This enables the user to assess the validity and accuracy of the measurement process employed, to judge the statistical analysis, and to learn details of techniques

and methods utilized for work entailing the greatest care and accuracy. These papers also should provide sufficient additional information not found on the certificate so that new applications in diverse fields not foreseen at the time the SRM was originally issued to be sought and found. Inquiries concerning the technical content of this paper should be directed to the author. Other questions concerned with the availability, delivery, price, and so forth of reference

materials will receive prompt attention from: Office of Standard Reference Materials

National Bureau of Standards

Gaithersburg, MD 20899

Stanley D. Rasberry

Chief Office of Standard Reference Materials

ill
OTHER NBS PUBLICATIONS IN THIS SERIES

Catalog of NBS Standard Reference Materials

(1984-85 edition), Catherine H. Hudson, ed., NBS

Spec. Publ. 260 (February 1984). $5.50* SN003-

003-02558-5.

Michaelis, R. E., and Wyman, L. L. Standard

Reference Materials: Preparation of White Cast

Iron Spectrochemical Standards. NBS Misc. Publ. 260-1 (June 1964). COM74- 1 106 1 **

Michaelis, R. E., Wyman, L. L., and Flitsch, R., Standard Reference Materials: Preparation of NBS Copper-Base Spectrochemical Standards. NBS Misc. Publ. 260-2 (October 1964). COM74-

11063**

Michaelis, R. E., Yakowitz, H., and Moore, G. A., Standard Reference Materials: Metallographic

Characterization of an NBS Spectrometric LowAlloy Steel Standard. NBS Misc. Publ. 260-3 (October 1964). COM74-1 1060** Hague, J. L. Mears, T. W., and Michaelis, R. E., Standard Reference Materials: Sources of

Information, NBS Misc. Publ. 260-4 (February

1965). COM74-11059

Alvarez, R., and Flitsch R., Standard Reference

Materials: Accuracy of Solution X-Ray Spectrometric Analysis of Copper-Base Alloys. NBS

Misc. Publ. 260-5 (March 1965). PB 168068**

Shultz, J. L, Standard Reference Materials: Methods for the Chemical Analysis of White

Cast Iron Standards, NBS Misc. Publ. 260-6

(July 1965). COM74-11068**

Bell, R. K., Standard Reference Materials: Methods for the Chemical Analysis of NBS

Copper-Base Spectrochemical Standards. NBS

Misc. Publ. 260-7 (October 1965). COM74-

11067** Richmond, M.S., Standard Reference Materials: Analysis of Uranium Concentrates at the

National Bureau of Standards. NBS Misc. Publ. 260-8 (December 1965). COM74-1 1066** Anspach, S. C, Cavallo, L. M. Garfinkel, S. B. Hutchinson, J. M. R., and Smith, C. N., Standard Reference Materials: Half Lives of Materials Used in the Preparation of Standard Reference Materials of Nineteen Radioactive Nuclides

Issued by the National Bureau of Standards NBS Misc. Publ. 260-9 (November 1965). COM74-11065**

Yakowitz, H., Vieth, D. L., Heinrich, K. F. J., and

Michaelis, R. E., Standard Reference Materials: Homogeneity Characterization of NBS Spectrometric Standards II: Cartridge Brass and LowAlloy Steel, NBS Misc. Publ. 260-10 (December

(1965). COM74-11064**

Napolitano, A., and Hawkins, E. G., Standard Reference Materials: Viscosity of Standard

Lead-Silica Glass, NBS Misc. Publ. 260-11 (November 1966). NBS Misc. Publ. 260-11** Yakowitz, H., Vieth, D. L„ and Michaelis, R. E., Standard Reference Materials: Homogeneity

Characterization of NBS Spectrometric Standards III: White Cast Iron and Stainless Steel Powder Compact, NBS Misc. Publ. 260-12

(September 1966). NBS Misc. Publ. 260-12**

Spijkerman, J. L., Snediker, D. K., Ruegg, F. C,

and DeVoe, J. R., Standard Reference Materials: Mossbauer Spectroscopy Standard for the Chemical Shift of Iron Compounds, NBS Misc. Publ. 260-13 (July 1967). NBS Misc. Publ.

260-13**

Menis, O., and Sterling, J. T., Standard Reference

Materials: Determination of Oxygen in Ferrous

Materials - SRM 1090, 1091, and 1092, NBS

Misc. Publ. 260-14 (September 1966). NBS Misc.

Publ. 260-14**

Passaglia, E., and Shouse, P. J., Standard Refer- ence Materials: Recommended Method of Use

of Standard Light-Sensitive Paper for Calibrating Carbon Arcs Used in Testing Textiles for Colorfastness to Light, NBS Misc. Publ. 260-15 (June 1967). (Replaced by NBS Spec. Publ.

260-41.) Yakowitz, H., Michaelis, R. E., and Vieth, D. L., Standard Reference Materials: Homogeneity

Characterization of NBS Spectrometric Standards IV: Preparation and Microprobe Characterization of W-20% MO Alloy Fabricated by Powder Metallurgical Methods, NBS Spec.

Publ. 260-16 (January 1969). COM74-1 1062** Catanzaro, E. J., Champion, C. E., Garner, E. L., Marinenko, G., Sappenfield, K. M., and Shields, W. R., Standard Reference Materials: Boric

Acid; Isotopic and Assay Standard Reference

Materials, NBS Spec. Publ. 260-17 (February

1970). Out of Print. Geller, S. B., Mantek, P. A., and Cleveland, N.

G., Standard Reference Materials: Calibration of NBS Secondary Standard Magnetic Tape (Computer Amplitude Reference) Using the Reference Tape Amplitude Measurement

"Process A," NBS Spec. Publ. 260-18 (November

1969). (See NBS Spec. Publ. 260-29.) Paule, R. C, and Mandel, J., Standard Reference

Materials: Analysis of Interlaboratory Measurements on the Vapor Pressure of Gold (Certifica- tion of Standard Reference Material 745). NBS

Spec. Publ. 260-19 (January 1970). PB190071**

Paule. R. C, and Mandel, J., Standard Reference

Materials: Analysis of Interlaboratory Measure- ments on the Vapor Pressures of Cadmium and

Silver, NBS Spec. Publ. 260-21 (January 1971). COM74-11359**

Yakowitz, H., Fiori, C. E., and Michaelis, R. E., Standard Reference Materials: Homogeneity

Characterization of Fe-3 Si Alloy, NBS Spec.

Publ. 260-22 (February 1971). COM74-1 1357**

Napolitano, A., and Hawkins, E. G., Standard

Reference Materials: Viscosity of a Standard

Borosilicate Glass, NBS Spec. Publ. 260-23 (December 1970). COM71-00157**

Sappenfield, K. M., Marineko, G., and Hague, J. L., Standard Reference Materials: Comparison

of Redox Standards, NBS Spec. Publ. 260-24 (January 1972). COM72-50058**

iv
Hicho, G. E., Yakowitz, H., Rasberry, S. D., and

Michaelis, R. E., Standard Reference Materials: A Standard Reference Material Containing

Nominally Four Percent Austenite, NBS Spec.

Publ. 260-25 (February 1971). COM74-1 1356** Martin, J. F., Standard Reference Materials:

National Bureau of Standards-US Steel Corporation Joint Program for Determining Oxygen and Nitrogen in Steel, NBS Spec. Publ. 260-26

(February 1971). 85 cents* PB 81 176620

Garner, E. L„ Machlan, L. A., and Shields, W. R., Standard Reference Materials: Uranium

Isotopic Standard Reference Materials, NBS

Spec. Publ. 260-27 (April 1971). COM74-

I 1358**

Heinrich, K. F. J., Myklebust, R. L., Rasberry, S. D., and Michaelis, R. E., Standard Reference Materials: Preparation and Evaluation of SRM's 481 and 482 Gold-Silver and GoldCopper Alloys for Microanalysis, NBS Spec.

Publ. 260-28 (August 1971). COM71-50365**

Geller, S. B., Standard Reference Materials: Cali- bration of NBS Secondary Standard Magnetic Tape (Computer Amplitude Reference) Using

the Reference Tape Amplitude Measurement

"Process A-Model 2," NBS Spec. Publ. 260-29 (June 1971). COM7I-50282

Gorozhanina, R. S., Freedman, A. Y., and

Shaievitch, A. B. (translated by M. C. Selby), Standard Reference Materials: Standard

Samples Issued in the USSR (A Translation from the Russian). NBS Spec. Publ. 260-30 (June

1971). COM71-50283**

Hust, J. G., and Sparks, L. L., Standard Reference

Materials: Thermal Conductivity of Electrolytic Iron SRM 734 from 4 to 300 K, NBS Spec. Publ. 260-31 (November 1971). COM71-50563**

Mavrodineanu, R., and Lazar, J. W., Standard

Reference Materials: Standard Quartz Cuvettes,

for High Accuracy Spectrophotometry, NBS

Spec. Publ. 260-32 (December 1973). 55 cents* SN003-003-01213-1 Wagner, H. L., Standard Reference Materials: Comparison of Original and Supplemental SRM 705, Narrow Molecular Weight Distri- bution Polystyrene, NBS Spec. Publ. 260-33 (May 1972). COM72-50526**

Sparks, L. L., and Hust, J. G., Standard Reference

Materials: Thermoelectric Voltage, NBS Spec.

Publ. 260-34, (April 1972). COM72-50371**

Sparks, L. L., and Hust, J. G., Standard Refer- ence Materials: Thermal Conductivity of

Austenitic Stainless Steel, SRM 735 from 5 to 280 K, NBS Spec. Publ. 260-35 (April 1972.) 35 cents* COM72-50368**

Cali, J. P., Mandel, J., Moore, L. J., and Young, D.

S., Standard Reference Materials: A Referee Method for the Determination of Calcium in Serum, NBS SRM 915, NBS Spec. Publ. 260-36 (May 1972). COM72-50527**

Shultz, J. I. Bell., R. K. Rains, T. C, and Menis,

O., Standard Reference Materials: Methods of Analysis of NBS Clay Standards, NBS Spec.

Publ. 260-37 (June 1972). COM72-50692**

Richmond, J. C, and Hsia, J. J., Standard Refer- ence Materials: Preparation and Calibration of Standards of Spectral Specular Reflectance, NBS Spec. Publ. 260-38 (May 1972). COM72-

50528**

Clark, A. F., Denson, V.A.. Hust, J. G., and

Powell. R. L., Standard Reference Materials: The Eddy Current Decay Method for Resistivity Characterization of High-Purity Metals, NBS

Spec. Publ. 260-39 (May 1972). COM72-50529**

McAdie, H. G., Garn, P.D., and Menis, O., Standard Reference Materials: Selection of Thermal

Analysis Temperature Standards Through a Cooperative Study (SRM 758, 759, 760), NBS

Spec. Publ. 260-40 (August 1972.) COM72-

50776** Wood, L. A., and Shouse, P. J., Standard

Reference Materials: Use of Standard LightSensitive Paper for Calibrating Carbon Arcs Used in Testing Textiles for Colorfastness to Light, NBS Spec. Publ. 260-41 (August 1972) COM72-50775**

Wagner, H. L. and Verdier, P. H., eds.. Standard

Reference Materials: The Characterization of Linear Polyethylene, SRM 1475, NBS Spec. Publ. 260-42 (September 1972). COM72-

50944**

Yakowitz, H., Ruff, A. W„ and Michaelis, R. E., Standard Reference Materials: Preparation and Homogeneity Characterization of an Austenitic Iron-Chromium-Nickel Alloy, NBS Spec. Publ. 260-43 (November 1972). COM73-50760**

Schooley, J. F„ Soulen, R. J., Jr., and Evans, G. A.,

Jr., Standard Reference Materials: Preparation and Use of Superconductive Fixed Point

Devices, SRM 767, NBS Spec. Publ. 260-44 (December 1972). COM73-50037**

Greifer, B., Maienthal, E. J., Rains, T. C, and

Rasberry, S. D., Standard Reference Materials: Powdered Lead-Based Paint, SRM 1579, NBS

Spec. Publ. 260-45 (March 1973). COM73-

50226**

Hust, J. G.,and Giarratano, P. J., Standard Refer- ence Materials: Thermal Conductivity and

Electrical Resistivity Standard Reference Materials: Austenitic Stainless Steel, SRM's 735 and

798, from 4 to 1200 K, NBS Spec. Publ. 260-46 (March 1975). SN003-003-0 1278-5* Hust, J. G., Standard Reference Materials: Electrical Resistivity of Electrolytic Iron, SRM 797, and Austenitic Stainless Steel, SRM 798, from 5 to 280 K. NBS Spec. Publ. 260-47 (February

1974). COM74-50176** Mangum, B. W., and Wise, J. A., Standard Refer- ence Materials: Description and Use of Precision Thermometers for the Clinical Laboratory, SRM 933 and SRM 934, NBS Spec. Publ. 260-48 (May 1974). 60 cents* SN003-003-0 1278-5 Carpenter, B. S., and Reimer, G. M., Standard

Reference Materials: Calibrated Glass Standards for Fission Track Use, NBS Spec. Publ. 260-49 (November 1974). COM74-51185

v
Hust, J. G., and Giarratano, P. J., Standard Refer- ence Materials: Thermal Conductivity and Electrical Resistivity Standard Reference Materials:

Electrolytic Iron, SRM's 734 and 797 from 4 to 1000 K, NBS Spec. Publ. 260-50 (June 1975). $1.00* SN003-003-0 1425-7 Mavrodineanu, R., and Baldwin, J. R., Standard

Reference Materials: Glass Filters As a Standard Reference Material for Spectrophotometry;

Selection; Preparation; Certification; Use-SRM

930, NBS Spec. Publ. 260-51 (November 1975). $1.90* SN003-003-OI481-8

Hust, J. G., and Giarratano, P. J., Standard Refer- ence Materials: Thermal Conductivity and Electrical Resistivity Standard Reference Materials 730 and 799, from 4 to 3000 K, NBS Spec. Publ. 260-52 (September 1975). $1.05* SN003-003-

01464-8 Durst, R. A., Standard Reference Materials: Standardization of pH Measurements, NBS

Spec. Publ. 260-53 (December 1975, Revised). $1.05 SNO03-O03-O1551-2

Burke, R. W., and Mavrodineanu, R., Standard

Reference Materials: Certification and Use of

Acidic Potassium Dichromate Solutions as an

Ultraviolet Absorbance Standard, NBS Spec.

Publ. 260-54 (August 1977). $3.00* SN003-003-

01828-7

Ditmars, D. A., Cezairliyan, A., Ishihara, S., and

Douglas, T. B.. Standard Reference Materials: Enthalpy and Heat Capacity; Molybdenum SRM 781, from 273 to 2800 K, NBS Spec. Publ. 260-55 (September 1977). $2.20* SN003-003-

01836-8

Powell, R. L., Sparks, L. L., and Hust, J. G„

Standard Reference Materials: Standard

Thermocouple Materials, Pt.67: SRM 1967, NBS

Spec. Publ. 260-56 (February 1978). $2.20* SN003-003-0 18864

Cali, J. P. and Plebanski, T., Guide to United

States Reference Materials, NBS Spec. Publ. 260-57 (February 1978). $2.20* PB 277173

Barnes, J. D., and Martin, G. M., Standard Refer- ence Materials: Polyester Film for Oxygen Gas

Transmission Measurements SRM 1470, NBS

Spec. Publ. 260-58 (June 1979) $2.00* SN003-

003-02077 Chang, T., and Kahn, A. H. Standard Reference

Materials: Electron Paramagnetic Resonance

Intensity Standard; SRM 2601, NBS Spec.

Publ. 260-59 (August 1978) $2.30* SN003-

003-01975-5 Velapoldi, R. A., Paule, R. C, Schaffer, R., Mandel, J., and Moody, J. R., Standard Refer- ence Materials: A Reference Method for the Determination of Sodium in Serum, NBS Spec.

Publ. 260-60 (August 1978). $3.00* SN003-003

01978-0

Verdier, P. H., and Wagner. H. L., Standard Refer- ence Materials: The Characterization of Linear Polyethylene (SRM 1482, 1483, 1484), NBS

Spec. Publ. 260-61 (December 1978). $1.70* SN003-O03-O2OO6-1

Soulen, R. J., and Dove, R. B., Standard Reference

Materials: Temperature Reference Standard

for Use Below 0.5 K (SRM 768). NBS Spec.

Publ. 260-62 (April 1979). $2.30* SN003-003-

02047-8 Velapoldi, R. A., Paule, R. C, Schaffer, R. Mandel, J., Machlan, L. A., and Gramlich, J. W., Standard Reference Materials: A Reference Method for the Determination of Potassium in Serum. NBS Spec. Publ. 260-63 (May 1979). $3.75* SN003-003-02068

Velapoldi, R. A., and Mielenz, K. D., Standard

Reference Materials: A Fluorescence Standard

Reference Material Quinine Sulfate Dihydrate (SRM 936), NBS Spec. Publ. 260-64 (January

1980). $4.25* SNO03-O03-O2 148-2 Marinenko, R. B., Heinrich, K. F. J., and Ruegg,

F. C, Standard Reference Materials: Micro- Homogeneity Studies of NBS Standard Reference

Materials, NBS Research Materials, and Other Related Samples. NBS Spec. Publ. 260-65

(September 1979). $3.50* SN003-003-021 14-1 Venable, W. H., Jr., and Eckerle, K. L., Standard

Reference Materials: Didymium Glass Filters for Calibrating the Wavelength Scale of Spectro- photometers (SRM 2009, 2010, 2013). NBS Spec.

Publ. 260-66 (October 1979). $3.50* SN003-003-

02127-0

Velapoldi, R. A., Paule, R. C, Schaffer, R., Mandel,

J., Murphy, T. J., and Gramlich, J. W., Standard

Reference Materials: A Reference Method for the Determination of Chloride in Serum, NBS Spec.

Publ. 260-67 (November 1979). $3.75* SN003-

003-02136-9 Mavrodineanu, R. and Baldwin, J. R., Standard

Reference Materials: Metal-On-Quartz Filters as a Standard Reference Material for Spectrophoto- metry-SRM 2031, NBS Spec. Publ. 260-68

(April 1980). $4.25* SN003-003-02 167-9 Velapoldi, R. A., Paule, R. C, Schaffer, R., Mandel, J., Machlan, L. A., Garner, E. L., and

Rains, T. C, Standard Reference Materials: A

Reference Method for the Determination of Lithium in Serum, NBS Spec. Publ. 260-69 (July)

1980). $4.25* SNO03-O03-O2214-4 Marinenko, R. B., Biancaniello, F., Boyer, P. A., Ruff, A. W., DeRobertis, L., Standard Reference

Materials: Preparation and Characterization of an Iron-Chromium-Nickel Alloy for Microanalysis, NBS Spec. Publ. 260-70 (May 1981). $2.50* SN0O3-O03-O2328-1

Seward, R. W., and Mavrodineanu, R., Standard

Reference Materials: Summary of the Clinical Laboratory Standards Issued by the National Bureau of Standards, NBS Spec. Publ. 260-71 (November 1981). $6.50* SN003-003-O238I-7

Reeder, D.J., Coxon, B., Enagonio, D., Christensen, R. G., Schaffer, R., Howell, B. F., Paule, R. C,

Mandel, J., Standard Reference Materials: SRM

900, Antiepilepsy Drug Level Assay Standard, NBS Spec. Publ. 260-72 (June 1981). $4.25* SN003-003-02329-9

vi
Interrante, C. G., and Hicho, G. E , Standard Refer- ence Materials: A Standard Reference Material Containing Nominally Fifteen Percent Austenite (SRM 486), NBS Spec. Publ. 260-73 (January

1982). $2.75* SN003-003-02386-8 Marinenko, R. B., Standard Reference Materials: Preparation and Characterization of K-411 and

K-414 Mineral Glasses for Microanalysis: SRM

470. NBS Spec. Publ. 260-74 (April 1982). $3.50 SN003-003-023-95-7

Weidner, V. R., and Hsia, J. J., Standard Reference

Materials: Preparation and Calibration of First Surface Aluminum Mirror Specular Reflectance Standards (SRM 2003a), NBS Spec. Publ. 260-75 (May 1982). $3.75 SN003-003-023-99-0

Hicho, G. E. and Eaton, E. E., Standard Reference Materials: A Standard Reference Material

Containing Nominally Five Percent Austenite (SRM 485a), NBS Spec. Publ. 260-76 (August

1982). $3.50 SN003-003-024-33-3 Furukawa, G. T., Riddle, J. L., Bigge, W. G., and

Pfieffer, E. R., Standard Reference Materials: Application of Some Metal SRM's as Thermometric Fixed Points, NBS Spec. Publ. 260-77 (August 1982). $6.00 SN003-003-024-34-1

Hicho, G. E. and Eaton, E. E., Standard Reference

Materials: Standard Reference Material Containing Nominally Thirty Percent Austenite (SRM

487), NBS Spec. Publ. 260-78 (September 1982). $3.75* SN003-003-024-35-0 Richmond, J. C, Hsia, J. J. Weidner, V. R., and

Wilmering, D. B., Standard Reference Materials: Second Surface Mirror Standards of Specular

Spectral Reflectance (SRM's 2023, 2024, 2025), NBS Spec. Publ. 260-79 (October 1982). $4.50* SN003-003-024-47-3

Schaffer, R„ Mandel, J., Sun, T., Cohen, A., and

Hertz, H. S., Standard Reference Materials: Evaluation by an ID/ MS Method of the AACC

Reference Method for Serum Glucose, NBS

Spec. Publ. 260-80 (October 1982). $4.75* SN003-

003-024-43-1 Burke, R. W., and Mavrodineanu, R. (NBS retired). Standard Reference Materials: Accuracy in Analytical Spectrophotometry, NBS Spec. Publ. 260-81 (April 1983). $6.00* SN003-003-024-8

Weidner, V. R., Standard Reference Materials: White Opal Glass Diffuse Spectral Reflectance Standards for the Visible Spectrum (SRM's 2015 and 2016). NBS Spec. Publ. 260-82 (April 1983). $3.75* SN003-003-024-89-9**

Bowers, G. N., Jr., Alvarez, R„ Cali, J. P. (NBS

retired), Eberhardt, K. R., Reeder, D. J., Schaffer, R., Uriano, G. A., Standard Reference

Materials: The Measurement of the Catalytic

(Activity) Concentration of Seven Enzymes in NBS Human Serum SRM 909, NBS Spec.

Publ. 260-83 (June 1983). $4.50* SN003-003-024-

99-6

Gills, T. E., Seward, R. W„ Collins, R. J., and

Webster, W. C, Standard Reference Materials: Sampling, Materials Handling, Processing, and Packaging of NBS Sulfur in Coal Standard

Reference Materials, 2682, 2683, 2684, and 2685, NBS Spec. Publ. 260-84 (August 1983). $4.50* SN003-003-025-20-8

Swyt, D. A., Standard Reference Materials: A Look

at Techniques for the Dimensional Calibration of Standard Microscopic Particles, NBS Spec. Publ. 260-85 (September 1983). $5.50* SN003-003-

025-21-6

Hicho, G. E. and Eaton, E. E., Standard Reference Materials: A Standard Reference Material

Containing Two and One-Half Percent Austenite. SRM 488, NBS Spec. Publ. 260-86 (December

1983) . $1.75* SN003-003-025-41-1 Mangum, B. W., Standard Reference Materials: SRM 1969: Rubidium Triple-Point - A Temperature Reference Standard Near 39.30 °C, NBS

Spec. Publ. 260-87 (December 1983). $2.25* SN003-003-025-44-5 Gladney, E. S., Burns, C. E., Perrin, D. R., Roelandts, I., and Gills, T. E., Standard Reference Materials: 1982 Compilation of Elemental

Concentration Data for NBS Biological, Geological, and Environmental Standard Reference

Materials. Spec. Publ. 260-88 (March 1984). $7.00* SNOO3-OO3-02565-8

Hust, J. G., Standard Reference Materials: A Fine- Grained, Isotropic Graphite for Use as NBS

Thermophysical Property RM's from 5 to 2500 K, NBS Spec. Publ. 260-89 (September 1984). $4.50* SN003-003-02608-5

Hust, J. G., and Lankford, A. B., Standard

Reference Materials: Update of Thermal

Conductivity and Electrical Resistivity of

Electrolytic Iron, Tungsten, and Stainless Steel, NBS Spec. Publ. 260-90 (September 1984). $3.00* SN003-003-02609-3

Goodrich, L. F., Vecchia, D. F., Pittman, E. S., Ekin, J. W., and Clark, A. F., Standard Reference

Materials: Critical Current Measurements on an NbTi Superconducting Wire Standard Reference

Material, NBS Spec. Publ. 260-91 (September

1984) . $2.75* SN003-003-026I4-0

Carpenter, B. S., Standard Reference Materials: Calibrated Glass Standards for Fission Track Use (Supplement to NBS Spec. 260-49). NBS

Spec. Publ.. 260-92 (September 1984). $1.50* SN003-003-02610-7

Ehrstein, J., Preparation and Certification of Standard Reference Materials for Calibration of Spreading Resistance Probes, NBS Spec. Publ. 260-93 (January 1985).

Gills, T. E., Koch, W. F. Stolz, J. W., Kelly, W. R., Paulsen, P. J., Colbert, J. C. Kirklin. D. R., Pei, P.T.S., Weeks, S., Lindstrom, R. M. Fleming, R. F., Greenberg, R. R., and

Paule, R. C, Methods and Procedures Used at the National Bureau of Standards to Certify Sulfur

in Coal SRM's for Sulfur Content, Calorific Value, Ash Content, NBS Spec. Publ. 260-94 (December 1984). Mulholland, G. W., Hartman, A. W., Hembree,

G. G., Marx, E., and Lettieri, T. R., Standard

Reference Materials: Development of a 1 m

Diameter Particle Size Standard, SRM 1690, NBS Spec. Publ. 260-95 (May 1985).

vii
Carpenter, B. S., Gramlich, J. W., Greenberg, R. R., and Machlan, L. A., Standard Reference

Materials: Uranium-235 Isotopic Abundance Standard Reference Materials for Gamma

Spectrometry Measurements, NBS Spec. Publ. 260-96 (In Press). Mavrodineanu, R. and Gills, T. E., Standard

Reference Materials: Summary of the Coal, Ore,

Mineral, Rock, and Refractory Standards Issued by the National Bureau of Standards, NBS Spec.

Publ. 260-97 (In Press). Hust, J. G., Standard Reference Materials: Glass Fiberboard SRM for Thermal Resistance, NBS

Spec. Publ. 260-98 (In Press). Callanan, J. E., Sullivan, S. A., and Vecchia, D. F., Standard Reference Materials: Feasibility Study

for the Development of Standards Using

Differential Scanning Calorimetry, NBS Spec.

Publ. 260-99 (In Press). Taylor, J. K., Standard Reference Materials: Hand- book for SRM Users, NBS Spec. Publ. 260-100

(In Press).

* Send order with remittance to Superintendent

of Documents, US Government Printing Office Washington, DC 20402. Remittance from

foreign countries should include an additional one-fourth of the purchase price for postage.

** May be ordered from: National Technical Information Services (NTIS). Springfield

Virginia 22161.
ABSTRACT

This handbook was prepared to provide guidance for the use of Standard Reference Materials

(SRM's) to provide an accuracy base for chemical measurements. The general concepts of precision and accuracy are discussed and their realization by quality assurance of the measurement

process. General characteristics of SRM's are described and guidance is given for their selection for specific applications. Ways to effectively use SRM's are recommended, utilizing

control charts to evaluate and monitor measurement accuracy. Appendices provide statistical

guidance on the evaluation of measurement uncertainty.

Key words: accuracy; calibration; chemical analysis; control charts; measurement uncertainty;

precision; quality assurance; standard reference materials; statistical control.

ix
TABLE OF CONTENTS

Page PREFACE

ABSTRACT T ix

1 . Introduction 1 2. Precision and Accuracy 2 2.1 Concepts of Precision and Accuracy 2 2.1.1 Precision and Bias in a Measurement System 3 2.2 Dependence on Standards 4 2.3 Physical and Chemical Standards 4 2.4 Calibration, Standardization, and Analytical Response Function 5 2.5 National Measurement System for Analytical Chemistry 6 3. Quality Assurance 8 3.1 Quality Assurance of a Measurement Process 8 3.2 Statistical Control 8 3.3 Control Charts 9 3.1 Frequency of Use of Reference Materials 12

4. Reference Materials 14 4.1 Role of Reference Materials 14 4.2 Concept of Traceability 14

5. Standard Reference Materials 16 5.1 Philosophy of SRM Production 16 5.2 How an SRM is Produced 16 5.3 Differences Among Measurement Methods 18 5.4 Understanding Certificate Information 18 5.5 Uncertainty of Certified Values 19

6. Use of SRM's 22

6.1 Kinds of SRM's 22 6.2 Choosing an SRM 24

6 . 3 Use of SRM' s 25 6.4 Interpretation of Reference Material Analyses 27 6.5 Evaluation of Measurement Error 30

7. Reporting Analytical Data 32 7.1 Limits of Uncertainty for Data 32 7.2 Significant Figures 32 7.3 Guidelines for Reporting Results of Measurements 33

8. NBS Services Related to SRM's 34

9. Bibliography 35 9.1 Reference Cited 35 9.2 Publications of the NBS Center for Analytical Chemistry Related to SRM's 35 10. Information 40 Appendix A. Glossary of Terms 41 Appendix B. Conversion Factors and Appendix B 46 Appendix C. Statistical Tools 54 C.1 Introduction 54 C.2 Estimation of Standard Deviation 55 C.2.1 Estimation from Replicate Measurements 56 C.2. 2 Estimation from Duplicate Measurements 56 C.2. 3 Estimation from the Range 57 C.2. 4 Pooling Estimates of Standard Deviations 58 C.3 Do Two Estimates of Precision Differ? 58 C.4 What are the Confidence Limits for an Estimate of a Standard Deviation? 59 C.5 Do Two Measured Values Agree? 59 C.6 Confidence Intervals for a Mean 59 C.7 Tolerance Intervals 61 C.8 Pooling Means to Obtain a Grand Average 62 C.9 Outliers 63

C. 10 Use of Random Number Tables 64 Appendix D. Reprints 65

D. 1 Quality Assurance of Chemical Measurements 65 D.2 Sampling for Chemical Analysis 70 D.3 Reference Materials - What They Are and How They Should Be Used 78 D.4 Validation of Analytical Measurements 81

x
LIST OF TABLES

Page Table 1. Quality Assessment Using Reference Materials 12 Table 2. Quality Assessment Using Duplicate/Splits 13 Table 3. Inventory of SRM's, 1 969 - 1 984 22 Table 4. Some Major New SRM Needs Forecasts for the Period 1984 - 1989 24 Table 5. Uses of SRM's in Measurement Systems 25 Table B.1 Conversion Factors 46 Table B.2 Use of Range to Estimates Variability 47 Table B.3 Critical Values for the F Test 48 Table B.4 Factors for Computing Two-Sided Confidence Limits for o 49 Table B.5 Percentiles of the t Distribution 50 Table B.6 Factors for Two-Sided Tolerance Limits for Normal Distributions 51 Table B.7 Short Table of Random Numbers 52 Table B.8 Z-Factors for Two-Sided Confidence Intervals 53

xi
LIST OF FIGURES

Figure 1. Unbiased measurement processes 2 Figure 2. Biased measurement processes 2 Figure 3. National measurement system for analytical chemistry 6 Figure 4. Measurement process quality assurance 8 Figure 5. Control chart 10 Figure 6. Measurement compatibility by i n t er compar i son , using SRM's 15 Figure 7. Systems approach to measurement accuracy 26 Figure 8. Interpreting SRM measurements 28 Figure 9. Identifying measurement bias 29 Figure 10. Uncertainty of measured value 30 Figure C.I Expected distribution of means of random samples/measurements 5^ Figure C.2 Confidence interval for o 55 Figure C.3 Computed 50% confidence intervals for the population mean, m, from 100 samples of H; 40 samples of 100; and 4 samples of 1000 55

xii
1 . Introduction

Standard Reference Materials (SRM's) have become well established as benchmarks for the quality assurance of measurements. Some analytical chemists find them i nd i spe ns i b 1 e for this purpose and use them systematically; others use them sporadically. Yet, there are others and those especially in some areas of analytical chemistry who rarely if ever use reference materials. From casual observation, the frequency of use of reference materials is closely

coupled with one or more of the following factors:

- familiarity with the philosophy of their use

- degree of appreciation of the benefits of their use

- availability of d i r e c t 1 y- ap p 1 i ca b 1 e SRM's

- understanding of the role of directly and indirectly related SRM's in a measurement

system

- degree of full appreciation of measurement as a system.

The National Bureau of Standards has pioneered and continues to be the leader in the development of Standard Reference Materials (SRM's) for quality assurance of measurements.

The program to provide such materials, originally known as standard samples, was initiated in 1906, largely in response to needs of the metals industry. It has since grown to a multimaterial program of over 1000 items that serves most of the areas of modern analytical chemistry. A large number of materials useful in physical metrology and engineering are also included. Some areas of analysis are covered more completely than others, due to historical

reasons, priorities for national issues, and to some extent the degree of industrial awareness

of the quality assurance concept. For the early users, SRM's were identical, in most respects, to the materials ordinarily analyzed. Thus the results of measurements of SRM's

were easily interpreted. As the program has grown, it has become impossible to provide SRM's

with a one-to-one correspondence to every conceivable application; as a result, generic standards are commonly produced which serve multi-purposes. This concept broadens the scope of applications and conserves effort and cost of production.

This handbook was prepared with the objective to improve the understanding and the basis

for use of SRM's. While written from the viewpoint of a chemist, the basic concepts described

are believed to be applicable to most areas of metrology. The handbook is arranged in a logical progression, starting with the basic concepts of precision and accuracy, followed by dis- cussions of the calibration and quality assurance of the measurement process, the use of Standard Reference Materials to evaluate various kinds of measurements, and the reporting of data with evaluated limits of uncertainty. The statistical considerations most frequently

applicable for the evaluation and interpretation of measurement data are reviewed in the Appendix. Each section is written with some degree of independence so that it can be understood without undue reference to the contents of other Sections.

The treatment of each subject is not claimed to be exhaustive but is often an overview. Accordingly, a list of selected references is included which contain both background and other information supplemental to that in the text. A listing of recent research papers from the NBS Center for Analytical Chemistry, related to the preparation, analysis, and certification

of specific SRM's is also included.

SOURCES OF INFORMATION

(See page 40 for more details)

NBS Standard Reference Materials

Telephone Number: 3 01-921-2045

Mailing lists are maintained to keep SRM users updated with catalogs and information on new SRM's. Call the number above to have your name added.

The free magazine American Laboratory has a monthly column called "Reference Materials to provide an information forum for SRM users.
2. Precision and Accuracy

2.1 Concepts of Precision and Accuracy

Accuracy is an intuitively understandable and desirable requirement for most measurements. Data which are knowingly inaccurate or whose accuracy is unknown have little

appeal to most users. Yet precision is sometimes confused with accuracy and the agreement of successive results can inspire a degree of confidence that the measurements may not merit. Accuracy, the closeness of a measured value to the true value, includes the concepts of bias and precision (see figure 1 and figure 2) and is judged with respect to the use to be made of the data. A measurement process must be unbiased to be capable of producing accurate

values. In such a case, it must be sufficiently precise, as well, or else the individual results will be inaccurate due to unacceptable variability. The following discussion is pre- sented to clarify these concepts. The term uncertainty is used widely in describing the results of measurement and denotes an estimate of the bounds of inaccuracy. Strictly speaking, the actual error of a reported value is usually unknowable. However, limits of error ordinarily can be inferred, with some risk of being incorrect, from the precision and- reasonable limits for the possible bias of the measurement process.

Figure 1. Unbiased Measurement Processes

The distributions of results from three unbiased processes are shown.

The precision decreases in the order A>B>C. While the limiting

means of all will approach the "true value," process C is relatively

inaccurate (compared with A) due to its imprecision.

Figure 2. Biased Measurement Processes

All of the processes are biased and hence inaccurate since the limiting means do not coincide with the "true value." However, it will be noted that most of the results for process A' will be more accurate than those of process C and even B (figure 1), due to precision considerations.

2
The concept of precision is concerned with the variability of the individual results of replicate measurements. A process which shows a small scatter is said to be precise and vice

versa. Obviously such judgments are subjective and based on the intended use of the data. What might be considered as very precise for one purpose could be grossly imprecise for another. Random errors are responsible for the observed scatter of measured values. These may

be reduced to the point at which they are negligible with respect to the tolerable error of the measured value, or are limited by inherent characteristics of the instrumentation or the methodology used. The averages of several series of measurements will show a smaller vari- ability than the individual values and the grand average of such is expected to approach a limiting value (limiting mean) as the number of measurements is increased.

The concept of bias is concerned with whether or not the limiting mean differs from the true (or accepted) value of the property measured. Here again, judgment is ordinarily

involved since it is impossible to eliminate all error or even to know if this has been achieved. Such decisions are thus based on whether or not bias exists for all practical

pur poses . In the case of individual measurements, each will exhibit some degree of inaccuracy, that

is to say it will deviate from the true value. This will occur because of random error together with any bias of the measurement system. Indeed, it is highly improbable that any individual measurement made by an unbiased measurement system will be accurate, since the probability of zero random error is zero. Many individual values may appear to have the correct value but this is due to truncation resulting from i nsensi ti vity of the measurement

process or from rounding of the data.

A measurement process should be sufficiently precise to minimize the number of replicate measurements required for the intended use. A very precise system may need only a few mea- surements, even one, to provide data that would not be significantly improved by further replication. Also, a measurement system must be sufficiently precise to identify whether or not biases of a comparable magnitude are present in the system. While possible in principle,

an unbiased measurement process of low precision may be incapable of providing accurate data, from a practical point of view, because of the large number of measurements required to reduce

the uncertainty of the random error to reasonable limits. Precision may be evaluated by the redundant process of replicate measurement. Results on

a single material may be used for this purpose, or the information obtained on a number of samples (even duplicate measurements, see Appendix C.2.2) may be pooled. Accordingly, there

is no reason why a laboratory cannot evaluate its own precision without external assistance

[1]. While SRM's may be helpful in this regard, they are not necessary for this purpose.

In order to properly estimate precision, a number of measurements over an extended period

of time may be required. A small number of measurements tend to underestimate the standard deviation since small random errors are more probable than large ones and less likely to be observed during a limited set of measurements. Also, it is common experience that it is much easier to repeat a measurement than to reproduce it over a period of time. The r e pe a t i b i 1 i t y

,

or short-term standard deviation is needed to answer questions about the number of repetitive

measurements, that may be required while the long-term standard deviation, or reproducibility

is needed to answer such questions as the agreement of data obtained at different times, or the statistical control of a measurement process. Though precise measurements can serve useful purposes when limited comparisons are required, accuracy is more often an essential requirement. Whenever the true value of the measured quantity is needed, or when data from different laboratories, different methodologies, or that from the same laboratory using the same method over a period of time needs to

be interrelated, bias can be a serious problem. The analysis of appropriate reference materials is the best and easiest way to investigate bias. While methods may be compared with reference methods to assess accuracy, this is ordinarily a more difficult and time-consuming

process (see Appendix D . k ) . 2.1.1 Precision and Bias in a Measurement System

The precision of a measurement system may be influenced by a number of factors, each having its own precision. The precision of each factor, quantified in terms of the variance, contributes to the precision of the process. The variance is simply the square of the standard deviation, s. In measurement processes, the variances of the individual steps, sf , add

up to define the variance of the process, i.e., s

2

= s \

+ s \ + s 3 + . . + s^. Some of the steps (or factors) can be easily identified and the individual variances estimated. Examples

are weighing and extraction. As steps are identifiable, improvements conceiveably can be made when there are "assignable causes" for undesirable imprecision. Because of addition in quad- rature, it is evident that one or a few sources of variance can be the major contributors to the total variance. Knowledge of the magnitude of the individual variances can indicate both directions for improvement and possible sources of trouble when " ou t

- of - co n t r ol " measurements

occur

3
It is conceivable that variance can be reduced to very low levels, with diligent effort. Laboratories commonly improve their precision as they gain experience with their methodology.

Ordinarily, a laboratory will improve its quality control practices to the point where the precision attained is adequate for a particular application or when peer performance has been attained. Because analysis must be pragmatic, cost-benefit decisions will often dictate how

far to go. For example, it is a matter of record that laboratories using the same methodology

will differ in their precisions. This may be due to difference in levels of skill but also to different levels of tolerance for permissible error.

Bias in measurement systems can result from several sources. The commonly recognized

ones are: control of measurement variables; interferences; erroneous calibration; contamination; losses; deteriorations; inefficiencies in extractions or sample dissolution. Variability in some of these can contribute to random error as well, and often to a major degree.

Inappropriate calibration techniques can be a serious source of bias. Reliance on spiking

which may not simulate ma t r i x - i n cor p or a t e d analyte, or the use of a pure matrix (e.g., pure water) to simulate a natural matrix (waste water) are typical examples. A reference material

that closely simulates the analytical samples is needed to identify and evaluate such biases. Unlike random errors, systematic errors or biases from several sources are not necessarily randomly distributed; hence one must consider that biases can add up algebraically. That is to say, the total bias B = B

1 + B

2

+ • • • + B . Thus, a large number

of small biases can equal or even exceed a large bias from a single source. While the_effect

of random error decreases as the number of measurements, n, is increased (s- = s

x //n), the effect of bias is independent of the number of measurements.

2.2 Dependence on Standards

All measurements depend on standards. Physical measurements depend almost entirely on physical standards with little or no dependence on chemical standards. Chemical measurements

on the other hand depend on both with greater dependence on the latter. The early recognition

of the need for universally acceptable physical standards, and the chaos that could result

from their unavailability led to the development of the now universally accepted physical standards for the primary units of length, mass, time, temperature, and radiant luminosity and

the units derived from them such as pressure, force, acceleration, power, and density. No corresponding chemical standards have ever been developed. There are, of course, the useful standards of atomic weights and a variety of physi cochemi cal standards.

The early chemical analytical measurements were largely absolute in nature, which means

that they depended almost entirely on physical standards. Thus, classical analysts used gravimetry in which chemical constituents were removed quantitatively or isolated from their matrix, purified, and weighed. Relation of such masses to the chemical information desired was calculated by stoichiometry . The critical sources of error in such measurements were incomplete separations, mechanical losses, and contamination due to co pr e c i p i t a t i on and analytical

blanks. Physical standards were the primary standards and provided adequate and sufficient

means to control the accuracy of such chemical measurements.

While classical methods augmented by such ph y s i ca 1 - chem i ca 1 techniques as coulometry,

still provide the basis for the most accurate measurement of major constituents or for the assay of pure materials, the bulk of modern chemical measurements are made by comparative

techniques in which, in essence, an instrument is used to compare an unknown sample with one

of known composition. Some measurements require the removal of the substance of interest

prior to analysis, or its isolation from the matrix using physical or chemical techniques. In others, the analytical process may combine the separation and measurement steps. Separation

of a group of analytes, followed by selective detection is another approach to analysis.

The trend toward comparative measurements has shifted the need in chemical analysis from heavy dependence on physical standards to heavy dependence on chemical standards. However,

there is usually no problem in obtaining chemicals of requisite purity to serve as chemical standards so that essentially no national or i n t er na t Lanal—"^t andar d chemicals have been developed or exist today, in the same sense as the physical standards. When reference materials

exist, they are ordinarily not chemical standards in the hierarchal sense of physical standards of measurement but rather are quality assurance materials as will be discussed later.

Of course, some reference materials are high purity chemicals which may be used as primary

standards in some areas of chemical analysis.

2.3 Physical and Chemical Standards

Seven basic units for physical measurements have been ado-pted by international agreement.

From these, all other units of measurement may be derived (2). The basic units are defined by appropriate artifacts or measurements. Transfer standards may be calibrated with respect to the basic standards maintained in national laboratories. Such calibrations must be done with

a sufficient degree of reliability, traceable to national standards. For most chemical measurements, uncertainties in the physical standards used do not contribute significantly to the analytical uncertainty.

4
Chemical standards differ from physical standards in several ways. They are chemical

elements or compounds, usually identical with or related by stoi chi ometry , to the analytes

measured. It is ordinarily possible to obtain such standards in sufficient purity or to purify them adequately so there is no need to maintain them in a national laboratory. Due to the complexity and variety of chemical measurements it would be infeasible if not impossible

to do so

The problem in the use of chemical standards is the degree to which they can be blended

or incorporated into a sample matrix to produce a substance that can reliably calibrate or define the response function of a chemical analyzer. Matrix match between standard and analytical sample is often critical but difficult to achieve. When standards are carried through

an entire analytical process, spikes, surrogates, and other artificially introduced constituents may not respond in the same manner as naturally occurring analytes, thus causing cali- bration problems. On the other hand, standards prepared to simulate the final analytical

sample (e.g., an extract or a solution of the original sample) may not calibrate the entire analytical process.

No matter what kind of standards are used, they must be prepared with care from reliable

starting materials. The mode of preparation should be such that the uncertainty of the standards does not contribute significantly to the overall analytical uncertainty. Chemists ordinarily assume that standards can be prepared with negligible error. Standards for very

low concentration levels may be exceptions. Furthermore, the stability of such standards and

the degree of protection required to safeguard them from contamination, deterioration, or losses always needs consideration.

Standards should never be used in an e x t r a po 1 a t i ve mode. They should always bracket the measurement range. No measurement should be reported at a value lower or higher than the lowest or highest standard used to calibrate the measurement process.

2.H Calibration, Standardization, and Analytical Response Function Calibration may be defined as the comparison of a measurement standard or instrument with another standard or instrument to identify or eliminate by adjustment any variation (deviation) of the accuracy of the item being compared. Physical standards such as masses, and instruments such as thermometers are calibrated. Physical standards or calibrated instruments, traceable to national standards are required for calibration of other standards or instruments. The uncertainty of the calibrations will depend on the uncertainty of the values

of the standards used and the measurement processes used for the i n t er com par i s ons . Chemical measurements require standards consisting of pure chemicals or liquid, solid, or gaseous mixtures prepared from them. For most applications, chemicals of sufficient purity

for use as standards or for their preparation, can be obtained from suppliers. For critical applications, chemical standards are sometimes assayed to determine their purity or analyzed

for impurities in order to calculate their composition. The latter practice can be erroneous

unless it is ascertained that all significant impurities have been determined. The concentrations of solutions used as analytical reagents or as calibrants are sometimes defined on the basis of their pr e par a t i on al data and knowledge or assumptions of purity. When concentrations

are determined by comparison with other solutions of known concentrations, the process is called standardization.

In general, the calibration of a chemical analyzer consists in the evaluation of its response function, in terms of chemical composition of the samples to be analyzed. The analyzer responds to some property of the analyte, the value of which needs to be quantified by use of known substances. Then it is tacitly assumed that the instrument will respond analogously to the standard and test samples. The sources of uncertainty in this case are the uncertainty in composition of the known samples and the validity of the analogy.

'it is a generally accepted principle of reliable analysis that chemical analyzers should

be calibrated over the full range of measurement and that measurement data be restricted to the range calibrated. It is not good measurement practice to report extrapolated data, i.e., data outside of the range calibrated. The range of reliable calibration can be considered as the range of reliable measurement and conversely.

The necessary frequency of re-calibration or re-evaluation of a response function will depend on the stability of the measurement system and the accuracy requirements for the data.

To ensure confidence in measured values, such re-evaluations should be made before significant

changes are to be expected.

The terms primary and secondary standards are used frequently and need some discussion. Strictly speaking, a primary standard is one whose value may be accepted without further veri- fication by the user. It, in turn, may be used to establish or ascertain a value for a secondary standard. Thus, a secondary standard provided by one laboratory (for example, a mass standard calibrated at NBS) could serve as a primary standard for another laboratory. In any case, the uncertainty of the value of any standard must be known since the adjective

designation (primary or secondary) does not define any limits of uncertainty for its value.

5
Analytical chemists have used the terms primary and secondary to indicate relatively pure materials that may be used to prepare solutions with accurately known compositions (3). The International Union of Pure and Applied Chemistry CO has set minimum levels of purity for primary and secondary chemicals. Specifications for certain classes of physical standards, have been established which include design characteristics and permissible departures (tolerances) from nominal values. Thus a 1 gram weight of Class 1 will have a tolerance of 0.03^ mg while the tolerance is 2 mg for a Class 6 weight of the same denomination (5). The nominal weight is assumed, when used,

but it should be recognized that the true value may lie anywhere within the tolerance range.

If such an uncertainty is too large, the standard may be calibrated, but upgrading may be difficult due to design considerations.

2.5 National Measurement System for Analytical Chemistry

What might be called the National Measurement System for Analytical Chemistry is shown in Figure 3. The measurement of any specific sample requires a measurement system, individually

designed with consideration of the requirements for the data. This system must be calibrated,

using physical and chemical standards. As already discussed, the physical standards may be traceable to national primary standards maintained by the National Bureau of Standards and compatible with those of other nations. The chemical standards, generally, will be prepared

by the measurement laboratory. Ordinarily, they serve as quality assurance materials to evaluate measurement accuracy, to i n t er ca 1 i br a t e laboratories in a measurement program, and to provide compatibility of measurement data. SRM's can serve as calibrants in some cases.

National

Physical Standards

Measurement

ManufacSynthesis Chemicals

I SRM'S

(National Primary Chemical

Standards)

Physico- Chemical

Constants

Science/ \

Technology J

Scientific Technical Research

Figure 3. National Measurement System for Analytical Chemistry

The figure illustrates a number of points that have been discussed earlier. The critical dependence of modern analysis on both physical and chemical standards is indicated although

the former of requisite reliability usually are available to the analyst from external

sources. Ordinarily, the chemist must prepare all chemical standards used, starting with source materials as indicated. Questions about the matrix match of standards and test samples

always must be considered. The measurement process is highly dependent on broad areas of science and technology, as well.

6
Quality assurance of the measurement process is essential for reliable data. The important role of SRM's in controlling the calibration process and in assessing data quality

is shown and will be elaborated on throughout this handbook.

7
3. Quality Assurance

Quality assurance is the name given to the procedures used to ascertain that measurement

data are good enough for their intended purpose (1,6). It involves two distinct but related activities:

quality control - those procedures and activities developed and implemented to produce a measurement of requisite quality

quality assessment - those procedures and activities utilized to verify that the quality

control system is operating within acceptable limits and to evaluate the quality of the data

.

The basic requirements for producing reliable data are appropriate methodology,

adequately calibrated, and properly used. These, together with good laboratory and measurement practices, are the basic ingredients of a quality control program. The quality of the data may be assessed by use of reference materials to evaluate bias and the time-consuming

process of redundancy to evaluate precision.

3.1 Quality Assurance of a Measurement Process

There is a growing awareness that analytical data for use in any decision process must be technically sound and defensible. Limits of uncertainty are required which need to be sup- ported by suitable documentary evidence. Professional analytical chemists have always

espoused this philosophy. Regulatory agencies and contracting parties increasingly are spe- cifying it as a routine requirement. The formal and even informal procedures used to establish the limits of uncertainty of measurement data are generally referred to as quality assurance, in which replicate measurements and independent procedures support claims for the accuracy of the data. When a measurement process can be established and demonstrated to be in

a state of statistical control, the accuracy of the process can be imputed to characterize

the accuracy of all data produced by it. Hence the requirements for redundancy can be greatly

reduced

.

A measurement process of the type described above is illustrated in Figure 4. It utilizes methodology appropriate for the measurement program and appropriate quality control practices are followed. Statistical control is demonstrated by the measurement of replicate

samples and internal reference materials, using control charts. This also permits the evaluation of the precision of the process.

Accept/ Use

Figure 4. Measurement Process Quality Assurance

When the process is demonstrated to be in a state of statistical control, reference materials such as SRM's may be analyzed to assess measurement accuracy. The resulting judgment of precision and accuracy can be assigned to the sample data output of the process. The figure shows also how data quality assessment is used in a feedback mode to monitor the process, to initiate corrective actions as required, and in a decision mode for the release or use of data . 3.2 Statistical Control

A stable measurement system is expected to produce reproducible data. Statistical control

may be defined as the attainment of a state of predictability. Under such a condition, the

8
mean of a large number of measurements will approach a limiting value (limiting mean) and the individual measurements should have a stable distribution, described by their standard deviation. Under such a condition, the limits within which any new measured value would be expected

to lie can be predicted with a specified probability, the confidence limits for a measurement

or mean of set of measurements can be calculated, and the number of measurements required to obtain a mean value with a given confidence may be estimated.

It is axiomatic that attainment of statistical control is the first objective of a measurement process. This is just another way of stating that it must achieve stability.

Yet, it has the further connotation that the data produced are statistically describable.

Eisenhart has stated -- "Until a measurement operation has been 'debugged 1 to the extent that

it has attained a state of statistical control it cannot be regarded in any logical sense as measuring anything at all (7)." When a measurement system is altered or disturbed, a new or modified measurement system

may result with a limiting mean and/or a standard deviation different from the previous

values. During normal use of a measurement system, changes can occur as well, unbeknown to the laboratory personnel. A well designed quality assurance program will monitor the system

for such changes and indicate when corrective actions are required.

3.3 Control Charts

The philosophy of the use of control charts is based on the premise that analytical measurements may be systematized to provide a process simulating a manufacturing process in many respects. As the result of quality control procedures, a system may be debugged and attain a state of statistical control of its data output. The accuracy of the system can be evaluated for typical test samples and thus can be assigned to all similar measurement data generated by the system.

A control chart is simply a graphical way to interpret test data. In its simplest form,

a selected reference sample is measured periodically and the results are plotted sequentially

(or time-ordered) on a graph. Limits for acceptable values are defined and the measurement

system is assumed to be in control (variability is stable and due to chance alone) as long as the results stay within these limits. A second useful form of control chart is one in which

the standard deviation or range (even differences between duplicates) of a series of measurements is plotted in a similar manner. The residence of the values within expected limits is accepted as evidence that the precision of measurement remains in control. The monitored

precision of measurement and the accuracy of measurement of the reference sample may be transferred, by inference, to all other appropriate measurements made by the system while it is in a state of control. Examples of each kind of control chart described above are given in Figure 5. In Figure

5A, the mean, x,_of 2 measurements is plotted sequentially. The central line is the most pro- bable value for x (i.e., the grand average, x, of measurements of x) and the limits LWL to UWL (lower and upper warning limits) define the area in which 95 percent of the plotted points are expected to lie. The limits LCL to UCL (lower and upper control limits) define the area in which almost all (99.7$) of the plotted points are expected to lie when the system is in a state of statistical control. It should be clear that when more than 5 percent of the points

lie outside of the warning limits or when values fall outside of the control limits, the system is behaving unexpectedly and corrective actions, and even rejection of data, may be required

.

A discussion of the strategy to follow in the use of control charts is beyond the scope

of the present presentation but laboratories using them need to develop such. Results are expected to scatter randomly within the limits. Systematic trends or patterns in the data plots may be early warning of incipient problems and are cause for concern, hence techniques

to identify such should be practiced. Control charts, including the factors for calculating control limits are discussed more thoroughly elsewhere, of which ASTM Special Technical Publication STP 15D is an excellent

source of information [8]. Briefly, the central line is either the known value for the test sample (e.g., certified value if an SRM is used), or the mean of at least 15 sets of independent measurements. The standard deviation estimate, s, should be based on at least 15 such measurements. Control limits can then be calculated according to the following table.

9
A

Sequence

Sequence

Figure 5. Duplicate measurements made on SRM 122G. A (upper) - x chart; B (lower) - R control chart

Control Limits 1

Central Line X (mean of = 15 sets of measurements)

*For a more extensive treatment of control limits, see Ref.

For the above limits, n represents the number of repetitive measurements of the reference

sample, the mean of which will be plotted on the X chart. For an X chart (single measurement

of the reference sample) n = 1.

1 0
Figure 5B represents a range (R) control chart. In chemical measurements , the difference

of duplicates is a good choice to plot on such a chart. The line R represents the average

range obtained as the result of a reasonably large number (e.g., >15) sets of duplicate mea- surements. The warning and control limits are appropriate multiples of R and have the same significance as discussed in Figure 5A. The range is calculated without regard to sign (absolute value) so the lower limits are zero.

The factors for calculating limits are discussed in the reference [8]. For duplicate measurements, they are

R mean of the differences of >15 sets of duplicate measurements

UWL 2.512 R UCL 3.267 R LWL 0 LCL 0 In use, the differences of duplicate determinations are plotted on the control chart and statistical control is assumed as long as they fall within the expected limits. Again they should not fall disproportionately outside of the warning limits and trends should not be observed . The R chart is based on the known relation between the range and the standard deviation,

hence it is a form of standard deviation or precision chart. When used with an X or X chart,

it is useful when deciding whether an observed deviation is due to bias or to a change in precision. When used alone, an R chart will monitor precision (but not bias).

The test samples, themselves, when measured in duplicate, may be control charted to monitor precision. The ranges for duplicate measurements of a class of samples can be plotted

on the same control chart, as long as they are expected to be measurable with comparable

precision.

An s control chart is based on plotting the estimate of the standard deviation obtained

from measurments of n replicates of the reference sample. Since a number of measurements are required (at least seven is recommended) to estimate the standard deviation each time it is charted, with any degree of reliability, and since some calculations are required, such charts

are seldomly used in chemical measurements. R charts can provide sufficient monitoring of precision with a reasonable amount of effort. They also offer the advantage of using a rea- sonable number of the actual test samples to monitor precision. The use of an R chart for test samples and an X chart utilizing an SRM may be ideal choices for many laboratories.

An X control chart is more robust than an X chart. Since it is based on the mean of two

or more measurements, an occasional outlier will have limited influence on the decision process. However, it requires additional work and this should be considered when using such in a quality assessment program. If the assessment strategy calls for confirmatory measurements of reference samples when out-of-control is indicated, the advantage of an X chart is lessened.

Such a strategy is most effective when control charts are maintained and used in a real-time

mode which will also provide the advantage of ability to take immediate corrective actions and thus minimize the uncertainty of data.

The question of how to obtain the statistical information necessary to construct a control chart needs to be considered. Once the decision to develop a control chart is made,

one might want to acquire the standard deviation and mean data as quickly as possible, but this could be misleading. It has been mentioned that measurements made over a short period of time show greater consistency than those obtained over a long period of time. Since the control chart will be used over a period of time, the latter is more appropriate for judging

performance

To develop control limits based on long-term behavior, it is recommended that at least 15 data points be accumulated and that no two points be obtained on the same day. This recommendation applies only to obtaining the standard deviation data to establish control limits for

an X or X chart and for preparing an s or R control chart.

If an SRM is used as the control chart reference sample, the value for the central line

is known, namely the certified value. If a laboratory's own internal reference materials are used, much work may be required if the "true value" for the central line is to be used. Some laboratories use an analytical mean value for the central line, and assume that this is essentially the "true value". This may be true only if the measurement process has been demonstrated to have negligible bias. The use of an analytical mean as the value for the central line can be useful in indicating stability of a process but bias can be evaluated only when true values are known.

1 1
3.1 Frequency of Use of Reference Materials

The optimum frequency of use of reference samples and also of replicates of actual test samples will depend on the stability of the measurement system and the risk involved when the system departs from statistical control (9). Since all data obtained during the period last- known- i n-control to f irst-known-out-of-control are suspect, such intervals may need to be minimized. The real-time use of control charts and/or reference material data is a further consideration. While the following discussion is directed toward control chart maintenance,

the same philosophy applies, whether this is done or whether the results on reference samples

are interpreted by other means. There are several empirical approaches to deciding on the frequency of use of reference

samples. The experience of the laboratory may indicate the expected frequency of occurrence

of trouble, in which case reference sample measurements, at least three in number, should be equally spaced within such an interval. Another approach is the "length of run" concept. In this, recognizable breaks in the production (of data) process are identified which could cause significant changes in precision or bias. Such breaks could include change of work shift;

rest periods; change, modification, or adjustment of apparatus; use of new calibration standards; significantly long down-times; use of a new lot of reagents. At least three reference

samples should be measured during any of these periods when the periods are considered to be potentially significant.

In summary, the measurement of reference materials is a risk-reducing procedure.

However, if it involves more than 10 percent of a laboratory's measurement effort, either the quality control process may need improvement or too much effort is being exerted in this direction. If less than 5 percent of effort is devoted to such measurements, the laboratory

may be taking too high a risk of producing unacceptable data, or may not even know the quality

of the data it is producing. The above statements are made with a laboratory making a significant number of high-quality routine measurements in mind. If a laboratory's program involves occasional or one-of-a-kind measurements, the amount of quality assurance effort required, including the number of measurements of reference materials to be made may be significantly more than that indicated above. Suggested measurement schedules for efficient utilization of reference materials are given in Table 1 and Table 2 (9). The sequence in Table 1 utilizes a combination of an internal reference material (IRM) and a SRM. The sequence in Table 2 utilizes a limited number

of duplicate or split samples together with reference materials. In either case, the use of control charts is recommended on a real-time basis. Recommended critical decision points in the measurement sequences are also indicated.

Table 1. Quality Assessment Using RM's Daily/Event Schedule

Daily/Event Schedule

All BRATION FULL EXPECTED RANGE

RMEST SAMPLES CROUP 1 RMEST SAMPLES - GROUP 2

EST SAMPLES

AL I BRAT ION MI DRANGE POINT NOTES

• DECISION MAINTAIN C0NTR0I

X- CONTROL CHART

R CONTROL CHART SYSTEM MUST BE AT LEAST 2 CR0UI

£ I RM CONTROL AT DECISION POINTS MAXIMUM OF 10 SAMPLES IN EACH GROUP

AT LEAST ONE SRM MEASUREMENT SHOULD BE MADE DURING

EACH SEQUENCE/DAY

1 2
Table 2. Quality Assessment Using Dupl i ca t e/ S p 1 i t

s

CAL I BRA SAM? SAMPL

SAMPL SAMPL

Sequence Schedule

FULL EXPECTED RANGE

ION CHECK • MIORANGE POINT

SAMP I

• SAMPI

• CALIBRATION CHECK • MIDRAI1CE POIN1

• CALIBRATION CHECK • MI DRANGE POINT/DUPLICATE

NOTES

• - DECISION POINT

1. MAINTAIN CONTROL CHARTS

a. DUPLICATE MI DRANGE CALIBRATION

b. DUPLICATE/SPLIT SAMPLE

c. X-CONTROL CHARTS, SRM AND IRM

2. SYSTEM MUST bE IN CONTROL AT DECISION POINTS

3. IF MORE THAN 20 SAMPLES, REPEAT SEQUENCE

4. IF LESS THAN 20 SAMPLES, DIVIDE INTO TWO CROUPS AND follow Similar pun

s. at least one srm measurement should be made our1nc each sequence day

13
4 . Reference Materials

4.1 Role of Reference Materials

In the most general terminology, a reference material (RM) is a substance for which one

or more properties are established sufficiently well for use to calibrate a chemical analyzer

or to validate a measurement process (10,11,12). An internal reference material (IRM) is such

a material developed by a laboratory for its own internal use. An external reference material

(ERM) is one provided by someone other than the end-user. A certified reference material

(CRM) is a RM issued and certified by an organization generally accepted to be technically

competent to do so. A Standard Reference Material (SRM) is a certified reference material

issued by NBS.

A reference material is for use in a decision process, hence the requirement for reliability of the value of the property measured must be consistent with the risk associated

with a wrong decision. The appropriateness of the reference material in the decision process

must also be considered. For some purposes, a simple substance, mixture, or solution will be adequate and the value of the property may be calculated from the data for its preparation.

However, even this is best verified by suitable check measurements to avoid blunders. Many decision processes require a natural matrix reference material which may necessitate extensive blending and homogeni zation treatments and complex analytical measurements. In such cases,

only a highly competent organization may have the resources and experience to do the necessary

wor k . The terms certificate and certification merely refer to the documentation that supports

the reference material. Guidelines for the content of certificates for reference materials

have been prepared by the International Standards Organization (13,14,15). They recommend the kind of information the certificate should contain but do not describe how it should be obtained. Furthermore, there are no guidelines for judging the relative quality of reference

materi als . The guiding principle in issuing a SRM is that it will be used for measurement quality assessment, hence the property certified must be accurately known. The uncertainty in the certified values takes into account that due to measurement and any variability (inhomogeneity) between and/or within samples of the material (16). Definitive methods are used for establishing the values of the certified properties or they are measured by two or more inde- pendent reliable methods in which case the results must agree to minimize the chance for mea- surement bias. All certification measurements are described in the certificate or are referenced. The certification measurements are preceeded by stability studies as appropriate

to set limits on the life expectancy of the material.

4.2 Concept of Traceability

The concept of traceability to national standards has been advanced in recent years to facilitate i n t er ca 1 i br a t i on of laboratories and compatibility of measurements. Traceability

as related to a standard may be likened to genealogy in that it may describe the chain of cal- ibrations related to establishing its value, including the intermediate standards that were

used and the various measurements involved. In the area of physical measurements, calibrations of standards or artifacts with respect to the national measurement standards can be made

at NBS with high precision. These may be made for secondary calibration laboratories who in turn calibrate standards for others, and so forth. Each time this is done, the uncertainty is increased due to uncertainties in a laboratory's own standards and propagation of the uncertainty of measurement. Measurement assurance programs (MAP's) are designed to minimize the latter and thus decrease the accumulation of uncertainty as measurements go lower down the measurement chain. The various measurements must be made with adequate quality assurance if reliable limits of uncertainty are assignable. The responsibility for such is that of the measurement laboratory.

While chemical measurements rely to some degree on physical measurements and require calibrated physical standards, very few chemical standards are disseminated in the same manner

as the physical ones are. Hence it is difficult if not impossible to establish the traceability of most chemical standards to other such standards and especially to national standards.

An exception to the above is when SRM's are used either as calibrants for a measurement process or as primary standards for chemical analysis. All measurements using such SRM's have

the capability of being traceable to a common set of standards and the i n t er c a 1 i br a t i on of laboratories is facilitated. Relatedly, certain commercial suppliers are producing reference

materials, certified with respect to specific SRM's and protocols for issuing such materials

as Certified Reference Materials have been developed (17). While an SRM ordinarily does not provide traceability in its narrowest interpretation, it may serve a broader and more useful function to provide measurement assurance which ensures

both proper calibration and acceptable utilization of methodology. When specific SRM's are commonly used in a systematic manner, as by means of control charts, i n t er c al i br a t i on of all laboratories using such and compatibility of data may be achieved as shown by Figure 6. Thus measurement networks can specify the SRM's to be used and the quality assessment procedure to

be followed to attain compatibility of monitoring data, for example. While acceptable SRM

1 4
data indicate acceptable performance of the measurement system, discrepant results may not be simple to interpret since such could indicate, calibration uncertainties, application problems, or both. One cannot rule out, completely misapplication of methodology or inappropriate

methodology as a source of trouble. However, a well-designed quality assurance program should facilitate the identification of the source of the problem.

NBS

National

Standards

SRM

/ -1

NBS

Measurements

Compatible

Data

User

Measurements

Figure 6. Measurement compatibility by i n t er ca 1 i br a t i on , using SRM's

1 5
5. Standard Reference Materials

5.1 Philosophy of SRM Production

Standard reference materials are considered to be services to the individual user who

must pay the full cost of the service provided. Costs of development, preparation, certification, and marketing are accumulated and pro-rated on the basis of the number of saleable units

that are produced. Thus the costs and benefits are prime considerations in authorizing and issuing an SRM. The production of low demand, h i gh- pr od uc t i on- c os t , and hence high unit-cost

SRM's is accordingly difficult, though not impossible.

SRM production is often preceeded by a substantial research effort. Methodology may need

to be developed or potential bias problems must be solved if accurate certification is to be done. Materials-related problems such as stability, homoge ni za t i on techniques, and proper conditions for packaging and storage may need investigation. Often the results of such research are applicable to wider areas of science and technology or at least to broader areas

of SRM certification. In such cases, the costs of such work may be supported from general research funds and not charged to production of an SRM. Otherwise all costs, including research and development, must be recovered from sales. This increases the unit-costs of SRM's and impacts on the development of new items for which substantial research and development costs are necessary.

5.2 How an SRM is Produced Identification of Need SRM's are developed to meet measurement needs. The need may be specific, as the result

of a regulatory issue, or general as the result of a wide-spread measurement problem. The

need may come to the attention of NBS in the form of a specific request, or as the result of NBS scientists' interactions with the measurement community. Because the reference material

program must be self-supporting, the magnitude of the need, cost of development, and the pro- spect of cost recovery through sales together with the technological chances of success are important considerations in establishing the feasibility of issuing an SRM. Determination of c har a c t e r i s t i c s / p r o pe r t i es / s pe c i f i c a t i ons The necessary properties of a useful reference material need careful consideration. The kind and level of parameters certified, the matrix and other physical characteristics, homo- geneity requirements, and the maximum acceptable uncertainties for the certified values are

key considerations. While a reference material is developed for a specific use, it is often possible to extend its usefulness to other areas by certification of additional parameters or by modifying the matrix. In doing the above, it must be considered that modification from a specific to a generic standard could possibly limit its usefulness for the initial purpose

while not significantly extending its areas of application. Moreover, the certification of additional parameters can increase costs unless compensated by sufficient additional sales,

and users do not ordinarily like to pay for information (in this case certificate values) which is not of direct use to them. From considering factors such as those discussed above, and from discussions with the user community, minimum specifications for a candidate SRM may be drafted. These may take

into consideration materials available on the market or suitable materials may need to be pro- duced to meet the specifications. In some cases, NBS must prepare the material or at least a prototype for initial testing.

Often, preliminary research and development efforts are necessary to evaluate the feasibility of production of SRM's and/or to develop specifications.

Preliminary Studies

After a material has been obtained, measurements are made to evaluate its compliance with

the specifications. While the exact level of the analyte is often not a controlling requirement, homogeneity is always an important requirement including both within and between units

of issue. Ordinarily, it is desirable to certify the material as a lot rather than as individual items, in which case homogeneity between units of issue must be acceptable.

Homogeneity

Homogeneity evaluation may be done in two phases. Preliminary measurements may need to be made to accept material for conformance with specifications and to decide on such questions

as pre-mixing and subdivision into units of issue (e.g., bottling) prior to certification

analysis. When a mul t i component/ par ameter SRM is involved, this can be a major undertaking if homogeneity determinations for each co ns t i t uen t / pr o pe r t y are to be undertaken at this time. When possible, a quick and precise method is sought to evaluate homogeneity. In multiparameter materials, this may not be possible for each component in which case initial homogeneity

may need to be judged on the basis of that of a limited number of typical constituents.

1 6
Final homogeneity evaluation is made from interpretation of certification data on each individual constituent or property. This requires design and execution of the measurement

program so that variance of measurement and sample composition can be individually evaluated. Measurement

The certification measurements are conducted according to a quality assurance plan established before the work is actually begun. This requires development of a statistical

plan for sampling and measurement, selection of methodology which has been demonstrated to be reliable, maintenance of statistical control of the measurement process, and quality assessment of the data by concurrent measurement of suitable reference materials as possible.

The methodology is selected on the basis of the following considerations. When possible,

the attainable accuracy of measurement should be better than that required for use of the data. The first choice for methodology is a method of known and demonstr atable accuracy. The term "definitive method" has been coined for such and is finding considerable usage, especially in relation to reference material analysis. A definitive method is one based on sound theoretical principles and which has been experimentally demonstrated to have negligible sys- tematic errors and a high level of precision. While a technique, that is to say a measurement

principle, may be conceptually definitive, a method based on such a technique, must be demonstrated to deserve such a status for each individual application.

An example of a definitive technique is isotope dilution mass spectrometry for trace analysis in which one relates the concentration of unknown samples directly to the actual weights of spikes of isotopes or isotopically labeled compounds. A mass spectrometer is used

to measure isotopic ratios, obviating the need for instrumental corrections. The only theoretical uncertainty in such a process is the question of the ability to recover a natural

analyte as compared with that of a spike. The accuracy attainable will depend on isotopic and chemical purity of the spike and the care used in preparation and measurement.

Examples of other definitive techniques are gravimetry and coulometry. Both are based on fundamental measurements that can be made with high accuracy. As in the case of any methodology, it must be demonstrated that no significant systematic errors are relatable or present

in their use in a specific application. When using such, possible biases of application are minimized by the use of multiple analysts/instruments to the extent possible. Redundancy of measurements in random sequence is another technique to avoid application bias. Because definitive methods are not always available, the mul t

i - t e c hni q ue approach is one often used in certification of SRM's. Parameters are measured by at least two independent

techniques when possible and such measurements must agree within reasonable limits to permit certification. Whenever significant discrepancies occur, additional work is carried out to reconcile them, otherwise the values cannot be certified but may be reported for informational

purposes , only. Another mode of certification, which may be called the m ul t

i - 1 abor a t or y approach, is used

for renewal of certain compositional SRM's. A group of laboratories of recognized competence

use methods of proven accuracy and the corresponding existing SRM as a control to analyze a renewal SRM. Any significant discrepancies are resolved by careful scrutiny of the data or by reanalysis using the same or independent methodology.

In a few cases, SRM's are certified for the value of a constituent or property that is method dependent, because existing technology requires such. An example of such is the Kjeldahl nitrogen value. In such cases, demonstration of statistical control of the measurement process and agreement of results by independent analysts is a requirement for certification. Evaluation of Data

All SRM data are given a thorough statistical analysis to establish limits of uncertainty. This will include that due to measurement and to any variability of the units of issue. The advance cooperation of statisticians in planning the experimental programs is essential if the proper measurements are to be made to enable a thorough evaluation of the reported values for the SRM. The interpretation of the certified values is discussed later in this handbook (see 5.4 and 5.5).

Fol 1 ow- up SRM production is ordinarily preceeded by studies of the stability of candidate

materials. When possible, only materials which have a long shelf life are selected. If there

is any limitation on stability, it is indicated on the certificate. In addition, NBS does 'shelf life' analysis on certain SRM's when it is considered that some de t er i or i a t i on could be possible .

17
NBS ordinarily prepares a SRM in sufficient quantity so that a several-year supply is available, at the time of issue, based on anticipated demand. Sometimes demand exceeds expectations. A few SRM's are prepared in limited lots due to various considerations, such as shelf

life, for example

.

NBS aims to keep most SRM's in stock for ready issue and to renew SRM's before the stock

is depleted. However, unanticipated demands can cause delays, and changes in technology may cause cancellation of plans for continual stocking because of conflicting priorities of competitive items.

It is the further aim of NBS to make SRM's as useful as possible to purchasers. Customer

service can be provided in many cases including advice on use. In the case of questions

arising from use, inquiry to the Office of Standard Reference Materials (OSRM) will get quick response and every effort will be made to provide satisfactory solutions to application

problems

.

A SRM is ordinarily certified using state-of-the-art methodology. This may be the methodology widely used in practical analysis with special care given to calibration, to quality control, and to elimination of sources of bias. In other cases, the methodology may be suitable only for research laboratory use. For example, isotope dilution mass spectrometry is often used-which would be an inappropriate routine technique, due to time and cost considerations. In any case, the certified value is ordinarily independent of the method of measurement. When certified values are method dependent, the methodology used in certification is always named in the certificate together with references where detailed information can be found. For a number of SRM's, a so-called NBS 260 publication describes the measurement

process in detail (see front of this publication for current listing).

5.3 Differences Among Measurement Methods Agreement of measured values by two or more independent measurement methods is one of the approved conditions for certification. Of course, measured values never agree perfectly so the statistical significance of disagreement must be considered. Results may not agree within

their respective uncertainty for several reasons.

1. Matrix effects in one or each method may not be fully compensated by the calibration

procedure used.

2. Systematic errors may not be fully compensated or unsuspected ones may exist.

3. It is in the nature of things that the more precise one can make a measurement, the smaller the difference that can be detected.

4. A fourth reason for two methods to disagree is perhaps the most common cause - the standard deviation of one method, or both, is underestimated.

In any event, systematic differences in measured values must be examined for their practical significance and values are not certified unless reasonable discrepancies can be resolved

.

5. 1

) Understanding Certificate Information

SRM certificates provide a variety of information about the particular material. Compositional values with uncertainty limits are given for all certified analytes. Ordinarily

the latter are for the 95? level of confidence and include allowances for the uncertainties of known sources of systematic error as well as the random error of measurement. Many certificates also will include values for other parameters or analytes which are reported for "infor- mational purposes" only. These values are so reported because they were measured by only one technique, they are the results from discrepant measurements by several techniques, or there

are homogeneity problems which detract from their analytical usefulness. Such values may have uncertainty values assigned to them, as well, but they represent the analysts' best judgment

of the random error uncertainty.

The certificate sometimes will describe restrictions in the use of the sample which must

be adhered to for reliable results. One of these concerns drying. Whenever this is critical, instructions for doing so are included and must be followed. In the case of several SRM's,

some elements must be determined on pre-dried samples while others are determined for moist samples with subsequent correction to dry weight, based on a moisture determination.

For heterogeneous materials, the minimum weight of an analytical sample may be specified.

This requirement should be followed if certified values are to be realized.

In the case of some SRM's, segregation is a potential or actual problem in that the material, though mixed at the time of certification, may segregate on standing. The certificate may instruct the user to shake, rotate, stir, or otherwise reconstitute the material.

Failure to do so will not only invalidate the present measurement but may jeopordize further measurement from the same container, due to disproportionate withdrawal of constituents.

18
Storage of some SRM's may need to be done under prescribed conditions. Refrigeration

and/or freezing may be necessary, and protection from moisture, once opened, or from radiant

energy may be necessary. Because of such problems, some SRM's are certified for first use, only . In some cases certification is valid only for a finite lifetime (e.g., 1 year, 5 years).

This is to limit NBS liability to individually notify users in case there is a change in the material. The lifetime is always calculated from the time of shipment -- it is never related

to packaging dates marked on the container.

These and other restrictions are necessary to protect the integrity of the sample or to ensure results that will be consistent with the certified values. NBS can accept no responsibility for validity of the material if such instructions are not faithfully followed.

5.5 Uncertainty of Certified Values 1 For the purpose of this discussion, SRM certification can be divided into two classes:

A. Each unit is measured and carries its own value (e.g., permeation tubes).

B. Samples chosen statistically from the lot of SRM are measured, and one certificate

gives the value for all units (most chemical types).

The uncertainty of the certified values for group A SRM's will depend entirely on the uncertainty of measurement. This will be based on the standard deviation and best estimates

of uncertainties of the systematic errors which have been corrected for, to the extent

poss i bl e

For group B SRM's, any differences in the certified property within the units or between

units of the lot poses a problem. A sampling and measurement scheme has to be devised to determine whether i nhomogen e i t y exists and to estimate its magnitude whenever it is important

to the use of the SRM. Homogeneity checks may be made using two different sampling schemes. In one, a batch of material is subsampled, using a statistically developed scheme, and measurements are made to detect significant differences in the compositions of the samples. This has the advantage

that grossly heterogeneous material would be rejected, thus saving the time and cost of packaging unacceptable material. It has the disadvantage that further heterogeneity could be introduced in acceptable material by segregation, discrimination, or contamination during

packaging. For material believed to be essentially homogeneous, bulk examination may be the method of choice. Once homogeneity is confirmed, the material may be analyzed and packaged as required, which could have advantages in some cases. Material which is considered to have measurable heterogeneity is best checked after packaging into bottles, vials, or whatever. Not only is it possible to detect original

heterogeneity but also any that might result from the packaging process. Three kinds of heterogeneity are generally possible:

a. Between units vs. within units

b. Trend or pattern — along a rod, within a sheet or block of material, in the order of preparation , etc

c. Between blocks of units — processed on different days, between dr urns , between lots,

etc . The sampling scheme used for each SRM depends to a large extent on the subject expert's knowledge and experience of what particlar type of heterogeneity is most likely to occur, and

the sampling scheme will be designed predominately to check on variability due to that source.

A knowledge of the details of the packaging process is also required, such as the sequence of filling bottles or the order in which specimens were cut from a massive material.

If the material is found to be essentially homogeneous, it is accepted; if the material

shows large variability, it is rejected. Often the variability is at about the level of what

can be detected by a particular analytical method. In that case, the analytical error and the heterogeneity of the material both contribute to the uncertainty in the final product — SRM

units .Let o m be the standard deviation of the analytical method, and o c be the standard deviation of the value of the individual units about the mean value of the lot. Then the standard deviation o of a single measurement on a unit, drawn at random from the lot would be

From a lecture by H. H. Ku, National Bureau of Standards, presented at Precision and Accuracy,

Seminar, 27 March 1980. See also Ref. 10, p. 296, and Ref. 12.
Reliable estimates of two of the three sigmas allow an estimate of the third.

When possible, o m is evaluated independently of the measurement of the SRM. In this

case, the standard deviation, o, of the measured values of individual samples, together with

the value for o m

, permits an estimation of o Q

. Often, possible matrix effects considerations preclude or raise questions about the independent estimation of o m

. And even if o m can be assumed to have a certain value, it may

be necessary to verify it for the SRM certification measurements.

By duplicate measurements of portions of n randomly selected samples, both o m and o c may

be estimated. Let x

i and y^ be the first and second measurements on portions of the ith unit (bottle, disc, sub-sample, etc.). The results may be tabulated as:

2 - y2 (x ?

+ y?) = z- 2 ^2

y n > =

s estimates o 2 estimates o.

Another way in which o c may be estimated is by the use of an independent method of measurement. Occasionally a highly precise method is available for i n t er com par i son of samples

but may not be feasible for use for certification measurement, due to calibration problems.

Such a procedure is especially useful for confirmation of the homogeneity status of a candidate SRM.

In any evaluation of homogeneity, it must be remembered that each analyte certified must

be individually examined for homogeneity considerations. It is not justifiable to extend con- clusions on the homogeneity for one analyte to another even though they may be closely related

i n other respects . Homogeneity statements always must be coupled with the size (mass) of sample to be used. Basically, heterogeneous materials such as bulk solids may exhibit gross heterogeneity as the sample size is diminished (see for example Appendix D.2). In crushed material, for example, individual particles could have widely different compositions. Apparent homogeneity is improved as larger sample sizes are considered since individual differences will be averaged

out. Accordingly, the minimum sample size necessary to realize the certified values often

will be specified in the certificate. The NBS certified values cannot be extended to the composition of subsamples smaller than the recommended size. Materials of group B which are found to be essentially homogeneous are certified on a lot

or bulk basis. All sub-samples are considered to have the same composition which is certified

together with a confidence interval based on estimates of uncertainties for both random and systematic errors of measurement. Materials with significant but usable levels of i nhomogen e i t y may be certified as a batch, in which case the statistical tolerance limits are given. This includes the average

value of all samples in the batch and limits within which individual samples are expected to lie, with a stated confidence. Because only a limited number of samples have been analyzed,

one cannot say, with certainty, the limits for a given percentage of samples but only a pro- bability that the limits are valid. Thus one could say that there is a 95 percent confidence

that 95 percent of the samples in the batch lie within some specified limits (statistical tolerance limits) and this is often what is stated on a certificate for this kind of material.

20
In the case of most granular SRM's, the within uni t-of -issue heterogeneity is essentially

the same for all un i ts-of - i ss ue and no significant average difference is to be expected

between individual units. In such a case, the average composition of sub-samples within all units would not be expected to differ, significantly. In using such SRM's it should be remembered that the composition of any sub-sample is expected to be within the tolerance

limits and the average composition of a number of sub-samples is expected to approach the certified value .

21
6. Use of SRM'a

6.1 Kinds of SRM's Standard Reference Materials may be described as well-characterized and certified

materials, produced in quantity, to improve measurement science and technology. They fall into three general categories (see Table 3): (a) certified chemical composition/purity standards; (b) certified physical property standards; (c) engineering type standards. Categories

(a) and (b) may be further subdivided into those materials related to basic measurements and those to applied measurements.

Table 3- Inventory of SRM's, - 1969 - 1984 §RM_Categor_£ Number_of_SRNP s 1£69 1979 1_984 Chemical Compos i t i on/ Pur i ty Steels and steel-making alloys 141 161 159 Cast, white, ductile, and blast furnace irons 16 23 25 Nonferrous metals and alloys 75 130 120 Gases in metals 9 29 13 High-purity metals 1 8 8 Electron probe m i croanal y t i c al 0 6 12 High purity chem i ca 1 / mi cr ochem i cal 16 26 18 Clinical analysis 1 22 28 Biological/botanical 0 9 9 Environmental analysis (gases, liquids, solids) 3 72 109 Forensic analysis 0 3 2 Oil-soluble metallo-or ganic compounds 24 24 22 Fertilizers 0 3 3 Ores 10 22 21 Cements 5 7 9 Minerals, refractories, carbides, glass 17 22 29 Glass trace elements 0 13 8 Special nuclear materials 18 33 30 Isotopic reference standards 9 J_5 _T4 Subtotals 345 628 639 Physical Properties

Ion activity 6 17 13 Physical properties of glass 7 13 15 Elasticity 0 1 1 Density 4 3 2 Polymer molecular weight 2 7 10 Polymer rheology 0 1 1 Temperature fixed points 5 12 14 Calorimetry 3 13 8 Thermometers/thermocouples 0 4 4 Vapor pressure 0 4 3 Thermal co nd uc t i v i t y / e xp a n s i on 0 29 16 Thermal resistance 0 1 10 Magnetic properties 0 11 10 Optical properties 4 20 24 Radioactivity 40 1 56 a

1 1

8

a Permittivity 6 7 6 Electrical resistivity 0 J_4 1 5 Subtotals 177 333 270 Special Engineering Properties

Standard rubbers 20 14 12 Computer tapes 0 3 4 Optical character recognition 0 4 1 Sieve sizing 3 5 4 Cement t ur b i d i me t r i c and fineness 1 1 1 Color 36 2 2 Fading standards 4 4 1 Fl ammab i 1 i ty/ smoke density 1 3 3 X-ray and photographic step tablets 1 4 4 Tear resistance-tape adhesion 1 1 1 Metal coating thickness 35 32 10 Octane rating 0 2 0 Subtotals 102 76 43 Total 544 1037 952

a Many of the radioactivity SRM's consist of short-lived isotopes and are available only on special order for limited time periods during the year.

22
Industrial materials that must be analyzed frequently for quality control of production

processes constitute a major fraction of all SRM's. Predominant in this group are metals in which essentially all major alloy types are specifically represented. Ores, minerals, cement,

glass, and ceramics are also included. Ordinarily, these SRM's are sampled directly from the container and analyzed by the user in the same manner as the day-to-day samples of the laboratory. The results of such SRM analyses are frequently control-charted to monitor the measurement process.

High purity chemicals for use as primary standards in a wide variety of chemical analyses constitute an important group of SRM's. Typically, the user will prepare solutions from these materials that may be used directly in the analytical process or for standardizing other analytical reagents. Clinical laboratory standards compose a large and growing group of SRM's. Originally,

such SRM's consisted largely of pure substances from which spikes or calibration solutions

could be prepared. They are now being augmented by natural matrix materials containing

analytes of interest that are analyzed directly without preliminary preparation.

The environmental group satisfies most of the routine monitoring requirements and some special situations as well. SRM's related to all of the criteria air pollutant analyses were introduced early into the program. These were followed by SRM's related to the measurement

of emissions from mobile and stationary sources, priority pollutants, and hazardous wastes.

The SRM's for the gaseous pollutants of the atmosphere are particularly slanted toward the calibration of analyzers and to provide traceability for i nd us t r i al 1 y- prod uced working standards. Because of the wide variety of sample types and the number of constituents of interest, it is virtually impossible to provide matrix matches for most of the samples encountered

by organic analysts. Accordingly, the SRM's in this area represent either high-priority

sample types or generic materials that should be widely applicable. Some SRM's useful for spiking or other types of standards preparation are also available.

A number of natural matrix SRM's certified for most of the inorganic constituents of environmental interest and some organic substances have been produced. These include several biological matrix samples (orchard leaves, now replace by citrus leaves was the first SRM in this group) and also urban particulate matter and river and marine sediments. Industrial

hygiene analysis materials are a small but important sub-group in the environmental category.

This list will be augmented as possible, and as demand is shown for additional items.

The physical property standards reflect many of the kinds of measurements made in testing laboratories. The gamut runs from those useful for the conventional physical measurements of temperature, melting point, vapor pressure, calorimetry, conductivity, and thermal expansion

to color, thickness of el ec t r ode pos i t s , and fineness of powders. Radioactivity

standards are also classified in this category. Engineering standards are a small but growing group which is rather diverse. Standard

rubbers, SRM's for evaluating the performance of magnetic tapes, and flammability standards

are examples.

NBS Special Publication 260, Catalogue of Standard Reference Materials, lists all SRM's, research materials, and special reference materials that are available and those that are in progress at the time it is issued. The catalogue is updated periodically, and supplements are issued in the interim. See page 3 for how to receive a copy. The SRM program tries to keep abreast of and even anticipate changes in technology, since

it may take a period of several years to develop and certify a new SRM. Input from the user community, from contacts with professional colleagues, and NBS's own measurement experience

are influential in guiding and establishing priorities for SRM development. SRM sales provide

guidance on inventory maintenance and priorities when questions of renewal must be decided.

While present contacts are extensive, additional input to the decision process is sought. It

is believed that there are areas of technology, and especially new technologies, where SRM's

are not significantly utilized and which would benefit from their use. Information about

these is especially solicited.

Table 4 lists the major areas into which SRM development is expected to expand in the near future. The list may be revised as technology advances and as new technologies appear.

User input is actively sought to confirm the wisdom of the proposed plans, or to provide information on which revisions might be considered.

While SRM's constitute the largest category, two other types of reference materials

described below are produced or distributed by NBS. Research Materials (RM's) are in addition to and distinct from the SRM's issued by NBS. The distinctions between Research Materials and Standard Reference Materials are in the infor- mation supplied with them and the purpose for which they should be used. Unlike SRM's, the RM's are not issued with Certificates of Analysis; rather they are accompanied by a "Report of

23
Table 4. Some Major New SRM Needs Forecast for the P er i od / 1 98 4 - 1 989 .

Trace Organic Analysis

Organic pollutants in natural matrices Nutrients and toxic substances in food and agricultural products

Enzymes, individual proteins, and therapeutic drugs in human serum Additives in plastics

Trace Elemental Analysis

High-performance alloys Plastics

Glass and ceramic materials Semiconductor materials

Fibers

Bulk Compositional Analysis

Recycled materials

Uranium and plutonium nuclear fuels (for nuclear safeguards)

Fibers Quantification of inorganic chemical species

Density Standards Dimensional Standards

Electron microscope magnification

Particle sizing Photomask linewidth

Voltage Standards (Josephson Junction)

Optical Properties Fluorescence

Reflectance

Wavelength

Electronic Properties

Nondestructive Evaluation Standards Radiographic sharpness

Visual acuity

Dye penetrant crack plate Nuclear Waste Disposal

Leach rate testing

Thermal expansion and conductivity of waste forms Polymer Molecular Weight Star-branched polystryenes

Ethylene-propylene copolymers

Spreading and sheet resistance

Glass dielectric

Investigation," the sole authority of which is the author of the report. A Research Material

is intended primarily to further scientific or technical research on that particular material.

One of the principal considerations in issuing an RM is to provide homogeneous material so that an investigator in one laboratory can be assured that the material he has is the same as that being investigated in a different laboratory. There are presently several materials in this category

.

Special Reference Materials called GM ' s are distributed by NBS to meet industry needs. These materials have been standardized either by some Government agency other than NBS, or by some standards-making body such as the American Society for Testing and Materials (ASTM), the American National Standards Institute (ANSI), and the Organization for International Standardization (ISO). For this class of materials, NBS acts only as a distribution point and does

not participate in their standardization.

6.2 Choosing an SRM

The large number of SRM's available may cause some confusion as to which to choose for a given purpose. Obviously, matrix match is a major consideration since there is little or no difficulty in interpreting test results of such materials. Close match is only possible when recurring analysis of well-defined materials is of concern, i.e., large volume industrial pro- ducts. However, all of the SRM's have been developed as the result of wide-spread needs and much consideration has been given to providing matrices that are either typical or that can satisfy generic purposes.

When a matrix match is possible, analysts are advised to use such SRM's. In consideration

of this, many users stock a relatively large number of them, encompassing the variety of materials that they expect to analyze. For many users, a perfect matrix match will not be possible, hence professional judgement will be required to select the ones most useful for

24
each situation. The Office of Standard Reference Materials, and especially the NBS scientists

who certify them, have special experience in most of the measurement areas represented by the SRM inventory. Inquiry to OSRM (see p. 3

1*) will provide access to the scientists who may be able to advise in the selection and use of appropriate SRM's for a given purpose.

6.3 Use of SRM's Because of the high reliability of the certified values, Standard Reference Materials,

find a wide variety of uses ranging from special occasions when a material of known properties

is needed to test some aspect of measurement, to the continual quality assurance of measurement systems. Table 5 is a summary of the most common kinds of applications.

Table 5. Uses of SRM's in Measurement Systems

Method Development and Evaluation Verification and evaluation of precision and accuracy of test methods Development of reference test methods Evaluation of field methods Validation of methods for a specific use Establishment of Measurement Traceability

Development of secondary reference materials

Development of traceability protocols

Direct field use Assurance of Measurement Compatibility

Direct calibration of methods and instrumentation

Internal ( i nt r al abor a t or y ) quality assurance

External ( i nter labor atory ) quality assurance

Any use of a reference material depends on the ability to make valid inferences from the measurement results. This involves the tacit assumption or demonstrated evidence that the material is reliable and capable of challenging the measurement process. Furthermore, the measurement process must be known to be in a state of statistical control, since limited measurements of the reference material will be used for predictive or evaluative purposes. Examples of one-time uses of SRM's as known test materials are numerous. Whenever an analytical method is developed or modified, a well- character i zed test material is needed to evaluate its performance characteristics. SRM's, as appropriate, are obvious choices in such

cases and numerous examples are cited in the literature. A survey during an 18 month period

(10) identified 40 research articles citing the use of SRM's in the development or evaluation

of a wide variety of different methods for chemical analysis and in particular for trace analysis. Likewise, performance checks of instrumentation, such as linearity, stability, and sensitivity are highly dependent on reliable test materials. Here again, an SRM is a logical

choice for such a purpose. When new methodology is adopted by a laboratory, familiarization measurements must be made in order to gain proficiency in its use. The use of SRM's will eliminate questions of stability and homogeneity that might complicate the test results when using other materials.

Some laboratories use SRM's to confirm a new analyst's capability to perform tests before undertaking measurements in their test programs. When a contract laboratory is needed to provide analytical services to an individual or in a monitoring program, evidence of the capability to do so is often a requirement. The analysis of test samples provided by the client is one approach to evaluate the competence of candidates. SRM's are virtually unexcelled for this purpose. The only questions in such

usage are the selection of an appropriate SRM and the possibility of falsification of data due

to recognition of the test sample as an SRM with a known composition.

The use of SRM's for educational purposes should not be overlooked. Understanding of analytical chemistry is best demonstrated by practical laboratory work in which students

analyze real samples. No better ones are available than SRM's which provide the opportunity

to test both the precision and the accuracy of the analytical results.

SRM's find use as calibrants in certain cases. For example, the practical pH scale is defined by NBS SRM's, and SRM's for fixed temperature points are available. The use of SRM's

as primary chemical standards has already been discussed. Some industrial matrix SRM's, and

25
particularly metals, are used for calibrating chemical analyzers. Many of the standard methods developed by ASTM Committee E-2 on Emission Spectroscopy can be calibrated directly with appropriate SRM's. As an example, ASTM Standard Method E 322 is used when analyzing low alloy steels by X-ray fluorescence and NBS D-800 and 1200 series of low-alloy steel SRM's are recommended as calibrants.

One of the major uses, and the original driving force behind SRM development, is for the quality assurance of measurement processes. When various analysts use different methodologies

(and even the same methods), unacceptable discrepancies can arise, usually attributable to calibration or procedural differences. The analysis of commonly available reference materials

can identify such problems and lead to their solution.

Raid Applications Figure 7. Systems Approach to Measurement Accuracy

This figure depicts a hierarchical system of measurement methods and reference materials.

The function of each component (1 to 6) is to transfer accuracy to the level immediately below

it and help provide traceability to the level immediately above it, thus helping to assure

overall measurement compatibility. Proceeding from the bottom to the top of the measurement

hierarchy, accuracy requirements increase at the expense of decreased measurement efficiency.

At the top are the so-called definitive methods of analysis or test, which give the most accurate values obtainable. Unfortunately, most definitive methods (for example, gravimetric

techniques for preparing analyzed gas SRM's) are usually time consuming and sophisticated.

Thus, they are not economically acceptable for widespread and routine use. Definitive methods, however, are used whenever possible to certify NBS SRM's. With these materials, accuracy

can be transferred throughout a measurement system. SRM's are commonly used in developing reference methods and assuring their accuracy.

Such methods may be suitable for direct use. Alternatively, they may serve as a basis for developing or evaluating other methods. Reference methods are also commonly used for producing secondary reference materials, which, in turn, are directly used in routine field measurement applications.

In principle, the accuracy of numerous field methods can be traced to a definitive method

in a hierarchical accuracy-based measurement system. SRM's and other reference materials are essential in the transfer of accuracy. Also essential are good methods, good laboratory

practices, well qualified personnel, and adequate quality assurance procedures.

The complexity of modern chemical analysis provides many sources of error and opportunities for introduction of bias and imprecision. Accordingly, such systems must be operated under a rigid quality assurance system if results are to be meaningful. It is not sufficient to check the calibration of instruments although this is always necessary. Rather,

the performance of the entire system needs to be monitored on a regular basis. SRM's are finding increasing use as test materials to monitor system performance.

26
SRM's are best used on a regular basis. The sporadic use of reference materials when trouble is suspected is a legitimate use but systematic measurement in a control- chart mode of operation will generally be more informative and is highly recommended. SRM's may be used as the sole reference material or they may be used with internal reference materials in a systematic manner, thus conserving the former and adding credence to the latter.

The use of SRM's as quality assurance materials is discussed in more detail in the article contained in Appendix (D.3).

6.4 Interpretation of Reference Material Analyses

Some SRM's have a matrix identity with test samples and can be used directly to establish

the response function of chemical analyzers. Others may be used by a laboratory as their pri- mary standards. However, the majority of the SRM's are quality assurance materials and should

be analyzed regularly or on occasion to monitor the performance of a measurement system.

The four general cases for use of SRM's as quality assurance materials are illustrated in Figure 8 (a-d). When a matrix match is possible (8a), the uncertainty in the sample measurements can be equatable to that observed in measurement of the SRM. When such a match is not possible but an SRM with a related matrix is available (8b), the test sample uncertainty may

be relatable to those observed when measuring the SRM's. Even when the above situations do not apply, the measurement of an appropriate SRM (8c) can monitor the measurement system and

its performance when measuring test samlples can be inferred in many cases. When an SRM is unavailable or not used, measurement uncertainty must be inferred from other evidence such as physical calibrations and the experience of others, for example. Obviously it is to the advantage of a laboratory to evaluate its own performance, using SRM's or other reliable

reference materials whenever possible.

The results obtained when analyzing reference materials should be interpreted after due consideration. When measured consistently and utilizing control charts, they can effectively

monitor a measurement process. When measured in isolation the results could be inconclusive

or even misleading.

The inability to correctly analyze a reference material may cast serious doubts on the reliability of a measurement process but provide no diagnostic information. Also, the correct analysis of an SRM may not necessarily indicate the converse. Referral to Figure 9 will clarify this point. In this figure, measured values are plotted with respect to the expected

values, certified values, for example. For an unbiased system the data would be represented

by line A

Various kinds of linear measurement bias are illustrated in Figure 9. Line B corresponds

to a constant bias (negative in this case but it could be positive, as well) while line C results from bias which is proportional to the concentration level of the sample. The propor- tionality factor could be less or greater than unity (shown). Line D results from a combination of constant and level- proportional bias. It is obvious that the measurement of one reference sample will not evaluate the performance of a measurement system throughout a con- centration range unless supplemented by other information. One could even obtain a result, 2, and conclude -that a system was unbiased when the analysis of additional reference materials

might indicate performance representable by line D, for example.

Occasionally, situations may occur where linear treatment of biases does not apply, but these are not described in the present paper. When possible, the analysis of several reference samples, spanning the concentration

range of interest, is the most useful way to investigate measurement bias. The three sample

approach - analysis of a low, middle, and upper range sample - is practical in most cases, provided that the reference samples are sufficiently homogeneous and that the range of analytical interest is covered. Bias is even identifiable using relatively non-homogeneous samples,

provided that a sufficient number are analyzed. It is highly unlikely that n randomly selected samples from a lot would all deviate in a systematic manner from a population mean

value, provided n is 5 or more. Thus the measurement of such should indicate the kind of bias, that may be present. Statistical advice may be necessary, in such cases to plan the number of samples and the replicate measurements needed and to evaluate the test results.

When supported by other data, the measurement of even a single reference sample can be meaningful. Thus a knowledge of the standard deviation of measurement, obtained from other

data, would answer whether point (1) or point (2) could be considered as represented by line

A. Measurement of a series of non-reference-material samples might provide some knowledge

about the slope and hence assist in the interpretation of the SRM measurement data. The best diagnostic information would be obtained from the measurement of a series of SRM's containing

graduated levels of analyte. When such are available, the use of all of them will maximize

the information on the performance characteristics of an analytical system.

27
^2 SRM v//sy///A Material

Measurement

USRM = U M

(A) Matrix-Match

SRM Material

Measurement

USRM = k U M

(B) Matrix-Related

SRM Material Usrm U M

Measurement

USRM ~ k U M

(C) Matrix-Relation Inferred

(D) SRM - Not Used

Figur Interpreting SRM measurements

28
Expected Value

Figure 9. Identifying measurement bias

An SRM may have a reasonable matrix match with test samples but differ from them in level

of concentration. If the level of analyte in the SRM is higher than that of the test sample,

it may be possible to quantitatively dilute the SRM. The best diluent is the matrix of the SRM but a neutral matrix may be used in some cases. Two SRMs containing different levels of

an analyte may be proportionally mixed to obtain a series of materials, ranging from the con- centration level of the lower to that of the higher. These techniques are described in ASTM

D-3975. - Preparation of Samples for Collaborative Testing of Methods for Analysis of Sediments. T-he expression used to calculate the composition of a blend of two samples, A and

B, is as follows:

weight percent (or ppm) of constituent a in sample A weight percent (or ppm) of constituent a in sample B weight percent (or ppm) of constituent a in mixture

weight of sample A in mixture

weight of sample B in mixture

When a material is diluted with a second material containing an the analyte of interest, the expression to be used is: nsignificant amount of

weight of diluent sample mixed with W

A

29
All dilutions must be made with care. Because uniform mixing may be difficult to achieve, the entire mixture that has been prepared may need to be used, rather than sub- samples of it. Despite such problems, the technique is attractive since it can provide reference materials that simulate the test samples more closely, and to evaluate a measurement

process over a range of concentration levels, as discussed in Section 6.4. When possible, the analysis of several reference samples, spanning the concentration

range of interest, is the most useful way to investigate measurement bias. The three sample

approach - analysis of a low, middle, and upper range sample - is practical in most cases, provided that the reference samples are sufficiently homogeneous and that the range of analytical interest is covered. Bias is even identifiable using relatively non-homogeneous samples,

provided that a sufficient number are analyzed. It is highly unlikely that n randomly

selected samples from a lot would all deviate in a systematic manner from a population mean

value, provided n is 5 or more. Thus the measurement of such should indicate the kind of bias, that may be present. Statistical advice may be necessary, in such cases to plan the number of samples and the replicate measurements needed and to evaluate the test results.

6.5 Evaluation of Measurement Error

The values measured by a user for an analyte or a parameter will rarely agree fully with

the certified value due to uncertainties in each. The question naturally arises as to how large a difference is significant. This will depend on the uncertainty of the measurement by the user (see Figure 10) and the certification limits for the SRM. The former can be calculated, using the expression (see also Section C.5):

X ± + B) /n (where X is the mean of n measurements by the user whose estimated standard deviation of measurement is s. Student's t value will depend on the number of degrees of freedom in the estimation of s (n-1 if s is based on the measurement of the moment) for a 95? confidence

level which is the usual level for certified values of an SRM. The value, B, is the user's estimate of the magnitude of any uncorrected biases inherent in his measurement and is based

on experience and professional judgment.

Figure 10. Uncertainty of measured value

C m= Uncertainty of Measured

B = Biases, Errors Inherent in Measurement

s = Precision of Measurement

i = Precision of Mean of n Measurements (really s~)

30
If the confidence interval intersects the confidence or tolerance interval of the SRM, there is agreement. If not, then a discrepancy exists which should be investigated. In the case of heterogeneous SRM's, several sub-samples may need to be measured to evaluate measurement bias.

If an apparent discrepancy is found, it is advisable to look close r at the estimates of uncertainty. Rarely will a user's uncertainty (^=) be less than that of the NBS measurements

which are done with state-of-the-art techniques. "Perhaps there are unsuspected biases in the user's laboratory, which the SRM has uncovered. If an explanation cannot be found, the user should communicate with NBS OSRM who will look into the matter and advise as possible. The sample may have deteriorated or become contaminated, so the possibility of such may need to

be considered.

It cannot be too strongly emphasized that statistical control must be attained before any data can be believed and any errors identified or corrected. There is no easy way to identify

assignable causes for either unacceptable bias or precision, which is the first step for cor- rective actions. Consultation with experienced users of the methodology employed may be helpful to suggest approaches to follow, if not the specific solutions. The magnitude of the errors encountered may rule out certain sources and indicate likely ones. However, the simultaneous existence of several sources of unacceptable error cannot be discounted.

In diagnosing error, it should be remembered that random errors add up in quadrature,

which is to say the variance of random errors is additive, as discussed in 2.1.1. When the measurement system is well-understood, it may be possible to estimate the variance of the individual steps or operations of which it is composed and to compare such with the magnitude

of the errors of concern. Obviously, the step or operation with largest variance is the first

one to be considered when other information is not available.

On the other hand, there is no reason to believe that biases are randomly distributed but rather they add up, algebraically. According, small systematic errors contribute differently

than small random errors. Whenever excessive bias or imprecision is found to be present, corrective action needs to be taken, otherwise the measurement process will have limited usefulness. The first question

that needs to be answered, in this regard, is whether the unsatisfactory situation is inherent

to the methodology or is due to its application in a given laboratory or even by specific persons. Collaborative test data and/or the research findings of others may indicate the magnitude of the former. If the experience of a laboratory is not consistent with this, excess application imprecision or bias would be suspected. Factors to be considered in reducing operational (non-state-of-the-art) bias include: better quality of calibrants

improvement in calibration

reducing contamination

reducing mechanical losses reducing sol ut i on/ ex t r ac t i on i n ef f i c i ence

s

removal of interferences.

Factors to be considered in reducing operational random error include: improvement of technical skills improvement of manipulative skills improvement of environmental control

closer tolerances in operational parameters

improved instrumentation

reducing variability of blanks.

31
7. Reporting Analytical Data

7.1 Limits of Uncertainty for Data

Data are of limited use and even can be useless unless limits of uncertainty can be estimated and assigned to them [1]. The limits should include the limits of uncertainty of any systematic error (bias) and the random errors of measurements. Estimations of limits of systematic error are based on judgment and require a full understanding of the measurement

system used. The experience of the analytical community is helpful in this respect. The random error component is based on the skill and experience of the laboratory making the measurements and is evaluated from the standard deviation of the measurement process.

When the measurement process is demonstrated to be in a state of statistical control, the process standard deviation may be used to evaluate the confidence interval for the mean of n measurements (see C.5). The use of control charts is the best way to demonstrate that a pro- cess is in a state of statistical control at the time the measurements are made and this can minimize the amount of work needed to establish confidence limits for the data.

In the absence of a control chart, a sufficient number of replicate measurements must be made to demonstrate statistical control and to estimate the standard deviation of measurement

with a measurable degree of confidence. The minimum number of replicate measurements required

is somewhat arbitrary and depends on the risk concerned with exceeding the limits of confi- dence that are stated. Metrologists often recommend 7 to 30 determinations as a reasonable

number of replicates. The uncertainty of the standard deviation increases rapidly below 7 and little is to be gained by increasing the number above 30.

It is not considered good practice to correct for biases without understanding their origin. Biases such as analytical blanks should be measured as accurately as necessary and possible and the results are corrected directly for them [18]. This is proper because analytical chemists believe that blanks are additive errors. Biases such as found when measuring

SRM's are investigated to identify their source so that they can be eliminated, minimized, or corr ected-f or in a proper manner. As already pointed out (see 6.4) the method of correction

will be dictated by the nature of the bias. The most reliable approach is to remove the bias rather than to correct for it. The treatment of bias related to the question of recovery often troubles the trace analyst. Usually corrections are not made but recoveries are reported as one of the qualifications for the data. The recovery, no matter what its value, should be shown to be in a state of statistical control, and this should be a requirement for reporting data of this

kind. When a recovery determination is made and the value obtained is variable or does not fall within control limits, corrective action is indicated and control should be re-established before data may be reported.

7.2 Significant Figures Numerical data are often obtained (or at least calculations can be made) with more digits

than are justified by its accuracy or precision. So that it is not misleading, such data when reported should be rounded to the number of figures consistent with the confidence that can be placed on it (see guidelines for Reporting Results 7.3). Accordingly, metrologists have adopted the terminology of significant figures in describing the resulting data. The number

of significant figures is said to be the number of digits remaining when the data is so rounded. The last digit, or at most the last two digits are expected to be the only ones that would be subject to change on further experimentation, for example. Thus, for a measured

value of 20.5, only the 5 and, at most the 0.5 would be expected to be subject to change. Such

data would be described as having three significant figures.

In counting significant figures, any zeros used to locate a decimal point are not considered as significant. Thus 0.0025 contains only two significant figures. Any zeros to the right of the digits are considered as significant, thus only those that have significance

should be retained. Thus 2500 and 2501 each have four significant figures. Zeros should not

be added to the right of significant digits to define its magnitude, unless they are significant, since this would confuse the significance of the value. For example, it is not good practice to report a value as 2500 ng but rather 2.5 mg if the data is reliable to two signi- ficant figures. The use of exponential notation, e.g., 3-5 x 10^, is an acceptable way to report data with two significant figures which would otherwise have to be reported as 3500, suggesting 4 significant figures.

In multiplication and division, the operation with the least number of significant

figures determines the numbers to be reported in the result. For example, the product 1256 x 12.2 = 15323.2 is reported as 1.53 x 10 . In addition and subtraction, the least number of figures to either the right or the left of the decimal point determines the number of significant figures to be reported. Thus the sum of 120.05 + 10.1 + 56.323 = 156.473 is reported as 156.5 because 10.1 defines the reporting level. In complex calculations involving multiplications and additions, for example, the operation is done serially, and the final result is rounded according to the least number of significant figures involved. Thus (1256 x 12.2) + 125 = 1 .53 x 10 4

+ 1 25 = 1 .54 x 10 4

.

32
The following rules should be used in rounding data, consistent with its significance:

When the digit next beyond the one to be retained is less than five, the retained

figure is kept unchanged. For example: 2.541 becomes 2.5 to two significant

figures

.

When the digit next beyond the one to be retained is greater than five, the retained

figure is increased by one. For example: 2.453 becomes 2.5 to two significant

f i gur es . When the digit next beyond the one to be retained is exactly five, and the retained

digit is even, it is left unchanged and conversely. Thus, 3.450 becomes 3-4 but 3-550 becomes 3-6 to two significant figures.

When two or more figures are to the right of the last figure to be retained, they are

to be considered as a group in rounding decisions. Thus in 2.4(501 ), the group (501

)

is considered to be >5 while for 2.5(499), (499) is considered to be <5. 7.3 Guidelines for Reporting Results of Measurements

The number of significant figures to be used in reporting results is often asked. This

will depend on the number of figures in the original data and the confidence limits to support

the results. Analysts sometimes feel that observed data have more digits than are meaningful

and are tempted to round them to what is felt to be significant. This should be resisted and rounding should be deferred as the last operation. The following guidelines are recommended

when deciding what is significant.

The number of figures to retain in experimental data and even in preliminary calculations

is unimportant, provided a certain minimum is exceeded. At least the last figure should vary between successive trials and variability of at least the last two figures is preferred. If this is not the case, the data are probably truncated by the operation (e.g., low attenuation), rounded off by the observer, or imprecisely read. Training of observers can often improve the precision of reading. Observers can have preconceived ideas of the attainable

precision (or that required for some application) and will round off readings with this in mind. Thus they may be actually throwing away data. The average of several values should be calculated with at least one more significant

figure than that of the data. This will then be rounded for reporting, consistent with the confidence limits estimated.

The standard deviation (necessary for computing confidence intervals) should be computed

to three significant figures and rounded to two when reported as data. The confidence interval should be calculated, then rounded to two significant figures (use more than this number

in the calculations as available) and the result reported should be consistent with this. While any confidence level may be used, the 95 percent level is commonly used. However, the level used for the calculation must be reported.

As an exa'mple of the above, the following data were observed:

5.2, 14.7, 15.1, 15.0, 15.3, 15.2, 14.9

x = 15.057

s = 0.207 Confidence interval calculation:

ts 2.517 x 0.207 -= = T= = 0.1969

/n /7 The result reported is x = 15.06 ± 0.20 where the uncertainty represents the 95 percent confidence interval for the mean of seven measurements

.

33
8. NBS Services Related to SRM's

The NBS Office of Standard Reference Materials and the various scientists that are engaged in their development and certification believe that the use of SRM's in a systematic

manner can provide a high level of confidence in analytical measurement data. To the extent possible, assistance will be provided related to their use. While detailed advice on specialized measurement problems cannot be provided, generic advice is available and may be all that

is needed in many situations. A list of the kinds of services that can be provided and the telephone number to call to make initial contacts follows.

- SRM General

o General catalogues will be sent on request

o Special catalogues will be sent to those identifying special interests and updates

will be sent as available

o Announcement of new SRM's are sent to those on the special interest lists

o Replacement of lost certificates will be made on request

- Assistance in Ordering/Customer Services

o Call 301 - 921 -20145 for special assistance in ordering, quotations on current

prices, and availability of specific SRM's.

- Technical Assistance

o Questions concerning applications, experimental results when measuring specific

SRM's, stability selection of SRM's, details of certification and certified values,

and other technical matters are directed to the appropriate project manager (see p. 57) or to Customer Services.

- SRM Workshops

o Quality Assurance of Chemical Measurements

A 2-day seminar, offered semi-annually, ordinarily announced through the SRM mailing list. Call 301 - 921-3197 for current information.

o Special SRM Workshops

Special workshops concerned with development of new SRM's or utilization of SRM's.

Call Customer Services

- Calibration Services

NBS provides a limited amount of calibration services in several areas of physical measurement. The services available and the current test fee may be obtained by inquiry to the NBS Office of Measurement Services, 301 - 921-2805.

34
9. Bibliography

9.1 References Cited

1. J. K. Taylor, Principles of Quality Assurance, NBSIR 85-3105 (1985), National Bureau of Standards, Gai ther sbur g , MD 20899.

2. Brief History and Use of the English and Metric System of Measurement. NBS SP 304A

( 1 968) . 3. Kolthoff, I. M . , et al. Quantitative Chemical Analysis, 4th Edition, p. 687 , Macmillian

( 1 969 ) . 4. The Analyst, 90 251 (1965).

5. ASTM E617, Laboratory Weights and Precision Mass Standards; 1978; ASTM, Philadelphia, PA 19103.

6. Taylor, J. K. Quality Assurance of Chemical Measurements. Anal. Chem. 53 : 1 588A-1 596A

(1981 ). 7. Eisenhart, C, Realistic Evaluation of the Precision and Accuracy of Instrument Calibration Systems, In Ref. 9, pp. 21-47.

8. ASTM Committee E-1 1 . ASTM Manual on Presentation of Data and Control Chart Analysis,

STP-15D, ASTM, Philadelphia, PA 19103.

9. Taylor, J. K. Reference Materials - What They Are and How They Should Be Used. J. Testing and Evaluation. 11:385-86 (1983).

10. Urlano, G. A. and Gravatt, C. C. The Role of Reference Materials and Reference Methods

in Chemical Analysis. CRC Critical Reviews in Analytical Chemistry, October 1977.

11. Cali, J. P. et al. The Role of Standard Reference Materials in Measurement Systems, National Bureau of Standards (U.S.) Monogr. 148; 1975.

12. Cali, J. P. and Stanley, C. L. Measurement Compatabi 1 i ty and Standard Reference

Materials; Annual Review of Materials Science 5:329~342, (1975).

13. ISO Guide 31 - Contents of Certificates of Reference Materials; 1981. Available from

ANSI, 1430 Broadway, New York, NY 10018.

14. ISO Guide 30 - Terms and Definitions Used in Connection with Reference Materials; 1981. Available from ANSI, 1430 Broadway, New York, NY 10018.

15. ISO Directory of Certified Reference Materials: 1982. Available from ANSI, 1430 Broadway, New York, NY 10018.

16. Ku, H.; Editor. Precision Measurement and Calibration Statistical Concepts and Procedures. National Bureau of Standards (U.S.) Spec. Publ. 300, Vol. 1; 1969.

17. Hughes, E. E. and Mandel , J. A Procedure for Establishing Traceability of Gas Mixtures

to Certain NBS SRM's. NBSIR 81-2777; 1981.

18. Taylor, J. K. Guidelines for Evaluation of the Blank Correction, J. Testing and Evaluation \Z, 54 (1984).

19. Natrella, M. G. Experimental Statistics. National Bureau of Standards (U.S.) Handbook

91 ; 1 963 .

9.2 Publications of the NBS Center for Analytical Chemistry

Related to SRM's

Alvarez, R ; Rasberry, S. D.; and Uriano, G. A. NBS Standard Reference Materials. Update 1982; Anal. Chem. 54:1226A (1982). Alvarez, R; Seward, R. W.; and Rasberry, S. D. Clincial Standard Reference Materials from

NBS; ACPR 19 (1983).

35
ASTM E305. Standard Practice for Establishing and Controlling Spectrochemi cal Analytical

Curves; 1983; ASTM, Philadelphia, PA 19103. ASTM E826. Standard Practices for Testing Homogeneity of Materials for the Development of Reference Materials; 1981; ASTM, Philadelphia, PA 19103. Bowers, G. N . , Jr.; McComb, R . B.; Christensen, R. G.; and Schaffer, R. High-Purity

4-ni trophenol : Purification, Characterization, and Specifications for Use as a Spectrophotometr i c Reference Material. Clin. Chem. 26(6), 724 (1980), SRM 938. Chesler, S. N . ; Guenther, F.'R.; May, W. E.; and Parris, R. M. SRM's for Accurate Analyses of PCB's in Oil. ASTM Standardization News J_0(6), 15 (1982), SRM 1581. Christensen, R. G.; White V. E . ; Meiselman, S.; and Hertz, H. S. Quantitative Trace Analysis

by Reversed-Phase Liquid Chromatogr aphy-Mass Spectrometry J. Chromatogr. 271 , 61 (1983), SRM 1599. Cohen, A.; Hertz, H. S.; Mandel, J.; Paule, R. C; Schaffer, R.; Sniegoski, L. T.; Sun, T.; Welch, M. J.; and White, V. E. Total Serum Cholesterol by Isotope Dilution/MaS3

Spectrometry: A Candidate Definitive Method. Clin. Chem. 26(7), 854 (1980). SRM 911a. Coxon, B. and Schaffer, R. Characterization and Quantitative Analysis of D-Glucose for Use in Clincial Analysis. Anal. Chem. 43, 1565 (1971), SRM 917. Coxon, B. and Schaffer, R. Analysis of Cortisol Clincial Standard by Fourier Transform,

Proton Magnetic Resonance Spectroscopy. Anal. Lett. 6(4), 291 (1973). Doumas, B. T. ; Bayse, D. D . ; Carter, R. J.; Peters, T. Jr.; and Schaffer, R. A Reference

Method for the Determination of Total Serum Protein. I. Development and Validation:

Clin. Chem. 27, 1642 (981), SRM 927. Doumas, B. T.; Bayse, D. D.; Bauer, K . ; Carter, R. J.; Elevitch, F . ; Garber, C. C.; Gradby, R. A.; Hause, L. L.; Mathes, A.; Peters, T., Jr., Rand, R. N . ; Reeder, D. J., Russell, S. M.; Schaffer, R.; and Westgard, J. 0. A Reference Method for the Determination of Total Protein. II. Test for Transferability. Clin. Chem. 27(10), 1651 (1981), SRM 927. Duncan, P.; Goshman, N.; Bayse, D. D.; and Schaffer, R., e_t a 1 . A Candidate Reference Method

for Uric Acid in Serum. II. I nt er 1 abor a t or y Testing. Clin. Chem. 28, 291 (1982), SRM

913. Epstein, M. S.; et al . Application of Laser-Excited Atomic Fluorescence Spectrometry to the Determination of Iron. Spectrochem. Acta, 35B, 233 (1980), SRM 394, 1633, 1643 (See also Applied Spectroscopy 34, 372 (1980)). Fatiadi; A. J. and Schaffer, R. An Improved Procedure for Synthesis of DL-4 -Hydroxy-3"

Methoxymandelic Acid ( DL- "V ani 1 1 y

1 " -Mandel i c Acid, V M A ) . J. Res. Nat. Bur. Stand. (U.S.) 78A(3), 136 (1974), SRM 925. Gladney, E. S. Compilation of Elemental Concentration Data for NBS Biological and Environmental SRM's. LA-8438-A-MS , UC-4, July 1980, Los Alamos Scientific Laboratory.

Gramlich, J. W.; Machlan, L. A.; Brletic, K. A.; and Kelly, W. R. Thermal Ionization Isotope Dilution Mass Spectrometry as a Definitive Method for Determination of Potassium in Serum, Clin. Chem. 28, 1309 (1982), SRM 909, 985. Greenberg, R. R. and Kingston, H. M. Trace Element Analysis of Natural Water Samples by Neutron Activation Analysis with Chelating Resin. Anal. Chem. 55(7), 1160 (1983), SRM

164 3a. Guenther, F. R . ; Parris, R. M . ; Chesler, S. N .

; and Hilpert, L. R. Determination of Phenolic Compounds in Alternate Fuel Matrices. J. Chromatogr. 207, 256 (1981), SRM 1580. Howell, B. F . ; Margolis, S. A.; and Schaffer, R. Detection of Inhibitors in Reduced Nicotinamide Adenine Dinucleotide by Kinetic Methods. Clin. Chem. 22, 1648 (1976), SRM

for NADH. Howell, B. F.; Margolis, S. A.; and Schaffer, R. Residual Fluorescence as an Index of Purity

of Reduced Nicotinamide Adenine Dinucleotide. Clin. Chem. 19(11), 1280 (1973), SRM for NADH. Hughes, E. E. Role of the National Bureau of Standards in Calibration Problems Associated

with Air Pollution Measurements, in Calibration in Air Monitoring. ASTM STP, 598; 1976. ASTM, 1916 Race St., Philadelphia, PA 19103.

36
Kingston, H. M. and Pella, P. A. Preconcentrat i on of Trace Metals in Environmental and Biological Samples by Cation Exchange Resin Filters for X-ray Spectrometry. Anal. Chem.

53 j 223 ( 1 981), SRM 1 632

Kline, W. R . ; Enagonio, D.; Reeder , D. J.; and May, W. E. Liquid Chromatographic

Determination of Valprioc Acid in Human Serum. J. Liq. Chromatog. 5(9), 1697 (1982), SRM

1 599 . Kratochvil, B. G. and Taylor, J. K. Sampling for Chemical Analysis. Anal. Chem. 5.3, 924A

(1981). Kuehner , E. C. and Pella, P. A. Ener gy- D i s pe r s i ve X-ray Spectrometr i c Analysis of NBS Standard Reference Material 1571, Orchard Leaves After Oxidation and Borate Fusion. Applied Spectroscopy 33, 632 (1979).

Koch, iff. F . Sample Preparation in I on- Chr omat ogr a ph y . J. Res. Nat. Bur. Stand. (U.S.). 84,

241 (1979). Lindstrom, R. M., et al . Neutron Capture Prompt Y-Ray Activation Analysis for Multielement Determination in Complex Samples. Anal. Chem. 51 (13). 2209 (1979). Maienthal, E. J. Application of Linear Sweep Voltammetry to the Determination of Trace Elements in Biological and Environmental Materials. Trace Substances for Environmental

Health VIII 243-6 (1974), SRM 1571. Maienthal, E. J. Analysis of Botanical Standard Reference Materials by Cathode Ray Polarography J.A.O.A.C. 55, 1109 (1972), SRM 1571. Margolis, S. A.; Howell, B. F.; and Schaffer, R. The Purification and Analysis of the Purity

of Reduced Nicotinamide Adenine D i nuc 1 eo t i de . Clin. Chem. 22, 1322 (1976 ), SRM for NADH. Margolis, S. A.; Howell, B. F.; and Schaffer, R. Lactate Dehydrogenase Inhibitors in NADH Preparations. Clin. Chem. 23, 1581 (1977), SRM for NADH. Margolis, S. A. and Konash, P. J. Non-Peptide Impurities in Angiotensin I and Other Commercial Peptides. J. High Res. Chromatog. and Chromatog. 3 , 317 (1980), SRM 998. Margolis, S. A. and Konash, P. L. The HPLC Analysis of Diasteromers and Structural Analogs of Angiotensins I and II. Anal. Biochem. In Press. SRM 998. Margolis, S. A. and Schaffer, R. Reversed-Phase Liquid Chromatographic Analysis of the Impurities of Nicotinamide Adenine D i nuc 1 eot i des . J. Liq. Chromatog. 2, 837 (1979), SRM

for NADH. Margolis, S. A. and Schaffer, R. Development of a Standard Reference Material for Angiotensin

I. Final Report on Agreement # 1 - Y 0

1 -HU - 7 0 0 4 2 -0 6 ; 1 979, SRM 998 . Margolis, S. A.; Yap, W. T. ; Matthews, B.; and Schaffer, R. Reversed-Phase Liquid

Chr omatograph Analysis of the A c i d- C at al y ze d Rearrangement of NADH: Separation of New Products and an Analysis of the First Two Reactions of the Rearrangements. J. Liq. Chromatog. ]_, 669 (1978), SRM for NADH. Marinenko, G . ; Koch, W. F.; and Etz, E. S. High Precision Coulometric Titration of Uranium J. Res. NBS 88, 117 (1982), SRM 950. May, W. E.j Brown, J. M.j Chesler, S. N . ; Guenther, R. F . ; Hilpert, L. R.; Hertz, H. S.; and Wise, S. A. Development of an Aqueous Polynuclear Aromatic Hydrocarbon Standard 'Reference Material. Polynuclear Aromatic Hydrocarbons, P. W. Jones and P. Leber, Eds. Ann Arbor Science Publishers, Inc., Ann Arbor, MI; (1979), SRM 1644.

May, W. E . ; Brown-Thomas, J. M . ; Hilpert, L. R.; and Wise, S. A. Certification of Selected Polynuclear Aromatic Hydrocarbons in SRM 1580, Organics in Shale Oil. Anal. Methods and Biol. Fate of Polynuclear Aromatic Hydrocarbons, M. Cooke, and A. J. Dennis, Eds. Battelle Press, Columbus, OH. 1-16; (1981), SRM 1580.

May, W. E . ; Chesler, S. N . ; Hertz, H. S.; and Wise, S. A. Analytical Standards and Methods

for the Determination of Polycyclic Aromatic Hydrocarbons in Environmental Samples.

Intern. J. Environ. Anal. Chem. 1_2, 259 (1982 ), SRM's 1 580 , 1 64 4 , 1 647 , and 1 649 . Mavrodineanu , R., Editor. Procedures Used at the National Bureau of Standards to Determine Selected Trace Elements in Biological and Botannical Materials, National Bureau of Standards (U.S.) Spec. Publ. 492; 1977. Mavrodineanu, R.; Shultz, J. I.j and Menis, 0. Accuracy in Spectrophotometry and Luminescence

Measurements. National Bureau of Standards (U.S.) Spec. Publ. 378; 1973 May.

37
Orvini, E.; Gills, T. E.; and LaFleur, P. D. Method for Determination of Selenium, Arsenic,

Zinc, Cadmium, and Mercury in Environmental Matrices by Neutron Activation Analysis.

Anal. Chen. 46, 1294 (1974) SRM 1571, 1577, 1630, 1632, and 1633. Pella, P. A.; Kingston, H. M. j Sieber, J. R . ; and Feng, L-Y. Effect of Sample Dissolution

Procedures on X-ray Spectrometr i c Analysis of Biological Materials. Anal. Chem. 55, 1193 (1983 ), SRM* s 1 575 and 1 577 . Pella, P. A.; Lorber, K . E.; and Heinrich, K. F. J. Ener gy- D i s per s i ve X-ray Spectrometric

Analysis of Environmental Samples after Borate Fusion. Anal. Chem. 50, 1268 (1978), SRM's

1633 and 1648. Pella, P. A. and Sieber, J. R. I n t er com par i sons of Selected Semi -Empi r i cal and Fundamental

Parameter Interelement Correction Methods in X-ray Spectrometry. X-ray Spectrometry 11,

167 (1 982) , SRM 1633. Perry, B. W. and Doumas , B. T. (Chairman); Bayse, D. D . ; Butler, T.; Cohen, A.; Fellows, W.; Garber, C. C; Howell, B.; Koch, T.; K r i s hnam ur t hy , S.; Louderback, A.; McComb, R. B. ; Miller, D.; Miller, R. R. ; Rand, R. N. ; and Schaffer, R. A Candidate Reference Method

for Determination of Bilirubin in Serum. Test for Transferability. Clin. Chem. 29, 297

( 1 983) , SRM 91 6. Rains, T. C; Rush, T. A.; and Butler, T. A. Innovations in Atomic Absorption

Spectrophotometry with Electrothermal Atomlzation for Determinating Lead in Foods. J.A.O.A.C. 65, 994 (1982), SRM 1566. Rasberry, S. D. The Role of NBS/SRM's in Quality Assurance. 1983 ASQC Quality Congress Transactions; pp. 343"8. Rasberry, S. D. and Heinrich, K. F. J. Calibration for Interelement Effects in X-ray Fluorescence Analysis. Anal. Chem. 46, 81 (1974), SRM 1188. Reeder, D. J.; Enagonio, D. P.; Chrlstensen, R. G .

; and Schaffer, R. Development of a Standard Reference Material for Antiepilepsy Drugs in Serum, Trace Org. Anal.: A New Frontier in Anal. Chem. National Bureau of Standards (U.S.) Spec. Publ. 519; 1979, 447-453, SRM

900. Rook, H. L.j Gills, T. E.j and LaFleur, P. D. Method for Determination of Mercury in Biological Materials by Neutron Activation Analysis. Anal. Chem. 44, 1114 (1972), SRM

1571. Schaffer, R .

, Editor. Organic Chemistry Section: Summary of Activities, July 1967 to June

1968. National Bureau of Standards (U.S.) Tech. Note 457; 1968, SRM's 911a, 912a, 913, and 914. Schaffer, R., Editor. Organic Chemistry Section: Summary of Activities, July 1968 to June

1969. National Bureau of Standards (U.S.) Tech. Note 507; 1969, SRM's 911a, 912a, 913,

914, 916, and 91 7. Schaffer, R., Editor. Organic Chemistry Section: Summary of Activities, July 1969 to June

1970. National Bureau of Standards (U.S.) Tech. Note 547; 1970, SRM's 911a, 912a, 916,

91 7, 920, 921 , and 925 . Schaffer, R.; Margolis, S. A.; and Longenbach, P. J. Consideration in the Preparation and Certification of Pure Analyte Reference Materials. Proc. of the 1979 Tenovus Workshop on Quality Control in Clin. Endoc., D. W. Wilson, S. J. Gaskell, and K. W. Kemp, Eds., Alpha Omega Publishing, Cardiff, Wales 37-42 (1979). General. Schaffer, R.; Sniegoski, L. T.; Welch, M. .J.; White, V. E.; Cohen, A.; Hertz, H. S.; Mandel

,

J.; Paule, R. C.; Svensson, L.; Bjorkhem, I.; and Blomstrand, R. Comparison of Two Isotope Dilution/Mass Spectrometric Methods for the Comparison of Total Cholesterol.

Clin. Chem. 28(1), 5 (1982), SRM 911a. Schaffer, R.; Velapoldi , R. A.; Paule, R. C; Mandel, J.; Bowers, G. N . , Jr.; Copeland, B. E . ; Rodgerson, D. 0.; and White, J. C. A M ul t i 1 a bor a t or y -E val ua t ed Reference Method for Determination of Serum Sodium. Clin. Chem. 27, 1842 (1981), SRM 919. Schaffer, R.; White, V. E.; Sniegoski, L. T.; and Cohen, A. A Candidate Definitive Method for

the Determination of Total Cholesterol in Serum, Trace Org. Anal.: A New Frontier in Anal. Chem. Nat. Bur. Stand. (U.S.) Spec. Publ. 519; (1979) 405-410, SRM 911a. Schwartz, M. K.; Blatt, S.; Blumenfeld, T. D.; Fleinsker, M . ; Free, A. H.; Goechman, N.; Hainline, A., Jr.; Laessig, R. H . ; Nino, H. V.; Richards, A. H.; Schaffer, R.; and Vanderlinde, R. F. Clincial Chemistry in Quality Assurance Practices for Health Laboratories, S. Inhorn, M. D., Ed., American Public Health Assoc. Washington, DC, 451-508; 1978. General.

38
Seward, R. W., Editor. Standard Reference Materials and Meaningful Measurements. Nat. Bur. Stand. (U.S.) Spec. Publ. 408. Small, J. A. Production and Characterization of Glass Fibers and Spheres for Microanalysis.

Scanning Electron Microscopy 1_, 445 ( 1 978). Small, J. A. and Steel, E. B. An Overview of the NBS-EPA Program for Development of Standards

for Use in the Analysis of Environmental Samples for Asbestos by Electron Microscopy.

Proc. Third Intern. Colloq. on Dust Meas. Techniques. Cannes, France 1980; p. 256. Small, E. B. ; Newbury, D. E. ; and Pella, P. A. Preparation of Thin-Film Glass Standards for Analytical Electron Microscopy. Anal. Elect. Microscopy 1981; 65-70 (San Francisco

Press, 1981). Velapoldi, R. A.; White, P. A.; May, W. E. ; and Eberhardt, K. Spectrof luorometric Determination of Polycyclic Aromatic Hydrocarbons in Aqueous Effluents from Generator

Columns. Anal. Chem. 55, 1896-1901, SRM 1 644 . Welch, M. J.; Cohen, A.; Hertz, H. S.; Ruegg, F. C; Schaffer, R . ; Sniegoski, L . T. ; and White, V. E. An Isotope Dilution Mass Spectrometr i c Method for the Accurate Determination of Serum Urea. Anal. Chem., Submitted for Publication, SRM 912a. White, V. E. ; Welch, M. J.; Schaffer, R.; and Hertz, H. S. Definitive Measurement of Constituents in Human Serum. Dimensions; 1980; March, SRM's 911a, 912a, 913, and 917. White, V. E. ; Welch, M. J.; Sun, T.; Sniegoski, L. T . ; Schaffer, R.; Hertz, H. S. ; and Cohen,

A. The Accurate Determination of Serum Glucose by Isotope Dilution/Mass Spectrometry -- Two Methods. Biomed. Mass Spectrom. 9, 395 (1982), SRM 917. Wise, S. A.; Bowie, S. L.; Chesler, S. N.; Cuthrell, W. F . ; and Rebbert, R. E. Analytical

Methods for the Determination of Polycyclic Aromatic Hydrocarbons on Air Particulate

Matter. Polynuclear Aromatic Hydrocarbons: Phys. and Biol. Chem., M. Cooke, and A. J. Dennis, Eds., Battelle Press, Columbus, OH; 1982; 919-929, SRM's 1648 and 1649.

39
10. Information

Office of Standard Reference Materials

Room B311, Chemistry Bldg. National Bureau of Standards

Washington, D.C. 20231 (Telephone 301-921-2045)

Chief Stanley D. Rasberry

Deputy Chief William P. Reed

Manager, Marketing and Customer Services

Leonara T. Klein

Manager, Production and Certification Programs

Thomas E. Gills Project Managers

Robert L. Alvarez

Thomas E. Gills

Lee J. Kieffer

Raymond L. McKenzie

Lura J. Powell William P. Reed Richard W. Seward

no
APPENDIX A. GLOSSARY OF TERMS Absolute Method - A method in which characterization is based entirely on physically

(absolute) defined standards. Accreditiation - A formal process by which a labortory is evaluated, with respect to established criteria, for its competence to perform a specified kind(s) of measurement.

Also, the decision based upon such a process. When a certificate is issued, the process

is often called certification.

Accuracy - The degree of agreement of a measured value with the true or expected value of the quantity of concern. Aliquant - A divisor that does not divide a sample into a number of equal parts without leaving a remainder; a sample resulting from such a divisor.

Aliquot - A divisor that divides a sample into a number of equal parts, leaving no remainder;

a sample resulting from such a divisor. Analyte - The specific component measured in a chemical analysis; also called analate. Assignable cause - A cause believed to be responsible for an identifiable change of precision

or accuracy of a measurement process.

Blank - The measured value obtained when a specified component of a sample is not present during the measurement. In such a case, the measured value/signal for the component is believed to be due to artifacts, hence should be deducted from a measured value to give a net value due to the component contained in a sample. The blank measurement must be made

so that the correction process is valid. Blind Sample - A sample submitted for analysis whose composition is known to the submitter but unknown to the analyst. A blind sample thus is one way to test proficiency of a measurement process.

Bias - A systematic error inherent in a method or caused by some artifact or idiosyncrasy of the measurement system. Temperature effects and extraction inefficiencies are examples

of this first kind. Blanks, contamination, mechanical losses and calibration errors are examples of the latter kinds. Bias may be both positive and negative and several kinds

can exist concurrently, so that net bias is all that can be evaluated, except under special conditions.

Bulk sampling - Sampling of a material that does not consist of discrete, identifiable,

constant units, but rather of arbitrary, irregular units. Callbrant - A substance used to calibrate or to establish the analytical response of a measurement system. Calibration- - Comparison of a measurement standard or instrument with another standard or instrument to report or eliminate by adjustment any variation (deviation) in the accuracy

of the item being compared. Cause-Effect Diagram - A graphical representation of the causes that can produce a specified

kind of error in measurement. A popular one is the so-called fish bone diagram, first described by Ishikawa, given this name because of its suggestive shape. Central Line - The long-term expected value of a variable displayed on a control chart. Certification - See accreditation.

Certified Reference Material (CRM) - A reference material one or more of whose property values

are certified by a technically valid procedure, accompanied by or traceable to a certificate or other documentation which is issued by a certifying body. Certified Value - The value that appears in a certificate as the best estimate of the value

for a property of a reference material.

Chance Cause - A cause for variability of a measurement process that occurs unpredictably, for unknown reasons, and believed to happen by chance, alone. Check Standard - In physical calibration, an artifact measured periodically, the results of which typically are plotted on a control chart to evaluate the measurement process.

*For other definitions, and particularly those related to industrial quality assurance, see: "Quality Systems Terminology", ANSI/ASQC Standard A 3 - 1 9 7 8, American National Standards

Institute, 1430 Broadway, New York, NY 10018.

41
Coefficient of Variation - The standard deviation divided by the value of the parameter measured . Common Cause - A cause of variability of a measurement process, inherent in and common to the process itself, as contrasted to a special cause (defined).

Comparative Method - A method which is based on the i nt er com par i son of the sample with a chemical standard. Confidence Interval - That range of values, calculated from an estimate of the mean and the standard deviation, which is expected to include the population mean with a stated level

of confidence. Confidence intervals in the same context also may be calculated for standard deviations, lines, slopes, points. Control Limit - The limits shown on a control chart beyond which it is highly improbable that

a point could lie while the system remains in a state of statistical control. Control Chart - A graphical plot of test results with respect to time or sequence of measurement together with limits within which they are expected to lie when the system is in a state of statistical control. Control Sample - A material of known composition that is analyzed concurrently with test samples to evaluate a measurement process (see also Check Standard). Composite Sample - A sample composed of two or more increments selected to represent a population of interest.

Cross Sensitivity - A quantitative measure of the response obtained for an undesired con- stituent ( i nt erf err ent ) as compared to that for a constituent of interest. Detection Limit - The smallest concentration/amount of some component of interest that can be measured by a single measurement with a stated level of confidence.

Double Blind - A sample, known by the submitter but submitted to an analyst in such a way that neither its composition nor its identification as a check sample are known to the latter. Duplicate Measurement - A second measurement made on the same (or identical) sample of material to assist in the evaluation of measurement variance. Duplicate Sample - A second sample randomly selected from a population of interest (see also split sample) to assist in the evaluation of sample variance. Education - Disciplining the mind through instruction or study. Education is general and prepares the mind to react to a variety of situations.

Error - Difference betwen the true or expected value and the measured value of a quantity or par amet er . Figure of Merit - A performance characteristic of a method believed to be useful when deciding

its applicability for a specific measurement situation. Typical figures of merit

include: selectivity; sensitivity; detection limit; precision; bias. Good Laboratory Practice (GLP) - An acceptable way to perform some basic operation or activity

in a laboratory, that is known or believed to influence the quality of its outputs. GLP's ordinarily are essentially independent of the measurement techniques used. Good Measurement Practice (GMP) - An acceptable way to perform some operation associated with

a specific measurement technique, and which is known or believed to influence the quality

of the measurement.

Gross Sample (also called bulk sample, lot sample) - One or more increments of material taken

from a larger quantity (lot) of material for assay or record purposes. Homogeneity - The degree to which a property or substance is randomly distributed throughout a material. Homogeneity depends on the size of the subsample under consideration. Thus a mixture of two minerals may be i nhomogeneous at the molecular or atomic level, but homogeneous at the particulate level. Incrememt - An individual portion of material collected by a single operation of a sampling

device, from parts of a lot separated in time or space. Increments may be either tested individually or combined (composited) and tested as a unit. Individuals - Conceivable constituent parts of a population. Informational Value - Value of a property, not certified but provided because it is believed

to be reliable and to provide information important to the certified material.

42
Intercalibration - The process, procedures, and activities used to ensure that the several laboratories engaged in a monitoring program can produce compatible data. When compatible data outputs are achieved and this situation is maintained, the laboratories can be said to be i n t er cal i br at ed

.

Laboratory Sample - A sample, intended for testing or analysis, prepared from a gross sample

or otherwise obtained. The laboratory sample must retain the composition of the gross sample. Often reduction in particle size is necessary in the course of reducing the quanti ty

.

Limiting Mean - The value approached by the average as the number of measurements, made by a stable measurement process, increases indefinitely.

Limit of Linearity (LOL) - The upper limit of concentration or amount of substance for which incremental additions produce constant increments of response.

Limit of Quantitation (LOQ) - The lower limit of concentration or amount of substance that must be present before a method is considered to provide quantitative results. By convention LOQ = 10s o

* wnere s 0 is tne estimate of the standard deviation at the lowest

level of measurement.

Lot - A quantity of bulk material of similar composition whose properties are under study. Method - An assemblage of measurement techniques and the order in which they are used. Outlier - A value which appears to deviate markedly from that for other members of the sample

in which it occurs. Pareto Analysis - A statistical approach to ranking assignable causes according to the frequency of occurrence. Performance Audit - A process to evaluate the proficiency of an ana 1 y s t / 1 abor at or y by evaluation of the results obtained on known test materials. Population - A generic term denoting any finite or infinite collection of individual things,

objects, or events; in the broadest concept, an aggregate determined by some property

that distinguishes things that do and do not belong. Precision - The degree of mutual agreement characteristic of independent measurements as the result of repeated application of the process under specified conditions. It is concerned with the closeness together of results. Primary Standard - A substance or artifact, the value of which can be accepted (within specific limits) without question when used to establish the value of the same or related

property of another material. Note that the primary standard for one user may have been

a secondary standard of another. Probability - The likelihood of the occurrence of any particular form of an event, estimated

as the ratio of the number of ways or times that the event may occur in that form to the total number of ways that it could occur in any form. Procedure - A set of systematic instructions for using a method of measurement or of sampling

or of the steps or operations associated with such. Protocol - A procedure specified to be used when performing a measurement or related

operation, as a condition to obtain results that could be acceptable to the specifier.

Protocol for a Specific Purpose (PSP) - Detailed instructions for the performance of all aspects of a measurement program. This is sometimes called a project QA plan. Quality - An estimation of acceptability or suitability for a given purpose of an object,

item, tangible, or intangible thing.

Quality Assessment - The overall system of activities whose purpose is to provide assurance

that the quality control activities are being done effectively. It involves a continuing

evaluation of performance of the production system and the quality of the products

prod uced

.

Quality Assurance - A system of activities whose purpose is to provide to the producer or user

of a product or a service the assurance that it meets defined standards of quality. It consists of two separate but related activities, quality control and quality assessment

(defined) . Quality Circle - A small group of individuals with related interests that meets at regular intervals to consider problems or other matters related to the quality of outputs of a process and to the correction of problems or to the improvement of quality.

4 3
Quality Control - The overall system of activities whose purpose is to control the quality of

a product or service so that it meets the needs of users. The aim is to provide quality

that is satisfactory, adequate, dependable, and economic. Random Sample - A sample selected from a population, using a randomization process. Reduction - The process of preparing one or more subsamples from a sample. Reference Material (RM) - A material or substance one or more properties of which are sufficiently well established to be used for the calibration of an apparatus, the assessment of a measurement method, or for the assignment of values to materials. Reference Method - A method which has been specified as capable, by virtue of recognized

accuracy, of providing primary reference data. Relative Standard Deviation - The coefficient of variation, expressed as a percentage. Replicate - A counterpart of another, usually referring to an analytical sample or a measurement. It is the general case for which duplicate is the special case consisting of two samples or measurements.

Routine Method - A method used in recurring analytical problems.

Sample - A portion of a population or lot. It may consist of an individual or groups of indi- viduals. It may refer to objects, materials, or to measurements, conceivable as part of

a larger group that could have been considered. Secondary Standard - A standard whose value is based upon comparison with some primary

standard. Note that a secondary standard, once its value is established, can become a primary standard for some other user. Segment - A specifically demarked portion of a lot, either actual or hypothetical.

Selectivity - The ability of methodology or instrumentation to respond to a desired substance

or constituent and not to others. It is sometimes quantified as cross sensitivity, which

see

,

Sensitivity - Capability of methodology or instrumentation to discriminate between samples

having differing concentrations or' containing differing amounts of an analate. Significant Figure - A figure(s) that remains to a number or decimal after the ciphers to the right or left are cancelled. Special Cause - A cause of variance or bias that is external (not inherent) to the measurement

system.

Split Sample - A replicate portion or sub-sample of a total sample obtained in such a manner

that it is not believed to differ significantly from other portions of the same sample. Standard - A substance or material, the properties of which are believed to be known with suf- ficient accuracy to permit its use to evaluate the same property of another. In chemical measurements, it often describes a solution or substance, commonly prepared by the analyst, to establish a calibration curve or the analytical response function of an

i ns t r umen t

.

Standard Addition - A method in which small increments of a substance under measurement are added to a sample under test to establish a response function or, by extrapolation, to detemine the amount of a constituent orginally present in the test sample. Standardization - (In analytical chemistry) the assignment of a compositional value to one standard on the basis of another standard. Standard Method - A method (or procedure) of test developed by a s t an dar ds - wr i t i ng organization, based on consensus opinion or other criteria, and often evaluated for its reliability by a collaborative testing procedure. Standard Operations Procedure (SOP) - A procedure adopted for repetitive use when performing a specific measurement or sampling operation. It may be a standard method or one developed

by the user . Standard Reference Material - A reference material distributed and certified by the National

Bureau of Standards.

Strata - Segments of a lot that may vary with respect to the property under study.

4 4
Subsample - A portion taken from a sample. A laboratory sample may be a subsample of a gross sample; similarly, a test portion may be a subsample of a laboratory sample.

Technique - A physical or chemical principle utilized separately or in combination with other techniques to determine the composition (analysis) of materials.

Test Portion (also called specimen, test specimen, test unit, aliquot) - That quantity of

a material of proper size for measurement of the property of interest. Test portions may

be taken from the gross sample directly, but often preliminary operations, such as mixing

or further reduction in particle size, are necessary. Tolerance Interval - That range of values, calculated from an estimate of the mean and the standard derivation, within which a specified percentage of individual values of population (measurements or sample) are expected to lie with a stated level of confidence Traceability - The ability to trace the source of uncertainty of a measurement or a measured

value

Training - Formal or informal instruction designed to provide competence of a specific nature. Uncertainty - The range of values within which the true value is estimated to lie. It is a best estimate of possible inaccuracy due to both random and systematic error. Validation - The process by which a sample, measurement method, or a piece of data is deemed

to be useful for a specified purpose. Variance - The value approached by the average of the sum of the squares of deviations of in- dividual measurements from the limiting mean. Mathematically, it may be expressed as l(x t - m) 2 - 2

1 » o c as n + «• n Ordinarily it cannot be known but only its estimate, s

2

, which is calculated by the expression

3

2 . LL*j - x) 2 3 n-1 Warning Limits - The limits shown on a control chart within which most of the test results are expected to lie (within a 95% probability) while the system remains in a state of statistical control. Youden Plot - A graphical presentation of data, recommended first by W. J. Youden, in which

the result(s) obtained by a laboratory on one sample is plotted with respect to the result(s). it obtained on a similar sample. It helps in deciding whether discrepant

results are due to random or systematic error.

15
APPENDIX B. CONVERSION FACTORS AND TABLES

B.1 Conversion Factors

In the metric system of weights and measures, designations of multiples and subdivisions

of any unit may be arrived at by combining with the name of the unit, the prefixes deka

,

hecto , and kilo , meaning, respectively, 10, 100, and 1 000, and dec 1 , centl , and mil 1 T, meaning, respectively, one-tenth, one-hundredth, and one- thousandth . In some of the following

metric tables, some such multiples and subdivisions have not been included for the reason that these have little, if any actual usage.

In certain cases, particularly in scientific usage, it becomes convenient to provide for multiples larger than 1 000 and for subdivisions smaller than one- thousandth . Accordingly,

the following prefixes have been introduced and these are new generally recognized:

exa , ( E ) mean i ng peta , ter a

,

giga , mega , kilo , hecto

deka ,

(P) , (T) , (G) , (m) , (k) ,

, (h) (da)

mean i ng 10 5 meaning loj 2 meaning 10;: meaning 10 meaning 10^ meaning 1 0

^ meaning 10

deci , cent i mill!

mi cro

(d) , (c)

(m)

(u)

meaning 10" mean i n i ngg 10

10 meaning 3 meaning 10" nano , (n), meaning 10 pico , f emto atto

,

(P)

(f

)

(a)

,

meaning 10 meaning 10 meaning 10~ 18 Thus a kilometer is 1 000 meters and a millimeter is 0.001 meter. LINEAR MEASURE

1 0 mi 11 imeters

10 centimeters

10 decimeters

10 meters

1 0 dekameters

10 hectometers

(mm

)

1 centimeter (cm)

1 decimeter (dm) » 100 millimeters

1 meter (m) -1 000 millimeters

1 dekameter (dam)

1 hectometer (hm) - 100 meters

1 kilometer (km) - 1 000 meters

100 square millimeters (mm ) - 1 100 square centimeters » 1 100 square decimeters = 1 100 square meters = 1 100 square dekameters » 1 100 square hectometers - 1

AREA MEASURE

square centimeter (cm 2

) square decimeter (dm 2

) square meter (m 2

) square dekameter (dam ) - 1 are square hectometer (hm 2

) - 1 hectare (ha) square kilometers (km ) FLUID VOLUME MEASURE

10 milliliters (mL) - 1 10 centiliters » 1 10 deciliters - 1 10 liters - 1 10 dekaliters » 1 10 hectoliters » 1

centiliter (cL) deciliter (dL) - 100 milliliters

liter - 1 000 milliliters

dekaliter (daL) hectoliter (hL) - 100 liters kiloliter (kL) - 1 000 liters

1 000 cubic millimeters (mm-*) - 1

1 000 cubic centimeters » 1

1 000 cubic decimeters = 1

- 1

SOLID VOLUME MEASURE

cubic centimeter (cm^) cubic decimeter (dm') 000 000 cubic millimeters

cubic meter (m^) 000 000 cubic centimeters

000 000 000 cubic millimeters

WEIGHT

10 milligrams

10 centigrams

10 decigrams

1 0 grams

10 dekagrams

10 hectograms

1 000 kilograms

(mg) centigram (eg) decigram (dg) = 100 milligrams

gram (g) 1 000 milligrams

dekagram (dag) hectogram (hg) » 100 grams kilogram (kg) - 1 000 grams megagram (Mg) or 1 metric ton (t)

H6
Table B.2. Use of Range to Estimate Variability

Number of Number of Measurements in a Set

Sets, k 2 3 4 5 6

3 4 1 .23 1 .77 2.12 2. 38 2.58

V 2.83 5.86 8.44 1 1 . 1 13.6

5 4 1.19 1 .74 2.10 2 . 36 2.56

V 4.59 9.31 13.9 1 8. 4 22. 6

1 0 d

2 1.16 1 .72 2. 08 2 . 34 2.55

8. 99 18.4 27.6 36. 5 44.9

20 d* 1.14 1 .70 2 .07 2. 35 2.54

17.8 36.5 55.0 72. 7 89.6

d

2 1.13 1 .69 2 .06 2. 33 2.53

R = mean of k sets of replicate measurements

v = degrees of freedom in estimate of standard deivation

For k > 20, v = 0.876 k

Adapted from Lloyd S. Nelson, J. Qual. Tech. 7(1) January (1975)

47
Table B.3 Critical Values for the F Test Critical values for a 2-tailed test of equality of standard deviation

estimates at 5% level of significance

F975 ("i. "2)

n, = degrees of freedom for numerator

" \

J 2 4 7 ( ,0 1, 1 j 20

" 24 30 40 6( 120

1 647.8 799.5 864.2 899.6 921.8 937.1 948.2 956.7 963.3 968.C 976.7 984.9 993.1 997.2 1001 1006

,_. 1010 1014 1018

2 38.51 39.00 39.17 39.25 39.30 39.33 39.36 39.37 39.39 39.40 39.41 39.43 39.45 39.46 39.46 39.47 39 4 i 39.49 39.50

' 17.44 16.04 15.44 15.10 14.88 14.73 14.62 14.54 14.4T 14.42 14.34 14.25 14.17 14.12 14.08 14.04 13 9) 13.95 13.90

12.22 10.65 9.98 9.60 9.36 9.20 9.07 8.98 8.84 8.75 8.66 8.56 8.51 8.46 8.41 8 3 i 8.31 8.26

S 10.01 8.43 7.76 7.39 7.15 6.98 6.85 6.76 6.68 6.62 6.52 6.43 6.33 6.28 6.23 6.18 6 1! 6.07 6.02

8.81 7.26 6.60 6.23 5.99 5.82 5.70 5.60 5.52 5.46 5.37 5.27 5.17 5.12 5.07 5.01 4 9i 4.90 4.85 7 8.07 6.54 5.89 5.52 5.29 5.12 4.99 4.90 4.82 4.76 4.67 4.57 4.47 4.42 4.36 4.31 4 2) 4.20 4.14

* 6.0( 5.45 5.0: 4. 85 4.6: 4.53 4.43 4.36 4.3C 4.20 4.10 4.00 3.95 3.89 3.84 3 7! 3.73 3.67 721 4.20 3.87 3.77 3.67 3.61 3.51 3.83 10 6.94 6.46 4.83 4.47 4.24 4.07 3.95 3.85 3.78 3.72 3.62 3.52 3.42 3.37 3.31 3.26 3 2'l 3.14 3.08

6.72 5.26 4.63 4.28 4.04 3.76 3.66 3.59 3.53 3.43 3.33 3.23 3.17 3.12 3.06 3 Oil 2.94 2.88 12 6.55 5.10 4.47 4.12 3.89 3.73 3.61 3.51 3.44 3.37 3.28 3.18 3.07 3.02 2.96 2.91 2.8 i 2.79 2.72

6.41 4.91 4.3! 4.0C 3. Ti 3.6C 3.4* 3.3S 3.31 3.2E 3.15 3.05 2.95 2.89 2.84 2.78 2 7'! 2.66 2.60 JJ 3.21 3.05 2.84 2.79 2.73 2.67 2.61 2.65 2.49

1 J 6.20 4.77 4.15 3.80 3.58 3.41 3.29 3.20 3.12 3.06 2.96 2.86 2.76 2.76 2.64 2.59 2.52 2.46 2.40 16 6.12 4.69 4.08 3.73 3.50 3.34 3.22 3.12 3.05 2.99 2.89 2.79 2.68 2.63 2.57 2.51 2 4

r

) 2.38 2.32 17 6.04 4.62 4.01 3.66 3.44 3.28 3.16 3.06 2.98 2.92 2.82 2.72 2.62 2.56 2.50 2.44 2 38 2.32 2.25

5.98 4.56 3.95 3.61 3.38 3.22 3.10 3.01 2.93 2.87 2.77 2.67 2.56 2.50 2.44 2.38 2.32 2.26 2.19 19 5.92 4.51 3.90 3.56 3.33 3.17 3.05 2.96 2.88 2.82 2.72 2.62 2.51 2.45 2.39 2.33 2.27 2.20 2.13

5.87 4.46 3.86 3.51 3.13 3.01 2.91 2.84 2.77 2.68 2.57 2.46 2.41 2.35 2.29 2.22 2.16 2.09

6.83 4.42 3.82 3.48 I'll 3.09 2.97 2.87 2.80 2.73 2.64 2.53 2.42 2.37 2.31 2.25 2.1>! 2.11 2.04

6.79 4.38 3.78 3.44 3.22 3.05 2.93 2.84 2.76 2.70 2.60 2.50 2.33 2.27 2.21 2.1< 2.08 2.00

5.75 4.3E 3.75 3.41 3.18 3.02 2.90 2.81 2.73 2.67 2.57 2.47 2.3t 2.30 2.24 2.18 2.1 2.04 1.97 5.72 3.72 3.38 3.15 2.99 2.87 2.78 2.70 2.64 2.54 2.44 2.27 2.21 2.15 2.): 2.01 1.94 5.69 3.69 3.35 3.13 2.97 2.85 2.75 2.68 2.61 2.51 2.41 2.30 2.24 2.18 2.12 2.) 1.98 1.91 5.66 it'i 3.67 3.33 3.10 2.94 2.82 2.73 2.65 2.59 2.49 2.39 2.28 2.22 2.16 2.09 2. ): 1.95 1.88

5.63 4.24 3.65 3.31 3.08 2.92 2.80 2.71 2.63 2.57 2.47 2.36 2.25 2.19 2.13 2.07 2. )i 1.93 1.85

5.61 4.22 3.63 3.29 3.06 2.90 2.78 2.69 2.61 2.55 2.45 2.34 2.23 2.17 2.11 2.05 1.91 1.83

6.59 4.20 3.61 3.27 3.04 2.88 2.76 2.67 2.59 2.53 2.43 2.32 2.21 2.15 2.09 2.03 1.89 1.81 5.57 4.18 3.59 3.25 3.03 2.87 2.75 2.65 2.57 2.51 2.41 2.31 2.20 2.14 2.07 2.01 1.87 1.79

5.42 4.05 3.46 3.13 2.90 2.74 2.62 2.53 2.45 2.39 2.29 2.18 2.07 2.01 1.94 1.88 l.n 1.64 5.29 3.93 3.34 3.01 2.79 2.63 2.51 2.41 2.33 2.27 2.17 2.06 1.94 1.88 1.82 1.74 1.58 1.48 110 5.15 3.80 3.23 2.89 2.67 2.52 2.39 2.30 2.22 2.16 2.05 1.94 1.82 1.76 1.69 1.61 1.43 1.31 5.02 3.69 3.12 2.79 2.57 2.41 2.29 2.19 2.11 2.05 1.94 1.83 1.71 1.64 1.57 1.48 1.27 1.00

Excerpted from "Experimental Statistics" (19) Table A. 5 which may be consulted for more extensive listings.

48
Table B .

1) Factors for Computing Two-Sided Confidence Limits for o

Dtgr**i a - .03 a » .01 a " .001

r« °d mm o >L Bu BL Bu Bt

1 17.79 .3576 86.31 .2969 844.4 .2480

2 4.859 .4581 10.70 .3879 33.29 .3291

3 3.183 .5178 5.449 .4453 11.65 .3824 2.567 .5590 3.892 .4865 6.938 .4218

s 2.248 .5899 3.175 .5182 5.085 .4529 6 2.052 .6143 2.764 .5437 4.128 .4784 7 1.918 .6344 2.498 .5650 3.551 .5000

t 1.820 .6513 2.311 .5830 3.167 .5186 9 1.746 .6657 2.173 .5987 2.894 .5348 10 1.686 .6784 2.065 .6125 2.689 .5492

11 1.638 .6896 1.980 .6248 2.530 .5621 12 1.598 .6995 1.909 .6358 2.402 .5738 13 1.564 .7084 1.851 .6458 2.298 .5845 1.534 .7166 1.801 .6549 2.210 .5942

13 1.509 .7240 1.758 .6632 2.136 .6032 16 1.486 .7308 1.721 .6710 2.073 .6116

17 1.466 .7372 1.688 .6781 2.017 .6193

It 1.448 .7430 1.658 .6848 1.968 .6266 19 1.432 .7484 1.632 .6909 1.925 .6333 20 1.417 .7535 1.609 .6968 1.886 .6397

21 1.404 .7582 1.587 .7022 1.851 .6457 22 1 .391 .7627 1 .568 .7074 1.820 .6514

23 1.380 .7669 1.550 .7122 1.791 .6568 24 1.370 .7709 1.533 .7169 1.765 .6619 23 1.360 .7747 1.518 .7212 1.741 .6668 26 1.351 .7783 1.504 .7253 1.719 .6713 27 1.343 .7817 1.491 .7293 1.698 .6758 21 1.335 .7849 1.479 .7331 1.679 6800 29 1.327 .7880 1.467 .7367 1.661 .6841 30 1.321 .7909 1.457 .7401 1 .645 .6880

31 1.314 .7937 1.447 .7434 1.629 .6917 32 1 .308 .7964 1.437 .7467 1 .615 .6953 33 1.302 .7990 1.428 .7497 1.601 .6987 34 1.296 .8015 1.420 .7526 1.588 .7020 33 1.291 .8039 1.412 .7554 1.576 .7052 36 1.286 .8062 1.404 .7582 1.564 .7083 37 1.281 .8085 1.397 .7608 1.553 .7113 38 1.277 .8106 1.390 .7633 1.543 .7141 39 1.272 .8126 1.383 .7658 1.533 .7169 40 1 .268 .8146 1 .377 .7681 1 . 523 . 7197

41 1.264 .8166 1.371 .7705 1.515 .7223 42 1.260 .8184 1.365 .7727 1.506 .7248 43 1.257 .8202 1.360 .7748 1.498 .7273 44 1.253 .8220 1.355 .7769 1.490 .7297 43 1.249 .8237 1.349 .7789 1.482 .7320 46 1.246 .8253 1.345 .7809 1.475 .7342 47 1.243 .8269 1.340 .7828 1.468 .7364

1. 2i0 1.335

1.331 . /Sb4 1.455

.73i6

.7407 1.234 ]8314 1.327 .7882 1.449 .7427

Excerpted from "Experimental Statistics" (19) Table A. 20 which may be consulted for more extensive listings.

49
Table B.5 Percentiles of the t Distribution

Confidence level

of 2-sided interval 20 40 60 80 90 95 98 99 975 c .99 1 .995

1 . 325 . 727 1.376 3.078 6 31 4 1 2 706 31 . 821 63. 657

2 . 289 .61 7 1.061 1 . 886 2 920 4 303 6

.

965 9. 925

3 .277 .584 . 978 1 . 638 2 353 3 1 82 4

.

541 5.841

4 . 271 . 569 . 941 1.533 2 1 32 2 776 3

.

747 4. 604

5 .267 .559 . 920 1 .476 2 01 5 2 571 3. 365 4.032

6 . 265 . 553 .90 6 1.440 943 2 4 4 7 3 • 1 43 3.707

7 .263 .549 .896 1.415 1 895 2 365 2

.

998 3.499

8 . 262 .54 6 .889 1.397 860 2 306 2 . 896 3 .355

9 .261 .543 . 883 1 .383 ] 833 2 262 2. 821 3.250

1 0 .260 . 542 . 879 1 .372 1 81 2 2 228 2. 764 3.169

1 1 .2 60 .54 0 .876 1.363 1 796 2 201 2 . 71 8 3.106

1 2 .259 .539 . 873 1.356 1 782 2 1 79 2 . 681 3. 055

1 3 .259 .538 .870 1.350 ' 771 2 1 60 2 . 650 3.012

1 4 .258 .537 .86 8 1.345 761 2 1 45 2 . 62 4 2.977

1 5 .258 .536 . 866 1-341 \ 753 2 1 31 2. 602 2.947

1 6 .258 .53 5 .865 1.337 1 7 4 6 2 1 2 0 2 . 583 2.921

1 7 .257 .534 .863 1.333 1 7 4 0 2 1 1 0 2

.

567 2.898

1 8 .257 . 534 .862 1.330 1 73 4 2 1 01 2 . 552 2.878

1 9 .257 .533 .861 1 . 328 729 2 093 2 . 539 2.861

20 . 257 .533 .860 1 . 325 725 2 086 2. 528 2.845

21 . 257 .532 . 859 1 . 323 1 7 2 1 2 080 2 . 51 8 2.831

22 .256 . 532 .858 1 . 321 4- 71 7 2 074 2 . 508 2.819

23 . 256 . 532 .858 1.319 1 71 4 2 069 2 . 500 2.807

2 4 .256 • 53

1

. 857 1.318 7 1 1 2 0 64 2

.

4 92 2.797

25 .256 .531 . 856 1 .316 708 2 060 2. 485 2.787

26 .256 .531 .856 1 .31 5 706 2 056 2 . 479 2.779

27 .256 .531 .855 1.314 703 2 052 2. 473 2.771

28 .256 .530 .855 1.313 701 2 048 2. 467 2.763

29 .256 .530 . 854 1 .31 1 699 2 045 2. 462 2. 756

30 .256 .530 .854 1 .310 697 2 042 2. 457 2.750

HO .255 . 529 .851 1 .303 684 2 021 2. 423 2.704

60 .254 . 527 . 848 1 . 296 671 2 000 2. 390 2.660

20 .254 .526 . 845 1 .289 658 1 980 2. 358 2.617

.253 . 524 . 842 1 . 282 645 1 960 2 . 326 2.576

Excerpted from "Experimental Statistics" (19) Table A-4, which may be consulted for more extensive listings.

50
Table B.6 Factors for Two-Sided Tolerance Limits for Normal Distributions

y = 0.95 7 = 0.99

H \

0.75 0.90 0.95 0.99 0.999 0.75 0.90 0.95 0.99 0.999

2 22.858 32.019 37.674 48.430 60.573 114.363 160 . 193 188.491 242.300 303.054

3 5.922 8.380 9.916 12.861 16.208 13.378 18.930 22.401 29.055 36.616 4 3.779 5.369 6.370 8.299 10.502 6.614 9.398 11.150 14.527 18.383

5 3.002 4.275 5.079 6.634 8.415 4.643 6.612 7.855 10.260 13.015 6 2.604 3.712 4.414 5.775 7.337 3.743 5.337 6.345 8.301 10.548 7 2.361 3.369 4.007 5.248 6.676 3.233 4.613 5.488 7.187 9.142 • 2.197 3.136 3.732 4.891 6.226 2.905 4.147 4.936 6.468 8.234

9 2.078 2.967 3.532 4.631 5.899 2.677 3.822 4.550 5.966 7.600 10 1.987 2.839 3.379 4.433 5.649 2.508 3.582 4.265 5.594 7.129

11 1.916 2.737 3.259 4.277 5.452 2.378 3.397 4.045 5.308 6.766 12 1.858 2.655 3.162 4.150 5.291 2.274 3.250 3.870 5.079 6.477

13 1.810 2.587 3.081 4.044 5.158 2.190 3. 3.727 4.893 6.240 14 1.770 2.529 3.012 3.955 5.045 2.120 3.029 3.608 4.737 6.043

15 1.735 2.480 2.954 3.878 4.949 2.060 2.945 3.507 4.605 5.876 16 1.705 2.437 2.903 3.812 4.865 2.009 2.872 3.421 4.492 5.732

17 1.679 2.400 2.858 3.754 4.791 1.965 2.808 3.345 4.393 5.607

IS 1.655 2.366 2.819 3.702 4.725 1.926 2.753 3.279 4.307 5.497

19 1.635 2.337 2.784 3.656 4.667 1.891 2.703 3.221 4.230 5.399 20 1.616 2.310 2.752 3.615 4.614 1.860 2.659 3.168 4.161 5.312

21 1.599 2.286 2.723 3.577 4.567 1.833 2.620 3.121 4.100 5.234 22 1.584 2.264 2.697 3.543 4.523 1.808 2.584 3.078 4.044 5.163 23 1.570 2.244 2.673 3.512 4.484 1.785 2.551 3.040 3.993 5.098 24 1.557 2.225 2.651 3.483 4.447 1.764 2.522 3.004 3.947 5.039 25 1.545 2.208 2.631 3.457 4.413 1.745 2.494 2.972 3.904 4.985 26 1.534 2.193 2.612 3.432 4.382 1.727 2.469 2.941 3.865 4.935 27 1.523 2.178 2.595 3.409 4.353 1.711 2.446 2.914 3.828 4.888

p - proportion of population covered

Y » confidence level

n m number of individuals (measurements, samples) used to compute x and s Excerpted from "Experimental Statistics" (19) Table A. 6 which may be consulted for more extensive listings.

51
Table B.7 Short Table of Random Numbers

77 27 86 26 21 89 91 71 42 64 64 58 74

44 19 !l5 55 33 90 44 27 22 07 62 17 34 39 80 62 24 33 81 67 28 11 34 79 26 35 34 23 09 94 00 80 55 31 63 27 91

74 97 80 30 65 07 71 30 01 84 47 45 89 70 74 13 04 90 51 27 61 34 63 87 44

2" 14 61 60 86 38 33 71 13 33 72 08 16 13 50 56 48 51 29 48 30 93 45 66 29

40 03 96 40 03 47 24 60 09 21 21 18 00 05 86 52 85 40 73 73 57 68

52 33 44 78 98 62 42 05 32 55 02

37 59 20 40 93 17 82 24 19 90 80 87 32 74 59 84 24 49 79 17 23 75 83 42 00

11 02 55 57 48 84 74 36 22 67 19 20 15 92 53 37 13 75 54 89 56 73 23 39 07

10 33 79 26 34 54 71 33 89 74 68 48 23 17 49 18 81 05 52 85 70 05 73 11 17 67 28 25 47 89 ,

65 65 42 23 96 64 20 30 89 87 64 37 91

50 7

. ">0 18 54 34 68 02 87 23 05 43 93 08 30 92 98

24 43 23 72 80 64 34 27 23 46 15 36 10 63 21 59 69 76 02 62 31 62 47 60 34 39 91 63 18 38 27 10 78 88 84 42 32 00 97 92 00 04 94 50 05 75 82 70 80 35

74 62 19 67 54 18 28 92 33 69 98 96 74 35 72 11 68 25 08 95 31 79 79 54 oi AO fin 42 57 66 76 72 91 03 63 48 46 44 01 33 53 62 •>8 80 59 55 05 02 16 13 17 54 06 36 63 06 15 03 72 38 01 58 25 37 66 48 56 19 56 41 29 28 76 49 74 39 50

92 70 96 70 89 80 87 14 25 49 25 94 62 78 26 15 41 39 48 75 64 69 61 06 38

91 08 88 53 52 13 04 82 23 00 26 36 47 44 04 08 84 80 07 44 76 51 52 41 59 97 74 47 90 90 87 48 01 43 15 60 40 11 9 54 13 09 13 80 42 29 63 03 24 64 12 43 28 10 01 65 62 07 79 83 05 9 61 39 18 32 69 33 46 58 19 34 03 59 28 97 31 02 65 47 47 70 39 74 17 30 22 65

67 43 31 09 12 60 19 57 63 78 11 80 10 97 15 70 04 89 81 78 54 84 87 83 42

61 75 37 19 56 90 75 39 03 56 49 92 72 95 27 52 87 47 12 52 54 62 43 23 13

10 00 19 51 77

93 23 71 58 09 78 08 03 07 71 79 32 25 19 6 04 40 33 12 06 78 91 97 88 95 37 55 48 82 63 89 92 59 14 72 19 17 22 51 90 20 03 64 96 60 48 01 95 44 84 62 13 11 71 17 23 29 25 13 85 33 35 07 69 25 68 57 92 57 11 84 44 01 33 66 29 89 97 47 03 13 20 86 22 45 59 98 64 53 89 64 94 81 55 87 73 81 58 46 42

16 94 85 82 89 07 17 30 29 89 89 80 98 36 25 36 53 02 49 14 34 03 52 09 20

01 93 10 59 75 12 98 84 60 93 68 16 87 60 11 50 46 56 58 45 88 72 50 46 11 95 71 43 68 97 18 85 17 IS 08 00 50 77 50 46 92 45 26 97 21 48 22 23 08 32

86 05 39 14 35 48 68 18 36 57 09 62 40 28 87 08 74 79 91 08 27 12 43 32 03 39 30 60 10 41 31 00 69 63 77 01 89 94 60 19 02 70 88 72 33 38 88 20 60 86 05 45 35 40 54 03 98 96 76 27 77 84 80 08 64 60 44 34 54 24 85 20 85 77 32

71 83 17 74 66 27 85 19 55 56 51 36 48 92 32 44 40 47 10 38 22 52 42 29 96

80 20 32 80 98 00 40 92 57 51 52 83 14 55 31 99 73 23 40 07 64 54 44 99 21

13 SO 78 02 73 39 96 82 01 28 67 51 75 66 33 97 47 58 42 44 88 09 28 58 06

67 92 65 41 45 36 77 96 46 21 14 39 56 36 70 15 74 43 62 69 82 30 77 28 77 72 56 73 44 26 04 62 81 15 35 79 26 99 S< za '£t za »« su M 90 to »o oo

28 86 85 64 94 11 58 78 45 36 34 45 91 38 51 S® 68 36 87 81 16 Tl 30 19 36

71 20 03 30 79 25 74 17 78 34 54 45 04 77 42 59 75 78 64 99 37 03 18 03 36

89 98 55 98 22 45 12 49 82 71 57 33 28 69 50 59 15 09 25 79 39 42 84 18 70 U 74 82 81 14 02 01 05 77 94 65 57 70 39 42 48 56 84 31 59 18 70 41 74 60

50 54 73 81 91 07 81 26 25 45 49 61 22 88 41 20 00 15 59 93 51 60 65 65 63 49 33 72 90 10 20 65 28 44 63 95 86 75 78 69 24 41 65 86 10 34 10 32 00 93

11 85 01 43 65 02 85 69 56 88 34 29 64 35 48 15 70 11 77 83 01 34 82 91 04 34 22 46 41 84 74 27 02 57 77 47 93 72 02 95 63 75 74 69 69 61 34 31 92 13

Excerpted from "Experimental Statistics" (19) Table A. 36 which may be consulted for more

52
Table B.8 Z-Factors for Two-Sided Confidence Interval

Confi dene e _ Lev e 1 Z_Factor

50$ 0.67

67 1.00

75 1.15

90 1.615

95 1.960

95. 45 2.000

99.00 2.575

99.74 3 99.9934 4 99.99995 5 100 - 10" 9

6 100 - 10~ 12

7 100 - 10~ 15 8

1 00 - 10" 18 - 9

9 100 - 10" 23 10

53
APPENDIX C. STATISTICAL TOOLS

C.1 Introduction

The following pages contain a brief description, with examples, of statistical calculations related to some of the questions that arise when evaluating chemical measurement

data. The reader is referred to the many excellent books that are available which discuss

these matters in more detail and the basis for the relationships used. General information on precision measurement is contained in reference [16], and NBS Handbook 91 [19] is especially

recommended for a detailed discussion of statistical concepts. It contains many numerical examples as well as extensive tables, from which most of the ones included in Appendix B were

taken

The results of repetitive measurements are usually considered to be normally distributed

and r epr esentable by a bell-shaped curve. If a series of n measurements were made many times,

one would obtain data sets represented by distributions such as those in Figure C.I. The means of each set will differ from each other. If the sample standard deviation, s, is cal- culated for each set of such measurements, a different result would be expected each time. Figure C.2 shows the two-sided (assymetric) confidence limits for o based on such estimates,

for several probability levels.

I i

1 1 1 1 1 1 1 1 1 1 r I 0 1 2 3 4 5 6 7 8 9 10 11 15 13

Series Number

Figure C.1 Expected distribution of the means of random samples/measurements. The individual measurements are indicated by x and the means, x, by dots

When several series of measurements are made, both the means and the standard deviations

will vary from measurement to measurement, as illustrated in Figure C.3. As n increases from

U to 1000, the variation of the means decreases but never disappears.

On considering the above, it should be obvious that even the best of measurements will differ amongst themselves, whether made by the same or different laboratories or scientists.

One often needs to answer questions such as the confidence that can be placed in measurement

data and the significance of apparent differences resulting from measurements. The various equations given in this appendix take into account both the expected variability within popu- lations and the uncertainties in the estimates of the population parameters that must be considered when answering such questions.

54
C.2 Estimation of Standard Deviation

The basic parameters which characterize a population (universe) of samples or measurements

on a given sample are the mean, p, and the standard deviation, o. Unless the entire population is examined, p and o cannot be known but ar_e estimated from sample(s) randomly selected

(assumed) from it. The result is a sample mean, x, and an estimate of the standard deviation,

Number of Measurements Figure C.2 Confidence Interval for o This figure illustrates the expected variability of estimates of standard deviations

made on various occasions, as a function of the number of measurements involved. The factor, when multiplied by the estimate of the standard deviation gives the interval

that is expected to include the population standard deviation for a given percentage of occasions. The labels, e.g., 10$, indicate the percentage of time that such an interval

would not be expected to include o. See section C.4 for a discussion and Table B . 4 for

the factors to be used in such calculations.

Figure C.3 Computed 50% confidence intervals for the population mean, m, from 100 samples of 4, 40 samples of 100, and 4 samples of 1000 [19]. The vertical lines essentially are error bars. The sample means, located at the center

of each, are not indicated. The sample means and standard deviations (proportional to the error bars) vary with each set of measurements. The error bars decrease inversely

as the square root of the sample size is increased and the means show correspondingly

smaller deviations from the population mean.

55
s, which must be used if such things as confidence intervals, population characteristics,

tolerance intervals, comparison of precision, and the significance of apparent discrepancies

in measured values are to be evaluated.

Several ways by which the standard deviation may be estimated are given in the following

sections.

C . 2 . 1 E s 1 1 ma t i_ on_of_S t a nd ar d_D e v j^a t^on_f r om_R e£M c a t e_M e a su r erne n t s For a series of n measurements

x

= n

s is estimated with v = n-1 degrees of freedom.

Example: C.2.1 - Series of Measurements (x^x) (x^x)'

15.2 .143 . 0204

14.7 -.357 . 1 257

15.1 .043 .0018

15.0 -*057 . 0033

15.3 .243 .0590

15.2 .143 . 0204

14.9 -.157 .0247

x = 1 5.057 Z = .2572

n = 7V.

2572

,— = o.207

C . 2 . 2 Es t i^ma t _i on_o f _S t an da r d_De v ^a t i. on_f roin_Du£licate_Mea3urements

If 2k where k = number of sets of duplicate measurements

d = difference of a duplicate measurement

v = k degrees of freedom

Note: It is not necessary that the duplicate measurements be made on the same materials. It

is only necessary that the materials measured are expected to have the same standard deviation of measurement.

Example A : C.2.2 - Dupl i cat es , Same I

x

f

x

s M d

2 14.7 15.0 0.3 0.09

15.1 14.9 0 . 2 0 .04 15.0 15.1 0 . 1 0.01 14.9 14.9 0 . 0 0 . 0 15.3 14.8 0.5 0.25

14.9 15.1 0. 2 0 .04 14.9

I 15.0 0 . 1 0.01 0.44

56
v = 7 degrees of freedom

Example B: C.2.2 - Estimation from Duplicates, Different Materials

x

f

x

s |d| d

2 14.7 15.0 0.3 0.09

20 . 1 19.8 0.3 0.09

1 2.5 13.0 0.5 0.25

23.6 23.3 0.3 0.09

15.1 14.9 0 . 2 0.04

18.2 18.0 0 . 2 0. 04 20.7 20. 9 0 . 2 0.04

Z 0. 64

= 0.21

v = 7 degrees of freedom

C . 2 . 3 Estimati on of Standard Deviation from the Range

The range, R, of a series of measur ements_ is defined as the difference of the highest and lowest value obtained. The average range, R, based on several sets ( k ) of measurements is calculated

R

1 + R2

+ Rg + . . . . + R

k

s = R/d 2 The value_for d

2 is obtained from Table B.2 and will depend on the number of sets, k, used

to calculate R and the number of measurements in a set. The table shows also the number of degrees of freedom for the estimate of the standard deviation. The materials used to estimate

R may be different, with the same restrictions as noted in C.2.2.

Example C.2.3 - From the Range of Duplicate Measurements

First Result Second Result Range

1 4 5 1 4 2 0.3

1 4 8 1 4 9 0 . 1

1 4 05 1 4 3 0.25

1 4 2 1 4 8 0.6

1 4 9 1 4 9 0.0

1 4 3 1 4 4 0. 1 1 4 7 1 4 1 0.6

1 4 4 1 4 7 0.3

1 4 1 1 4 25 0.15

1 4 95 1 4 65 0.3

1 4 25 1 4 95 0.7

0.3 + 0.1 + 0-25 + 0.6 +0+0.1 + 0.6 + 0.3 + 0-15 + 0.3 + 0.7

1 1 0.309

R/d 2 1.16 for 11 estimates of R (see Table B.2 by interpolation)

0.27

10 degrees of freedom for s (from Table B.2, rounded)

57
C . 2 . 4 P oo_l i_ng_Es t .1 ma t e s_o f _S t a n d a r d_De v .i a t i. on s Several estimates of the standard deviation may be pooled to obtain a better estimate

Given several estimates of the standard deviation obtained on several occasions, with the corresponding measurements:

'2 "2 v 2 "3

'3 n

3 v

3 = n 3"

I 2 2 V

1 S

1 + V2

S

2

+ 2

'k sk pooled

s pooled wil1 be ba sed on (v

1 + v2

+ • • • + v k

) degrees of freedom

Note: Ordinarily, v = n-1

Example C.2.4 - Pooling Standard Deviations

The standard deviation of a measurement process was estimated on five occasions. These

are to be pooled to improve the estimate of o.

1 0.171 7 6 2 0.205 5 H 3 0. 1 85 7 6

1 0.222 4 3 5 0. 1 80 5 4

6 ( 0 . 1 85 ) 2

+ 3 ( 0 . 222 ) 2+ 4(0. 1 80 ) 2

0.1755 + 0.1681 + 0.2054 + 0.1479 + 0.1296

23 Sp = 0.190 with 23 degrees of freedom.

C.3 Do Two Estimates of Precision Differ?

Conduct an F test, as follows:

Let s-| = estimate of standard deviation (larger value) based on n^ measurements.

Let s

2

= estimate of standard deviation (smaller value) based on n

2 measurements.

In each case, the respective degrees of freedom, v = n-1.

2 2 Calculate F = s

1 /s 2 Look up critical value of F

Q in Table B.3, based on the respective degrees of freedom for the estimates of s-| and s

2

. If F>F C consider >s 2 at the chosen level of confidence

If F<F C there is no reason to believe that Si>s 2 at the chosen level

of confidence

Example C.3 _ Comparison of Precision Estimates

2.00 n

1 = 6 v, = 5

2 n, = > v, =

F = 4.00/1 . 00 = 4 .0

F

Q

= 7.15 at 5? level of significance

Conclusion: There is no reason to believe that s

58
I

C.4 What are the Confidence Limits for an Estimate of a Standard Deviation?

The width of the confidence interval for an estimated standard deviation will depend on

the number of degrees of freedom, v, upon which the estimate is based (v=n-1). The interval

is not symmetrical (see Figure C.2), as in the case for a mean, since a small number of mea- surements tend to underestimate the standard deviation. To calculate the bounds of the interval, one may use a table such as Table B.4 and find the factors By and B

L corresponding to the number of degrees of freedom involved and the confidence level sought. In the table, a = 0.05 corresponds to a confidence of 95% for the interval so calculated. The confidence interval is then, sB L to sBy.

Example C.I - Confidence Limits for Estimate of Standard Deviations

s = 0. 1 5 n=10, v = 9 For a = .05. v = 9 (see Table B . 4) one finds B

y

= 1 .746; B L

- 0.6657

The confidence interval for s is 0.15 x 0.6657 to 0.15 x 1.746 or 0.10 to 0.26.

C.5 Confidence Interval for a Mean

The confidence interval for the mean will depend on the number of measurements, n, the standard deviation, s, and the level of confidence desired. The confidence interval is calculated using the expression

ts

x ± —

/n The value for t (see Table B.5) will depend on the level of confidence desired and the number

of degrees of freedom, v, associated with_the estimation of s. If s is based on the set of measurements used to calculate the mean, x, then v = n-1. If the measurements are made by a system under statistical control, as demonstrated by a control chart, v will depend on the number of measurements made to establish the control limits. Example C.5 - Confidence Interval Based on s Estimated from Data Set of Seven Measurements

x = 10.05

s = 0.11

n = 7 v = 6 For a 95 percent level of confidence, t = 2.447, hence 2.447 x 0.11 10.05 ± = 10.05 ± 0.10, or 9.95 to 10.15

/7

Example C.5 - Confidence Interval Based on s Obtained from Control Chart Limits,

One Measurement of x x = 10.05

s = 0.11

v = 45 (control chart)

n = 1 For a 95 percent level of confidence, t = 2.016, hence

2.016 x 0.11 10.05 ± = 10.05 ± 0.22 or 9.83 to 10.27

/I Values of t in the above were obtained from Table B.5, by interpolation

Note: There is no statistical basis for a confidence level statement for one measurement

unless supported by a control chart or other evidence of statistical control.
C.6 Do the Means of Two Measured Values Disagree, significantly?

The decision on disagreement is based on whether the difference, A, of the two values exceeds its statistical uncertainty, U. The method used for calculation of the uncertainty

depends on whether or not the respective standard deviation estimates may be considered to be significantly different.

£3Ji.e_I No reason to believe that the standard deviations differ (e.g., same method, analyst, experimental conditions, etc.). Step 1 Chose the significance level of the test. Step 2 Calculate a pooled standard deviation from the two estimates to obtain a better estimate of the standard deviation.

A B Sp will be based on v A

+ v R degrees of freedom

Step 3 Calculate the uncertainty, U , of the difference V

n

A

+ 1 n

A

n, Step 4 Compare A = | x A

- x B | with U If A < U, there is no reason to believe that the means disagree,

Example

x. = 4.25 x R

= 4.39

= 0.13 s R

= 0. 1 7 n

A

= 7 n

B

= 10

v

A

= 6 v B= 9 A = | x, - x B | = 1.25 - 1.39 | =0.11

Step 1 a = 0.05 (95? confidence)

Step 2 V6

( 0 . 1 3

)

2 + 9 (.17)' I

V.

1 01 4 + .2061 »

0.155 jim \ 70 Step 3 U =2.131x0.155

U = 0.080

Step 1 .14 > .080 Conclude that 4.39 differs from 4.25 at the 95% level of confidence.

Case_I_I Reason to believe that the standard deivations differ (e.g., different experimental conditions, different laboratories, etc.) Step 1 Chose a, the significance level of the list. Step 2 Compute the estimated variance of each value

s

2 S

2 A B
Step 3 Compute the effective number of degrees of freedom, f (v A v

B r

f = 2

Step 4 Compute the uncertainty, U, of the difference

u = t- yTAv

B

, Step 5 Compute A with U If A is < U there is no reason to believe that the means disagree

Exampl

e

x„ = 4.25 x R

= 4.39 0.13 0.17

Step 1

Step 2

a = 0.05 (95? confidence)

2.414 x 10'

Step 3

( 2. 41 4 x 10 3 + 2.89 x 10 3 )' 2.414 x 10' 2.89 x 10"

Step 4 U

U Step 5 A

= 1 7 2.11 V2.41 4 x 0.153

0.14 : U = 0.

•3 +

Conclude there is no reason to believe that x, at 95? level of confidence

C.7 Statistical Tolerance Intervals

A tolerance interval represents the limits within which a specified percentage of the population is expected to lie with a given probability. It is especially useful to specify

the variability in composition of samples. If the standard deviation of the population of samples were known, the limits for a given percentage of the population could be calculated

with certainty. Because only an estimate of the standard deviation is usually known, based on

a limited sampling of the population, a tolerance interval, based on inclusion of a percentage

of the population with a specific probability of inclusion, is all that can be calculated.

The calculation is made as follows: Tolerance Interval = x ± ks where k = a factor (obtained from Table B.6 for example) based on the percentage of population to be included, the probability of inclusion, and the number of measurements used to calculate x and s.

Example C.7 - Statistical Tolerance Interval

For measurements of ten samples of a shipment of coal, the sulfur content was found to be

x = 1 . 62? s = 0.

1

0% n = 1

0

From Table B.6, k = 3-379 for Y = 0.95, p = 0.95, n = 10. The tolerance interval is thus 1.62% ± 0.34? or 1.28? to 1.96?.

61
C.8 Pooling Means to Obtain a Grand Average, x Case_i A11 means based on same number of measurements of equal precision

+ x

2

+ x

3

+ . . . + x n

Case_I_I^ Means based on different number of measurements, but no reason to believe the precisions differ

Case II_I Means based on different number of measurements with differing precisions

Step 1 Compute weight to be used for each mean,

n

i n

1 w, = — e.g. , w, = —

Step 2

Example C.8 Case - Calculation of Grand Average, Case I To calculate the grand average, x, of the following means, all believed to be equally

precise

.

*1 = 1 0 50

*2 = 1 0 37

*3 = 1 0 49 m - 1 0 15

x

5

" 1 0 47

1 0 50 0. 37 0.45 + 10.47

Example C. Calculation of Grand Average, Case II

1 0. 50 10.37

10.49 10.45

10.47

10.50 xl

0

n = 1 0 n = 5 n = 20

n = 5 n = 7 10.49 x 20 0.45 x 5

Example C, Calculation of Grand Average, Case III

1 0. 50 x 1 000

i x

i n

i si w^

1 0 . 50 1 0 . 1 0 1 000

2 1 0 . 37 5 . 1 5 222

3 1 0. 49 20 . 1 1 1 652

4 1 0. 45 5 . 1 0 500

5 1 0 . 47 7 . 1 6 273

37 x 222 0.49 x 1652 + 10.45 x 500 + 1000 + 222 + 1 652 + 500 + 273

62
x = 1 0. H78

s= = 2.71 x 10 ^ s= = 0.0166

C.9 Outliers

Outliers are data values that do not belong or have a very low probability of belonging to the data set in which they occur. They can result from such causes as blunders or malfunctions of the methodology, or from unusual losses or contamination. If outliers occur too often, there may be deficiencies in the quality control program which can be corrected and

thus improve the measurements. One should always look for causes when data are rejected. Outliers can be identified when data are plotted, when results are ranked, and when control limits are exceeded. Only when a measurement system is well understood and the variance is well established, or when a large body of data are available, is it possible to distinguish between extreme values and true outliers with any degree of confidence.

The following rules for rejection of data should be used with caution since an outlier in

a well-behaved measurement system should be a rare occurrence.

A. Rejection for Assignable Cause System malfunction, m i s i de n t i f i ca t i on of known contamination, are examples.

a sample, suspected transcription error,

Rule of Huge Error

If the questioned value differs from the mean by some multiple, M, of the standard

deviation, it may be considered to be an outlier. The size of the multiple depends on the confidence required for rejection. One evaluates

A practical rule might be to use M > 4 as a criterion for rejection. This corresponds

to a significance level of < 2% when the standard deviation is well established, such

as based on a data set of 15 or larger.

If s is not well established but depends on the data set in question, the odds for rejection are much larger. For example, if x and s are based on 6 measurements, M > 6 would be the criterion for rejection for a 2% level of significance.

C. Statistical Tests Several statistical tests are available for identifying outliers based on ranking data

and testing extreme values for credibility. The Dixon criterion is described on page

17-3 of NBS Handbook 91 (19) and the critical values for decision on rejection using

this criterion are given in Table A - 1 4 of the same reference.

A method for identifying outlier laboratories in a collaborative test or proficiency

testing program is described by Youden on page 118 of NBS Special Publication 300 (16) where a table of the test score values necessary to use his criterion also will be found.

63
Example C.9 - Outliers, Huge Error Concept

x (original order) x (ranked order)

10.50 10.M5

1 0. 47 10.47

10.49 10.47

10.45 1 0.48

10.47 10.49

10.57 10.50

10.52 10.50 10.50 1 0.52 10.48 10.53 10.53 10.57

1. 10.57 appears to be an outlier

2. Calculate mean and sample standard deviation, s, ignoring 10.57

x = 10.490 s = 0.0255

3.

1 °- 57 -

1 °- 49

= 3.13 0.0255

4. Since 3.13 < 4 conclude that 10.57 should be retained in the data

5. Calculate mean and sample standard deviation including 10.57

x = 10. 498 s = 0.0349

C.10 Use of Random Number Tables

It is often desirable to randomize the sequence in which measurements are made, samples

are chosen, and other variables of an analytical program are set. Tables of random numbers,

such as Table B.7, are a convenient and simple way to accomplish this. The following

procedure may be used.

1. Number the samples (or measurements) serially, say 00 to xy . For example, 00 to 15 for 16 i terns

.

2. Start at any randomly selected place in the table and proceed from that point in any systematic path. The order in which the item numbers are located becomes the random sequence number to be assigned to them. Example: Start at Row 7, Column 3 (chosen by chance) of Table B.7 and proceed from left to right as in reading. The first number is 76 which is not usable for the above

series of items. The first usable number is 15. Proceeding as above, the items are located in the following order: 15, 06, 02, 03, 05, 00, 11, 13, 07, 10, 09, 08, 04,

14, 01, 12. If a number already chosen is encountered, pass over it to the next usable number

.

64
John K.Taylor APPENDIX D.l

Center for Analytical Chemistry

National Bureau of Standards Washington, D.C. 20234 QualityAssurance of

Figure 1. Measurement tolerances and errors The objective of quality assurance programs for analytical measurements

is to reduce measurement errors to tolerable limits and to provide a means of ensuring that the measure- ments generated have a high probability of being of acceptable quality. Two

concepts are involved. Quality control

is the mechanism established to control errors, while quality assessment

is the mechanism to verify that the system is operating within acceptable

limits. General handbooks that dis- cuss quality assurance in more detail are given in References 1-3. Quality is a subjective term. What is high quality in one situation may be low or unacceptable quality in another

case. Clearly the tolerable limits of

error must be established for each. Along with this there must be a clear understanding of the measurement

process and its capability to provide

the results desired. The tolerance limits for the property to be measured are the first conditions to be determined. These are based upon the considered judgment

of the end user of the data and represent the best estimate of the limits within which the measured property must be known, to be useful for its in- tended purpose. The limits must be

realistic and defined on the basis of cost-benefit considerations. It is better to err on the side of too-narrow

limits. Yet, measurement costs nor- mally increase as tolerances are de- creased, so that the number of measurements possible for a fixed budget may be inadequate when coupled with

material-variability considerations. Once one has determined the toler- ance limits for the measured property, the permissible tolerances in measure- ment error may be established. The

basis for this is shown in Figure 1. The

tolerance limits for the measured

property are indicated by Lp

. Uncertainties in the measurement, based on

the experience and judgment of the

analyst, are indicated by Cm . These

include estimates of the bounds for the biases (systematic errors), B, and

the random errors as indicated by s, the estimate of the standard deviation. Obviously, Cm must be less than Lp

if the data are to be useful. The

confidence limits for x, the mean of n

replicate measurements, are:

in which t is the so-called student factor. While the effect of random error is minimized by replication of measurements, there are practical limitations, and any measurement process that re- quires a large number of replicates has

a serious disadvantage. Weil-designed and well-implement- ed quality assurance programs provide

the means to operate a measurement

system in a state of statistical control, thereby providing the basis for establishing reliable confidence limits for the data output.

Until a measurement operation . . . has attained a state of statistical control, it cannot be regarded in any logi- cal sense as measuring anything at

all. C. E. Eisenhart

The Analytical System

Analytical measurements are made

because it is believed that compositional information is needed for some

end use in problem solving. Explicitly or implicitly, a measurement system

such as that depicted in Figure 2 is in- volved. One must have full understanding of the measurement system

for each specific situation in order to generate quality data. The conceptualization of the problem, including the data requirements and their application, constitutes the model. The plan, based on the model,

includes details of sampling, measure- ment, calibration, and quality assur- ance. Various constraints such as time, resources, and the availability of samples may necessitate compromises in the plan. Adequate planning will re- quire the collaboration of the analyst, the statistician, and the end user of the data in all but the most routine

Published in Analytical Chemistry, December 1981, pp. 1588A-1596A, by the American Chemical Society 65
Report

Chemical Measurements

cases. In complex situations, planning may be an iterative process in which

the actual data output may require re- consideration of the model and revi- sion of the plan. Sampling has been discussed in a recent paper (4). Obviously, the sample is one of the critical elements of the measurement process. Closely re- lated is the measurement methodology to be used. The method used must

be adequate for the intended purpose and it must be properly utilized. The

necessary characteristics of a suitable method include: adequate sensitivity,

selectivity, accuracy, and precision. It

is desirable that it also have the fol- lowing characteristics: large dynamic measurement range; ease of operation; multiconstituent applicability; low

cost; ruggedness; portability. To judge

its suitability, the following information must be known about it: type of sample; forms determined; range of

applicability; limit of detection; biases; interferences; calibration require- ments; operational skills required;

precision; and accuracy. Obviously all of the above characteristics must

match the measurement require- ments. In case of doubt, trial measure- ments must be made to demonstrate

applicability to a given problem. A

cost-benefit analysis may be needed

to determine which of several candi- date methods is to be selected. A

method, once adopted, must be used

in a reliable and consistent manner, in order to provide reproducible data. This is best accomplished by following

detailed written procedures called Standard Operating Procedures (SOPs) in quality assurance terminology. Standard methods developed by

voluntary standardization organizations are often good candidates for SOPs, when they are available. Two kinds of calibrations are re- quired in most cases. Physical calibra- tions may be needed for the measure- ment equipment itself and for ancil- lary measurements such as time, temperature, volume, and mass. The measurement apparatus may include

built-in or auxiliary tests such as volt- age checks, which may need periodic

verification of their stability if not of

their absolute values. But especially, most analytical equipment requires some kind of chemical calibration, often called standardization, to establish the analytical function (i.e., the

relation of instrument response to chemical quantification). Obviously,

the analyst must thoroughly understand each of the calibrations required

for a particular measurement. This in- cludes a knowledge of the standards needed and their relation to the measurement process, the frequency of

calibration, the effect on a measure- ment system due to lack of calibration, and even the shock to the system

resulting from recalibration.

Quality Control

Quality control encompasses all of the techniques used to encourage re- producibility of the output of the measurement system. It consists of the use

of a series of protocols developed in advance and based on an intimate un- derstanding of the measurement process and the definite requirements of the specific measurement situation. Protocols, i.e., procedures that must

be rigorously followed, should be es- tablished for sampling, measurement,

calibration, and data handling. Some

of these, or at least selected portions, may be applicable to most or all of the measurements of a particular labora- tory and become the basis of a good

laboratory practices manual (GLPM).

Planning Primary Secondary "=——»

Data Flow

Figure 2. Analytical measurement system

66
I Measurement 1

Inspection |

I

Data

Inspection » Reject

Accept

Figure 3. Quality control by inspection

In fact, the GLPM should cover the

generalities, if not the specifics, of all measurement practices of the laboratory. The protocols for a specific measurement process include the GLPs

together with any requirements of the

specific situation. The GLPM and protocols should be developed collaboratively by all of those involved in the measurements, and this development process may be

the most important aspect of their function. It encourages a keen consid- eration of the measurement process and creates an awareness of potential problems that GLPs attempt to avert. Protocols are of little use unless they are followed rigorously, and the

attitudes of laboratory personnel are certainly key factors in this regard. Analysts must aspire to produce high

quality data and must be their own

most severe critics. Notwithstanding, good quality control systems should

include provisions for inspection, both

periodically and aperiodically (unan- nounced) to ascertain how well they

are functioning. Large laboratories may have a quality control officer or group, independent of the laboratory management, that oversees the operation of the quality control system. Quality Control by Inspection An informal kind of quality control involves the frequent if not constant

inspection of certain aspects of the measurement system for real or ap- parent problems (5). The essential

features of such a system are depicted

in Figure 3. Based on an intimate knowledge of the measurement process, samples may be casually inspect- ed for their adequacy. The rejection and possible replacement of obviously unsuitable ones can eliminate not only

extra work but also erroneous data

that might be difficult to identify

later. Difficulties in the actual measurement may often be identified as they occur and remedial measures, in- cluding remeasurement, may be taken

either to save data that might other- wise be lost or at least to provide valid reasons for any rejections. Likewise, data inspection can identify problems and initiate remedial actions, including new measurements, while it is still possible to do so. Control Charts The performance of a measurement

system can be demonstrated by the measurement of homogeneous and

stable control samples in a planned re- petitive process. The data so generat- ed may be plotted as a control chart in a manner to indicate whether the measurement system is in a state of

statistical control. Either the result of

a single measurement on the control sample, the difference between dupli- cate measurements, or both may be

plotted sequentially. The first mode may be an indicator of both precision and bias, while the second monitors

precision only. To effectively use such a chart, the standard deviation of a single measurement of the control sample must

be known. This may be obtained by a

series of measurements of the control sample, or it may be obtained from

the experience of the laboratory on

measuring similar samples. Control

limits, i.e., the extreme values believed

to be credible, are computed from the standard deviation. For example, the

2<j limit represents those within which

the values are expected to lie 95% of the time. The 3<r limit represents the 99.7% confidence level. Departures from the former are warnings of possi- ble trouble, while exceeding the latter usually means corrective action is needed. In the event that the standard

deviation cannot be estimated with

sufficient confidence initially, the control chart may be drawn using the best

estimate, and the limits may be modified on the basis of increasing measurement experience. The development of a control chart must include the rationale for its use. There must be a definite relation be- tween the control measurements and

the process they are designed to control. While the control chart only sig- nifies the degree of replication of measurements of the control sample, its purpose is to provide confidence in the

measurement process. To do this, the

control measurements must simulate

the measurements normally made. In chemical measurements, this means

simulation of matrix, simulation of concentration levels, and simulation of sampling. The latter objective may be

difficult if not impossible to achieve.

It must be further emphasized that

the control measurements should be random members of the measurement

routine, or at least they should not oc- cupy biased positions in any measure- ment sequence. To the extent that control samples

are representative of the test samples, and to the extent that measurements

of them are representative of the measurement process, the existence of statistical control for these samples can imply such control of the measure- ment process and likewise of the re- sults obtained for the test samples. No specific statements can be made

about the frequency of use of control samples. Until a measurement process is well understood, control samples may need to be measured fre- quently. As it is demonstrated to be in control, the need may become less and

the incentive to do "extra" work may

diminish. Along with the decision on how much effort should be devoted to quality control the risks and conse- quences of undetected loss of control must be weighed. Many laboratories consider that the 5-15% extra effort ordinarily required for all aspects of

quality control is a small price to pay

for the quality assurance it provides. When measurements are made on a frequently recurring schedule, internal

controls, such as duplicate measure- ments of test samples, can provide evi- dence of reproducibility so that control samples may be used largely to

identify systematic errors, drifts, or other types of problems. When laboratories are engaged in a

variety of measurements, the use of representative control samples may be

difficult if not impossible. In such

cases, often only the measurement

methodology can be tested, and evaluation of the quality of the measure- ment output requires considerable judgment. In such cases, the experi- ence of the lab becomes a key factor. In some complex measurement sys- tems, certain steps or subsystems are more critical than others, and hence it may be more important to develop

control charts for them than for the

entire system. The control of such

steps may indeed prevent propagation

of error into the end result. An example is the sampling step, which may be

very critical with respect to the end

result. In such a case, the records of periodic inspections may be adaptable

to the control chart technique of quality control. 67
Quality Assessment

Procedures used to evaluate the ef- fectiveness of the quality control sys- tem may be classified according to whether the evidence arises from in- ternal or external sources. Internal procedures, useful largely for estimating precision, include the use of inter- nal reference samples and control charts to monitor the overall perfor- mance of the measurement system as described in an earlier section. Replicate measurements on replicate or

split samples can provide valuable in- sight into the reproducibility of both

the measurement and sampling processes. Comparison of the results ob- tained as a consequence of inter- change of analysts, equipment, or combinations of these can attest to operational stability as well as identify malfunctions. Measurements made on

split samples using a completely inde- pendent method can lend confidence

to the method normally in use or indi- cate the presence of measurement

bias. External quality assessment is al- ways needed since it can detect prob- lems of bias that are difficult to identify by internal procedures. Participation in collaborative tests, exchange of samples with other laboratories, and

the use of certified reference materials

are time-honored assessment devices. NBS Standard Reference Materials (SRMs) (6) are especially useful for quality assessment in cases where they

are available and applicable. The in- formation that can be obtained or in- ferred by their use is described in a

later section. Operators of monitoring networks may provide proficiency

testing or audit samples to assess labo- ratory performance. Ordinary practices should be used here, so that nor- mal rather than optimum perfor- mance is measured. A laboratory should diligently use

the information obtained in the quali- ty assessment process. Adverse data should not be treated in a defensive manner but the reason for it should be

investigated objectively and thoroughly. When laboratory records are reli- ably and faithfully kept, the task of identifying causes of problems is made

easier. This is an important reason for developing data handling protocols and ensuring that all protocols are

strictly followed. Systematic Errors Systematic errors or biases are of two kinds—concentration-level inde- pendent (constant), and concentationlevel related. The former are sometimes called additive while the latter are called multiplicative. Both kinds may be present simultaneously in a given measurement system. An example of the first kind is the reagent

blank often present in measurements

involving chemical processing steps. The second kind can result from, for example, use of an inaccurately certi- fied calibrant. Systematic errors may arise from

such sources as faulty calibrations, the use of erroneous physical constants,

incorrect computational procedures, improper units for measurement or re- porting data, and matrix effects on'the measurement. Some of these can be eliminated or minimized by applying

corrections or by modification of the measurement technique. Others may

be related to fundamental aspects of the measurement process. The most

insidious sources of error are those un- known or unsuspected of being

present. One of the most important sources

of error in modern instrumental measurements concerns uncertainties in the calibrants used to define the analytical function of the instrument. The

measurement step essentially consists of the comparison of an unknown with

a known (calibrant) so that any error

in the latter results in a proportional

error in the former. The need to use

calibrants of the highest reliability is obvious. The measurement protocol should

include a detailed analysis of the sources of error and correction for them to the extent possible. The

uncertainties, B, referred to earlier, represent the uncertainties in the cor- rections for the systematic errors. In making such an estimate, the 95% confidence limits should be assigned to the extent possible. The magnitudes

of these uncertainties can be estimat- ed from those assigned by others in the case of such factors as calibration standards and physical constants. Other constant sources of error may

be more subtle both to identify and to evaluate, and the judgment and even

intuition of the experimenter may be

the only sources of information. The effectiveness of elimination of, or correction for, systematic errors is best evaluated from external quality assessment procedures. Differences found between known and measured

values of test samples, such as SRMs,

need to be reconciled with the laboratory's own estimates of bounds for its random and systematic errors. When

the random error is well established,

as by the quality control process, sig- nificant discrepancies can be attrib- uted to unsuspected or incorrectly es- timated systematic errors. The Use of SRMs for Quality Assessment An SRM is a material for which the

properties and composition are certi- fied by the National Bureau of Stan- dards (6, 7). To the extent that its compositional properties simulate

Figure 4. Typical analytical systematic

errors (bias), (a) = unbiased; (b) =

measurement-level related; (c) = constant error; and (d) = combination of b and c those of the sample ordinarily measured, its "correct" measurement can imply "correct" measurement of the usual samples. Such a conclusion re- quires that the protocol of measure- ment was the same in each case. Hence it is necessary that no special care be exercised in measuring the SRM, other than that ordinarily used. Analysis of SRMs has been recom- mended as a means of providing "trace- ability" to national measurement

standards. However, a word of caution

is appropriate on this point. Measure- ment processes are seldom identical, so that traceability is most often based on inference. Also, the fact that an ac- ceptable result is or is not obtained for an SRM provides no unique explanation for such a result. The use of an SRM should never be attempted until the analytical system

has been demonstrated to be in a state of statistical control. An SRM is not needed for such a purpose and such

use is discouraged. Ordinarily, the SRM will be available in limited amount so that the statistics of the measurement process should be demonstrated by measurements on other

materials. Only under such a situation can the results of an SRM measure- ment be considered as representative

of the measurement system. A consideration of the nature of analytical errors, shown in Figure 4, will clarify why the measurement of a sin- gle SRM may not be fully informative.

It will be noted that errors may be

constant, measurement-level related, or a combination of these, and a single right or wrong result will not indicate on which of several possible curves it might lie. Measurement of a series of SRMs may clarify the nature of the measurement process and this should be done whenever possible. An inti- mate understanding of the operation

of a particular measurement system may also make it possible to eliminate some of the possible sources of error and to better interpret the data from measurement of SRMs.

G8
Record Keeping

Adequate record keeping in an easily retrievable manner is an essential part of the quality assurance program. Records needed include the description of test samples, experimental pro- cedures, and data on calibration and

testing. Quality control charts should be diligently prepared and stored. A

chain of custody of test materials should be operative and such materials should be retained and safe- guarded until there is no doubt about

their future use or need. Data Control The evaluation, review, and release of analytical data is an important part

of the quality assurance process. No

data should be released for external use until it has been carefully evaluated, Guidelines for data evaluation, applicable to almost every analytical

situation, have been developed by the ACS Committee on Environmental Improvement (8). A prerequisite for release of any data should be the as- signment of uncertainty limits, which

requires the operation of some kind of

a quality assurance program. Formal

release should be made by a professional analytical chemist who certifies that the work was done with reason- able care and that assigned limits of uncertainty are applicable. Laboratory Accreditation Laboratory accreditation is one form of quality assurance for the data output of certified laboratories. Accreditation is based on criteria that

are considered essential to generate

valid data and is a formal recognition that the laboratory is competent to carry out a specific test or specific type of test (9, 10). The certification is as meaningful as the care exercised in developing certification criteria and

evaluating laboratory compliance. Generic criteria developed by national and international standardization or- ganizations have been influential in this respect (11). These criteria are well conceived and provide general guidance for the sound operation of

analytical laboratories, whether or not

certification is involved. Implementation

Detailed quality assurance plans are

ineffective unless there is commitment

to quality by all concerned. This com- mitment must be total, from manage- ment to technical staff. The former must provide the resources, training,

facilities, equipment, and encourage- ment required to do quality work. The

latter must have the technical ability and motivation to produce quality

data. Some may argue that if there is such commitment, there is no need for a formal quality assurance program.

However, the experience of many lab- oratories has demonstrated that a for- mal quality assurance program pro- vides constant guidance for the attain- ment of the quality goals desired. References

(1) "Quality Assurance Handbook for Air Pollution Measurement Systems: Principles"; Vol. 1, E.P.A. Publication No.

600/9-76-005.

(2) "Handbook for Analytical Quality Control in Water and Wastewater Laboratories"; EPA Publication No. 600/4-

79-019.

(3) Juran, J. M. "Quality Control Handbook," 3rd ed.; McGraw-Hill: New York,

1974.

(4) Kratochvil, B. G.; Taylor, J. K. Anal. Chem. 1981,53, 924 A.

(5) Brewers, J. M., et al. "Data Are for Looking At, or Quality Control by Inter- pretation." In "Water Quality Paramters"; American Society for Testing and

Materials: Philadelphia, 1975, ASTM

STP573

(6) "Catalogue of NBS Standard Refer- ence Materials"; National Bureau of Standards: Washington, NBS Special Publication 260.

(7) Cali, J. P., et al. "The Role of Standard

Reference Materials in Measurement

Systems"; National Bureau of Standards: Washington, January 1975, NBS

Monograph 148.

(8) ACS Subcommittee on Environmental

Analytical Chemistry. "Guidelines for Data Acquisition and Data Quality Eval- uation in Analytical Chemistry"; Anal. Chem. 1980, 52, 2242.

(9) "Quality Control System-Require- ments for a Testing and Inspections Laboratory"; American Council of Indepen- dent Laboratories: Washington.

(10) "Testing Laboratory Performance:

Evaluation and Accreditation"; Berman,

G. A., Ed.; National Bureau of Standards: Washington, NBS Special Publi- cation 591.

(11) "Standard Recommended Practice for Generic Criteria for Use in Evaluation of Testing and/or Inspection Agencies"; American Society for Testing and Materials: Philadelphia, ASTM Publication No. E-548.

John K. Taylor, coordinator for quality assurance and voluntary stan- dardization activities at the National Bureau of Standards Center for Analytical Chemistry, received his BS

from George Washington University, and his MS and PhD degrees from the University of Maryland. His research

interests include electrochemical

analysis, refractometry, isotope separations, standard reference materials, and the application of physical methods to chemical analysis.

69
Appendix D.2 Sampling for

Chemical

Analysis

A major consideration in the reli- ability of any analytical measurement

is that of sample quality. Too little at- tention is directed to this matter. The

analyst often can only report results obtained on the particular test speci- men at the moment of analysis, which may not provide the information desired or needed. This may be because

of uncertainties in the sampling process, or in sample storage, preservation, or pretreatment prior to analysis. The sampling plan itself is often so poorly considered as to make relation of the analytical results to the population from which the sample was drawn

uncertain, or even impossible to inter- pret. All of the above aspects of sampling

merit full consideration and should be

addressed in every analytical determination. Because the scope is so broad, We will limit the present discussion to

a small segment of the total problem,

that of sampling bulk materials. For

such materials the major steps in sampling are:

• identification of the population from which the sample is to be obtained,

• selection and withdrawal of valid gross samples of this population, and

• reduction of each gross sample to a laboratory sample suitable for the analytical techniques to be used.

The analysis of bulk materials is one of the major areas of analytical activity. Included are such problems as the analysis of minerals, foodstuffs, environmentally important substances, and many industrial products. We shall discuss the major consider- ations in designing sampling programs

for such materials. While our discus- sion is specifically directed toward

solid materials, extension to other

materials will often be obvious. A brief list of definitions commonly

used in bulk sampling is provided in the glossary. Preliminary Considerations in Sampling

Poor analytical results may be

caused in many ways—contaminated

reagents, biased methods, operator er- rors in procedure or data handling, and so on. Most of these sources of

error can be controlled by proper use

of blanks, standards, and reference samples. The problem of an invalid sample, however, is special; neither

control nor blank will avail. Accordingly, sampling uncertainty is often treated separately from other uncertainties in an analysis. For random er- rors the overall standard deviation, sQ , is related to the standard deviation for the sampling operation, s s , and to that

for the remaining analytical operations, s„, by the expression: s% = s„ +

Sg- Whenever possible, measurements

should be conducted in such a way

that the components of variance aris- ing from sample variability and measurement variability can be separately

evaluated. If the measurement process

is demonstrated to be in a state of statistical control so that s a is already known, ss can be evaluated from s0 , found by analysis of the samples. Otherwise, an appropriate series of repli- cate measurements or replicate samples can be devised to permit evaluation of both standard deviations. Youden has pointed out that once

the analytical uncertainty is reduced

to a third or less of the sampling uncertainty, further reduction in the analytical-uncertainty is of little importance (/ ). Therefore, if the sampling

uncertainty is large and cannot be re- duced, a rapid, approximate analytical method may be sufficient, and further refinements in the measurement step may be of negligible aid in improving

the overall results. In fact, in such

cases a rapid method of low precision that permits more samples to be ex- amined may be the best route to re- ducing the uncertainty in the average

value of the bulk material under test. An excellent example of the importance of sampling is given in the deterPublished in Analytical Chemistry, July 1981, pp. 924A-938A, by the American Chemical Society

70
Report

Byron Kratochvil

Department of Chemistry

University of Alberta Edmonton, Alberta, Canada T6G 2G2 John K. Taylor

National Bureau of Standards Washington, D.C. 20234

Figure 1. Relative standard deviation associated with the sampling and

analysis operations in testing peanuts

for aflatoxins (after T. B. Whittaker, Pure and Appl. Chem., 49, 1709 (1977))

0 40 Concentration of Aflatoxin (ppb)

mination of aflatoxins in peanuts (2). The aflatoxins are highly toxic compounds produced by molds that grow

best under warm, moist conditions. Such conditions may be localized in a warehouse, resulting in a patchy dis- tribution of highly contaminated kernels. One badly infected peanut can contaminate a relatively large lot with unacceptable levels (above about 25 ppb for human consumption) of afla- toxins after grinding and mixing. The

standard deviations of the three operations of sampling, subsampling, and

analysis are shown in Figure 1. The

analytical procedure consists of sol- vent extraction followed by thin-layer chromatography and measurement of the fluorescence of the aflatoxin spots. Clearly, sampling is the major source

of the analytical uncertainty. Types of Samples Random Samples. In common with

the statistician, the analytical chemist

ordinarily wishes to generalize from a small body of data to a larger body of

data. While the specimen/sample ac- tually examined is sometimes the only matter of interest, the characteristics of the population of specimens are fre- quently desired. Obviously, the samples under examination must not be

biased, or any inferences made from them will likewise be biased.

Statisticians carefully define several terms that are applied to statistical in- ference. The target population de- notes the population to which we

would like our conclusions to be applicable, while the parent population

designates that from which samples

were actually drawn. In practice these two populations are rarely identical, although the difference may be small. This difference may be minimized when the selection of portions for ex- amination is done by a random process. In such a process each part of the population has an equal chance of being selected. Thus, random samples

are those obtained by a random sampling process and form a foundation from which generalizations based on

mathematical probability can be made. Random sampling is difficult. A

sample selected haphazardly is not a random sample. On the other hand, samples selected by a defined protocol

are likely to reflect the biases of the

protocol. Even under the most favor- able circumstances, unconscious selec- tion and biases can occur. Also, it can

be difficult to convince untrained in- dividuals assigned t he task of obtaining samples that an apparently unsystematic collection pattern must

be followed closely for it to be valid. Whenever possible, the use of a

table of random numbers is recom- mended as an aid to sample selection. The bulk material is divided into a number of real or imaginary segments. For example, a body of water can be

conceptually subdivided into cells, both horizontally and vertically, and

the cells to be sampled selected ran- domly. To do this each segment is as- signed a number, and selection of seg- ments from which sample increments

are to be taken is made by starting in an arbitrary place in a random number table and choosing numbers ac- cording to a predecided pattern. For

example, one could choose adjacent,

alternate, or nth entries and sample

those segments whose numbers occur

until all of the samples decided upon

have been obtained. The results obtained for these and

other random samples can be analyzed by some model or plan to identify whether systematic relations exist. This is important because of the possible introduction of apparent correla- tions due to systematic trends or biases in the measurement process. Accordingly, measurement plans should

always be designed to identify and

minimize such problems.

Despite the disadvantages, sampling at evenly spaced intervals over

the bulk is still often used in place of random sampling owing to its simplic71
Define goals.

Select analytical procedures, number of analyses, and sampling sites on basis of goals, time and cost constraints, and

personnel and apparatus available.

Collect samples; reduce to suitable test portions.

Carry out preliminary operations (dissolve, ad|ust conditions, separate interferences); acquire data on test portions.

Select best value from data, estimate

reliability of value, assess validity of model,

revise model and repeat if necessary.

Figure.2. The place of sampling in the overall analytical process

ity. Because this procedure is more

subject to bias than random sampling,

it is not recommended. If it is used, the results must be closely monitored

to ensure that errors from periodicity

in the material are not introduced. Systematic Samples. Frequently, samples are obtained and analyzed to

reflect or test some systematic hypothesis, such as changes in composition with time, temperature, or spatial

location. Such samples, if collected in

a systematic manner, may each be

considered to represent a separate dis- crete population under the existing conditions. However, the results may

still be statistically tested for the sig- nificance of any apparent differences. In a carefully designed sampling

plan, consideration should be given to the possible concurrence of unantici- pated events or phenomena that could

prejudice the information on the sample measured. For example, measure- ments to be taken at time intervals are sometimes made with a random start or other superimposed random time

element. Needless to say, the less known about a given process, the more

randomness is merited. Conversely, as

a process is more fully understood,

systematic approaches can provide maximum efficiency of data acquisition.Representative Samples. The

term "representative sample" is fre- quently used in analytical discussions

to connote a single sample of a uni- verse or population (e.g., waste pile, lagoon, ground water) that can be ex- pected to exhibit average properties of the population (see glossary). Obviously, such a sample cannot be se- lected by a random process. And even

if it could, to ascertain the validity of

its representativeness would require considerable effort. The concept of a truly representative sample would appear to be valid

in only two cases. The first case in- volves samples defined a priori as rep- resentative for a specific purpose. For

example, the Hazardous Waste Management System prescribes seven pro-

.ocols for sampling wastes—ranging from viscous liquids, solids, or containerized liquids to reservoirs—to provide samples that "will be consid- ered by the Agency (EPA) to be repre- sentative of the waste" (.3). The sec- ond case involves the sampling of

truly homogeneous materials. While the measurement of samples

defined as representative may reduce

analytical costs, the information so obtained ordinarily does not enjoy the

status of that obtained from valid ran- dom samples of the population. An ex- ception is when effort has been vigor- ously exerted to homogenize the population prior to sampling. Such processes are difficult and are ordinarily only justified when the objective is to produce a number of subsamples of

essentially similar properties. Because of the difficulties of se- lecting or producing a "representative sample" it is recommended that this concept be discouraged for general purposes and reserved only for cases where the effort required to prepare such a sample is justified. An appreciation of the compositional information that is lost as a result is a further reason to discourage the practice. With a properly designed and execut- ed random sampling plan, the valu- able characteristics of sample mean

and variation between members can

be ascertained, neither of which can

be obtained by measurement of one

"representative sample." Composite Samples. A composite sample (see glossary) may be consid- ered as a special way of attempting to produce a representative sample. Many sampling procedures are based on the assumption that average composition is the only information desired. Such averages may be bulk averages, time-weighted averages, and

flow-proportional averages, for example, and may be obtained by measure- ment of a composite, suitably pre- pared or collected. Elaborate proce- dures involving crushing, grinding, mixing, and blending have been devel- oped and even standardized for the preparation of solid composites, while sampling systems for liquids (especially water) have been developed to obtain various composite samples.

Analysis of a number of individual samples permits determination of the average (at the expense of extra analytical effort) and the distribution of samples within the population (be- tween-sample variability). In some

cases, it may be of interest to isolate the within-sample variability as well. All this information is necessary for collaborative test samples and in ref- erence material usage, especially when

apparent differences in analytical re- sults within and between laboratories need to be evaluated.

72
Table I. Confidence Intervals and Statistical Tolerance Limits 3

n t» -7= Kc Ks

2 12.70 ±18 37.67 ±75

4 3.18 ±3.2 6.37 ±12.9

8 2.36 ±1.7 3.73 ±7.4

16 2.18 ±1.1 2.90 ±5.8

32 2.04 ±0.7 2.50 ±5.0

100 1.98 ±0.4 2.23 ±4.4

1.96 0 1.96 ±4.0

8 Calculated for s = 2, based on measurement of n samples

b 95% confidence limits for the mean of n samples

c Based on a 95% confidence that the interval will contain 95% of the samples

Because of the limited information provided by a composite sample, full consideration should be given to the consequences before deciding between

this approach and the analysis of indi- vidual samples. Subsampling. Usually, the sample

received by the analytical laboratory

will be larger than that required for a

single measurement, so some sub- sampling (see glossary) will be re- quired. Often, test portions (see glos- sary) must be taken for replicate measurements or for measurement of dif- ferent constituents by several techniques. Obviously, such test portions must be sufficiently alike that the re- sults are compatible. Frequently it is necessary to reduce particle size, mix,

or otherwise process the laboratory sample (see glossary) before with- drawing portions (subsamples) for analysis. The effort necessary at this stage depends on the degree of homogeneity of the original sample. In general, the subsampling standard deviation should not exceed one-third of the sampling standard deviation. Al- though this may sound appreciable, it is wasteful of time and effort to de- crease it below this level. But this does

not mean care is unnecessary in sub- sampling. If a sample is already homogeneous, care may be needed to avoid introducing segregation during sub- sampling. Even though analysts may

not be involved with sample collection, they should have sufficient knowledge of sampling theory to sub- sample properly. They should also be provided with any available information on the homogeneity of the samples received so that they can subsample adequately and efficiently. Model of the Sampling Operation

Before sampling is begun, a model

of the overall operation should be es- tablished (Figure 2). The model

should consider the population to be

studied, the substance(s) to be measured, the extent to which speciation

is to be determined, the precision re- quired, and the extent to which the

distribution of the substance within

the population is to be obtained. The model should identify all as- sumptions made about the population under study. Once the model is complete, a sampling plan can be established. The Sampling Plan The plan should include the size, number, and location of the sample in- crements and, if applicable, the extent

of compositing to be done. Procedures

for reduction of the gross sample (see glossary) to a laboratory sample, and

to the test portions, should be specified. All of this should be written as a

detailed protocol before work is begun. The protocol should include procedures for all steps, from sampling through sample treatment, measurement, and data evaluation; it should be revised as necessary during

execution as new information is obtained. The guidelines for data acquisition and quality evaluation in envi- ronmental chemistry set out by the ACS Subcommittee on Environmental

Analytical Chemistry are sufficiently general to be recommended reading

for workers in all fields (4). The sampling protocol should in- clude details of when, where, and how

the sample increments are to be taken. On-site criteria for collection of a valid sample should be established before- hand. Frequently, decisions must be made at the time of sampling as to components likely to appear in the sample that may be considered for- eign, that is, not part of the population. For example, a portion of dredged sediment in which the mercury content is to be determined might

contain cans, discarded shoes, rocks or other extraneous material. For the in- formation sought these items might be considered foreign and therefore legit- imately rejected. Decisions as to rejec- tion become less clear with smaller

items. Should smaller stones be reject- ed? How small? And what about bits of metal, glass, leather, and so on? Criteria for such decisions should be made logically and systematically, if possible before sampling is initiated. The type of container, cleaning pro- cedure, and protection from contamination before and after sampling must

be specified. The question of sample

preservation, including possible addition of preservatives and ref rigeration, should be addressed. Some sampling

plans call for field blanks and/or field- spiked samples. The critical nature of the latter and the dif ficulties possible under field conditions require the ut- most care in planning and execution of

the sampling operation if the results are to be meaningful Whenever possible, the analyst should perform or directly supervise the sampling operation. If this is not

feasible, a written protocol should be provided and the analyst should en- sure that those collecting the samples

are well-trained in the procedures and

in use of the sampling equipment, so that bias and contamination are mini- mized. No less important is careful la- beling and recording of samples. A

chain of custody should be established such that the integrity of the samples from source to measurement is ensured. Often auxiliary data must be

recorded at the time the sample is taken: temperature, position of the

collecting probe in the sample stream,

flow velocity of the stream, and so on. Omission or loss of such information may greatly decrease the value of a sample, or even render it worthless. Sampling Bulk Materials. Once

the substances to be determined, to- gether with the precision desired, have been specified, the sampling plan can

be designed. In designing the plan, one must consider:

• How many samples should be taken?

• How large should each be?

• From where in the bulk material

(population) should they be taken?

• Should individual samples be analyzed, or should a composite be pre- pared? These questions cannot be an- swered accurately without some

knowledge of the relative homogeneity

of the system. Gross samples should

be unbiased with respect to the differ- ent sizes and types of particles present

in the bulk material. The size of the

gross sample is often a compromise

based on the heterogeneity of the bulk

material on the one hand, and the cost

of the sampling operation on the

other. When the properties of a material

73
2.9

b

<

• •T

' I* 2 5

'(0

Ol

(0c

3

O p i

•

• o

V--:-

'' V'.

:"

.

1.7 :

• j«8

Sample Weight, g

Figure 3. Sampling diagram of sodium-24 in human liver homogenate (from Refer- ence 7)

to be sampled are unknown, a good

approach is to collect a small number

of samples, using experience and intuition as a guide to making them as representative of the population as

possible, and analyze for the component of interest. From these prelimi- nary analyses, the standard deviation

ss of the individual samples can be

calculated, and confidence limits for the average composition can be established using the relation fi=x± tSs/y/n (1) where ju is the true mean value of the population, x is the average of the analytical measurements, and t is ob- tained from statistical tables for n measurements (often given as n — 1 degrees of freedom) at the desired

level of confidence, usually 95%. Table

I lists some t values; more extensive

tables are provided in books on quantitative analysis and statistics (5). On the basis of this preliminary in- formation, a more refined sampling

plan can be devised, as described in the following sections. After one or two cycles the parameters should be known with sufficient confidence that the optimum size and number of the samples can be estimated with a high

level of confidence. The savings in sampling and analytical time and

costs by optimizing the sampling pro- gram can be considerable. Minimum Size of Individual In- crements. Several methods have been

developed for estimation of the amount of sample that should be taken in a given increment so as not to exceed a predetermined level of sampling uncertainty. One approach is through use of Ingamells's sampling

constant (6). Based on the knowledge

that the between-sample standard deviation s s (Equation 1), decreases as the sample size is increased, Ingamells has shown that the relation WR 2 = Ks (2)

is valid in many situations. In Equation 2, W represents the weight of sample analyzed, R is the relative standard deviation (in percent) of sample composition, and Ks is the sampling constant, corresponding to the weight of sample required to limit the sampling uncertainty to 1% with 68% confidence. The magnitude of Ks may be determined by estimating ss from a series of measurements of samples of weight W.

Once Ks is evaluated for a given sample, the minimum weight W re- quired for a maximum relative stan- dard deviation of R percent can be

readily calculated. An example of an Ingamells sampling constant diagram is shown in Figure 3 for a human liver sample

under study in the National Environ- mental Specimen Bank Pilot Program

at the National Bureau of Standards (NBS) in conjunction with the Envi- ronmental Protection Agency (7). A

major goal of the program is to evaluate specimen storage under different conditions. This requires analysis of small test portions of individual liver specimens. The material must be sufficiently homogeneous that variability between test portions does not mask

small variations in composition owing

to changes during storage. The homogeneity of a liver sample for sodium

was assessed by a radiotracer study in which a portion was irradiated, added

to the remainder of the specimen, and

the material homogenized. Several

test portions were then taken and the

activity of 24 Na measured as an indi- cator of the distribution of sodium in the samples. From Figure 3 it can be

seen that the weight of sample re- quired to yield an inhomogeneity of 1% (±2.4 counts g

_1

s _1

) is about 35 g. For a subsample of one gram, a sampling uncertainty of about 5% can be

expected. Minimum Number of Individual Increments. Unless the population is known to be homogeneous, or unless a representative sample is mandated by some analytical problem, sufficient replicate samples (increments) must

be analyzed. To determine the mini- mum number of sample increments, a sampling variance is first obtained, ei- ther from previous information on the bulk material or from measurements made on the samples. The number of samples necessary to achieve a given

level of confidence can be estimated from the relation

t 2s

2

where f is the student's t -table value

for the level of confidence desired, s

2 and x are estimated from preliminary measurements on or from previous knowledge of the bulk material, and R

is the percent relative standard deviation acceptable in the average. Initially t can be set at 1.96 for 95% confi- dence limits and a preliminary value

of n calculated. The t value for this n

can then be substituted and the sys- tem iterated to constant n. This ex- pression is applicable if the sought-for component is distributed in a positive binomial, or a Gaussian, distribution. Such distributions are characterized by having an average, n, that is larger than the variance, a\. Remember that

values of <ts (and ss ) may depend

greatly on the size of the individual samples. Two other distributions that may be

encountered, particularly in biological materials, should be mentioned. One

is the Poisson distribution, in which

the sought-for substance is distributed randomly in the bulk material such

that a

2 is approximately equal to m- In

this case R 2x

(4) The other is the negative binominal

distribution, in which the sought-for substance occurs in clumps or patches, and a; is larger than fi. This pattern

often occurs in the spread of contamination or contagion from single

74
sources, and is characterized by two

factors, the average, x, and a term, k, called the index of clumping. P'or this system

1 (5) Here k must be estimated, along with

x, from preliminary measurements on

the system. Sometimes, what is wanted is not an

estimate of the mean but instead the two outer values or limits that contain

nearly all of the population values. If we know the mean and standard deviation, then the intervals fi ± 2a and

fi ± 3<t contain 95% and 99.7%, respectively, of all samples in the population. Ordinarily, the standard deviation a is not known but only its esti- mate s, based on n observations. In

this case we may calculate statistical tolerance limits of the form x + Ks

and x - Ks, with the factor K chosen

so that we may expect the limits to in- clude at least a fraction P of the samples with a stated degree of confi- dence. Values for the factor K (8) de- pend upon the probability 7 of includ- ing the proportion P of the population, and the sample size, n. Some val- ues of K are given in Table I. For ex- ample, when 7 = 0.95 and P = 0.95, then K = 3.38 when n = 10, and K =

37.67 for duplicates (n = 2). Sampling a Segregated (Stratified) Material. Special care must be taken when assessing the average amount of a substance distributed throughout a bulk material in a non- random way. Such materials are said

to be segregated. Segregation may be found/for example, in ore bodies, in different production batches in a plant, or in samples where settling is caused by differences in particle size or density. The procedure for obtaining a valid sample of a stratified material is as follows (9):

• Based on the known or suspected

pattern of segregation, divide the material to be sampled into real or imagi- nary segments (strata).

• Further divide the major strata into

real or imaginary subsections and se- lect the required number of samples by chance (preferably with the aid of a

table of random numbers).

• If the major strata are not equal in

size, the number of samples taken from each stratum should be proportional to the size of the stratum.

In general, it is better to use strati- fied random sampling rather than unrestricted random sampling, provided

the number of strata selected is not so

large that only one or two samples can be analyzed from each stratum. By

keeping the number of strata suffi- ciently small that several samples can

be taken from each, possible varia-

(a) (b) 10

1.0

0.1

0.01

0.001

\ 0%

1%

R = 0.1% \

1

9%

1 0 0.5 0 0.5 Fraction of Richer Particles

1.0

Figure 4. Relation between minimum sample size and fraction of the richer parti- cles in a mixture of two types of spherical particles (diameter 0.1 mm and density

1) for a sampling standard deviation (R) of (a) 0.1 % and (b) 1 %. Richer particles contain 10% of substance of interest, and leaner ones contain 0, 1,5, or 9%

(after Reference 12, p 554)

tions within the parent population can

be detected and assessed without in- creasing the standard deviation of the sampling step. Minimum Number of Individual Increments. When a bulk material is highly segregated, a large number of samples must be taken from different segments. A useful guide to estimating

the number of samples to be collected

is given by Visman (10), who proposed

that the variance in sample composition depends on the degree of homogeneity within a given sample increment and the degree of segregation between

sample increments according to the

relation A/W+B/n (6) where s., is the variance of the average

of n samples using a total weight W of sample, and A and R are constants for a given bulk material. A is called a homogeneity constant, and can be calcu- lated from Ingamells's sampling constant and the average composition by A = lQ4 x

2Ks (7) Sampling Materials in Discrete

Units. If the lot of material under

study occurs in discrete units, such as truckloads, drums, bottles, tank cars, or the like, the variance of the analytical result is the sum of three contributions: (1) that from the variance be- tween units in the lot, (2) that from

the average variance of sets of samples

taken from within one unit, and (3) that from the variance of the analytical operations. The contribution from

each depends upon the number of units in the lot and the number of samples taken according to the fol- lowing relation (9):

9 cb

2 (N - n b ) , ffu

. 2 N

(H)

75
Glossary

Bulk sampling—sampling of a material that does not consist of discrete, identifiable, constant units, but rather of arbitrary, irregular units. Composite—a sample composed of two or more Increments. Gross sample (also called bulk sample, lot sample)—one or more increments of material taken from a larger quantity (lot) of material for assay or record purposes. Homogeneity—the degree to which a property or substance is randomly distributed throughout a material. Homogeneity depends on the size of the units under consideration. Thus a mixture of two minerals may be inhomogeneous at the molecular or atomic level, but homogeneous at the particulate level. Increment—an individual portion of material collected by a single operation of a sampling

device, from parts of a lot separated in time or space. Increments may be either tested

individually or combined (composited) and tested as a unit. Individuals—conceivable constituent parts of the population. Laboratory sample—a sample, intended for testing or analysis, prepared from a gross sample or otherwise obtained. The laboratory sample must retain the composition

of the gross sample. Often reduction in particle size is necessary in the course of re- ducing'the quantity. Lot—a quantity of bulk material of similar composition whose properties are under

study'. Population—a generic term denoting any finite or infinite collection of individual things, objects, or events in the broadest concept; an aggregate determined by some property

that distinguishes things that do and do not belong. Reduction—the process of preparing one or more subsamples from a sample. Sample—a portion of a population or lot. It may consist of an individual or groups of in- dividuals. Segment—a specifically demarked portion of a lot, either actual or hypothetical. Strata—segments of a lot that may vary with respect to the property under study. Subsample—a portion taken from a sample. A laboratory sample may be a subsample

of a gross sample; similarly, a test portion may be a subsample of a laboratory sample.

Test portion (also called specimen, test specimen, test unit, aliquot)—That quantity of a material of proper size for measurement of the property of interest. Test portions may be taken from the gross sample directly, but often preliminary operations, such

as mixing or further reduction in particle size, are necessary.

where

ax

2 = variance of the mean, oV2 = variance of the units in the

lot, aw

2 = average variance of the samples taken from a segment,

<i t 2 = variance of the analytical operations, N = number of units in the lot,

rib = number of randomly

selected units sampled,

n w = number of randomly drawn

samples from each unit

selected for sampling, and

n t = total number of analyses, including replicates, run on

all samples.

If stratification is known to be absent, then much measurement time

and effort can be saved by combining

all the samples and mixing thoroughly

to produce a composite sample for analysis. Equation 8 is applicable to

this situation also. If the units vary

significantly in weight or volume, the

results for those units should be weighted accordingly. For homogeneous materials aw

2 is zero, and the second term on the right-hand side of Equation 8 drops

out. This is the case with many liquids

or gases. Also, if all units are sampled, then n h = N and the first term on the right-hand side of Equation 8 also drops out. Particle Size in Sampling

Particulate Mixtures Random sampling error may occur even in well-mixed particulate mixtures if the particles differ appreciably

in composition and the test portion contains too few of them. The problem

is particularly important in trace analysis, where sampling standard deviations may quickly become unacceptably large. The sampling constant di- agram of Ingamells and the Visman

expression are useful aids for estimating sample size when preliminary in- formation is available. Another ap- proach that can often provide insight

is to consider the bulk material as a two-component particulate mixture, with each component containing a dif- ferent pe rcentage of the analyte of in- terest (//). To determine the weight

of sample required to hold the sampling standard deviation to a preselected level, the first step is to deter- mine the number of particles n. The

value of n may be calculated from the

relation [didzl2 flOOfPj -P2 )l 2 „p(l-p) RP

(9) where d\ and d-2 are the densities of the two kinds of particles, d is the

density of the sample, Pi and P2 are the percentage compositions of the component of interest in the two kinds

of particles, P is the overall average composition in percent of the component of interest in the sample, R is the percent relative standard

deviation (sampling error) of the sampling operation, and p and 1 — p

are the fractions of the two kinds of

particles in the bulk material. With

knowledge of the density, particle diameter, and n, the weight of sample

required for a given level of sampling

uncertainty can be obtained through

the expression, weight = (4/3)wr 3 dn

(assuming spherical particles). Figure 4 shows the relation between

the minimum weight of sample that should be taken and the composition

of mixtures containing two kinds of

particles, one containing 10% of the sought-for substance and the other 9,

5, 1, or 0%. A density of 1, applicable

in the case of many biological materials, is used, along with a particle diameter of 0.1 mm. If half the particles in a mixture contain 10% and the other

half 9% of the substance of interest, then a sample of 0.0015 g is required if the sampling standard deviation is to be held to a part per thousand. If the second half contains 5%, a sample of 0.06 g is necessary; if 1%, 0.35 g would

be needed. In such mixtures it is the

relative difference in composition that

is important. The same sample

weights would be required if the compositions were 100% and 90, 50, or 10%, or if they were 0.1% and 0.09, 0.05, or 0.01%. The same curves can be used for any relative composition by

substitution of x for 10%, and 0.1 x,

76
0.5 x, and 0.9 x the curves corre- sponding to 1, 5, and 9% in Figure 4. If a standard deviation of 1% is acceptable, the samples can be 100 times

smaller than for 0.1%. An important point illustrated by

the figure is that if the fraction of

richer particles is small, and the leaner ones contain little or none of the sub- stance of interest, large test portions

are required. If a sample of gold ore containing 0.01% gold when ground to 140 mesh (0.1 mm in diameter) consists, say, of only particles of gangue and of pure gold, test portions of 30 g would be required to hold the sampling standard deviation to 1%. (An

ore density of 3 is assumed.) Concluding Comments

Sampling is not simple. It is most

important in the worst situations. If the quantities x, s, Ks , A, and B are known exactly, then calculation of the

statistical sampling uncertainty is easy, and the number and size of the samples that should be collected to provide a given precision can be readily determined. But if, as is more usual, these quantities are known only ap- proximately, or perhaps not at all, then preliminary samples and measurements must be taken and on the

basis of the results more precise sampling procedures developed. These

procedures will ultimately yield a sampling plan that optimizes the quality of the results while holding down

time and costs. Sampling theory cannot replace ex- perience and common sense. Used in concert with these qualities, however,

it can yield the most information about the population being sampled

with the least cost and effort. All analytical chemists should know enough

sampling theory to be able to ask in- telligent questions about the samples

provided, to take subsamples without

introducing additional uncertainty in the results and, if necessary, to plan and perform uncomplicated sampling

operations. It is the capability of un- derstanding and executing all phases

of analysis that ultimately characterizes- the true analytical chemist, even though he or she may possess special expertise in a particular separation or measurement technique.

References

(1) W. J. Youden, J Assoc. Off. Anal. Chem., 50, 1007 (1967).

(2) T. B. Whitaker, J. W. Dickens, and R.

J. Monroe, J. Am. Oil Chem. Soc.,51, 214 (1974); T. B. Whitaker, Pure Appl. Chem., 49, 1709 (1977).

(3) Hazardous Waste Monitoring System,

General, Fed. Regist., Vol. 45, No. 98, pp

33075-33127 (May 19, 1980).

(4) Staff, ACS Subcommittee on Environ- mental Analytical Chemistry, Anal. Chem., 52, 2242 (1980).

(5) See, for example, W. . Dixon and F. J. Massey, Jr., "Introduction to Statistical Analysis," 3rd ed., McGraw-Hilt, New

York, 1969; M. G. Natrella, "Experimental Statistics," National Bureau of Stan- dards Handbook 91, August 1963, U.S. Government Printing Office.

(6) C. 0. Ingamells and P. Switzer, Talanta, 20, 547 (1973); C. O. Ingamells, Talanta, 21, 141 (1974); 23, 263 (1976).

(7) S. H. Harrison and R. Zeisler, NBS In- ternal Report 80-2164, C. W. Reimann,

R. A. Velapoldi, L. B. Hagan, and J. K.

Taylor, Eds., U.S. National Bureau of Standards, Washington, D.C., 1980, p 66.

(8) M. G. Natrella, "Experimental Statistics," National Bureau of Standards Handbook 91, August 1963, U.S. Govern- ment Printing Office, pp 2-13 and Table

A6.

(9) ASTM E-300 Standard Recommended

Practice for Sampling Industrial Chemicals, American Society for Testing and

Materials, Philadelphia, 1973 (reap- proved 1979).

(10) J. Visman, Materials Research and

Standards, November, p 8 (1969).

(11) A. Benedetti-Pichler, in "Physical Methods of Chemical Analysis," W. M.

Berl, Ed., Academic Press, New York,

1956, Vol. 3, p 183; W. E. Harris and B. Kratochvil, Anal. Chem., 46, 313 (1974).

(12) W. E. Harris and B. Kratochvil, "In- troduction to Chemical Analysis," Saunders, Philadelphia, 1981, Chapter 21.

Kratochvil Taylor Byron Kratochvil, professor of chemistry at the University of Alberta, re- ceived his BS, MS, and PhD degrees from Iowa State University. His re- search interests include solvent ef- fects on solute properties and reactions, applications of nonaqueous

systems to chemical analysis, and

methods for determining ionic solutes.

John K. Taylor, coordinator for quality assurance and voluntary stan- dardization activities at the National Bureau of Standards Center for Analytical Chemistry, received his BS

from George Washington University, and his MS and PhD degrees from the University of Maryland. His research

interests include electrochemical

analysis, refractometry, isotope separations, standard reference materials, and the application of physical methods to chemical analysis.

11
Appendix D.3 SYMPOSIUM ON REFERENCE MATERIALS AND THEIR USE IN NUCLEAR FUEL CYCLE

John K. Taylor 1

Reference Materials—What They Are and

How They Should be Used

REFERENCE: Taylor. J. K., "Reference Materials— What They Are and How Thev Should be Used," Journal of Testing and Evaluation, JTEVA, Vol. 11, No. 6. Nov. 1983, pp. 385-387. ABSTRACT: The role of reference materials in monitoring the chemical measurement process is considered. Requirements for reliable reference

materials are reviewed. The use of reference material data in estimating

the uncertainties of the results of measurements on test samples is discussed. KEYWORDS: accuracy, chemical analysis, precision, quality assur- ance, quality control, reference materials, standard reference materials

The increasing requirements for accuracy in chemical analysis and the necessity to interrelate and combine data sets from several laboratories or from the same laboratory over intervals of time have

created a demand for well-characterized reference materials (RMs)

for quality assurance purposes. When properly used, such materials can provide a high degree of confidence in analytical data. On the basis of inquiries received and discussions with various

analysts, it is clear that RMs are not fully used in some situations and

are poorly used in others. It is the purpose of this paper to clarify the

role of RMs in the chemical measurement process and to suggest ways in which they may be used to the best advantage.

Role of Reference Materials An RM is any substance that may be measured simultaneously or se- quentially in a measurement process to provide information about

the process or the measurements arising therefrom. RMs may be in- ternally developed to monitor a specific measurement process, ot they may be provided by an externa! source. Externally developed

reference materials (ERMs) are usually certified by some organization and frequently called certified reference materials (CRMs) [/]. The National Bureau of Standards (NBS) Standard Reference Materials (SRMs) are a special class of CRMs that have been carefullyPresented at the Symposium on Reference Materials and Their Use in Nuclear Fuei Cycle, sponsored by ASTM Committee C-26 on Nuclear Fuel

Cycle on 9 Aug! 1982. Knoxville.'TN. 'Coordinator tor quality assurance and voluntary standardization. Center for Analytical Chemistrv. National Bureau of Standards. Washington. DC 20234.

analyzed (sometimes with the aid of cooperators) and certified by NBS [2-4]. While the RMs described above may differ in status, each can provide useful information to the analyst for the assess- ment of data quality. The only rational basis for use of a RM is as a monitor of a measurement system that is in a state of statistical control [5]. This means that a valid measurement principle has been identified and

put into practice using quality control procedures that assure a requisite degree of reproducibility. Indeed, such a measurement process should, conceptually, be capable of producing an infinite population of measurements, some of which at any moment may be

considered as a sample. The measurements of the RM may then be

considered as random samplings of the output of the measurement

system, which would permit their interpretation for evaluation of the measurement process.

Requirements for RMs

RMs of any type must be appropriate in matrix and composition and of stable composition over the intended period of use. They

must be sufficiently uniform in composition when subsampied (ho- mogeneous) and available in sufficient quantity to be usefui over a reasonable period of time. CRMs have the further requirement that they must be issued with a certificate in which their measured parameters and assigned

uncertainties are fully documented [6]. Internal reference materials (IRMs) must have an equal degree of reliability with respect to stability and homogeneity. The requirement for accuracy of the as- signed values of specified parameters of the latter will depend upon

the end use of the materials, but this may be of lesser importance

than homogeneity in some cases. Laboratories are well advised to upgrade the accuracy of their IRMs to the highest extent possible. Intcrcomparisons with high

quality CRMs, such as SRMs. can be used to accomplish this purpose.

Interpretation of RM Data The primary function cf IRMs (often called control samples) is to evaluate the attainment of statistical control of the measurement

system. As long as such samples are stable and homogeneous in 0090-3973/83/00 1 1 -0385SC0.C0 78
386 JOURNAL OF TESTING AND EVALUATION

composition, the precision observed in the analysis of the IRM may

be inferred as the precision of the measurement system for that particular measurement. Accordingly, it is clear that stability and uni- formity are the prime requirements of such materials and that accurate knowledge of compositions is only a secondary consideration. While such information is highly desirable, the proof of absence of bias using such samples may be difficult to establish based on inter- nally generated evidence alone. ERMs and CRMs in particular are best used to demonstrate ac- curacy, that is, the freedom from bias, of measurement systems that

are demonstrated to be in a state of statistical control. Because the CRM may be costly or available in limited amounts or both, this lat- ter demonstration is often best left to the use of IRMs. Because of

their high quality and the care used in their certification, SRMs

often stand at the top of the RM hierachy and, hence, are especially useful to evaluate the accuracy of a measurement process. Needless

to say. SRMs should be used in carefully designed test sequences

together with IRMs if maximum information is to be provided.

Figure 1 contains a typical sequence in which IRMs and SRMs

may be measured together with the test samples to monitor a measurement process. Figure 1 assumes that control charts are maintained [7], the kinds of which are indicated in the "Notes." The control limits of the charts are determined from the results of previous measurements of the IRM. Points on the control charts are plotted immediately after the data are obtained, and they must fall within

the control limits, at the decision points, in order to continue the measurements sequence. Otherwise any measurements obtained

since the last time the system was known to be in control are suspect and discarded or held in abeyance. Furthermore, the system must

Daily/Event Schedule

CALIBRATION - FULL EXPECTED RANGE

* IRM TEST SAMPLES - GROUP 1

* IRM TEST SAMPLES - GROUP 2

* IRM

« SRM

TEST SAMPLES - GROUP N-l

* IRM TEST SAMPLES - GROUP N

* IRM

* CALIBRATION - MIDRANGE POINT NOTES

* - DECISION POINT

1. MAINTAIN CONTROL CHARTS X-CONTROL CHART , IRM

R- CONTROL CHART , a IRM

2. SYSTEM MUST 3E IN CONTROL AT DECISION POINTS

3. AT LEAST 2 GROUPS: MAXIMUM OF 10 SAMPLES IN EACH CROUP 4^AT LEAST ONE SRM MEASUREMENT SHOULD BE MADE DURING

. EACH SEQUENCE/DAY FIG. 1

Quality assessment using IRM samples.

be demonstrated to have regained control before data may again be

accepted. Figure 2 is similar to Fig. 1 but uses duplicate or split samples to monitor statistical control. Control charts based on the differences between the results obtained for the duplicate/split samples are the

basis for monitoring statistical control. Such charts are described in several publications [7]. The rationale to be followed at the decision points is essentially the same as described in the discussion of

Fig. 1. No matter what kinds of RMs are used, their ability to monitor the measurement process and especially the measurements In progress must be demonstrated, and this is often a matter of inference. Though statistical control of the measurement system and freedom

from bias may be readily demonstrated for the case of measurement

of RMs, the performance of the system-Ton measurements of other

test samples is the matter of concern. To the extent that the RMs

simulate the test samples, the inference drawn from measurement of the former may be transferred to the latter. Conversely, the confidence may diminish as the degree of simulation is decreased. In every case, the experience and professional judgment of the analyst must be used to infer how well an RM monitors the actual measure- ment process. RMs may also be used to evaluate the suitability of a proposed method for a special purpose or to determine the performance characteristics of methods under development. Such use of RMs has much the same limitations as in the evaluation of monitoring a process. As stable test samples, RM analyses can provide data on the

CALIBRATION - FULL EXPECTED RANGE

• CALIBRATION CHECK - MIDRANGE POINT SAMPLE 1

• SAMPLE 1 D/S SAMPLE 2-9 SAMPLE 10

• SAMPLE 10 D/S

» IRM or SRM SAMPLE 11-19 SAMPLE 20

• SAMPLE 20 D/S

• CALIBRATION CHECK - MIDRANGE POINT

« CALIBRATION CHECK - MIDRANGE POINT/DUPLICATE

NOTES

• DECISION POINT

1. MAINTAIN CONTROL CHARTS

a. DUPLICATE MIDRANGE CALIBRATION

b. DUPLICATE/ SPLIT SAMPLE

c. X-CONTROL CHARTS, SRM AND IRM

2. SYSTEM MUST BE IN CONTROL AT DECISION POINTS

3. .IF MORE THAN 20 SAMPLES, REPEAT SEQUENCE

4. IF LESS THAN 20 SAMPLES, DIVIDE INTO T'.VC GROUPS AND

FOLLOW SIMILAR PLAN

5. AT LEAST ONE SRM MEASUREMENT SHOULD BE MADE DURINC EACH SEQUENCE DAY FIG. 2—Quality assessment using duplicates/splits. 79
TAYLOR ON REFERENCE MATERIALS 387

precision of a method of measurement. How well this may be trans- ferred to a practical measurement situation, and how well potential

biases are evaluated is again a matter of judgment, which may need

to be supported by additional information.

Conclusion

Laboratories should refrain from reporting data unless they are in a position to assign uncertainties to the reported values [<*]. Such an

assignment requires the attainment of statistical control of the measurement system and estimation of the bounds of systematic error. The analysis of reliable RMs in a planned measurement sequence

can provide the basis of estimating both the random and systematic components of the measurement uncertainty. However, the assign- ment of such uncertainties to the test results must be done with due

consideration of any matrix differences between the RMs and the

test samples. The analysis of high quality ERMs, such as SRMs, to- gether with the laboratory's IRMs (control samples) is the best ap- proach to monitoring a chemical measurement system for quality as- surance of the data output.

References

[/] "Terms and Definitions Used in Connection with Reference

Materials,'' ISO Guide 30-1981. International Standards Organization, Geneva. Switzerland. 1981.

[2] Caii. J. P. and Stanley, C. L., "Measurement Compatibility and Stan- dard Reference Materials." Annual Review o/ Materials Science, Vol. 5. 1975. pp. 329-242.

[3] Cali, J. P., Mears. T. W., Michaelis. R. E., Read, W. P., Seward.

R. W., Stanley, C. L.. and Yolken, H. T., "The Role of Standard Refer- ence Materials in Measurement Systems." NBS Monograph 148, National Bureau of Standards. Washington. DC 20234. Jan. 1975.

\4\ Catalogue of NBS Standard Reference Materials. SP 260, National Bureau of Standards, Washington, DC 20234.

[5] Taylor, J. K.. "Quality Assurance of Chemical Measurements,"

Analytical Chemistry, Vol. 53, 1981, pp. 1588A-1596A.

[6] "Contents of Certificates of Reference Materials," ISO Guide 31-198L

International Standards Organization, Geneva. Switzerland, 1981.

(7] ASTM Committee E-ll on Statistical Methods. Manual on Presentation of Data and Control Chart Analysis. STP 15D. American Society

for Testing and Materials. Philadelphia. 1976.

[8] American Chemical Society Subcommittee on Environmental Chemistry, "Guidelines for Data Acquisition and Data Quality Evaluation in Analytical Chemistry," Analytical Chemistry. Vol. 52, 1980, p. 2242.

80
Report

Appendix D.H

John K. Taylor

Center for Analytical Chemistry

National Bureau of Standards Washington, D C. 20234 ^klidatioim of

Analytical Methods

Validation of analytical methods is a subject of considerable interest. Documents such as the "ACS Guidelines for Data Acquisition and Data

Quality Evaluation" (1) recommend

the use of validated methods. The

promulgation of federal environmental regulations requires the inclusion

of validated reference methods. Standards-writing organizations spend

considerable time in collaborative

testing of methods they prepare, vali- dating them in typical applications and determining their performance

characteristics. Nevertheless, questions about the appropriateness of methods and the validity of their use

in specific situations often arise. Some

of these questions may be due to dif- ferences, in understanding both what a method really is and what the signifi- cance of the validation process is. This

paper attempts to clarify the nomenclature of analytical methodology and

to define the process of validating methods for use in specific situations. Hierarchy of Methodology The hierarchy of methodology, pro- ceeding from the general to the specific, may be considered as follows: technique — method —* procedure —

*

protocol. A technique is a scientific principle that has been found to be useful for providing compositional information; spectrophotometry is an example. Analytical chemists historically have in- vestigated new measurement tech- niques for their ability to provide

novel measurement capability, or to replace or supplement existing methodology. As a result of innovative applications, analysts can now analyze

This REPORT is based on a talk given at the 184th ACS National Meeting, Sept. 12-17, 1982, Kansas City, Mo.

for myriad substances in exceedingly complex mixtures at ever lower trace

levels, with precision and accuracy un- dreamed of only a few years ago (2). A method is a distinct adaptation

of a technique for a selected measure- ment purpose. The pararosaniline method for measurement of sulfur dioxide is an example. It involves measuring the intensity of a specific dye, the color of which is "bleached" by the

gas. Several procedures for carrying out this method may be found in the

literature. Modern methodology is

complex and may incorporate several measurement techniques; a method may thus be interdisciplinary. A procedure consists of the written

directions necessary to utilize a method. The "standard methods" devel- oped by ASTM and AOAC are, in reality, standardized procedures. ASTM

D2914—Standard Test Method for the Sulfur Dioxide Content of the At- mosphere (West-Gaeke Method) —is an example {3). While a precise description is the aim, it is difficult, if not impossible, to describe every deHierarchy of Analytical Methodology

Definition Example Technique Scientific principle useful for providing compositional infor- mation

Spectrophotometry

Method Distinct adaptation of a technique for a selected measurement

purpose

Pararosaniline method

for measurement of

sulfur dioxide

Procedure Written directions necessary to use a method ASTM D2914—- Standard

Test Method for the

Sulfur Dioxide Content of the Atmosphere (West- Gaeke Method)

Protocol Set of definitive directions that must be

followed, without exception, if the analytical results are to be accepted for a given purpose

EPA Reference Method

for the Determination

of Sulfur Dioxide

in the Atmosphere

(Pararosaniline Method)

Published in Analytical Chemistry, May 1983, 600A-608A, by the American Chemical Society 81
tail of every operation in a procedure.

Accordingly, some level of sophistication is presumed for the user of every published procedure; if very sophisti- cated users are contemplated, only a minimum of detail will be provided and vice versa. However, it should be noted that any omission in the description of critical steps is a potential source of variance or bias, even in the hands of knowledgeable analysts. Because of the flexibility intentionally or unintentionally provided to the analyst, or because of differences in inter- pretation, it is fair to say that minorto-major differences of application occur in the use of even the most precisely defined procedures. Such differ- ences often account for the interlabo- ratory variability observed in many

collaborative tests. Further, at some

point of departure from a published

procedure, a new method results that may need its own validation. The term protocol is the most specific name for a method. A protocol is a set of definitive directions that must

be followed, without exception, if the

analytical results are to be accepted

for a given purpose. Protocols may

consist of existing methods or procedures, modifications of such, or they may be developed especially for specific purposes. Typically, they axe pre- scribed by an official body for use in a given situation such as a regulatory

process. The EPA Reference Method

for the Determination of Sulfur Dioxide in the Atmosphere (Pararosaniline Method) is an example of a protocol

(4). The test method specified as part

of a contractual arrangement for the acceptance of data or a product or material is another example of a protocol, although it may not be called that in the contract. A plethora of methods, procedures,

Figure 1. Basic concept of the validation process

and protocols based on the same measurement principle can arise for a given analytical determination. Usually, they are worded differently, and

they may contain subtle or major dif- ferences in technical detaiis. The ex- tent to which each needs to be individually validated is a matter of professional judgment. It is evident that some validation tests could be merely

a matter of experimentally testing the

clarity of the written word. Goals for Validation

Validation is the process of deter- mining the suitability of methodology

for providing useful analytical data. This is a value judgment in which the performance parameters of the method are compared with the require- ments for the analytical data, as illustrated in Figure 1. Obviously a method

that is valid in one situation could be

invalid in another. Accordingly, the establishment of firm requirements

for the data is a prerequisite for method selection and validation. When

data requirements are ill-considered, analytical measurement can be unnecessarily expensive if the method cho- sen is more accurate than required, in- adequate if the method is less accurate than required, or utterly futile if the accuracy of the method is unknown.

Fortunately, typical and even stan- dard measurement problems often

exist. Examples include a wide variety

of clinical analyses, environmental de- terminations, and recurring measure- ments for the characterization of in- dustrial products. The kinds of samples for which methods have been val- 82
idated should be clearly described, and users should be aware of the need

to demonstrate their own abilities to use the method in their own laboratories.Statements of precision and accura- cy are often a result of a validation

process, especially in the case of a col- laborative test exercise. Such state- ments are often misinterpreted; they merely describe the results of the exercise and are, at best, estimates of

typical performance expectations for the method. They should not be con- strued to be performance parameters

nor should they be used to estimate

the uncertainty of any future data ob- tained by using the method. However,

information on precision and accuracy should be obtained to the extent possible since it provides a quantitative

basis forjudging general performance

capability. Other information useful for characterizing methodology or forjudging

its suitability for a given use includes:

sensitivity to interferences, limits of detection, and useful range of measurement. The specific details for evaluating methodology in these re- spects are beyond the scope of the present paper. Ordinarily, such infor- mation is best obtained as a result of applied research during the method

development stage. Because the limit of detection is closely related to the attainable precision at the lower limit of measurement, both the limit of detection and the lowest concentration range measurable (often called limit of quantitation) should be evaluated, as pertinent, in every laboratory (i , 5). Validation Process The validation process verifies that the methodology is based on sound

technical principles and that it has been reduced to practice for practical measurement purposes. Both the need

to validate methodology and the pro- cedure to be followed are matters for professional judgment. The validation can be either general or specific. General Validation. Validation of measurement techniques depends on

the elucidation of the scientific princi- ples upon which they are based. Such

validation results from the research of the scientific community, and its soundness is evaluated by peer review. Better understanding of measurement

principles can extend their scope and

improve the quality of their use. To

confirm the above statement, one need only think about the varied re- search that has contributed to the un- derstanding of the principles of gas chromatography and that has led to development of its status as a prime measurement technique. Methods arise as the result of applied research, typically by individuals, that often involves both a comprehensive understanding of measure- ment techniques and a high degree of ingenuity and innovation in their application. Testing of the methods in typical practical situations plays a key

role in both the development process and in validation. While ordinarily limited in scope, validation at the re- search stage can be comprehensive and can apply to a wide variety of end

uses. Procedures are developed for the end use of methods in practical analytical situations. The user laboratory

ordinarily needs more experimental

details than are contained in a published research report of a method to use it in practical measurements. Fre- quently, as a method gains widespread

use, procedures evolve that the users may decide need to be standardized. This is often done by consensus in a standards organization forum. During

this process, the resulting standard procedure is examined both technically and editorially. A thorough review

process includes collaborative testing

in which typical stable test materials

are analyzed to verify the procedure's

usefulness and to identify both technical and editorial weaknesses. The process is illustrated in Figure 2. If the composition of the reference samples

is known, precision and bias, both

intra- and interlaboratory, can be

evaluated; otherwise, only precision can be evaluated. If a method of known accuracy is available, the col- laborative test may consist of its comparison with the candidate method, in which case both precision and bias can

be evaluated. The performance pa- rameters of the procedure so evalu- ated are for the conditions of the col- laborative test that are considered

typical. Any extension of them to other kinds of samples is by inference

only, and may need to be justified. Al- though it can be time-consuming, the development of a standard method is one of the best ways to validate a pro- cedure because of the breadth of ex- amination that is involved. A protocol is prescribed by fiat of an

organization requiring a specific kind

of measurement. Presumably it results from an intelligent decision based on

the organization's vaJidation process

or that of others. This may consist of an extensive collaborative test or publication of a proposed protocol for public comment. Unfortunately, expe- diency has overruled sound scientific judgment in some cases, resulting in the promulgation of unvalidated and

scientifically defective protocols (6). Protocols that are specified in a contractual arrangement may be selected

arbitrarily or through a well-conceived

selection process. Verification of their validity for the specific use should be

a prime consideration. Validation for Specific Use. The

83
Candidate Method

Stable Homogeneous

Reference Sample IE

Unknown

Composition Known

Composition

Precision Evaluation

Reference Method of Known

Accuracy

Precision and 8ias

Evaluation

Figure 2. Collaborative test process

ultimate use of analytical methodology is to produce compositional infor- mation about specific samples necessary for the solution of particular problems ranging from exotic research

investigations to the very mundane. The selection of appropriate measure- ment methodology is often a major

consideration. Methods or procedures, even if previously validated in general

terms, cannot unequivocally be as- sumed to be valid for the situation in hand, because of possible differences

in sample matrix and other considerations. Professional analytical chemists traditionally have recognized this and their responsibility to confirm or prove (if necessary) both the validity

of the methodology used for specific application (2) and their own ability to reduce it to practice. The classical validation process is il- lustrated in Figure 3. When reference samples are available that are similar

in all respects to the test samples, the process is very simple: It consists of analyzing a sufficient number of refer- ence samples and comparing the re- sults to the expected or certified val- ues (7). Before or during such an exercise, the analyst must demonstrate the attainment of a state of statistical control of the measurement system (8) so that the results can be relied upon as representative of those expected when

using the methodology-measurement

system.

When a suitable reference material

is not available, several other ap- proaches are possible. One consists of comparing the results of the candidate method with those of another method known to be applicable and reliable, but not useful in the present situation because of cost, unavailability of per- sonnel or equipment, or other reasons. Even the agreement of results with

those obtained using any additional independent method can provide some useful information. Spiked samples and surrogates may

be used as reference samples. This ap- proach is less desirable and less satis- factory because of the difficulty in the

reliable preparation of such samples and because artificially added materials such as spikes and surrogates may

exhibit matrix effects differing from

those of natural samples. Split samples of the actual test samples may be used to evaluate the precision of a method or procedure, but they provide no information about the pres- ence or magnitude of any measure- ment bias. Another approach is to infer the ap- propriateness of methodology from measurements on analogous but dis- similar reference materials. The criti- cal professional judgment of the analyst is necessary to decide the validity of the inference. In all cases, sufficient tests must be made to evaluate the methodology for

8 'A
Candidate Method

Quality Control Replicate Measurements

Spike/ Surrogate

Independent Method

Method Known

Accuracy- 1

Collaborative Test

Validated/ Evaluated Method

Figure 3. General process for evaluation/validation of methodology

the variety of matrices and ranges of composition expected during the mea- surement process. Ordinarily, the lat- ter should include three levels of concentration, namely, the extremes and

the mid-range of compositions expected. Statistical considerations suggest

that at least six degrees of freedom

(ordinarily seven measurements)

should be involved at each decision

point. Conclusion A valid method is necessary but not

sufficient for the production of valid data. Most methods require a degree

of skill on the part of the analyst; this

skill constitutes a critical factor in the measurement process. It is common

knowledge that data obtained by several laboratories on the same test sample using the same methodology may

show a high degree of variability. The

alleviation of such a problem is in the area of quality assurance of the measurements (S). Data obtained by a valid method used in a well-designed

quality assurance program should

allow the assignment of limits of uncertainty that can be used to judge the

data's validity.

It should be remembered that the

validity of any data will also depend upon the validity of the model and of the sample (<S, 9). The model repre- sents the conceptualization of the

problem to be solved, describes the samples that should be analyzed, the data base required, and the way the model will be utilized. Obviously, even

flawless measurement data will be of

little value if the basic concepts are

faulty. Likewise the samples analyzed must be valid if the results obtained

for them are to be intelligently inter- preted. The key role of reliable reference materials in the validation of analytical measurements cannot be overemphasized. Their use in validating the methodology has already been dis- cussed. A planned sequential analysis of reference materials in a quality as- surance program can assess the quality of the data output and thus validate the overall aspects of the analytical measurement system (7). References

(1) ACS Subcommittee on Environmental

Analytical Chemistry. Anal. Chem. 1980, 52, 2242.

(2) Taylor, John K. CHEMTECH 1982. 12, 225.

(3) Annual Book of ASTM Standards. Part 26. American Society for Testing and Materials, Philadelphia. Pa. 19103,

1981.

(4) National Primary and Secondary Ambient Air Quality Standards. Fed. Resist. April 30, 1971, Vol. 36, Part S4, p. 3137.

(5) Glaser, J. A.; Foerst. D. L.; McKee,

G. D.; Quave, S. A.; Budde, W. L. Enuiron. Sci. Technol. 1981, 15, 1426-35.

(6) Purdue, L. T. et al. Environ. Sci. Technol. 1972,6, 152-54.

(7) Taylor, John K. "Reference Materials—How Thev Are or How Thev Should Be Used," ASTM Journal of Testing and Technology, in press.

(8) Taylor, John K. Anal. Chem. 1981,53, 1588-96 A.

(9) Kratochvil, Byron; Taylor, John K.

Anal. Chem. 1981, 53, S24-38 A.

John K. Taylor is coordinator (or chemical measurement assurance and

voluntary standardization at the National Bureau of Standards' Center

for Analytical Chemistry. He received

his BS degree from George Washington University and his MS and PhD

degrees from the University of Maryland. His research interests include electrochemical analysis, refractometry, isotope separations, standard

reference materials, and the application of physical methods to chemical

analysis.

85
NBS-114A IREV. 2-BC) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR REPORT NO. NBS/SP-260/100

2. Performing Organ. Report No 3. Publication Date September 1985

4. TITLE AND SUBTITLE Standard Reference Materials: Handbook for SRM Users

5. AUTHOR(S) John K. Taylor

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) NATIONAL BUREAU OF STANDARDS

U.S. DEPARTMENT OF COMMERCE

GAITHERSBURG, MD 20899

7. Contract/Grant No.

8. Type of Report & Period Covered Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP) Same as No

SUPPLEMENTARY NOTES Library of Congress Catalog Card Number: 85-600576

[~_] Document describes a computer program; SF-185, FIPS Software Summary, is attached.

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

This handbook was prepared to provide guidance for the use of Standard Reference Materials (SRM's) to provide an accuracy

base for chemical measurements. The general concepts of precision

and accuracy are discussed and their realization by quality assurance of the measurement process. General characteristics

of SRM's are described and guidance is given for their selection

for specific applications. Ways to effectively use SRM's are recommended, utilizing control charts to evaluate and monitor measurement accuracy. Appendices probide statistical guidance

on the evaluation of measurement uncertainty.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons) accuracy; calibration; chemical analysis; control charts; measurement

uncertainty; precision; quality assurance; Standard Reference Materials

statistical control

13. AVAILABILITY g Unlimited

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