EPA-600/R-97/121

EPA TRACEABILITY PROTOCOL FOR ASSAY AND

CERTIFICATION OF GASEOUS CALIBRATION STANDARDS

September 1997

U.S. Environmental Protection Agency

National Exposure Research Laboratory

Human Exposure and Atmospheric Science Division

Research Triangle Park, NC 27711
EPA TRACEABILITY PROTOCOL FOR ASSAY AND

CERTIFICATION OF GASEOUS CALIBRATION STANDARDS

U.S. Environmental Protection Agency

National Exposure Research Laboratory

Human Exposure and Atmospheric Science Division

Research Triangle Park, NC 27711
iii

Section Page

List of Figures .................................................... ix

List of Tables ...................................................... x

Acknowledgments ................................................. xi

Glossary ......................................................... xiii

1 INTRODUCTION ................................................. 1-1

2 EPA TRACEABILITY PROTOCOL FOR ASSAY AND CERTIFICATION OF COMPRESSED GAS

CALIBRATION STANDARDS ........................................ 2-1

2.1 GENERAL INFORMATION ...................................... 2-1

2.1.1 Purpose and Scope of the Protocol ........................ 2-1

2.1.2 Reference Standards ................................... 2-1

2.1.2.1 Gas Manufacturer's Intermediate Standard ........... 2-4

2.1.2.2 Recertification of Reference Standards ............. 2-5

2.1.3 Using the Protocol ..................................... 2-5

2.1.4 Certification Documentation .............................. 2-5

2.1.5 Certification Label ..................................... 2-6

2.1.6 Assay/Certification of Compressed Gas Calibration

Standards ........................................... 2-6

2.1.6.1 Incubation of Newly Prepared Compressed

Gas Calibration Standards ....................... 2-6

2.1.6.2 Stability Test for Reactive Gas Mixtures ............. 2-6
iv

2.1.6.3 Certification Periods for Compressed Gas

Calibration Standards ........................... 2-7

2.1.6.4 Minimum Cylinder Pressure ...................... 2-9

2.1.6.5 Assay/Certification of Multicomponent

Compressed Gas Calibration Standards ............. 2-9

2.1.7 Analyzer Calibration ................................... 2-10

2.1.7.1 Basic Analyzer Calibration Requirements ........... 2-10

2.1.7.2 Analyzer Multipoint Calibration ................... 2-10

2.1.7.3 Zero and Span Gas Checks ..................... 2-13

2.1.7.4 Reference Standards for Multipoint Calibrations

and Zero and Span Gas Checks .................. 2-14

2.1.7.5 Uncertainty of the Calibration Curve ............... 2-14

2.1.8 Uncertainty of the Estimated Concentration of

the Candidate Standard ................................ 2-15

2.1.9 Zero Gas ........................................... 2-17

2.1.10 Accuracy Assessment of Commercially Available

Standards .......................................... 2-17

2.2 PROCEDURE G1: ASSAY AND CERTIFICATION OF A COMPRESSED GAS CALIBRATION ST

WITHOUT DILUTION ......................................... 2-18

2.1.1 Applicability ......................................... 2-18

TABLE OF CONTENTS (continued)

Section Page

2.2.2 Limitations .......................................... 2-18

2.2.3 Assay Apparatus ..................................... 2-18

2.2.4 Pollutant Gas Analyzer ................................. 2-20

2.2.5 Analyzer Calibration ................................... 2-20

2.2.5.1 Multipoint Calibration .......................... 2-20

2.2.5.2 Analyzer Range .............................. 2-20

2.2.5.3 Linearity .................................... 2-20

2.2.5.4 Zero and Span Gas Checks ..................... 2-21

2.2.6 Assay Gases ........................................ 2-22

2.2.6.1 Candidate Standard ........................... 2-22

2.2.6.2 Reference Standard ........................... 2-22

2.2.6.3 Zero Gas ................................... 2-23

2.2.7 Assay Procedure ..................................... 2-23

2.2.8 Stability Test for Newly Prepared Candidate Standards ........ 2-24

2.2.9 Certification Documentation ............................. 2-25

2.2.10 Recertification Requirements ............................ 2-25

2.3 PROCEDURE G2: ASSAY AND CERTIFICATION OF A COMPRESSED GAS CALIBRATION ST

USING DILUTION ............................................ 2-25

2.3.1 Applicability ......................................... 2-25

2.3.2 Limitations .......................................... 2-25

2.3.3 Assay Apparatus ..................................... 2-26

2.3.4 Pollutant Gas Analyzer ................................. 2-29

2.3.5 Analyzer Calibration ................................... 2-29

2.3.5.1 Multipoint Calibration .......................... 2-29

2.3.5.2 Analyzer Range .............................. 2-30
v

2.3.5.3 Linearity .................................... 2-30

2.3.5.4 Zero and Span Gas Checks ..................... 2-30

2.3.6 Selection of Gas Dilution Flow Rates or Gas

Concentration Settings ................................. 2-32

2.3.7 Flowmeter Type and Flowmeter Calibration ................. 2-32

2.3.8 Assay Gases ........................................ 2-33

2.3.8.1 Candidate Standard ........................... 2-33

2.3.8.2 Reference Standard ........................... 2-34

2.3.8.3 Zero Gas ................................... 2-34

2.3.9 Assay Procedure ..................................... 2-34

2.3.10 Stability Test for Newly Prepared Standards ................ 2-36

2.3.11 Certification Documentation ............................. 2-37

2.3.12 Recertification Requirements ............................ 2-37

3 EPA TRACEABILITY PROTOCOL FOR ASSAY AND CERTIFICATION OF PERMEATION DEVICE

CALIBRATION STANDARDS ........................................ 3-1

TABLE OF CONTENTS (continued)

Section Page

3.1 GENERAL INFORMATION ...................................... 3-1

3.1.1 Purpose and Scope of the Protocol ........................ 3-1

3.1.2 Reference Standards ................................... 3-1

3.1.3 Selecting a Procedure .................................. 3-2

3.1.4 Using the Protocol ..................................... 3-3

3.1.5 Certification Documentation .............................. 3-3

3.1.6 Certification Label ..................................... 3-4

3.1.7 Assay/Certification of Candidate Permeation Device

Calibration Standards .................................. 3-4

3.1.7.1 Permeation Device Design ....................... 3-4

3.1.7.2 Precautions for Use and Storage of

Permeation Devices ............................ 3-4

3.1.7.3 Equilibration of Newly Prepared Permeation

Devices ..................................... 3-5

3.1.7.4 Certification Conditions for Permeation

Device Calibration Standards ..................... 3-5

3.1.8 Technical Variances ................................... 3-5

3.2 PROCEDURE P1: ASSAY AND CERTIFICATION OF PERMEATION DEVICE CALIBRATION

STANDARDS REFERENCED TO A PERMEATION DEVICE REFERENCE STANDARD 3-6

3.2.1 Applicability .......................................... 3-6

3.2.2 Limitations ........................................... 3-6

3.2.3 Assay Apparatus ...................................... 3-7

3.2.4 Pollutant Gas Analyzer .................................. 3-9

3.2.5 Analyzer Calibration .................................... 3-9

3.2.5.1 Multipoint Calibration ........................... 3-9

3.2.5.2 Analyzer Range .............................. 3-10

3.2.5.3 Linearity .................................... 3-10

3.2.5.4 Zero and Span Gas Checks ..................... 3-10
vi

3.2.6 Selection of Gas Dilution Flow Rates ...................... 3-10

3.2.7 Flowmeter Type and Flowmeter Calibration ................. 3-10

3.2.8 Permeation Devices ................................... 3-11

3.2.8.1 Candidate Standard ........................... 3-11

3.2.8.2 Reference Standard ........................... 3-11

3.2.8.3 Zero Gas ................................... 3-11

3.2.9 Assay Procedure ..................................... 3-12

3.2.10 Stability Test for Newly Prepared Permeation

Devices ............................................ 3-14

3.2.11 Certification Documentation ............................. 3-14

3.2.12 Recertification Requirements ............................ 3-15

TABLE OF CONTENTS (continued)

Section Page

3.3 PROCEDURE P2: ASSAY AND CERTIFICATION OF PERMEATION DEVICE CALIBRATION

STANDARDS REFERENCED TO A COMPRESSED GAS REFERENCE STANDARD 3-15

3.3.1 Applicability ......................................... 3-15

3.3.2 Limitations .......................................... 3-15

3.3.3 Assay Apparatus ..................................... 3-15

3.3.4 Pollutant Gas Analyzer ................................. 3-17

3.3.5 Analyzer Calibration ................................... 3-18

3.3.5.1 Multipoint Calibration .......................... 3-18

3.3.5.2 Analyzer Range .............................. 3-19

3.3.5.3 Linearity .................................... 3-19

3.3.5.4 Zero and Span Gas Checks ..................... 3-19

3.3.6 Selection of Gas Dilution Flow Rates ...................... 3-19

3.3.7 Flowmeter Type and Flowmeter Calibration ................. 3-19

3.3.8 Candidate Standard ................................... 3-20

3.3.9 Reference Standard ................................... 3-20

3.3.10 Zero Gas ........................................... 3-21

3.3.11 Assay Procedure ..................................... 3-21

3.3.12 Equilibrium Test for Newly Prepared Permeation

Devices ............................................ 3-24

3.3.13 Certification Documentation ............................. 3-24

3.3.14 Recertification Requirements ............................ 3-24

3.4 PROCEDURE P3: ASSAY AND CERTIFICATION OF PERMEATION DEVICE CALIBRATION

STANDARDS REFERENCED TO A MASS REFERENCE STANDARD .... 3-24

3.4.1 Applicability ......................................... 3-24

3.4.2 Limitations .......................................... 3-24

3.4.3 Assay Apparatus ..................................... 3-25

3.4.3.1 Analytical Balance ............................ 3-25

3.4.3.2 Temperature-Controlled Chamber ................ 3-25

3.4.3.3 Electrostatic Charge Neutralization ................ 3-27

3.4.4 Weighing Interval ..................................... 3-27

3.4.5 Assay Procedure ..................................... 3-28

3.4.6 Number of Weighings of the Candidate Standard ............. 3-29
vii

3.4.7 Calculation of Certified Permeation Rate ................... 3-29

3.4.8 Uncertainty of Certified Permeation Rate for

Candidate Standard ................................... 3-31

3.4.9 Certification Documentation ............................. 3-31

3.4.10 Recertification Requirements ............................ 3-31

4 REFERENCES ................................................... 4-1
viii

TABLE OF CONTENTS (continued)

Appendix Page

A INSTRUCTIONS FOR CALIBRATION WORKBOOK ...................... A-1

B INSTRUCTION FOR PERMEATION RATE WORKBOOK ................... B-1

C CALCULATION OF TOTAL ANALYTICAL UNCERTAINTY .................. C-1

D MATRIX NOTATION .............................................. D-1
ix
x

LIST OF FIGURES

Number Page

2-1 Example regression curve and confidence bands from 

multipoint calibration ............................................. 2-12

2-2 One possible design of the apparatus for the assay of compressed gas

calibration standards without dilution (Procedure G1) .................... 2-19

2-3 One possible design of the apparatus using flow controllers for assay of

compressed gas calibration standards with dilution (Procedure G2) ......... 2-27

2-4 One possible design of the apparatus using a gas dilution system for assay of

compressed gas calibration standards with dilution (Procedure G2) ......... 2-28

3-1 One possible design of the apparatus for the assay of permeation device

calibration standards referenced to a permeation device reference standard

(Procedure P1) .................................................. 3-8

3-2 One possible design of the apparatus for the assay of permeation device

calibration standards referenced to a compressed gas reference standard

(Procedure P2) ................................................. 3-16

3-3 Chamber for maintaining permeation tubes at constant

temperature ................................................... 3-26

3-4 Example of spreadsheet graphic output for calculating permeation rates ..... 3-30
xi

LIST OF TABLES

Number Page

2-1 SUMMARY OF COMPRESSED GAS SRMs THAT ARE AVAILABLE

FROM NIST .................................................... 2-2

2-2 SUMMARY OF COMPRESSED GAS PRMs THAT ARE AVAILABLE

FROM NMi ..................................................... 2-3

2-3 CERTIFICATION PERIODS FOR COMPRESSED GAS CALIBRATION STANDARDS IN ALUMINUM

CYLINDERS THAT ARE CERTIFIED UNDER THIS PROTOCOL ............ 2-8

2-4 SOME LINEARIZING TRANSFORMATIONS FOR MULTIPOINT CALIBRATION DATA 2-16

3-1 NIST SRM PERMEATION DEVICE REFERENCE STANDARDS ............ 3-2
xii

ACKNOWLEDGMENTS

The information in this document has been funded wholly by the U.S. Environmental Protection

Agency (EPA) under Contract No. 68D40091 to the Research Triangle Institute (RTI), Research Triangle

Park, North Carolina.

This traceability protocol was prepared by Robert S. Wright and Michael J. Messner of RTI under

RTI Project No. 91U-6699-208. It is a revision of an earlier protocol that was prepared in 1993 by the

same authors. The authors thank the EPA work assignment manager, Berne I. Bennett, for his guidance

and technical discussion as the protocol was being written. The authors also thank the following RTI

staff members who provided administrative, technical, editorial, word processing, and graphic arts

support: Malcolm J. Bertoni, Michael Y. Cross, W. Cary Eaton, Tonda J. Gentry, Beryl C. Pittman,

Helen M. Reading, Sue S. Preston, and Jan L. Shirley.

This protocol was reviewed by personnel of EPA, the National Institute of Standards and Technology

(NIST), and the Netherlands Measurement Institute (NMi) as it was being prepared. The authors wish to

thank the following individuals for their technical assistance:

Pamela M. Chu (NIST)

Ed W.B. DeLeer (NMi)

Willliam D. Dorko (NIST)

David L. Duewer (NIST)

Gerald D. Mitchell (NIST)

John T. Schakenbach (EPA)

Rob Wessel (NMi)

Numerous comments from specialty gas producers provided useful comments and suggestions for revisions

to this protocol. The authors thank the following organizations for their assistance:

Airgas, Inc.

Air Liquide America Corporation

Air Products and Chemicals, Inc.

BOC Gases

Matheson Gas Products

MG Industries

Praxair, Inc.

Scott-Marrin, Inc.

Scott Specialty Gases, Inc.

Spectra Gases, Inc.

xii

GLOSSARY

ANSI American National Standards Institute

ASTM American Society for Testing and Materials

GMIS Gas Manufacturer’s Intermediate Standard

ILAC International Laboratory Accreditation Program

ISO International Standardization Organization

NIST National Institute of Standards and Technology

Nmi Netherlands Measurement Institute

NTRM NIST Traceable Reference Material

NVLAP National Voluntary Laboratory Accreditation Program

PRM Primary Reference Material

RGM Research Gas Mixture

SRM Standard Reference Material
1-1

SECTION 1

INTRODUCTION

In 1993, the U.S. Environmental Protection Agency (EPA) in Research Triangle Park, North

Carolina, revised its 1987 version of its traceability protocol for the assay and certification of

compressed gas and permeation-device calibration standards. The protocol allows producers of gaseous

1,2

standards, users of gaseous standards, and other analytical laboratories to establish traceability

between their protocol gases and gaseous Standard Reference Materials (SRMs) produced by the National

Institute of Standards and Technology (NIST). Parts 50, 58, 60, and 75 of Title 40 of the Code of Federal

Regulations (CFR) require using SRMs or gaseous standards traceable to SRMs for calibrating and auditing

ambient air and stationary source pollutant monitoring systems.3-6

As the protocol was being revised, the 1987 version was published in the January 11, 1993, issue

of the Federal Register. It was inserted as Appendix H to 40 CFR Part 75, which concerns the Acid Rain

Program. In April 1996, EPA's Acid Rain Program suggested that the 1987 and 1993 versions of the protocol

be consolidated into a single protocol. In discussions at that time, RTI suggested that the protocol be

revised in a manner that would allow EPA Protocol Gases to be produced either with the higher accuracy

(within ±2 percent) needed by EPA’s Acid Rain Division or with less stringent accuracy requirements that

might be acceptable to other users. In 1997, RTI solicited additional suggested revisions from specialty

gas producers and other interested parties.

The purpose of this work assignment was to revise the statistical procedures in the 1993 version

of the protocol and to consolidate its two published versions in order to make the revised protocol useful

to EPA’s Acid Rain Division as well as other users. Improvement of the statistical procedures had the

highest priority.

The current revision has several significant changes from the 1993 version as listed below:

1. Statistical techniques are used to calculate the total uncertainty of the candidate

standard. Data from the multipoint calibration and the assays are used in these calculations

(see Section 2.1.4);

2. The uncertainty of reference standards is now included in the calculation of the total

uncertainty of the candidate standard (see Section 2.1.2);

3. Statistical techniques are used to calculate the stability of candidate standards. The

intermediate performance standard of 1 percent agreement between assays has been deleted

(see Section 2.1.6.2);

4. Statistical spreadsheets were developed to assist in these calculations, but equivalent

statistical techniques may also be used. These spreadsheets replace most of the manual

calculations required in the 1993 version of the protocol (see Appendices A through D).

5. Multipoint calibration data may be fitted to straight-line, quadratic, cubic, or quartic

linear regression models by the spreadsheets, although the use of cubic and quartic models

is discouraged (see Appendix A);
1-2

6. If a quadratic or higher-order model is used to fit the multipoint calibration data, at least

two reference standards, having different concentrations, must be measured during the

assays (see Section 2.2.7);

7. The correction for minor calibration drift following the multipoint calibration is embedded

in the spreadsheets’ calculation of the uncertainty of a single assay;

8. Primary Reference Standards from the Netherlands Measurement Institute (NMi) are accepted

as being equivalent to SRMs from NIST (see Section 2.1.2);

9. The analyst may substitute a low-concentration reference standard in the place of the zero

gas during assays of the candidate standard (see Section 2.1.9);

10. A summary of EPA's audit results from 1992 to the present is available at an EPA website,

http://www.epa.gov/ttn (see Section 2.1.10);

11. A strip chart recorder is no longer required as part of the assay apparatus, but a highprecision data acquisition system must produce an electronic or paper record of the

analyzer's response during assays. This record must be maintained for 3 years after the

standard’s certification date (see Section 2.2.4).
2-1

SECTION 2

EPA TRACEABILITY PROTOCOL FOR ASSAY AND CERTIFICATION OF

COMPRESSED GAS CALIBRATION STANDARDS

2.1 GENERAL INFORMATION

2.1.1 Purpose and Scope of the Protocol

This protocol describes two procedures for assaying the concentration of compressed gas

calibration standards and for certifying that the assayed concentrations are traceable to a National

Institute of Standards and Technology (NIST) Standard Reference Material (SRM). This protocol is

mandatory for certifying the compressed gas calibration standards used for the pollutant monitoring that

is required by the regulations of 40 CFR Parts 50, 58, 60 and 75 for the calibration and audit of ambient

air quality analyzers and continuous emission monitors. This protocol may be used to assay and certify

gas mixtures that have the same components as compressed gas SRMs. A multiple-component standard may be

assayed and certified under this protocol if compressed gas SRMs that contain the individual components

in the standard exist. This protocol may be used by specialty gas producers, standard users, or other

analytical laboratories. The assay procedure may involve the direct comparison of the standards to

reference standards without dilution (i.e., Procedure G1) or the indirect comparison of the standards to

reference standards with dilution (i.e., Procedure G2). A candidate standard having a concentration that

is lower or higher than that of the reference standard may be certified under this protocol if both

concentrations (or diluted concentrations) fall within the well-characterized region of the pollution

gas analyzer's calibration curve. This protocol places no restrictions on cylinder sizes and the same

analytical procedures must be used in assays of all cylinder sizes.

2.1.2 Reference Standards

Parts 50, 58, 60, and 75 of the monitoring regulations require that gaseous pollutant

concentration standards used for calibration and audit of ambient air quality analyzers and continuous

emission monitors be traceable to either a NIST SRM or a NIST Traceable Reference Material (NTRM). In

7

1996, NIST and the Netherlands Measurement Institute (NMi) issued a joint declaration that specific NMi

Primary Reference Materials (PRMs) can be considered as being equivalent to the corresponding NIST SRMs.

8

The compressed gas SRMs that are available from NIST are listed in Table 2-1. The current SRM-equivalent

compressed gas PRMs that are available from NMi are listed in Table 2-2. Other gas mixtures are under

study by NIST and NMi and they may be added to the Declaration of Equivalence. PRMs produced by other

national metrology organizations will be considered equivalent to NIST SRMs when a declaration of

equivalence is issued jointly by NIST and the national metrology organization. The generic terms “Primary

Reference Material” and “PRM” are used in this document to refer to any SRM-equivalent standard that has

received such equivalency status.

The uncertainty of SRMs, NTRMs, and PRMs is expressed as a 95-percent confidence interval, which

is the one-sigma uncertainty multiplied by a coverage factor almost always equal to
2-2

TABLE 2-1. SUMMARY OF COMPRESSED GAS SRMs

THAT ARE AVAILABLE FROM NISTa

Certified component

Balance gas Concentration range b

for SRMs

Ambient nonmethane organics (15

components)

Nitrogen 5 ppb

Ambient toxic organics (19

components)

Nitrogen 5 ppb

Aromatic organic gasesc Nitrogen 0.25 to 10 ppm

Carbon dioxide Air 345 to 365 ppm

Carbon dioxide Nitrogen 0.5 to 16 percent

Carbon monoxide Air 10 to 45 ppm

Carbon monoxide Nitrogen 10 ppm to 13 percent

Carbon monoxide, propane, and carbon

dioxide

Nitrogen 1.6 to 8 percent CO

600 to 3,000 ppm C3H8

0 to 14 percent CO2

Hydrogen sulfide Nitrogen 5 to 20 ppm

Methane Air 1 to 10 ppm

Methane Nitrogen 50 to 100 ppm

Methane and propane Air 4 ppm CH4, 1 ppm C3H8

Nitric oxide Nitrogen 5 to 3,000 ppm

Oxides of nitrogen

(i.e., nitrogen dioxide plus

nitric acid)

Air 100 ppm

Oxygen Nitrogen 2 to 21 percent

Propane Air 0.25 to 500 ppm

Propane Nitrogen 100 ppm to 2 percent

Sulfur dioxide Nitrogen 50 to 3,500 ppm

All SRMs may not be available at all times. Other compressed gas SRMs may be developed in the future and a

could be used as reference standards. Contact NIST for information about SRM availability at (301) 975-

6776 or http://gases.nist.gov.

SRM concentrations are by mole. b

Aromatic organic gases are benzene, bromobenzene, chlorobenzene, and toluene. c
2-3

TABLE 2-2. SUMMARY OF COMPRESSED GAS PRMs 

THAT ARE AVAILABLE FROM NMia

Certified component Balance gas Concentration range for PRMsb

Carbon dioxide Nitrogen 100 ppm to 15 percent

Carbon monoxide Nitrogen 100 ppm to 6 percent

Ethanol Nitrogen 100 to 259 ppm

Nitric oxide Nitrogen 10 to 4000 ppm

Oxygen Nitrogen 2 to 22 percent

Propane Nitrogen 500 to 3000 ppm

Sulfur dioxide Nitrogen 100 to 3500 ppm

 Information about PRMs can be obtained from: The NMi office in the United States is: a

Nederlands Meetinstituut B.V. NMi USA, Inc.

Van Swinden Laboratorium 36 Gilbert Street South

Department of Chemistry Tinton Falls, NJ 07701

P.O. Box 654P.O. Box 7758

2600 AR DELFT Shrewsbury, NJ 07701

The Netherlands Telephone: (908) 842-8900

Telephone: 31 15 269 16 80 Telefax: (908) 842-0304

Telefax: 31 15 261 29 71 E-mail: NMiUSANJ@aol.com

E-mail: SecChemie@NMi.nl

 SRM-equivalent PRMs from other national metrology organizations may be added in the future. 

 Users of this protocol will be advised if such additions occur.

Within the listed ranges, any concentration is available. PRMs are prepared individually in 5-L cylinders b

according to ISO Standard 6142 (Gas Analysis–Preparation of calibration gas mixtures-weighing methods). 

After preparation, the composition is verified against Dutch Primary Standard Gas Mixtures. The stability is

normally guaranteed for a period of 2 years. Uncertainties depend on the certified concentration and vary

from 0.1 percent (relative) for binary mixtures to 1.0 percent (relative) maximum for certain constituents in

multicomponent mixtures.

2. This estimate includes allowances for the uncertainties of known sources of systematic error as well

9

as the random error of measurement. A value of one-half of the stated uncertainty of these reference

standards should be used in calculating the total analytical uncertainty of standards that are certified

under this protocol (see Appendix C).

The EPA regulations define a "traceable" standard as one that has been compared and certified,

either directly or via not more than one intermediate standard, to a primary standard such as a NIST SRM

or an NTRM. Comparison of a candidate standard directly to an SRM, an SRM-equivalent PRM, or an NTRM

3,4

is preferred and recommended. However, the use of a Gas Manufacturer's Intermediate Standard (GMIS) (see

Subsection 2.1.2.1) in the comparison is permitted. A GMIS is an intermediate reference standard that has

been compared directly to an SRM, an SRM-equivalent PRM, or a NTRM according to Procedure G1. It is an

acceptable reference standard for the assay of candidate standards. However, purchasers of standards that

have been compared to a GMIS should be aware that, in conformity with the above definition, such a standard
2-4

could only be used directly for calibration or audit. Such a standard could not be used as a secondgeneration intermediate reference standard to certify other compressed gas calibration standards.

Accordingly, the reference standard used for assaying and certifying a compressed gas calibration

standard under this protocol must be an SRM, a NTRM, an SRM-equivalent PRM, or a GMIS. The reference

standard must be within its certification period.

Volume reference standards must be traceable to NIST primary standards by calibration at a NISTaccredited state weights and measures laboratory or at a calibration laboratory that is accredited by the

National Voluntary Laboratory Accreditation Program (NVLAP) or by the International Laboratory

Accreditation Conference (ILAC). These volume reference standards are required for assays using 10,11

procedure G2 (see Subsection 2.3.7).

2.1.2.1 Gas Manufacturer's Intermediate Standard—

A GMIS is a compressed gas calibration standard that has been assayed by direct comparison to an

SRM, an SRM-equivalent PRM, or a NTRM, that has been assayed and certified according to Procedure G1, and

that also meets the following requirements:

1. A candidate GMIS must be assayed on at least three separate dates that are uniformly spaced

over at least a 3-month period. During each of these assays, the candidate GMIS must be

measured at least three times. All these assays must use the same SRM, SRM-equivalent PRM,

or NTRM as the reference standard to avoid errors associated with the use of different

reference standards for different assays. 

2. For each assay, the analyst must calculate the mean and 95-percent uncertainty for the three

or more measured concentrations of the candidate GMIS according to the statistical procedures

described in Appendix A or equivalent statistical techniques. The 95-percent uncertainty

must be less than or equal to 1.0 percent of the mean concentration.

3. After the three or more assays have been completed, the analyst must calculate the overall

mean estimated concentration and the 95-percent uncertainty for the candidate GMIS using the

spreadsheet described in Appendix C or equivalent statistical techniques.

4. If the 95-percent confidence limits (i.e., estimated concentration plus or minus

uncertainty) for the assays overlap, the candidate GMIS can be considered to be stable and

can be used as a reference standard for assays of candidate standards. In the Appendix C

spreadsheet, all cells in the comparisons table will be “true.” If the confidence limits do

not overlap, the candidate GMIS may be unstable or there may be analytical problems

associated with the assays or the reference standards. One or more cells in the comparisons

table will be “false.” The analyst must either disqualify the candidate GMIS or investigate

why the confidence limits do not overlap. The analyst may discard the data from a

questionable assay and then conduct another assay. The candidate GMIS can be used as a

reference standard if the confidence limits for the remaining assays and the new assay

overlap. The candidate GMIS cannot be used if it appears to be unstable.

5. A GMIS must be recertified every 2 years. Use the spreadsheet described in Appendix C or

equivalent statistical techniques to compare the confidence limits from a single

recertification assay with the confidence limits from the previous assays. If the confidence

intervals overlap, the GMIS can be recertified. If the reassayed GMIS fails to meet this

requirement, it must undergo a full certification as described in Step 1 above before it can

be used again. There is no requirement that the same reference standard must be used in the

original assays and the recertification assay, but this practice is desirable if possible.
2-5

2.1.2.2 Recertification of Reference Standards—

Recertification requirements for SRMs and NTRMs are specified by NIST. Recertification

requirements for PRMs are specified by NMi. See Subsection 2.1.2.1 for GMIS recertification requirements.

2.1.3 Using the Protocol

The assay/certification protocol described here is designed to minimize both systematic and

random errors in the assay process. Therefore, the protocol should be carried out exactly as it is

described. The assay procedures in this protocol include one or more possible designs for the assay

apparatus. The analyst is not required to use these designs and may use alternative components and

configurations that produce equivalent-quality measurements. Inert materials (e.g., Teflon , stainless ®

steel, or glass) and clean, noncontaminating components should be used in those portions of the apparatus

that are in contact with the gas mixtures being assayed. 

2.1.4 Certification Documentation

Each certified compressed gas calibration standard must be documented in a written certification

report and this report must contain at least the following information:

1. Cylinder identification number (e.g., stamped cylinder number).

2. Certified concentration for the compressed gas calibration standard, in parts per million

by mole or mole percent. This value should be reported to 3 significant digits. The

certified concentration is the mean of all assayed concentrations for which the candidate

standard is considered to be stable.

3. Balance gas in the gas mixture.

4. Cylinder pressure at certification and the statement that the standard should not be used

when its gas pressure is below 1.0 megapascals (i.e., 150 psig).

5. Date of the assay/certification.

6. Certification expiration date (i.e., the certification date plus the certification period)

(see Subsection 2.1.6.3).

7. Identification of the reference standard used in the assay: NIST SRM number, NIST sample

number, cylinder identification number and certified concentration for an SRM; cylinder

identification number and certified concentration for an SRM-equivalent PRM, a NTRM, or a

GMIS. The certification documentation must identify the reference standard as being an SRM,

an SRM-equivalent PRM, a NTRM, or a GMIS.

8. Statement that the assay/certification was performed according to this protocol and that

lists the assay procedure (e.g., Procedure G1) used.

9. The analytical method that was used in the assay.

10. Identification of the specialty gas producer or other laboratory (i.e., name and location)

where the standard was assayed and certified. This identification must be given in the same

or larger font as the other required information in the report.

11. Chronological record of all certifications for the standard.
2-6

12. If applicable, statement that the certified concentration of specified component has been

corrected for analytical interferences from other specified components.

13. An estimate of the total uncertainty associated with the assay of the candidate standard.

This estimate must include the uncertainties of the reference standards, the analyzer

multipoint calibration, and any interference correction. Use the spreadsheet described in

Appendix C or equivalent statistical techniques to calculate the total uncertainty.

This certification documentation must be given to the purchaser of the standard. The specialty

gas producer must maintain laboratory records and certification documentation for 3 years after the

standard's certification date. A specialty gas producer or other vendor may redocument an assayed and

certified standard that it has purchased from another specialty gas producer and that it wishes to sell

to a third party. However, the new certification documentation must clearly identify the specialty gas

producer or other laboratory (i.e., name and location) where the standard was assayed.

2.1.5 Certification Label

A label or tag bearing the information described in items 1-6, 8, and 10 of Subsection 2.1.4 must

be attached to the standard.

2.1.6 Assay/Certification of Compressed Gas Calibration Standards

2.1.6.1 Incubation of Newly Prepared Compressed Gas Calibration Standards—

Newlyprepared compressed gas calibration standards must be incubated at least 4 days before being

assayed and certified.

2.1.6.2 Stability Test for Reactive Gas Mixtures—

Compressed gas calibration standards that contain reactive gas mixtures, including hydrogen

sulfide (H S), nitric oxide (NO), oxides of nitrogen (NO ), sulfur dioxide (SO ), and carbon monoxide (CO), 2 x 2

and that have not been previously certified, must be tested for stability as discussed herein. Conduct

an initial assay of the candidate standard and determine a concentration for the standard. The candidate

standard must be measured at least three times during the assay. Reassay the standard at least 7 days

after the first assay. Use the spreadsheet described in Appendix C or equivalent statistical techniques

to compare the 95-percent confidence limits for the two assays. If the confidence limits overlap, the

candidate standard can be considered to be stable and can be certified. In the spreadsheet, all cells in

the comparisons table will be “true.” If the confidence intervals do not overlap, the candidate standard

may be unstable or there may be analytical problems associated with the assays or the reference standards.

The analyst must wait an additional 7 days or more and conduct a third assay. If the confidence interval

for the third assay overlaps either of the two previous assays, the candidate standard can be certified

using the data from the two overlapping assays to determine the certified concentration and the total

uncertainty. The analyst must disqualify the candidate standard if none of the three confidence intervals

overlap. The analyst should investigate the cause of the lack of agreement among the three assays and

should correct any problems that are discovered.

2.1.6.3 Certification Periods for Compressed Gas Calibration Standards—

The certification of a compressed gas calibration standard is valid for only a specified period

following its certification date, which is the date of its last assay. In general, the certification

period should be no longer than the period for which similar standards have been shown to be stable.12-14

The certification periods for various standards are specified in Table 2-3. These certification periods

are for standards that are contained in aluminum cylinders. In general, the certification period for

standards that are contained in nonaluminum cylinders is 6 months. However, an exception is made for the

following three gas mixtures: carbon dioxide with a concentration >0.5 percent; oxygen with a
2-7

concentration >0.5 percent; oxygen with a concentration >0.8 percent; and propane with a concentration

>0.1 percent. The certification period for standards containing these three gas mixtures in nonaluminum

cylinders is given in Table 2-3.

If a standard is to be used after its certification period has ended, it must be recertified in

accordance with this protocol. The recertification assay must be performed using the same analytical

procedure (e.g., Procedure G1) as was used for the original assay of the standard. The purpose of this

assay is to determine whether the standard has remained stable since its original certification. The

standard must be measured at least three times during the recertification assay. A second assay is not

needed for recertification of the standard. There is no requirement that the same reference standard must

be used in the original and recertification assays, although this practice is desirable if possible.

Record the results of the recertification assay in the laboratory's records. Use the spreadsheet

described in Appendix C or equivalent statistical techniques to compare the confidence limits for the

recertification assay with those for the previous assays. If the confidence limits overlap, the standard

can be recertified. The second certification period for the standard is the same as that given in Table

2-3.

A standard that was certified under this protocol may be recertified by a laboratory other than

the one that performed the original certification. In such a case, the 95-percent confidence limits for

the recertification assay must overlap the certified concentration plus or minus the total uncertainty

that was given in the original certification documentation. If the confidence limits do not overlap, a

second recertification assay must be conducted and the confidence limits for the two recertification

assays must overlap before the standard can be recertified. The recertification documentation must list

the information from the original certification documentation plus the corresponding information from

the recertification assays. Both the original and the recertification laboratories must be identified

in the recertification documentation.
2-8

TABLE 2-3. CERTIFICATION PERIODS FOR COMPRESSED GAS

 CALIBRATION STANDARDS IN ALUMINUM CYLINDERS THAT

ARE CERTIFIED UNDER THIS PROTOCOL

Certified components Balance gas

Applicable

concentration range Certification

period (months)

Ambient nonmethane organics (15

components)

Nitrogen 5 ppb 24

Ambient toxic organics (19 components) Nitrogen 5 ppb 24

Aromatic organic gases Nitrogen $0.25 ppm 36

Carbon dioxide Nitrogen or aira $300 ppm 36

Carbon monoxide Nitrogen or air $8 ppm 36

Hydrogen sulfide Nitrogen $4 ppm 12

Methane Nitrogen or air $1 ppm 36

Nitric oxide Oxygen-free

nitrogenb

$4 ppm 24

Nitrous oxide Air $300 ppb 36

Oxides of nitrogen

(i.e., sum of nitrogen dioxide

and nitric acid)

Air $80 ppm 24

Oxygen Nitrogen $0.8% 36

Propane Nitrogen or air $1 ppm 36

Sulfur dioxide Nitrogen or air 40 to 499 ppm 24

Sulfur dioxide Nitrogen or air $500 ppm 36

Multicomponent mixtures — — See text

Mixtures with lower concentrations — — See text

When used as a balance gas, "air" is defined as a mixture of oxygen and nitrogen where the minimum concentration of oxygen is 10 a

percent and the concentration of nitrogen is greater than 60 percent.

Oxygen-free nitrogen contains <0.5 ppm of oxygen. b

The spreadsheet described in Appendix C to calculate the total analytical uncertainty of a

candidate standard has provision for data from only three assays. If more than three assays are conducted,

only the data from the three most recent assays should be used in the spreadsheet.

The certification periods given in Table 2-3 apply to specific concentration ranges over which

the gas mixtures have been found to be stable. These concentration ranges match the concentration ranges

for NIST SRMs. The protocol described here allows the certification of standards with concentrations that

may be lower than those of the corresponding SRMs. If the concentration of the standard is less than the

applicable concentration range given in Table 2-3, the initial certification period for this standard is

6 months. After this period, the standard must be recertified before further use. The standard must be

measured at least three times during the recertification assay. If the confidence limits for the

recertification assay overlap those for the previous assays, the standard can be recertified for the

period shown in Table 2-3. For example, a 35-ppm sulfur dioxide in nitrogen standard will have an initial
2-9

certification period of 6 months. After a successful recertification, this standard will have a

recertification period of 24 months.

If the confidence limits from the recertification assay do not overlap those from the original

assays, the analyst must either disqualify the standard for further use under this protocol or investigate

why there is an apparent difference between the original assays and the recertification assay. This

difference may be due to an actual instability of the gas mixture, to a reference standard problem, to an

analytical instrumentation problem, or to some other problem. If the analyst can find a reasonable

explanation for the difference and if this cause is not instability, then the standard can be recertified.

The analyst must append a brief report on the investigation to the recertification documentation and to

the laboratory's records.

A multiple-component standard can be certified for a period equal to that of its most briefly

certifiable component. For example, a standard containing sulfur dioxide, carbon monoxide, and propane

in nitrogen can be certified for 24 months because the shortest certification period is 24 months.

A standard may be recertified if the gas pressure remaining in the cylinder is greater than 3.4

megapascals (i.e., 500 psig).

2.1.6.4 Minimum Cylinder Pressure—

In general, a compressed gas calibration standard should not be used when its gas pressure is below

1.0 megapascals (i.e., 150 psig). NIST has found that some gas mixtures (e.g., nitric oxide in nitrogen)

have exhibited a concentration change when the cylinder pressure fell below this value.

2.1.6.5 Assay/Certification of Multicomponent Compressed Gas Calibration Standards—

This protocol may be used to assay and certify a multiple-component standard if compressed gas

SRMs, SRM-equivalent PRMs, or NTRMs exist that contain the individual components of the multiplecomponent standard. If any component in the multiple-component standard interferes with the assay of any

other component, the analyst must conduct an interference study to determine an interference correction

equation. This study must be conducted using the same analyzer or analyzers as will be used to assay the

standard. The study must use single-component and multiple-component reference standards that have been

assayed using interference-free analyzers. The study must cover the same range of concentrations for all

components as will exist for the standards being assayed and certified according to this protocol.

Data from the interference study must be evaluated using multiple-variable least-squares regression

analysis. The analyst should consult with a statistician before beginning the study or evaluating its

data. The regression analysis must produce an interference correction equation and an estimate of the 95-

percent uncertainty associated with the corrected concentrations for the assayed components. The

interference correction equation will be valid for the range of concentrations covered in the study for

which the uncertainty of the corrected concentration is #1 percent of the corrected concentration. The

analyst must add the interference correction uncertainty to the total uncertainty of the standard. The

certification documentation must include a statement that the certified concentration of a specified

componenthas been corrected for interferences from other specified components. An interference study

is not needed if the assay analyzer is interference free.

2.1.7 Analyzer Calibration

2.1.7.1 Basic Analyzer Calibration Requirements—

The assay procedures described in this protocol employ a data reduction technique to calculate

the concentration of a candidate compressed gas standard that corrects for minor analyzer calibration

variations (i.e., drift). This technique does not require the absolute accuracy of the analyzer's

calibration curve at the time of the assay. Requirements for the analyzer follow: (1) it must have a well-
2-10

characterized calibration curve for the pollutant of interest (see Subsection 2.1.7.2); (2) it must have

good resolution and low noise; (3) its calibration must be known and must be reasonably stable or

recoverable during the assay/certification process; and (4) all measurements of candidate standards must

fall within a well-characterized region of its calibration curve.

2.1.7.2 Analyzer Multipoint Calibration—

The gas analyzer used for the assay must have had a multipoint calibration within 1 month prior

to the assay date. This calibration is not used directly to interpret analyzer response during the assay

of the candidate compressed gas calibration standard. The data reduction technique corrects the analyzer

response on the assay date for any minor calibration drift during the period between the multipoint

calibration and the assay date. The corrected analyzer response is then used with the multipoint

calibration data to calculate a concentration value for the candidate standard.

The analyzer's zero and span controls may be adjusted before the start of the multipoint

calibration. If a zero or span adjustment is made, allow the analyzer to stabilize for at least one hour

before beginning the multipoint calibration. The waiting period is necessary because some analyzers'

calibrations drift for a period of time following a zero or span control adjustment.

Themultipoint calibration must consist of one or more measurements of the analyzer responses to

at least five different concentrations. The use of a zero gas in the calibration is recommended, but is

not required. Record these measurements and the analyzer's zero and span control settings in the

laboratory's records. These calibration concentrations should be approximately evenly spaced over the

concentration range. The multipoint calibration is valid only for the concentration range lying between

the largest and smallest measured concentrations. The concentrations may be produced by undiluted

reference standards or by dilution of reference standards using a gas dilution system. See Subsection

2.1.7.4 for reference standard requirements. If a gas dilution system is used, it must have a specified

accuracy of no worse than 1.0 percent of the undiluted reference standard concentration. The accuracy of

the gas dilution system must be checked by the analyst at monthly intervals by comparing diluted reference

standards to undiluted reference standards having approximately the same concentration.

If the analyzer has multiple concentration ranges, a multipoint calibration should be done for

all ranges that will be used later for the assay of candidate standards. A multipoint calibration that

is conducted on one range is not valid for an assay that is conducted on another range.

Data from the multipoint calibration must be evaluated using least-squares regression analysis.15

This statistical analysis technique will be used to determine the analyzer's calibration curve and to

characterize the uncertainty associated with the calibration. The concentration values are the

independent (i.e., X) values in the analysis and their units may be parts per million, mole percent, or

any other appropriate units. The analyzer response values are the dependent (i.e., Y) values in the

analysis and their units may be volts, millivolts, percent of scale or any other measurable analyzer

response units. The analyzer response values should have a resolution of less than or equal to 1 percent

of the maximum measured analyzer response. 

Because an analyzer’s response has a random error component, repeated measurements of the same

reference standard will not produce identical analyzer responses. The analyst may investigate the

analyzer’s precision by making replicate measurements of multiple reference standards. Least-squares

regression analysis is normally conducted under the assumption that the precision is the same at all

concentrations. However, this assumption may not be true for real-world analyzers and the analyst may

need to use alternate statistical procedures to analyze the multipoint calibration data.

Calculate the least-squares regression coefficients of the calibration equation using the

spreadsheets described in Appendix A or using equivalent statistical techniques (e.g., the worksheet for
2-11

linear relationships given in Chapter 5 of Reference 15). The spreadsheets allow the multipoint

calibration data to be fitted to straight-line, quadratic, cubic, or quartic linear regression models.

EPA discourages the use of the cubic and quartic models and believes that better fits of the data can be

obtained by performing multipoint calibrations over more limited concentration ranges and by using

straight-line or quadratic models. Inclusion of cubic and quartic models in the spreadsheets is for

experimental use or for situations in which there is a theoretical basis for the use of such higher-order

models. Analysts should be aware that apparent higher-order calibration curves may be caused by artifacts

such as inaccurate reference standards or leaks in a gas dilution system. They should not use higher-order

regression models to fit multipoint calibration data that have inadequate precision and that should be

fitted to lower-order regression models. If analysts suspect that the precision is inadequate, they

should make replicate measurements at each different concentration. Additionally, a multipoint

calibration should not change regression model orders from one month to the next.

The spreadsheet described in Appendix A will suggest the best regression model for the multipoint

calibration data, but the analyst should choose the model that best fits the measurement process on

theoretical grounds.

Plot the values from the multipoint calibration and the regression curve with confidence bands

as shown in Figure 2-1. These plots will provide a graphical representation of the calibration and will

permit a qualitative assessment of the uncertainty associated with the calibration. Record the regression

coefficients and other statistical results in the laboratory's records.

However, a quantitative assessment of the calibration's uncertainty is needed to allow the

analyst to determine whether the multipoint calibration data adequately characterizes the "true"

calibration curve for the analyzer. The criterion to be used to evaluate the uncertainty of the multipoint

calibration is the 95-percent uncertainty (i.e., " = 0.05) for a concentration predicted from the

regression line using measured values of the analyzer response. This 95-percent uncertainty for the

predicted concentration can be calculated using the spreadsheets described in Appendix A or using

equivalent statistical techniques. Record the uncertainty calculations in the laboratory's records. A

multipoint calibration will be considered to be well-characterized for all concentrations that are within

the range of the multipoint calibration measurements and for which the magnitude of the 95-percent

confidence limits for the regression-predicted analyzer response are #±1 percent of the measured response

for the largest concentration in the multipoint calibration. For example, assume that a multipoint

calibration was conducted between 0 and 100 ppm and that the measured responses ranged between 0 and 10

volts. The calibration is well-characterized for all concentrations for which the 95-percent confidence

limits are #±0.1 volt, which is equal to ±1 percent of 10 volts. Step 4 of the spreadsheet described in

Appendix A allows the analyst to enter various concentrations and obtain the corresponding regression-
2-12

Figure 2-1. Example regression curve and confidence

bands from multipoint calibration.

predicted analyzer response and confidence limits.

In effect, the 95-percent uncertainty value is a measure of how well the multipoint calibration

data fit an equation which the analyst assumes is the "true" calibration equation for the analyzer.

Comparison of uncertainty values from straight-line and quadratic equations permits the analyst to select

the equation that best represents the calibration data. 

A multipoint calibration may fail to meet this uncertainty criterion for several possible

reasons:

• inadequate analytical precision;

• inaccuracy of the reference standards or the gas dilution system; or 

• excessive uncertainty in the analyzer's calibration equation due to incorrect assumptions

about the form of the equation.

The effect of inadequate analytical precision can be reduced by increasing the number of replicate

measurements at each calibration concentration or by increasing the number of different concentrations

used in the multipoint calibration. Additionally, precision can be improved by using an averaged analyzer

response,rather than an instantaneous analyzer response, for each measurement. Reference standard

inaccuracy is reduced by using the most accurate reference standards that are available. An inaccurate

gas dilution system can be detected by comparing measurements of the concentration of a diluted reference
Relative Difference ' 100 Current Response & Calibration Response

Calibration Response for Reference Standard

.

2-13

standard to the theoretically equal concentration of another, undiluted reference standard. It can also

be detected by comparing measurements of two theoretically equal concentrations obtained by dilution of

two reference standards having significantly different concentrations. An inaccurate gas dilution system

must not be used for the multipoint calibration. The effect of excessive uncertainty in a straight-line

calibration equation can be eliminated by using a quadratic calibration equation or by transforming the

calibration data mathematically so that they may be fitted to a straight line regression equation. See

Subsection 2.1.7.5 for a discussion of such mathematical transformations.

Note that possibly a more restrictive uncertainty criterion applies for the assay of the candidate

standard. The magnitude of the 95-percent confidence limits for the estimated concentration of the

candidate standard must be #±1 percent of the concentration of the reference standard (see Subsections

2.2.2 and 2.32). For example, assume that a 70-ppm candidate standard is being assayed using a 50-ppm

reference standard. The 95-percent confidence limits for the candidate standard’s estimated

concentration must be #±0.5 ppm.

2.1.7.3 Zero and Span Gas Checks—

On any day after the multipoint calibration that the analyzer will be used for the assay of a

candidate standard, its calibration drift must be measured. This drift is calculated relative to the

analyzer response during the multipoint calibration. The purpose of the zero and span gas checks is to

verify that the calibration drift has remained within acceptable limits since the multipoint calibration.

The criterion that is used to assess the drift is the relative difference between the analyzer's current

response and the corresponding value from the multipoint calibration. The following equation is used for

this calculation:

This calculation is performed in Step 6 of the spreadsheet described in Appendix A.

Note that the relative difference is always calculated relative to the calibration response for

the reference standard, even when the zero gas is being measured. This calculation is performed for the

zero gas measurements and for the reference standard measurements. If the reference standard was not

measured during the multipoint calibration, use the regression-predicted response for a concentration

equal to that of the reference standard.

If the relative differences for the zero and span gas checks are each less than or equal to 5.0

percent, the analyzer's current calibration is considered to be approximately the same as during the

multipoint calibration and the assay may be conducted. The zero and span controls do not have to be

adjusted following the zero and span checks because the data reduction technique used in this protocol

does not depend on the absolute accuracy of the analyzer calibration equation at the time of the assay.

If the relative differences for the zero or span gas checks are greater than 5.0 percent, the

analyzer is considered to be out of calibration. A new multipoint calibration may be conducted before the

candidate standard is assayed or the analyzer's zero and span controls may be adjusted to return the

analyzer's response to the original calibration levels. For some analyzers such as nondispersive infrared

instruments, daily changes in environmental variables such as barometric pressure may shift the

calibration. After any adjustment of controls, the analyst should repeat the zero and span gas checks and

recalculate the relative differences to verify that the analyzer is in calibration.
2-14

The zero gas and reference standard measurements that are performed for the assay of the candidate

standard may also be used for the zero and span gas checks.

Between the time of the multipoint calibration and the time of the zero and span gas checks, the

analyst may adjust the analyzer’s zero and span controls for assays that will not be certified according

to this protocol. However, these controls must be returned to their settings at the multipoint

calibration before the zero and span gas checks or assays under this protocol.

2.1.7.4 Reference Standards for Multipoint Calibrations and Zero and Span Gas Checks—

The reference standards for the multipoint calibration and for the span gas checks must be diluted

or undiluted SRMs, SRM-equivalent PRMs, NTRMs, or GMISs as specified in Subsection 2.1.2. The reference

standard for the span gas check need not be the same as one of those used for the multipoint calibration

or for the assay of the candidate standard.

Pure gases may be diluted to prepare gas mixtures for use in multipoint calibrations, but such

mixtures may not be used as the reference standards for the span gas check or for the assay of the candidate

standard. Pure gases may not be diluted by more than a factor of 100.

The zero gas must meet the requirements in Subsection 2.1.9. For some analyzers such as gas

chromatographs, the analyst may have reason to believe that the zero gas reading may not accurately

represent the zero-intercept of the calibration equation. The analyst may substitute a lowconcentration, NIST-traceable reference standard for the zero gas, providing that the concentration of

this standard is less than the concentration of the candidate standard.

2.1.7.5 Uncertainty of the Calibration Curve—

The data reduction technique used in this protocol is based on the assumption that the analyzer

has a well-characterized calibration curve. The accuracy of the certified concentration of a candidate

compressed gas calibration standard is dependent upon this assumption. The analyst cannot assume that

the analyzer's calibration curve is a straight line between the measured values for the zero gas and the

reference standard. The analyst must calculate the calibration equation and the uncertainty for its

predicted concentrations by statistical analysis of the measurements obtained during the multipoint

calibration.

The total uncertainty of the certified concentration for a candidate standard is composed of

several components. The first component is the accuracy associated with the certified concentration of

the reference standard. This uncertainty is minimized by using an SRM, an SRM-equivalent PRM, a NTRM, or

a GMIS as the reference standard. The second component is the precision of the measurements of the

reference and candidate standards. This uncertainty is minimized by making replicate measurements of

these standards. The third component is the uncertainty associated with the concentrations that are

predicted from the analyzer's calibration curve. This uncertainty concerns whether an assumed

calibration equation accurately represents the "true" calibration curve.

This third component of uncertainty does not exist if the concentrations of the reference and

candidate standards are equal. The assumed calibration equation and the true calibration curve will pass

through the data for the reference standard regardless of whether they diverge elsewhere and the equation

will be accurate for that single concentration. However, the uncertainty does exist if the concentrations

of the reference and candidate standards differ. The assumed and true calibration curves may pass through

different points for concentrations not equal to that of the reference standard. Analytical errors will

develop because of this difference.

The measure of this uncertainty that is most directly useful to the analyst is the 95-percent

uncertainty for a regression-predicted concentration given one or more measurements of the candidate
2-15

standard. The uncertainty may be calculated using the spreadsheet described in Appendix A or using

equivalent statistical techniques. Several points should be noted about this uncertainty value. First,

its magnitude decreases as n increases where n is the number of measurements in the multipoint

calibration. Second, its magnitude decreases as nN increases, where nN is the number of measurements of

the candidate standard. Third, its magnitude increases as the mean measured analyzer response (yN) for

)

the candidate standard diverges from the overall mean measured analyzer response (y) for the multipoint

)

calibration. These points mean that it becomes easier to satisfy the uncertainty criterion as one

increases the number of measurements in the multipoint calibration and in the assay of the candidate

standard. Additionally, the absolute uncertainty of the regression predicted concentration is larger at

the extremes of the calibrated concentration range than at the middle of the range.

For analyzers having an inherently nonlinear, but precise response, the calibration equation can

be calculated using quadratic or higher-order polynomial regression analysis. Alternatively, a nonlinear

equation may be linearized with a simple mathematical transformation of the multipoint calibration data.

Examples of some linearizing transformations are given in Table 2-4, which is reproduced from Reference

15. The multipoint calibration data may need to undergo several different transformations before the

optimum transformation is determined. Using appropriately transformed calibration data, a calibration

equation can be calculated with an acceptable 95-percent uncertainty for the regression-predicted

concentration. Subsequently, data obtained from the assay of the candidate standard must be similarly

transformed to calculate a concentration for the candidate standard. 

2.1.8 Uncertainty of the Estimated Concentration of the Candidate Standard

Uncertainty in the concentration estimated for a candidate standard is due to many different

sources, including uncertainty in the reference standards, uncertainty in the analyzer multipoint

calibration, uncertainty in the zero/span correction factors, and measurement imprecision. Some of these

sources can be assessed using standard statistical techniques, but others cannot be assessed with the

limited data that are produced when implementing this protocol.

For those cases where the candidate standard is assayed at the same time as the multipoint

calibration, the candidate standard's concentration is determined directly from the calibration curve.

The total uncertainty of the concentration is calculated by using the spreadsheets described in
YT

' XT' YT' b0% b1XTb0' b1'

Y ' a %

b

X Y

1

X

Y '

1

a % bXN

1

Y

' a % bX

1

Y X

Y '

X

a % bX

X

Y

X

Y ' ab x Y X

Y ' ae bx Y X

aX b Y X

Y ' a % bX n, X

n

2-16

TABLE 2-4. SOME LINEARIZING TRANSFORMATIONS

FOR MULTIPOINT CALIBRATION DATA

If the relationship

is of the form:

STEP ONE:

Plot the transformed

calibration data

STEP TWO:

Fit the

straight line

STEP THREE:

Convert straight line

constants (b and b ) 0 1

to original constants:

Use the normal

procedures for

calculating the

regression line using

the transformed

calibration data. 

Calculate the 95-

percent uncertainties

for the predicted

transformed

concentrations and

compare them to the

uncertainty

criterion.

a b

,

or a b

a b

log log a log b

log log a b log e

log log log a b

 where n is known

Y a b

Source: Reference 15.
UncertaintyTOTAL ' (UncertaintyASSAY)

2 % (UncertaintySTANDARD)2

.

UncertaintyTOTAL ' (UncertaintyASSAY)

2 % (UncertaintyCORRECTION)2 % (UncertaintySTANDARD)2

.

UncertaintyRELATIVE ' 100 UncertaintyTOTAL / Certified Concentration .

2-17

Appendices A and C or equivalent statistical techniques. It combines the uncertainty of the assay with

the uncertainty of the reference standard using the following equation:

For those cases where the candidate standard is assayed on a date following the multipoint

calibration, the spreadsheet includes the uncertainty associated with the zero gas and reference standard

measurements in the calculation of total uncertainty.

If an interference-correction equation has been used to obtain a corrected concentration for the

candidate standard, the 95-percent uncertainty for the corrected concentration must be included in the

assessment of the total analytical uncertainty of the candidate standard's concentration using the

following equation:

The analyst may report the total analytical uncertainty of the candidate standard's certified

concentration on the certification documentation or may report this estimate as a percentage that is

relative to the certified concentration using the following equation:

2.1.9 Zero Gas

Zero gas used for zero gas checks or for dilution of any candidate or reference standard should

be clean, dry, zero-grade air or nitrogen containing no detectable concentration of the pollutant of

interest. It should match the balance gas in the candidate standard and the reference standard, unless

it has been demonstrated that the analyzer is insensitive to differences in the balance gas composition.

The zero gas also should contain no contaminant that causes a detectable response on the analyzer or that

suppresses or enhances the analyzer's response. The oxygen content of zero air should be approximately

thatof ambient air, unless it has been demonstrated that varying the oxygen content does not suppress or

enhance the analyzer's response. The water vapor concentration in the zero gas should be less than 5 ppm.

The analyst may substitute a low-concentration, NIST-traceable reference standard for the zero

gas in zero gas checks and assays if there is reason to believe that the zero gas reading may not accurately

represent the zero-intercept of the calibration equation.

2.1.10 Accuracy Assessment of Commercially Available Standards

Periodically, the U.S. EPA will assess the accuracy of compressed gas calibration standards that

have been assayed and certified according to this protocol. The accuracy of representative standards will

be assessed by EPA audits. The audit results, identifying the specialty gas producers or other analytical

laboratories that assayed and certified the standards, will be published as public information. A summary

of EPA’s audit results from 1992 to the present is available as a WordPerfect 6.1 file at EPA’s Ambient

Monitoring Technology Information Center (Internet Address: http://www.epa.gov/ttn). This document can

be found in the Directory of TTNWeb Sites/ AMTIC/Publications/ORD-NERL Documents.
2-18

2.2 PROCEDURE G1: ASSAY AND CERTIFICATION OF A COMPRESSED GAS

CALIBRATION STANDARD WITHOUT DILUTION

2.2.1 Applicability

This procedure may be used to assay the concentration of a candidate compressed gas calibration

standard, based on the concentration of a compressed gas reference standard of the same gas mixture. This

procedure allows a specialty gas producer, a standard user, or other analytical laboratory to certify that

the assayed concentration for the candidate standard is traceable to the reference standard. The

procedure employs a pollutant gas analyzer to compare the candidate and reference standards'

concentrations by direct measurement without dilution of either gas.

This procedure may be used for the assay of more than one candidate standard during the same assay

session. Criteria that apply to the assay of one candidate standard apply to the assay of multiple

candidate standards.

2.2.2 Limitations

The concentration of the candidate standard may be greater than or lesser than the concentration

of the reference standard. However, both concentrations must lie within the well-characterized region

of the multipoint calibration (see Subsection 2.1.7.2). Additionally, the magnitude of the 95-percent

confidence limits for the estimated concentration of the candidate standard must #±1 percent of the

reference standard concentration. This criterion may be more restrictive than the corresponding

criterion for the multipoint calibration, but it allows the analyst greater flexibility in the selection

of a reference standard for the assay of a particular candidate standard. For example, assume that a 70-

ppm candidate standard is being assayed using a 50-ppm reference standard and that the analyzer’s

calibration was found to be well-characterized between 20 and 80 ppm. The 95-percent confidence limits

for the candidate standard’s estimated concentration must be less than or equal to ±0.5 ppm.

The balance gas must be the same in both the candidate standard and the reference standard, unless

it has been demonstrated that the analyzer's response is insensitive to differences in the balance gas

composition.

2.2.3 Assay Apparatus

Figure 2-2 illustrates one possible design of apparatus for the assay of compressed gas

calibration standards without dilution. This apparatus is designed to allow the convenient routing of

the gas mixtures to the pollutant gas analyzer. The gas mixture to be measured is selected by rotation of

two three-way valves (i.e., V1 and V2). Pressure regulators and gas flow controllers (i.e., C1 and C2)

control the flow rates from the individual cylinders. The gas flow controllers may be needle values,

capillary tubes, thermal mass flow controllers, or other flow control devices. The gas mixtures are

routed to the analyzer through a union tee tube fitting. Gas in excess of the analyzer's demand is vented,

which helps to ensure that the gas entering the analyzer is at near-ambient pressure. Normally, the excess

gas is vented to the atmosphere without any obstructions in the tubing. However, the excess gas can be

routed through an uncalibrated rotameter by rotation of a three-way valve (i.e., V3). The rotameter is

used to demonstrate that the total gas flow rate exceeds the sample flow rate of the analyzer and that no

room air is being drawn in through the vent line.
2-19

The apparatus may be modified in several ways that will not diminish its performance. The two

three-way valves could be replaced by solenoid valves or by a single four-way valve with three input ports

and one output port. Alternatively, a single length of tubing with a gas flow controller could be

connected manually to individual cylinders' pressure regulators in succession. See also Subsection

2.1.3.

2.2.4 Pollutant Gas Analyzer

The pollutant gas analyzer must have a well-characterized calibration curve and must be capable

of measuring directly the concentration of both the candidate and the reference standards without

dilution. See Subsection 2.1.7.1. It must have good resolution, good precision, a stable response, and

low output signal noise. In addition, the analyzer should have good specificity for the pollutant of

interest so that it has no detectable response to any other component or contaminant that may be contained

in either the candidate or reference standards. If any component in a multiple-component standard

interferes with the assay of any other component, the analyst must conduct an interference study to

determine an interference correction equation. If the candidate and reference standards contain

dissimilar balance gases (e.g., air versus nitrogen or different pro-portions of oxygen in the balance

air), it must have been demonstrated that the analyzer's response is not sensitive to differences in the

balance gas composition. This demonstration can be accomplished by showing that no difference exists in

the analyzer's response when measuring a compressed gas calibration standard that has been diluted with

identical flow rates of different balance gases.

The analyzer should be connected to a high-precision data acquisition system (e.g., a strip chart

recorder), which must produce an electronic or paper record of the analyzer's response during the assay.

A high-precision digital panel meter, a digital voltmeter, a data logger or some other data acquisition

system with four-digit resolution can be used to obtain numerical values of the analyzer's response. More

precise values will be obtained if this system has a data-averaging capability. The assay record must be

maintained for 3 years after the standard’s certification date.

If the analyzer has not been in continuous operation, turn it on and allow it to stabilize (e.g.,

for at least 12 hours) before beginning the measurements.

2.2.5 Analyzer Calibration

2.2.5.1 Multipoint Calibration—

See Subsections 2.1.7.2 and 2.1.7.4.

2.2.5.2 Analyzer Range—

The range of the analyzer must include the concentrations of the zero gas, the candidate standard

and the reference standard. The concentrations of the candidate and reference standards must fall within

the well-characterized region of the analyzer's calibration curve. In general, the analyst should use

a range that will produce the largest on-scale analyzer response.

2.2.5.3 Linearity—

The data reduction technique used in this procedure requires that the analyzer have a wellcharacterized, but not necessarily linear, calibration curve (see Subsection 2.1.7.5). Highconcentration-range analyzers of the type that are required for this procedure may not be inherently

linear, but in such cases they usually have a predictable, non-linear calibration curve that can be

described by a polynomial equation or can be mathematically transformed to produce a straight-line

calibration curve that is suitable for use in this procedure. Any such polynomial equation or

mathematical transformation should be verified during the multipoint calibration. Caution should be
s

n

#

RRS

100

RRS

2-20

exercised in using a transformed calibration curve because zero or span control adjustments to the

analyzer may produce unexpected effects in the transformed calibration curve.

2.2.5.4 Zero and Span Gas Checks—

See Subsections 2.1.7.3 and 2.1.7.4. Prior to carrying out the assay of the candidate standard,

use zero and span gases to check for calibration drift in the analyzer since the multipoint calibration.

Zero gas and span gas checks must be performed on any day after the multipoint calibration that candidate

standards are assayed. If multiple assays are being performed on the same analyzer range, the analyst

needs to perform only a single set of zero gas and span gas checks for this range. However, another set

must be performed if the range is changed.

The gas mixtures to be used during the zero and span gas checks need not be the same as any of the

reference standards used for the assay of the candidate standard or for the multipoint calibration. The

reference standard for the span gas check must be traceable to a NIST SRM, a SRM-equivalent PRM, or an

NTRM. Information concerning this standard (e.g., cylinder identification number, certified

concentration) must be recorded in the laboratory's records.

A source of clean, dry zero gas is recommended, but not required. The analyst may substitute a

low-concentration, NIST-traceable reference standard for the zero gas if there is reason to believe that

the zero gas reading may not accurately represent the zero-intercept of the calibration equation.

Make three or more discrete measurements of the zero gas and three or more discrete measurements

of the reference standard. "Discrete" means that the analyst must change the gas mixture being sampled

by the analyzer between measurements. For example, the analyst might alternate between measurements of

the reference standard and measurements of the zero gas. Record these measurements in the laboratory's

records. 

Next, verify that the analyzer's precision is acceptable. Calculate the mean and standard

deviation of the analyzer's responses to the zero gas. Repeat the calculations for the reference standard

measurements. These calculations are performed in Step 6 of the spreadsheet described in Appendix A.

Record these calculations in the laboratory's records. The standard error of the mean for each set of

measurements must be less than or equal to 1.0 percent of the mean response to the reference standard.

That is,

where

s = standard deviation of the analyzer's response;

n = the number of independent measurements of the gas mixture; and

= the mean analyzer response to the reference standard.

The value of the standard error of the mean can be made smaller by increasing the number of

measurements. This calculation will enable the analyst to determine how many replicate measurements are

needed during the assay of the candidate standard to obtain acceptable precision. The analyst may wish

to use a data logger or data acquisition system with averaging capability to obtain more precise

measurements. If the value of the standard error of the mean is not acceptable, then the analyzer must be

repaired or another analyzer must be used for the assay. 

Next, verify that excessive calibration drift has not occurred since the multipoint calibration.

For the zero gas measurements, calculate the relative difference (in percent) between the current mean
Relative Difference ' 100 Current Response & Calibration Response

Calibration Response for Reference Standard

.

2-21

analyzer response during the zero gas check and the corresponding response that is predicted from the

multipoint calibration regression equation. That is,

This calculation is performed in Step 6 of the spreadsheet described in Appendix A.

Note that the relative difference is always calculated relative to the calibration response for

the reference standard, even when the zero gas is being measured. Repeat this calculation for the

reference standard measurements. Record these calculations in the laboratory's records. If the reference

standard was not measured during the multipoint calibration, use the regression-predicted response for

a concentration equal to that of the reference standard. 

Then, if the relative differences for the zero and span gas checks are less than or equal to 5.0

percent, the analyzer is considered to be sufficiently in calibration. The zero and span controls need

not be adjusted and the assay may be conducted. The data reduction technique does not require the absolute

accuracy of the analyzer calibration. Some minor calibration drift is acceptable because the effect of

any drift will be corrected during the reduction of the assay data.

However, if the relative difference for either the zero or the span gas check is greater than 5.0

percent, then the analyzer is considered to be out of calibration. A new multipoint calibration may be

conducted before the candidate standard is assayed or the analyzer's zero and span controls may be

adjusted to return the analyzer's response to the original calibration levels. For some analyzers such

as nondispersive infrared instruments, daily changes in environmental variables such as barometric

pressure may shift the calibration. After any adjustment of controls, the analyst should repeat the zero

and span gas checks and recalculate the relative differences to verify that the analyzer is sufficiently

in calibration. The analyzer will be considered to be out of calibration if the relative differences

remain greater than 5.0 percent.

The zero gas and reference standard measurements that are performed for the assay of the candidate

standard may also be used for the zero and span gas checks.

2.2.6 Assay Gases

2.2.6.1 Candidate Standard—

See Subsections 2.1.6 and 2.2.2.

2.2.6.2 Reference Standard—

See Subsections 2.1.2 and 2.2.2. The reference standard used for the assay of the candidate

standard must be a NIST SRM, an SRM-equivalent PRM, an NTRM or a GMIS. This standard need not be the same

as any of the reference standards used for the span gas check or for the multipoint calibration.

Information concerning the reference standard (e.g., cylinder identification number, certified

concentration, etc.) must be recorded in the laboratory's records.

If the multipoint calibration data have been fitted to a linear (i.e., straight-line) regression

model, then only a single reference standard need be measured during the assay of the candidate standard.

If these data have been fitted to a quadratic or higher-order regression model, then at least two reference

standards must be measured. One reference standard is adequate to determine the slope of a linear

equation, but additional reference standards are needed to determine the curvature of quadratic and

higher-order polynomial equations. The concentrations of the additional reference standards should be
2-22

located at the maximum difference between the polynomial curve and the corresponding straight line between

the zero gas and the highest-concentration reference standard.

2.2.6.3 Zero Gas—

See Subsection 2.1.9. A source of clean, dry zero gas is recommended, but not required. The

analyst may substitute a low-concentration, NIST-traceable reference standard for the zero gas during

zero gas checks and assays if there is reason to believe that the zero gas reading may not accurately

represent the zero-intercept of the calibration equation. Information concerning the zero gas should

be recorded in the laboratory's records.

2.2.7 Assay Procedure

1. Verify that the assay apparatus is properly configured, as described in Subsection 2.2.3 and

shown in Figure 2-1. Inspect the analyzer to verify that it appears to be operating normally

and that all controls are set to their expected values. Record these control values in the

laboratory's records.

2. Verify that a multipoint calibration of the analyzer has been performed within 1 month prior

to the assay date. (See Subsections 2.1.7.2, 2.1.7.5 and 2.2.4). Additionally, verify that

the zero and span gas checks indicate that the analyzer is in calibration (see

Subsection 2.2.5.4). Finally, verify that the concentrations of the candidate and reference

standards fall within the well-characterized region of the analyzer's calibration curve (see

Subsection 2.2.2).

3. Measure and adjust the flow rates of the gas mixtures (i.e., reference standard(s), candidate

standard, and zero gas) to approximately the same value that will provide enough flow for the

analyzer and sufficient excess to assure that no ambient air will be drawn into the vent line.

4. In succession, measure the zero gas, the reference standard(s), and the candidate standard(s)

using the analyzer. Use valves V1 and V2 to select each of the gas mixtures for measurement.

For each measurement, allow ample time for the analyzer to achieve a stable response. If the

response for each measurement is not stable, the precision of the measurements will decline

and the candidate standard may not be certifiable under this protocol. Record the analyzer

response for each measurement in the laboratory's records, using the same response units

(e.g., volts, millivolts, percent of scale, etc.) as was used for the multipoint calibration.

At this point, do not convert these data into concentration values using the calibration

equation. Do not perform any necessary mathematical transformation of these data. These

steps will be done later. Do not make any zero control, span control, or other adjustments

to the analyzer during these measurements.

The analyst may assay multiple candidate standards during the same assay session. For

example, a single set of measurements may involve a zero gas, a reference standard and three

candidate standards. Criteria that apply to the assay of one candidate standard apply to the

assay of multiple candidate standards. The analyst should be aware that the effect of any

short-term calibration drift will be greater when multiple candidate standards are assayed.

This greater effect is due to the longer period of time between reference standard

measurements. Unacceptable uncertainties of the estimated concentrations for the candidate

standards may occur as a result of the longer assay session.

5. Conduct at least two additional sets of measurements, as described in step 4 above. However,

for these subsequent sets of measurements, change the order of the three measurements (e.g.,

measure reference standard, zero gas, and candidate standard for the second set and measure

zero gas, candidate standard, and reference standard for the third set). Changing the order
2-23

that the gas mixtures are measured helps the analyst to discover any effect of that one

measurement has on subsequent measurements. The number of sets of measurements will have

been determined during analysis of the multipoint calibration data such that the 95-percent

uncertainty for the regression-predicted concentration of the candidate standard is #1

percent of the concentration of the reference standard.

6. If any one or more of the measurements of a set of measurements is invalid or abnormal for any

reason, discard all three measurements and repeat the measurements. Such measurements may

be discarded if the analyst can demonstrate that the experimental conditions were

inappropriate during these measurements. Data cannot be discarded just because they appear

to be outliers but may be discarded if they satisfy statistical criteria for testing

outliers. The analyst must record any discarded data and a brief explanation as to why these

16

data were discarded in the laboratory's records.

7. The spreadsheet described in Appendix A or equivalent statistical techniques must be used to

calculate an estimated concentration and a 95-percent uncertainty for the candidate standard

based on data from the assay measurements and from the multipoint calibration. The use of

both sets of data in the statistical analysis produces an estimated concentration with

smaller uncertainty while correcting for any minor calibration drift which may have occurred

since the multipoint calibration. Record the estimated concentration and the 95-percent

uncertainty in the laboratory’s records.

The spreadsheet also calculates the percentage of the uncertainty that is due to the

multipoint calibration. This percentage is needed for the total uncertainty calculations

when two or more assays fall under the same multipoint calibration. Record this value in the

laboratory’s records. 

The analyst should investigate any of the measurements that appear to be outliers. Such data

may be discarded if the analyst can demonstrate that the experimental conditions were

inappropriate during these measurements. Data cannot be discarded just because they appear

to be outliers, but may be discarded if they satisfy statistical criteria for testing

outliers. The analyst must record any discarded data and a brief summary of the investigation

in the laboratory’s records.

8. If the multipoint calibration data and the assay data underwent any mathematical

transformations before their statistical analysis, perform the reverse transformations for

the estimated concentration and the 95-percent uncertainty. Record the transformed values

in the laboratory’s records.

2.2.8 Stability Test for Newly Prepared Candidate Standards

Newly prepared candidate standards that contain reactive gas mixtures must be assayed on at least

two dates that are separated by at least 7 days (see Subsections 2.1.6.1 and 2.1.6.2). The spreadsheet

described in Appendix C or equivalent statistical techniques must be used to evaluate the stability of the

candidate standard and to calculate the overall estimated concentration and the total uncertainty for the

candidate standard.

The stability is evaluated by comparing the 95-percent confidence limits (i.e., estimated

concentration ±95-percent uncertainty) for the candidate standard from the two or more assays. If the

confidence limits overlap, the candidate standard can be considered to be stable and may be certified.

In the spreadsheet, all cells in the comparisons table will be “true.” If the confidence limits do not

overlap, the candidate standard may be unstable or there may be analytical problems associated with the

assays or the reference standards. One or more cells in the comparisons table will be “false.” The
2-24

analyst must either disqualify the candidate standard or investigate why the confidence limits do not

overlap. The analyst may conduct additional assays until stability is achieved and add the additional

data to the spreadsheet. Data from a nonoverlapping assay may be discarded and the remaining data used

to determine the overall estimated concentration and the total uncertainty provided the confidence limits

overlap. Record these values and any discarded data in the laboratory’s records.

2.2.9 Certification Documentation

See Subsections 2.1.4 and 2.1.5.

2.2.10 Recertification Requirements

See Subsections 2.1.6.3 and 2.1.6.4.

2.3 PROCEDURE G2: ASSAY AND CERTIFICATION OF A COMPRESSED GAS

CALIBRATION STANDARD USING DILUTION

2.3.1 Applicability

This procedure may be used to assay the concentration of a diluted candidate compressed gas

calibration standard, based on the concentration of a diluted compressed gas reference standard of the

same gas mixture. This procedure allows a specialty gas producer, a standard user, or other analytical

laboratory to certify that the assayed concentration for the candidate standard is traceable to the

reference standard. The procedure employs a low-concentration-range (i.e., ambient air quality level)

pollutant gas analyzer to compare quantitatively diluted gas samples of both the candidate and reference

standards.

Dilution of the candidate and reference standards with zero gas allows greater flexibility in the

range of concentrations of both the candidate and reference standards that can be assayed. Additionally,

dilution allows the use of a low-concentration-range analyzer, which is more likely to have an inherently

linear response than a high-concentration-range analyzer. However, the dilution technique introduces

additional error into the assay which would not be present if the standards were assayed without dilution.

This additional error is measured by an accuracy check of the assay apparatus which is performed as part

of the multipoint calibration.

This procedure may be used for the assay of multiple candidate standards at the same time.

Criteria that apply to the assay of one candidate standard apply to the assay of multiple candidate

standards.

2.3.2 Limitations

1. The concentration of the diluted candidate standard may be greater than or lesser than the

concentration of the diluted reference standard. However, both concentrations must lie

within the well-characterized region of the analyzer's multipoint calibration (see

Subsection 2.1.7.2). 

Additionally, the magnitude of the 95-percent confidence limits for the estimated

concentration of the candidate standard must be #±1 percent of the reference standard

concentration. This criterion may be more restrictive than the corresponding criterion for

the multipoint calibration, but it allows the analyst greater flexibility in the selection

of a reference standard for the assay of a particular candidate standard. For example, assume

that a 70-ppm candidate standard is being assayed using a 50-ppm reference standard and that

the analyzer’s calibration was found to be well characterized between 20 and 80 ppm. The 95-
2-25

percent confidence limits for the candidate standard’s estimated concentration must be #±0.5

ppm.

2. An accurate system for flow measurement and gas dilution is required.

3. The balance gas in both the candidate and reference standards must be identical, unless

either a high dilution flow rate ratio (i.e., at least 50 parts zero gas to 1 part standard)

is used for the assay or it has been demonstrated that the analyzer is insensitive to

differences in the balance gas.

2.3.3 Assay Apparatus

The components of the assay apparatus can be assembled in several different configurations

without diminishing performance. Two possible designs of the assay apparatus are illustrated in Figures

2-3 and 2-4. The former figure shows a configuration in which discrete components (i.e., three-way

valves, gas flow controllers, and a mixing chamber) are used to dilute the reference and candidate

standards. The latter figure shows a configuration in which a commercially available gas dilution system

is used to dilute the standards. Both designs share the important characteristic that the candidate

standard is diluted by the same components that dilute the reference standard.

In Figure 2-3, either zero gas or a diluted standard can be routed to the analyzer by rotation of

three three-way values (i.e., V1, V2, and V3). One gas flow controller (i.e., C1) regulates the flow rates

of the reference and candidate standards. These flow rates can be measured by a single flowmeter connected

to an outlet port on valve V2 or by a flowmeter built into C1. Another gas flow controller (i.e., C2)

regulates the flow rate of the zero gas. This flow rate can be measured by a flowmeter connected to an

outlet port on valve V3 or by a flowmeter built into C2. The gas flow controllers may be needle valves,

capillary tubes, thermal mass flow controllers, or other suitable devices (see Subsection 2.3.7). If

different flow rates are used for the reference and candidate standards during the assay (see Subsection

2.3.6), separate gas flow controllers may be used for the two standards. However, the same flowmeter must

be used to measure the two flow rates to minimize error in the measurement (see Subsection 2.3.7). Flow

rates should be controlled and measured with a relative uncertainty of 1 percent or less. For large

dilutions of the standards, the reference and candidate standard flow rates may be quite small.

Therefore, the internal volume of the tubing and components should be kept small to minimize the flushing

time when valve V1 is rotated.

The mixing chamber combines the two gas streams and should be designed to produce turbulent flow

to ensure thorough mixing of the gas streams. The diluted gas mixtures are routed to the analyzer through

a union tee tube fitting, which vents excess gas flow. Normally, the excess gas is vented to the

atmosphere without any obstructions in the tubing and the gas entering the analyzer is at near-atmospheric

pressure. However, the excess gas can be routed through an uncalibrated rotameter by rotation of a threeway valve (i.e., V4). The rotameter is used to demonstrate that the total gas flow rate exceeds the sample

flow rate of the analyzer and that no room air is being drawn in through the vent line.
2-26
2-27
2-28

The apparatus in Figure 2-3 may be modified in several ways that will not diminish its performance.

For example, the three-way valves could be replaced by solenoid valves. Alternatively, valve V1 could be

replaced by a single length of tubing that is connected manually to the two standards' pressure regulators

in succession (see also Subsection 2.1.3).

In Figure 2-4, the reference and candidate standards are diluted with a gas dilution system. This

gas dilution system may use capillary tubes, positive-displacement pumps, thermal mass flow controllers,

or other suitable devices to dilute the standards. If a gas dilution system is used, it must have a

specified accuracy of not greater than 1.0 percent of the undiluted reference standard concentration.

The analyst must check the accuracy of the gas dilution system during the multipoint calibration (see

Subsections 2.1.7.2 and 2.3.5.1).

2.3.4 Pollutant Gas Analyzer

The pollutant gas analyzer must have a well-characterized calibration curve and must have a range

that is capable of measuring the diluted concentration of both the candidate and the reference standards

(see Subsection 2.1.7.1). It must have good resolution, good precision, a stable response, and low output

signal noise. In addition, the analyzer should have good specificity for the pollutant of interest so that

it has no detectable response to any other component or contaminant that may be contained in either the

candidate or reference standards. If any com-ponent in a multiple-component standard interferes with the

assay of any other component, the analyst must conduct an interference study to determine an interference

correction equation. A suitable analyzer with acceptable performance specifications may be selected from

the list of EPA-designated reference and equivalent method analyzers. If the candidate and reference

17

standards contain dissimilar balance gases (e.g., air versus nitrogen or different proportions of oxygen

in the balance air), either a high dilution flow-rate ratio (i.e., at least 50 parts zero gas to 1 part

standard) should be used or it must have been demonstrated that the analyzer's response is not sensitive

to differences in the balance gas composition. This demonstration may be accomplished by showing that no

difference exists in an analyzer's response when measuring a compressed gas calibration standard that has

been diluted with identical flow rates of different balance gases.

The analyzer should be connected to a high-precision data acquisition system (e.g., a strip chart

recorder) which must produce an electronic or paper record of the analyzer's response during the assay.

A high-precision digital panel meter, a digital voltmeter, a data logger or some other data acquisition

system with four-digit resolution can be used to obtain numerical values of the analyzer's response. More

precise values will be obtained if this system has a data-averaging capability. The assay record must be

maintained for 3 years after the standard’s certification date.

If the analyzer has not been in continuous operation, turn it on and allow it to stabilize (e.g.,

for at least 12 hours) before beginning any measurements.

2.3.5. Analyzer Calibration

2.3.5.1 Multipoint Calibration—

See Subsections 2.1.7.2 and 2.1.7.4. Following completion of the multipoint calibration, the

accuracy of the assay apparatus must be checked to verify that the error associated with the dilution is

not excessive. This accuracy check involves the measurement of an undiluted or diluted check standard.

The check standard must be an SRM, an SRM-equivalent PRM, or an NTRM, or a GMIS as specified in Subsection

2.1.2. It must have a certified concentration that is different from that of the reference standard used

in the multipoint calibration. Information concerning this standard (e.g., cylinder identification

number, certified concentration) must be recorded in the laboratory's records.
Relative Difference ' 100 Mean Analyzer Response & Predicted Response

Predicted Response

.

2-29

If an undiluted check standard is used, its concentration must fall in the well-characterized

region of the calibration curve. If a diluted check standard is used, the diluted concentration must fall

in the well-characterized region.

Make three or more discrete measurements of the undiluted or diluted check standard. "Discrete"

means that the analyst must change the gas mixture being sampled by the analyzer between measurements.

For example, the analyst might alternate between measurements of the check standard and the zero gas.

Record these measurements in the laboratory's records.

Next the analyst must verify that the dilution error is not excessive. For the check standard

measurements, calculate the relative difference (in percent) between the mean analyzer response and the

corresponding response that is predicted from the multipoint calibration regression equation and the

undiluted or diluted check standard concentration. That is,

If the relative difference is greater than 1.0 percent, the dilution error is considered to be

excessive. The analyst must investigate why the relative difference is excessive. The problem may be due

to errors in the reference standard and check standard concentrations, errors in assay apparatus or to

some other source. Assays may not be conducted until the relative difference for a subsequent accuracy

check is less than or equal to 1.0 percent.

2.3.5.2 Analyzer Range—

The range of the analyzer must include the concentrations of the zero gas and of the diluted

candidate and reference standards (see Subsection 2.3.6). The concentrations of the diluted reference

and candidate standards must fall within the well-characterized region of the analyzer's calibration

curve. Because the selection of the dilution ratio or ratios to be used in the assay provides great

flexibility in the choice of concentrations to be measured by the analyzer, the analyzer range should be

selected based on optimum accuracy, stability, and linearity.

2.3.5.3 Linearity—

The data reduction technique used in this procedure requires that the analyzer have a wellcharacterized, but not necessarily linear, calibration curve (see Subsection 2.1.7.5). Many

lower-concentration analyzers of the type that may be used for this procedure have straight-line

calibration curves. If not, they usually have a predictable nonlinear calibration curve that can be

described by a polynomial equation or can be mathematically transformed to produce a straight-line

calibration curve suitable for use in this procedure. Any such polynomial equation or mathematical

transformation should be verified during the multipoint calibration. Caution should be exercised in using

a transformed calibration curve because zero or span control adjustments to the analyzer may produce

unexpected effects in the transformed calibration curve.

2.3.5.4 Zero and Span Gas Checks—

See Subsections 2.1.7.3 and 2.1.7.4. Prior to carrying out the assay of the candidate standard,

use zero and span gases to check for calibration drift in the analyzer since the multipoint calibration.

Zero gas and span gas checks must be performed on any day after the multipoint calibration that candidate

standards are assayed. If multiple assays are being performed on the same analyzer range, the analyst

needs to perform only a single set of zero gas and span gas checks. However, another set must be performed

if the range is changed.

The gas mixtures to be used during the zero and span gas checks need not be the same as any of the

reference standards used for the assay of the diluted candidate standard or for the multipoint
s

n

#

RDRS

100

Relative Difference ' 100 Current Response & Calibration Response

Calibration Response for Diluted Reference Standard

.

RDRS

2-30

calibration. The reference standard for the span gas check must be traceable to a NIST SRM, an SRMequivalent PRM, or an NTRM. Information concerning this standard (e.g., cylinder identification number,

certified concentration) must be recorded in the laboratory's records.

Make three or more discrete measurements of the zero gas and three or more independent

measurements of the diluted reference standard. Record these measurements in the laboratory's records.

Next, the analyst must verify that the analyzer's precision is acceptable. Calculate the mean

and standard deviation of the analyzer's response to the zero gas. Repeat these calculations for the

diluted reference standard measurements. These calculations are performed in Step 6 of the spreadsheet

described in Appendix A. Record these calculations in the laboratory's records. The standard error of

the mean for each set of measurements must be less than or equal to 1.0 percent of the mean response to the

diluted reference standard. That is,

where

s = standard deviation of the analyzer's response;

n = the number of independent measurements of the gas mixture; and

 = the mean analyzer response to the diluted reference standard.

The value of the standard error of the mean can be made smaller by increasing the number of

measurements. This calculation will enable the analyst to determine how many replicate measurements are

needed during the assay of the diluted candidate standard to obtain acceptable precision. The analyst may

wish to use a data logger or data acquisition system with data averaging capability to obtain more precise

measurements. If the value of the standard error of the mean is not acceptable, then the analyzer must be

repaired or another analyzer must be used for the assay.

Next the analyst must verify that excessive calibration drift has not occurred since the

multipoint calibration. For the zero gas measurements, calculate the relative difference (in percent)

between the mean analyzer response during the zero gas check and the corresponding response that is

predicted from the multipoint calibration regression equation. That is,

This calculation is performed in Step 6 of the spreadsheet described in Appendix A.

Note that the relative difference is always calculated relative to the calibration response for

the diluted reference standard, even when zero gas is being measured. Repeat this calculation for the

diluted reference standard measurements. Record these calculations in the laboratory's records. If the

diluted reference standard was not measured during the multipoint calibration, use the regressionpredicted response for a concentration equal to that of the diluted reference standard.

Then, if the relative differences for the zero and span checks are less than or equal to 5.0

percent, the analyzer is considered to be in calibration. The zero and span controls need not be adjusted

and the assay may be conducted. The data reduction technique used in this procedure does not require the
2-31

absolute accuracy of the analyzer's calibration. Some minor calibration drift is acceptable because the

drift will be corrected for during the reduction of the assay data.

However, if the relative difference for either the zero or the span gas checks is greater than 5.0

percent, then the analyzer is considered to be out of calibration. A new multipoint calibration may be

conducted before the candidate standard is assayed or the analyzer's zero and span controls may be

adjusted to return the analyzer's response to the original calibration levels. For some analyzers such

as nondispersive infrared instruments, daily changes in environmental variables such as barometric

pressure may shift the calibration. After any adjustment of the controls, the analyst should repeat the

zero and span gas checks and recalculate the relative differences to verify that the analyzer is

sufficiently in calibration. The analyzer will be considered to be out of calibration if the relative

differences remain greater than 5.0 percent.

The zero gas and diluted reference standard measurements that are performed for the assay of the

diluted candidate standard may also be used for the zero gas and span gas checks. 

2.3.6 Selection of Gas Dilution Flow Rates or Gas Concentration Settings

The flow rates or settings used for the zero gas, reference standard, and candidate standard

should be selected carefully to provide diluted concentrations for both the candidate and reference

standards that fall in the well-characterized region of the analyzer's calibration curve. The diluted

concentration of the candidate standard may be greater than or lesser than the diluted concentration of

the reference standard. Any assay error due to the dilution process will be reduced if the same dilution

flow-rate ratio or concentration setting can be used for both the candidate and reference standards.

Select the diluted concentrations of the reference and candidate standards, and select flow rates or

concentration settings that will produce the highest analyzer responses within the well-characterized

region of the analyzer's calibration curve.

If the same dilution flow-rate ratio or concentration setting cannot be used for both the

candidate and reference standards, select different ratios or settings for the candidate and reference

standards to produce concentrations that are approximately equal and that fall in the well-characterized

region of the analyzer's calibration curve. Select flow rates or settings such that only one of the

apparatus controls must be adjusted when switching from the reference standard to the candidate standard,

or vice versa. Where a choice of analyzer ranges is available, higher dilution ratios or lower

concentration settings will reduce the consumption of the standards.

2.3.7 Flowmeter Type and Flowmeter Calibration

Figure 2-3 shows flow measurement ports on valves V2 and V3. In this configuration, a single

flowmeter can be used to measure both the standard flow rate and the zero gas flow rate. Such an approach

would reduce measurement errors arising from differences in the calibration of multiple flowmeters.

Alternatively, the flow rates can be measured at the outlet of the dilution apparatus, with the rotameter

vent temporarily plugged. In either case, a NIST-traceable volumetric flowmeter such as a wet test meter,

a thermal mass flowmeter, or a soap bubble flowmeter can be used (see Subsection 2.1.2). Each flow rate

must be measured separately while the other flow rates are set to zero. Care must be exercised to ensure

that each measured flow rate remains constant when combined with the other flow rate(s) and between the

time of measurement and the time of the assay. Additionally, care must be taken to ensure that the

flowmeter does not cause any back pressure in the gas stream and any resulting change in the flow rate

through the flow controller.

If in-line flowmeters are mounted directly downstream of the flow controllers, they may not

operate at atmospheric pressure because of back pressure from downstream components. Also, this back

pressure may vary as a function of the total flow rate. Thus, the flowmeters must compensate for the

variable in-line pressure. Thermal mass flowmeters do not need to be corrected for pressure effects.
Flow Rate '

Volume

Time

PM& PWV

PS

TS

TM

2-32

Measurements from pressure-sensitive flowmeters such as rotameters or from volumetric flowmeters such

as wet test meters must be carefully corrected for the actual gas pressure during the flow measurement.

An in-line flowmeter must not contaminate or react with the gas mixture passing through it.

The flowmeters used should be stable, repeatable, and linear and have good resolution. If

possible, select flow rates or a flowmeter range such that the flow rates to be measured fall in the upper

half of the flowmeter's range. The flowmeters should be carefully calibrated at several flow rates to

prove linearity. The calibration should be accurate to plus or minus 1 percent and must be referenced to

an accurate flow rate or volumetric standard traceable to a NIST primary standard. Flowmeter calibrations

should be checked and recertified periodically, as determined by stability information such as a

chronological control chart of calibration data. 

Allvolumetric flow-rate measurements must be corrected or referenced to the same temperature and

pressure conditions, such as EPA-standard conditions (i.e., 760 millimeters of mercury (mm Hg), 25 EC)

or the ambient temperature and pressure conditions prevailing in the laboratory during the assay.

Measurements using wet test meters and soap bubble flowmeters also must be corrected for the saturation

of the gas stream with water vapor in the moist interiors of these flowmeters. The equation to correct the

flow rate for temperature, pressure, and humidity effects is given below:

where

PM = measured barometric pressure (mm Hg);

PWV = partial pressure of water vapor (mm Hg);

P = standard pressure (mm Hg); S

TS = standard temperature (298.2 K); and

TM = measured ambient temperature (273.2 + EC).

Measurement of reference and candidate standard flow rates with the same flowmeter and

measurement of both dilution zero gas flow rates with the same flowmeter tend to reduce measurement

errors, associated with the use of multiple flowmeters. These errors are more pronounced at higher

dilution flow rate ratios. Note that the impact of any flow measurement error is reduced if the same

dilution ratio can be used for both the reference standard and candidate standard measurements.

2.3.8 Assay Gases

2.3.8.1 Candidate Standard—

See Subsections 2.1.6, 2.3.2, and 2.3.6.

2.3.8.2 Reference Standard—

See Subsections 2.1.2, 2.1.6.4, 2.3.2, and 2.3.6. The reference standard used for the assay of

the candidate standard must be a NIST SRM, an SRM-equivalent PRM, an NTRM or a GMIS. This standard need

not be the same as any of the reference standards used for the span gas check or for the multipoint

calibration. Information concerning the reference standard (e.g., cylinder identification number,

certified concentration, etc.) must be recorded in the laboratory’s records.

If the multipoint calibration data have been fitted to a linear (i.e., straight-line) model, then only a

single reference standard need be measured during the assay of the candidate standard. If these data have
Diluted Standard Conc. '

(Undiluted Standard Conc.) (Standard Flow Rate)

(Standard Flow Rate % Zero Gas Flow Rate)

.

2-33

been fitted to a quadratic or higher-order polynomial model, then at least two reference standards must

be measured. One reference standard is adequate to determine the slope of a linear equation, but

additional reference standards are needed to determine the curvature of quadratic or higher-order

polynomial equations. The concentrations of the additional reference standards should be located at the

maximum difference between the polynomial curve and the corresponding straight line between the zero gas

and the highest-concentration reference standard.

2.3.8.3 Zero Gas—

See Subsection 2.1.9. Use the same zero gas for dilution of both candidate and reference gases.

The analyst may substitute a low-concentration, NIST-traceable reference standard for the zero gas in zero

gas checks and assays if there is reason to believe that the zero gas reading may not accurately represent

the zero-intercept of the calibration equation. Information concerning the zero gas should be recorded

in the laboratory's records.

2.3.9 Assay Procedure

1. Verify that the assay apparatus is properly configured as shown in Figure 2-3 or Figure

2-4 and as described in Subsection 2.3.3. Inspect the analyzer to verify that it appears

to be operating normally and that all controls are set to their expected values. Record

these control values in the laboratory's records.

2. Verify that the flowmeters, if used in the assay apparatus, are properly calibrated (see

Subsection 2.3.7).

3. Verify that a multipoint calibration of the analyzer has been performed within 1 month

prior to the assay date and that the dilution error is not excessive (see Subsections

2.1.7.2, 2.1.7.5, 2.3.4, and 2.3.5.1). Additionally, verify that the zero and span gas

checks indicate that the analyzer is in calibration (see Subsection 2.3.5.4). Finally,

verify that the concentrations of the diluted reference and candidate standards fall

within the well-characterized region of the analyzer's calibration curve (see Subsection

2.3.2).

4. Determine and establish the flow rates or concentration settings of the gas mixtures

(i.e., reference standard(s), candidate standard, and zero gas) that will be used for the

assay (see Subsections 2.3.6, 2.3.7, and 2.3.5.2). Also check that the total flow rate

coming from the mixing chamber will provide enough flow for the analyzer and sufficient

excess to ensure that no ambient air will be drawn into the vent line. Changes in the

sample pressure may change the calibration curve. When using the same flow rates for both

candidate and reference standards, carefully set the delivery pressures of the two

standards' pressure regulators to the same value so that there is no change in the flow

rate when switching from one standard to the other.

Calculate the diluted reference standards' concentration using the following equation:

Record the measured flow rates and the undiluted and diluted reference standard

concentrations in the laboratory's records.
2-34

5. In succession, measure the zero gas, the diluted reference standard(s) and the diluted

candidate standard using the analyzer. For each measurement, adjust the flow rates, if

necessary, to those determined in step 4, and allow ample time for the analyzer to achieve

a stable reading. If the reading for each measurement is not stable, the precision of the

measurements will decline and the candidate standard might not be certifiable under this

protocol. Record the analyzer response for each measurement, using the same response

units (e.g., volts, millivolts, percent of scale, etc.) as was used for the multipoint

calibration. At this point, do not convert the data into concentration values using the

calibration equation. Do not perform any mathematical transformations of the data. These

steps will be done later. Do not make any zero control, span control, or other adjustments

to the analyzer during this set of measurements. Record these analyzer responses in the

laboratory's records.

The analyst may assay multiple candidate standards during the same assay session. For

example, a single set of measurements may involve a zero gas, a diluted reference

standard, and three diluted candidate standards. Criteria that apply to the assay of one

candidate standard apply to the assay of multiple candidate standards. The analyst should

be aware that the effect of any short-term calibration drift will be greater when multiple

candidate standards are assayed. This greater effect is due to the longer period of time

between reference standard measurements. Unacceptable uncertainties of the estimated

concentrations for the diluted candidate standards may occur as a result of the longer

assay session.

6. Conduct at least two additional sets of measurements, as described in step 5 above.

However, for these subsequent sets of measurements, change the order of the three

measurements (e.g., measure the reference standard, zero gas, and candidate standard for

the second set and measure the zero gas, candidate standard, and reference standard for

the third set, etc.). Changing the order that the gas mixtures are measured helps the

analystto discover any effect that one measurement has on subsequent measurements. The

number of sets of measurements will have been determined during the analysis of the

multipoint calibration data such that the 95-percent uncertainty for the regressionpredicted concentration of the candidate standard is #1 percent of the concentration of

the reference standard.

7. If any one or more of the measurements of a set of measurements is invalid or abnormal for

any reason, discard all three measurements and repeat the set of measurements. Such

measurements may be discarded if the analyst can demonstrate that the experimental

conditions were inappropriate during these measurements. Data cannot be discarded just

because they appear to be outliers, but may be discarded if they satisfy statistical

criteria for testing outliers. The analyst must record the discarded data and a brief 15

explanation as to why these data were discarded in the laboratory's records.

8. The spreadsheet described in Appendix A or equivalent statistical techniques must be used

to calculate an estimated concentration and a 95-percent uncertainty for the candidate

standard based on data from the assay measurements and from the multipoint calibration.

The use of both sets of data in the statistical analysis produces an estimated

concentration with smaller uncertainty while correcting for any minor calibration drift

that may have occurred since the multipoint calibration. Record the estimated

concentration and the 95-percent uncertainty in the labora-tory’s records.

The spreadsheet also calculates the percentage of the uncertainty that is due to the

multipoint calibration. This percentage is needed for the total uncertainty calcula-
Certified Undiluted Conc. '

(Mean Diluted Conc.) (Total Gas Flow Rate)

(Standard Flow Rate)

where Total Gas Flow Rate ' Standard Flow Rate % Zero Gas Flow Rate .

2-35

tions when two or more assays fall under the same multipoint calibration. Record this

value in the laboratory’s records. 

The analyst should investigate any of the measurements that appear to be outliers. Such

data may be discarded if the analyst can demonstrate that the experimental conditions were

inappropriate during these measurements. Data cannot be dis-carded just because they

appear to be outliers, but may be discarded if they satisfy statistical criteria for

testing outliers. The analyst must record any discarded data as well as a brief summary

of the investigation in the laboratory’s records.

9. If the multipoint calibration data and the assay data underwent any mathematical

transformations before their statistical analysis, perform the reverse transformations

for the estimated concentration and the 95-percent uncertainty. Record the trans-formed

values in the laboratory’s records.

10. Finally, the certified undiluted concentration for a candidate standard containing a

unreactive gas mixture and requiring only a single assay can be calculated from the mean

concentration of the diluted candidate standard as follows:

2.3.10 Stability Test for Newly Prepared Standards

Newly prepared candidate standards that contain reactive gas mixtures must be assayed on at least

two dates that are separated by at least 7 days. See Subsections 2.1.6.1 and 2.1.6.2. The spreadsheet

described in Appendix C or equivalent statistical techniques must be used to evaluate the stability of the

candidate standard and to calculate the overall estimated concentration and the total uncertainty for the

candidate standard.

The stability is evaluated by comparing the 95-percent confidence limits (i.e., estimated

concentration ±95-percent uncertainty) for the candidate standard from the two or more assays. If the

confidence limits overlap, the candidate standard can be considered to be stable and may be certified.

In the spreadsheet, all cells in the comparisons table will be “true.” If the confidence limits do not

overlap, the candidate standard may be unstable or there may be analytical problems associated with the

assays or the reference standards. One or more cells in the comparisons table will be “false.” The

analyst must either disqualify the candidate standard or investigate why the confidence limits do not

overlap. The analyst may conduct additional assays until stability is achieved and add the additional

data to the spreadsheet. Data from a nonoverlapping assay may be discarded and the remaining data used

to determine the overall estimated concentration and the total uncertainty provided the confidence limits

overlap. Finally calculate a certified undiluted concentration using the above equation. Record these

values and any discarded data in the laboratory’s records. 

2.3.11 Certification Documentation

See Subsections 2.1.4 and 2.1.5.

2.3.12 Recertification Requirements
2-36

See Subsections 2.1.6.3 and 2.1.6.4.
2-19

Figure 2-2. One possible design of the apparatus for the assay of compressed 

gas calibration standards without dilution (Procedure G1)
2-27

Figure 2-3. One possible design of the apparatus using flow controllers for assay

of compressed gas calibration standards with dilution (Procedure G2)
2-28

Figure 2-4. One possible design of the apparatus using a gas dilution system for

assay of compressed gas calibration standards with dilution (Procedure G2)
3-1

SECTION 3

EPA TRACEABILITY PROTOCOL FOR ASSAY AND CERTIFICATION OF

PERMEATION DEVICE CALIBRATION STANDARDS

3.1 GENERAL INFORMATION

3.1.1 Purpose and Scope of the Protocol

This protocol describes three procedures for assaying the permeation rate of a permeation device

calibration standard and for certifying that the assayed permeation rate is traceable to National

Institute of Standards and Technology (NIST) reference standards. This protocol is mandatory for

certifying the permeation device calibration standards used for the pollutant monitoring that is required

by the regulations of the Code of Federal Regulations, Chapter 40, Parts 50 and 58 for the calibration

3,4

and audit of ambient air quality analyzers. This protocol covers the assay and certification of sulfur

dioxide (SO2) and nitrogen dioxide (NO2) permeation device calibration standards. This protocol may be

used by permeation device producers, standard users, or other analytical laboratories. The assay

procedure may involve the comparison of these standards to permeation device reference standards (i.e.,

Procedure P1), to compressed gas reference standards (i.e., Procedure P2), or to mass reference standards

(i.e., Procedure P3).

3.1.2 Reference Standards

Thepermeation device reference standards that may be used under this protocol are NIST Standard

Reference Material (SRM) numbers 1625 and 1626. These SRMs (listed in Table 3.1) are permeation tubes

containing SO2. In the future, NIST may develop additional SRMs, which may be used as reference standards

under this protocol.

The compressed gas reference standards that may be used under this protocol are NIST SRMs,

Netherlands Measurement Institute Primary Reference Materials (NMi PRMs) that are equivalent to SRMs,

NIST traceable reference materials (NTRMs), or gas manufacturer's intermediate standards (GMISs). These

standards are described in Subsection 2.1.2 of this report.

The uncertainty of SRMs, NTRMs, and PRMs is expressed as a 95-percent confidence interval, which

is the one-sigma uncertainty multiplied by a coverage factor almost always equal to 2. This estimate 9

includes allowances for the uncertainties of known sources of systematic error as well as the random error

of measurement. A value of one-half of the stated uncertainty of these reference standards should be used

in calculating the total analytical uncertainty of standards that are certified under this protocol (see

Appendix C).

Mass reference standards that may be used under this protocol must be traceable to NIST mass

standards. Additionally, they must have an individual tolerance of no more than 0.05 mg. Examples of

18-20

mass reference standards that meet these specifications are American National Standards

Institute/American Society for Testing and Materials (ANSI/ASTM) Classes 1, 3, and 4. The mass reference
3-2

TABLE 3-1. NIST SRM PERMEATION DEVICE REFERENCE STANDARDS

NIST

 SRM no.

Permeation

 device type

Device

 length

(cm)

Nominal permeation

rate at 30 EC (μg/min)

Nominalconcentration (in μmol/mol)

at various dilution gas flow rates

(L/min)

1 5 10

1625 Sulfur dioxide 10 3.7 1.4 0.28 0.14

1626 Sulfur dioxide 5 2.1 0.8 0.16 0.08

standards must be recalibrated on a regular basis (e.g., yearly) at a NIST-accredited State weights and

measures laboratory or at a calibration laboratory that is accredited by the National Voluntary Laboratory

Accreditation Program (NVLAP), which is administered by NIST, or by the International Laboratory 10,11

Accreditation Conference (ILAC). The recalibration frequency is to be determined from records of previous

recalibrations of these standards.

Two separate sets of mass reference standards are recommended. Working calibration standards

should be used for routine permeation device weighings and should be kept next to the analytical balance

in a protective container. Laboratory primary standards should be handled very carefully and should be

kept in a locked compartment. The working standards should be compared to the laboratory primary

standards every 3 or 6 months to check for mass shifts associated with handling or contamination. The

current masses of the working standards as traced to the laboratory primary standards should be recorded

in a laboratory notebook and should be used to check the calibration of the analytical balance.

Always use smooth, nonmetallic forceps for handling mass reference standards. The standards are

handled only with these forceps, which are not used for any other purpose. Mark these forceps to

distinguish them from the forceps that are used to handle permeation devices. Handle the standards

carefully to avoid damage that may alter their masses.

The temperature reference standards that may be used under this protocol must be liquid-in-glass

thermometers having scale tolerances and uncertainties that conform to NIST Special Publication 250-23.21

They must have an uncertainty of no more than 0.05 (EC). The thermometers must have serial numbers etched

or permanently marked into the glass and a manufacturer's calibration certificate of traceability to NIST

standards. They must be recalibrated on a regular schedule (e.g., yearly) according to NIST guidelines22

by the user, a NIST-accredited State weights and measures laboratory, or an NVLAP- or ILAC-accredited

calibration laboratory.

3.1.3 Selecting a Procedure

Procedures P1 and P2 are applicable to the assay and certification of candidate permeation device

calibration standards using an ambient air quality analyzer. Procedure P1 provides for the assay to be

referenced to a permeation device reference standard. Procedure P2 provides for the assay to be

referenced to a compressed gas reference standard.

Procedure P3 is applicable to the assay and certification of candidate standards using an

analytical balance. This procedure provides for the assay to be referenced to a mass reference standard.
3-3

3.1.4 Using the Protocol

The assay/certification protocol described here is designed to minimize both systematic and

random errors in the assay process. Therefore, the protocol should be carried out exactly as it is

described. The assay procedures in this protocol include one possible design for the assay apparatus.

The analyst is not required to use this design and may use alternative components and configurations that

produce equivalent-quality measurements. Nonreactive materials (e.g., Teflon , stainless steel, or ®

glass) and clean, noncontaminating components should be used in those portions of the apparatus that are

in contact with the gas mixtures being assayed.

3.1.5 Certification Documentation

Each certified permeation device calibration standard must be documented in a written

certification report and this report must contain at least the following information:

1. Permeation device identification number;

2. The contents of the permeation device;

3. Certified permeation rate (in nanograms (ng) per minute);

4. The certification temperature (in EC to the nearest 0.1E);

5. The dilution gas (i.e., air or nitrogen) used during the assay (for procedures P1 and P2);

6. Date of the assay/certification;

7. Identification of the reference standards used in the assay: NIST SRM number, NIST sample

number, and certified concentration or permeation rate for an SRM; cylinder identification

number and certified concentration for an SRM-equivalent PRM, an NTRM or GMIS; manufacturer,

model number and serial number for a mass or temperature reference standard. The

certification documentation must identify the type of reference standard used in the assay;

8. Statement that the assay/certification was performed according to this protocol and that

lists the assay procedure (e.g., Procedure P1) used;

9. The analytical method that was used in the assay;

10. Identification of the laboratory where the standard was assayed and certified;

11. Chronological record of all certifications for the standard by the certifying laboratory;

12. A statement that the standard will retain its certification only as long as 5 percent of the

original liquid weight or a visible amount of liquid remains in it;

13. The environmental exposure conditions (e.g., temperature and moisture) that will invalidate

the certification; and

14. A statement of the overall analytical uncertainty estimate associated with the assay of the

candidate standard. The estimate must include the uncertainty associated with the reference

standard. 
3-4

This certification documentation must be given to the purchaser of the standard. The permeation device

producer must maintain laboratory records and certification documentation for 3 years after the

standard's certification date. A permeation device producer or other vendor may redocument an assayed

and certified standard that it has purchased from another permeation device producer and that it wishes

to sell to a third party. However, the new certification documentation must clearly list the permeation

device producer or other laboratory where the standard was assayed.

3.1.6 Certification Label

The permeation device calibration standard must be labeled with its identification number.

3.1.7 Assay/Certification of Candidate Permeation Device Calibration Standards

3.1.7.1 Permeation Device Design—

Permeation devices are designed and constructed in various ways, but all devices consist of a

sealed chamber containing liquified gas and a permeable area through which the gas is allowed to permeate.

The permeated gas is swept and diluted with a measured volumetric flow rate of dry air or nitrogen to

create a quantitative concentration of the pollutant gas.

3.1.7.2 Precautions for Use and Storage of Permeation Devices—

The permeation rate of all permeation devices is critically dependent on temperature; a

permeation device is useful as a concentration standard only when its temperature is precisely controlled

and accurately measured, and an accurately metered dilution gas flow rate is provided.

The inaccuracy of gaseous pollutant concentration standards that are produced by permeation

devices may increase due to physical or chemical sorption of the permeated gas in the permeation system.

This sorption will have a larger effect on the inaccuracy as the concentration decreases. Nonreactive

materials (e.g., Teflon , stainless steel, or glass) and clean, noncon-taminating components should be ®

used in those portions of the permeation system that are in contact with the permeated gas.

The reproducibility of the certified permeation rate of a permeation device may be adversely

affected by exposure of the device to temperatures greater than the specified operating or storage

temperature range for the device or by exposure to excessive moisture. NO2 permeation devices must be

stored under dry conditions and preferably at a temperature between 20 and 35 EC, or as otherwise

recommended by the manufacturer. SO permeation devices may be refrigerated for storage. 2

It appears that there is a limited temperature range at which NO2 permeation devices can be used

as standards. This temperature range is conservatively given as 20 to 35 EC. Low or high temperature

23

storage of NO permeation devices is not recommended. 2

NO2 permeation devices should be stored in and used in dry dilution gas. One study showed that NO 2

permeation rates were significantly lower in moderately humid air (i.e., 30 to 40 percent relative

humidity) than in dry air on the preceding day. Furthermore, the permeation rates did not return to the

24

original levels after dry air had passed over the device for 24 hours. Another study found that NO2

concentrations from a permeation device declined by about one-third as relative humidity levels increased

from 0 to 100 percent.25

Candidate standards being certified under Procedure P3 must be stored under constant temperature

conditions between assays. A storage container for this application is described in the procedure.

When stored at a temperature other than the assay temperature, some permeation devices require

an equilibration period at the assay temperature to reach thermal equilibrium and a stable, accurate
3-5

permeation rate. When transferred from a different storage temperature, thin-walled permeation devices

should be maintained at the assay temperature with a fixed dilution flow rate for at least 48 hours before

use or before certification. Temperature changes of >10 EC may require equilibration periods of up to 15

days for NO permeation devices to attain a stable permeation rate. Upon return to the original 2

23,26

temperature,some devices may not return to the same permeation rate as before the temperature change.

Other types of permeation devices may require longer equilibration periods. Observe any manufacturer's

recommendations for equilibration and use.

3.1.7.3 Equilibration of Newly Prepared Permeation Devices—

A newly prepared permeation device must be equilibrated for at least 48 hours at the assay

temperature before being assayed for the first time. The equilibration period may be 100 hours or longer

for some permeation devices. This period will vary as a function of the permeating compound, the material

26

and the thickness of the permeating surface and the temperature.

3.1.7.4 Certification Conditions for Permeation Device Calibration Standards—

A standard will retain its certification only as long as 5 percent of the original liquid weight

or a visible amount of liquid remains in it. A standard loses its certification if it is exposed for

prolonged periods of time to excessive moisture or to temperatures greater than 15 EC above its

certification temperature. A standard that loses its certification must be reassayed before it can be

certified for further use.

3.1.8 Technical Variances

Permeation device producers, standard users, and other analytical laboratories may petition the

U.S. EPA for technical variances to the assay procedures in this protocol. A technical variance allows

the use of a specific alternative assay procedure for candidate standards, which can be certified under

this protocol. The petitioner must send a written request with a detailed description of the alternative

assay procedure and supporting analytical data to Work Assignment Manager, EPA Traceability Protocol

Project, U.S. EPA, Mail Code 47, Research Triangle Park, NC 27711. The supporting analytical data must

demonstratethe equivalence of the alternative assay procedure with the procedures given in this protocol.

Technical variances may also be given for alternative temperature ranges of certifying or storing

permeation devices provided that supporting analytical data are provided with the written request.

Permeation device producers, standard users, and other analytical laboratories may petition the

U.S. EPA to allow the assay and certification of permeation devices that contain gases or liquified gases

other than SO2 and NO2. The petitioner must send a written request with a detailed description of the

permeation device and supporting analytical data to the EPA Work Assignment Manager at the address given

above. The supporting analytical data must demonstrate that the permeation rate for the proposed device

can be accurately determined, that only the specified compound is permeating, that the rate is stable over

the lifetime of the device, and that the rate is not changed by temperature and humidity effects.

3.2 PROCEDURE P1: ASSAY AND CERTIFICATION OF PERMEATION DEVICE

CALIBRATION STANDARDS REFERENCED TO A PERMEATION DEVICE

REFERENCE STANDARD

3.2.1 Applicability

This procedure may be used to assay the permeation rate of a candidate SO2 or NO 2 permeation device

calibrationstandard, based on the permeation rate of a permeation device reference standard of the same

pollutant compound, and to certify that the assayed permeation rate is traceable to the reference

standard. The procedure employs a low-concentration range (i.e., ambient air quality level) pollutant

gas analyzer to compare quantitatively diluted concentrations from the two permeation devices for the
3-6

assayof the candidate device. This procedure may be used for the assay of multiple candidate standards

during the same assay session. Criteria that apply to the assay of one candidate standard apply to the

assay of multiple candidate standards. This procedure may be used by permeation device producers,

standard users, or other analytical laboratories.

3.2.2 Limitations

1. The permeation rate of the candidate standard may be greater than or lesser than the

permeation rate of the reference standard. However, the diluted concentrations from both

standards must lie within the well-characterized region of the analyzer's multipoint

calibration (see Subsection 2.1.7.2). Additionally, the 95-percent uncertainty for the

regression-predicted concentration of the diluted candidate standard must be 1.0 percent

of the concentration of the diluted reference standard. This uncertainty is obtained from

the statistical analysis of the multipoint calibration data using the spreadsheet described

in Appendix A or using equivalent statistical techniques (e.g., the worksheet for linear

relationships given in Chapter 5 of Reference 15). This criterion means that the uncertainty

associated with the multipoint calibration determines the concentration range over which a

diluted candidate standard may be assayed.

2. A quantitatively accurate flow measurement and dilution system is required.

3. A source of clean, dry zero gas is required.

4. This procedure is designed to assay the permeation rate of a candidate standard that is

mounted in a specially designed assay dilution system; the procedure does not accommodate the

certification of a candidate standard that is mounted in its own self-contained dilution/flow

measurement system.

3.2.3 Assay Apparatus 

Figure 3-1 illustrates the components and configuration of one possible design for the assay

apparatus, including a common dilution system for both the reference and candidate standards. The

configuration is designed to allow convenient routing of zero gas and diluted concentrations of the

reference and candidate standards, in turn, to the analyzer for measurement, as selected by valves V1, V2,

and V3. Three gas flow controllers (i.e., C1, C2, and C3) regulate the total dilution flow rates for both

the reference and candidate permeation devices and the purge gas flow rate. These gas flow controllers

may be needle valves, capillary tubes, thermal mass flow controllers, or other suitable devices. The flow

rates must be controlled to within 1.0 percent variation during the assay.

The total dilution flow rate is measured by a single, common flowmeter (i.e., M1). Valve V1

directs a portion of the total dilution flow through one or the other of the two temperature-controlled

permeation device chambers to sweep up the permeated pollutant gas. This sweep flow rate is monitored by

an auxiliary flowmeter for each permeation device (i.e., M2 and M3). These auxiliary flowmeters need not

be accurately calibrated, since only the total dilution flow measured by flowmeter M1 is used in the

dilution calculation. Gas flow controllers C1 and C3 can be used to adjust and balance the flow rates of

the two gas streams sweeping through the permeation device chambers. The permeation device that is not

being analyzed receives a purge gas stream to avoid the buildup of high pollutant concentrations in the

chamber. This purge gas flow is vented through valve V2 and is not measured by flowmeter M1.

The assay apparatus illustrated in Figure 3-1 may be modified by the addition of multiple

candidate standard chambers. These chambers may be set to different temperatures.
3-7

If it is necessary to use different dilution flow rates for the candidate and reference permeation

devices (see Subsection 3.2.6), separate flow controllers for the two permeation devices may be used for

the two different flows. However, the same flowmeter should always be used to measure these two flow rates

to minimize systematic flow measurement errors.

The mixing chamber combines the gas streams and should be designed to provide turbulence in the

flow to ensure thorough mixing of the two gas streams. The diluted gas mixtures are routed to the analyzer

through a union tee tube fitting, which vents excess gas flow. Normally, the excess gas is vented to the

atmosphere without any obstructions in the tubing and the gas entering the analyzer is at near-atmospheric

pressure. However, the excess gas can be routed through an uncalibrated rotameter by rotation of a threeway valve (i.e., V4). The rotameter is used to demonstrate that the total gas flow rate exceeds the sample

flow rate of the analyzer and that no room air is being drawn in through the vent line (also see Subsection

3.1.4). Check the apparatus carefully for leaks and correct all leaks before use.

The mean temperatures of the reference standard chamber and the candidate standard chamber must

be controlled to within 0.05 EC of the setpoint with a temperature stability of ±0.05 EC. These

temperatures must be measured with a NIST-traceable thermometer having a measurement uncertainty of

±0.05 EC or less.
3-8
Relative Difference ' 100 Mean Analyzer Response & Predicted Response

Predicted Response

.

3-9

3.2.4 Pollutant Gas Analyzer

See Subsection 2.3.4. The pollutant gas analyzer must have a well-characterized calibration

curve and a range capable of measuring the diluted concentrations of both the candidate and the reference

standards. It must have good resolution, good precision, a stable response, and low output signal noise.

In addition, the analyzer must have good specificity for the pollutant of interest so that it has no

detectable response to any contaminant that may be contained in the standards. A suitable analyzer with

acceptable performance specifications may be selected from the list of EPA-designated reference and

equivalent method analyzers.17

The analyzer should be connected to a high-precision data acquisition system (e.g., a strip chart

recorder), which must produce an electronic or paper record for documentation of the analyzer responses

obtained during the assay. Additionally, a digital panel meter with four-digit resolution, a digital

voltmeter, data logger, or other data acquisition system must be used to obtain numerical values of the

analyzer's response. More precise values will be obtained if these instruments have some data averaging

capability. The assay record must be maintained for 3 years after the standard’s certification date.

If the analyzer has not been in continuous operation, turn it on and allow it to stabilize (e.g.,

for at least 12 hours) before beginning any measurements.

3.2.5 Analyzer Calibration

3.2.5.1 Multipoint Calibration—

See Subsections 2.1.7.2 and 2.1.7.4. Following completion of the multipoint calibration, the

accuracy of the assay apparatus must be checked to verify that the error associated with the dilution is

not excessive. This accuracy check involves the measurement of a diluted check standard. This check

standard must be a permeation device that is traceable to a NIST SRM. It must have a certified permeation

rate that is different from that of the reference standard used during the multipoint calibration.

Information concerning this standard (e.g., permeation device identification number, certified

permeation rate) must be recorded in the laboratory's records. The diluted concentration of the check

standard must fall in the well-characterized region of the calibration curve.

Make three or more discrete measurements of the diluted check standard. "Discrete" means that

the analyst must change the gas mixture being sampled by the analyzer between measurements. For example,

the analyst might alternate between measurements of the diluted check standard and the zero gas. Record

these measurements in the laboratory's records.

Next the analyst must verify that the dilution error is not excessive. For the diluted check

standard measurements, calculate the relative difference (in percent) between the mean analyzer response

and the corresponding response that is predicted from the multipoint calibration regression equation and

the diluted check standard concentration. That is,

If the relative difference is greater than 1.0 percent, the dilution error is excessive. The analyst must

investigate why the dilution error is excessive. The problem may be due to errors in the reference

standard and check standard permeation rates, errors in the assay apparatus or to some other source.

Assays may not be conducted until the relative difference for a subsequent accuracy check is 1.0 percent.

3.2.5.2 Analyzer Range—
3-10

See Subsection 2.3.5.2.

3.2.5.3 Linearity—

See Subsection 2.3.5.3.

3.2.5.4 Zero and Span Gas Checks—

See Subsection 2.3.5.4.

3.2.6 Selection of Gas Dilution Flow Rates

The dilution flow rates used for the reference and candidate standards should be selected

carefully to provide diluted concentrations for both standards that fall in the well-characterized region

of the analyzer's calibration curve. Potential errors in the assayed permeation rate due to dilution flow

rate measurement error will be greatly reduced if the same dilution flow rates can be used for both

standards. If the same dilution flow rates cannot be used for both standards, select different dilution

flow rates for the candidate and reference devices to provide approximately equal diluted concentrations

that fall in the well-characterized region. Additionally, the magnitude of the 95-percent confidence

limits for the estimated concentration of the diluted candidate standard must be ±1 percent of the

concentration of the diluted reference standard.

3.2.7 Flowmeter Type and Flowmeter Calibration

Flowmeter M1, as shown in Figure 3-1, measures in-line flow rates and does not operate at

atmospheric pressure because of backpressure from downstream components. Also, this backpressure is

variable, depending on the total dilution flow rate. Thus, the type of flowmeter used must compensate for

the variable in-line pressure. Measurements from a pressure-sensitive flowmeter such as a rotameter or

a wet test meter must be carefully corrected for the actual in-line pressure during the total dilution flow

rate measurement. 

Alternatively, the flow rates can be measured at the outlet of the dilution apparatus, with the

excess gas flow vent temporarily plugged. In this case, a volume-type meter such as a wet test meter or

a soap film flowmeter can be used, and flow measurements may be conveniently referenced to atmospheric

pressure. Each flow rate must be measured independently while the other flow rate is set to zero. Great

care must then be exercised to ensure that each measured flow rate remains constant between the time of

measurement and the time of the assay.

The flowmeter used should be stable, repeatable, linear, and have good resolution. The flowmeter

must not contaminate or react with the gas mixture passing through it. If possible, select flow rates or

a flowmeter range such that the measured flow rates fall in the upper half of the flowmeter's range. The

flowmeter should be carefully calibrated at several flow rates to prove linearity. The calibration should

be accurate to ±1.0 percent, referenced to an accurate flow or volume standard traceable to a NIST primary

standard (see Subsection 3.1.2). The flowmeter calibration should be checked and recertified on a regular

schedule (e.g., yearly). The recertification frequency is to be determined from stability information

such as a chronological control chart of calibration data.

All volumetric flow rate measurements must be corrected or referenced to the same temperature and

pressure conditions, such as EPA standard conditions (25 EC and 760 mm Hg) or the ambient temperature and

pressure conditions prevailing in the laboratory during the assay. Measurements using wet test meters

and soap bubble flowmeters also must be corrected for the saturation of gas stream with water vapor in the

moist interiors of these flowmeters. The equation to correct the flow rate for temperature, pressure, and

humidity effects is given below:
Flow Rate '

Volume

Time

PM& PWV

PS

TS

TM

3-11

where

PM = measured barometric pressure (mm Hg);

PWV = partial pressure of water vapor (mm Hg);

P = standard pressure (mm Hg); S

T = standard temperature (298.2 K); S

TM = measured ambient temperature (273.2 + EC).

Measurement of both dilution flow rates with the same flowmeter tends to reduce systematic flow

measurement error. Note particularly that flow measurement error is greatly reduced if the same dilution

flow rates can be used for both the reference and candidate standards.

3.2.8 Permeation Devices

3.2.8.1 Candidate Standard—

See Subsections 3.1.7 and 3.2.2. Follow the manufacturer's instructions for equilibration and

for use of the candidate standard and for selecting the temperature at which it is to be assayed and

certified. The candidate standard should be assayed at the same temperature at which it will be

subsequently used. The mean operating temperature of the candidate standard chamber must be controlled

to within 0.05 EC of the setpoint with a temperature stability of ±0.05 EC. This temperature must be

measured with a NIST-traceable thermometer with a measurement uncertainty of ±0.05 EC or less (see

Subsection 3.1.2).

3.2.8.2 Reference Standard—

See Subsections 3.1.2, 3.1.7.1, 3.1.7.2, and 3.2.2. Follow NIST's instructions for equilibration and use of the SRM reference standard and for selecting an operating temperature within its certified

range. The mean operating temperature of the reference standard chamber must be controlled to within

0.05 EC of the setpoint with a temperature stability of ±0.05 EC. This temperature must be measured with

a NIST-traceable thermometer with a measurement uncertainty of ±0.05 EC or less.

3.2.8.3 Zero Gas—

See Subsection 2.1.8. Use the same zero gas for dilution of both the candidate and reference

standards.

3.2.9 Assay Procedure

1. Verify that the assay apparatus is properly configured as shown in Figure 3-1 and described

in Subsection 3.2.3. Inspect the analyzer to verify that it appears to be operating normally

and that all controls are set to their expected values. Record these control values in the

laboratory's records.

2. Determine and establish the operating temperatures for the reference and candidate standards

in their respective temperature-controlled chambers. Install the standards and, with zero

gas flowing over both standards, allow ample time for the standards to equilibrate (see

Subsection 3.1.7.2). Record the temperatures in the laboratory's records.
Diluted Standard Conc. '

10&3 MV

MW

Permeation Rate

Dilution Flow Rate

3-12

3. Verify that flowmeter M1 is properly calibrated (see Subsection 3.2.7).

4. Verify that a multipoint calibration of the analyzer has been performed within 1 month prior

to the assay date (see Subsections 2.1.7.2, 2.1.7.5, and 2.3.4). Additionally, verify that

the zero and span gas checks indicate that the analyzer is in calibration (see Subsection

2.3.5.4).

5. Determine and establish the dilution flow rates and diluted concentrations for the reference

and candidate standards that will be used for the assay (see Subsections 3.2.6, 3.2.7, and

3.2.5.2). Use an estimated permeation rate for the candidate standard in these calculations.

Calculate the diluted standard concentrations (in ppm) using the following equation:

where

MV = Molar volume of the dilution gas (liters/mole);

= (0.08206) Tm

MW = Molecular weight of the dilution gas (grams/mole); permeation rate is given in

nanograms/minute; and dilution flow rate is given in liters/minute.

Ensure that the diluted candidate and reference standard concentrations are within the wellcharacterized region of the analyzer's calibration curve (see Subsection 2.3.2). Also check

that both dilution flow rates will provide enough flow for the analyzer, with sufficient

excess to ensure that no ambient air will be drawn into the vent line, and without increasing

the pressure of the sample delivered to the analyzer. If possible, use the same dilution flow

rate for both standards. Record the measured flow rates in the laboratory's records.

6. In succession, measure the zero gas, the diluted reference standard and the diluted candidate

standard using the analyzer. Use valves V1, V2, and V3 to select each of the three gas

mixtures for measurement. For each measurement, adjust the flow rates, if necessary, to those

determined in step 5, and allow ample time for the analyzer to achieve a stable reading. If

the reading for each measurement is not stable, the precision of the measurements will

decline and the candidate standard might not be certifiable under this protocol. Record the

analyzer response for each measurement, using the same response units (e.g., volts,

millivolts, percent of scale, etc.) as was used for the multipoint calibration. At this

point, do not convert the data into concentration values using the calibration equation. Do

not perform any mathematical transformations of the data. These steps will be done later.

Do not make any zero control, span control, or other adjustments to the analyzer during this

set of measurements. Record these analyzer responses in the laboratory's records.

The analyst may assay multiple candidate standards during the same assay session. For

example, a single set of measurements may involve a zero gas, a diluted reference standard,

and three diluted candidate standards. Criteria that apply to the assay of one candidate

standard apply to the assay of multiple candidate standards. The analyst should be aware that

the effect of any short-term calibration drift will be greater when multiple candidate

standards are assayed. This greater effect is due to the longer period of time between

reference standard measurements. Unacceptable uncertainties of the estimated
3-13

concentrations for the diluted candidate standards may occur as a result of the longer assay

session.

7. Conduct at least two additional sets of measurements, as described in step 6 above. However,

for these subsequent sets of measurements, change the order of the three measurements (e.g.,

measure the reference standard, zero gas, and candidate standard for the second set and

measure the zero gas, candidate standard, and reference standard for the third set, etc.).

Changing the order that the gas mixtures are measured helps the analyst to discover any effect

that one measurement has on subsequent measurements. The number of sets of measurements will

have been determined during the analysis of the multipoint calibration data such that the 95-

percent uncertainty for the regression-predicted concentration is 1 percent of the

concentration of the reference standard.

8. If any one or more of the measurements of a set of measurements is invalid or abnormal for any

reason, discard all three measurements and repeat the set of measurements. Such measurements

may be discarded if the analyst can demonstrate that the experimental conditions were

inappropriate during these measurements. Data cannot be discarded just because they appear

to be outliers, but may be discarded if they satisfy statistical criteria for testing

outliers. The analyst must record any discarded data and a brief explanation about why the

16

data were discarded in the laboratory's records.

9. The spreadsheet described in Appendix A or equivalent statistical techniques must be used to

calculate an estimated concentration and a 95-percent uncertainty for the diluted candidate

standard based on data from the assay measurements and from the multipoint calibration. The

use of both sets of data in the statistical analysis produces an estimated concentration with

smaller uncertainty while correcting for any minor cali-bration drift that may have occurred

since the multipoint calibration. Record the estimated concentration and the 95-percent

uncertainty in the laboratory’s records.

The spreadsheet also calculated the percentage of the uncertainty that is due to the

multipoint calibration. This percentage is needed for the total uncertainty calculations

when two or more assays fall under the same multipoint calibration. Record this value in the

laboratory’s records.

The analyst should investigate any of the measurements that appear to be outliers. Such data

may be discarded if the analyst can demonstrate that the experimental conditions were

inappropriate during these measurements. Data cannot be discarded just because they appear

to be outliers, but may be discarded if they satisfy statistical criteria for testing

outliers. The analyst must record any discarded data as well as a brief summary of the

investigation in the laboratory’s records.

10. If the multipoint calibration data and the assay data underwent any mathematical

transformations before their statistical analysis, the analyst must perform to reverse

transformations for the estimated concentration and the 95-percent uncertainty. Record the

transformed values in the laboratory’s records.

11. Finally, calculate the certified permeation rate (in nanograms/minute) and uncertainty for

the candidate standard using the equations below:
Certified Permeation Rate '

103 MW

MV

Diluted Standard

Conc.

Dilution Flow

Rate .

Uncertainty of Permeation Rate '

103 MW

MV

95&Percent

Uncertainty

Dilution Flow

Rate .

3-14

3.2.10 Equilibration Test for Newly Prepared Permeation Devices

A permeation device that has not been previously assayed must be tested for a stable permeation

rate as follows: Reassay the permeation rate at least 24 hours after the first assay and compare the two

assayed concentrations. The spreadsheet described in Appendix C or equivalent statistical techniques must

be used to evaluate the stability of the permeation rate by comparison of the confidence limits from the

two assays. If the confidence intervals overlap, the permeation rate can be considered to be stable and

the candidate standard may be certified for use. Otherwise, equilibrate the device longer at the

operating temperature and repeat the test, using the second and third assays as if they were the first and

second. This process may be repeated until the rate stabilizes. Permeation devices that are not stable

may not be used for calibration or audit purposes. Candidate standards that fail the initial and the

repeat stability tests are unstable and are disqualified for further use under this protocol.

3.2.11 Certification Documentation

See Subsections 3.1.5 and 3.1.6.

3.2.12 Recertification Requirements

See Subsection 3.1.7.3.

3.3 PROCEDURE P2: ASSAY AND CERTIFICATION OF PERMEATION DEVICE

CALIBRATION STANDARDS REFERENCED TO A COMPRESSED GAS 

REFERENCE STANDARD

3.3.1 Applicability

This procedure may be used to assay the permeation rate of a candidate SO2 and NO2 permeation device

calibration standard, based on the concentration of a compressed gas reference standard of the same

pollutant compound, and to certify that the assayed permeation rate is traceable to the reference

standard. The procedure employs a low-concentration range (i.e., ambient air quality level) pollutant

gas analyzer to compare quantitatively diluted concentrations from the permeation device calibration

standard with quantitatively diluted concentrations from the compressed gas reference standard. This

procedure may be used for the assay of multiple candidate standards during the same assay session.

Criteria that apply to the assay of one candidate standard apply to the assay of multiple candidate

standards. This procedure may be used by permeation device producers, standard users or other analytical

laboratories.

3.3.2 Limitations
3-15

1. The concentration of the diluted candidate standard may be greater than or less than the

concentration of the diluted reference standard. However, the diluted concentrations from

both standards must lie within the well-characterized region of the analyzer's calibration

curve (see Subsection 2.1.7.2). Additionally, the 95-percent uncertainty for the

regression-predicted concentration of the diluted candidate standard must be 1.0 percent

of the concentration of the diluted reference standard. This uncertainty is obtained from

the statistical analysis of the multipoint calibration data using the spreadsheet described

in Appendix A or using equivalent statistical techniques (e.g., the worksheet for linear

relationships given in Chapter 5 of Reference 15). This criterion means that the uncertainty

associated with the multipoint calibration determines the concentration range over which a

diluted candidate standard may be assayed.

2. A quantitatively accurate dilution and flow measurement system is required.

3. A source of clean, dry zero gas is required.

4. This procedure is designed to assay the permeation rate of a candidate standard that is

mounted in a specially designed assay dilution system. The procedure does not accommodate

the certification of a candidate standard that is mounted in its own self-contained

dilution/flow measurement system.

3.3.3 Assay Apparatus

Figure 3-2 illustrates the components and configuration of one possible design for the assay

apparatus, including a common dilution system for both the reference and candidate standards. 
3-16
3-17

The configuration is designed to allow convenient routing of zero gas and diluted concentrations of the

reference standard and the candidate standard, in turn, to the analyzer for measurement, as selected by

valves V1, V2, and V3. Three gas flow controllers (i.e., C1, C2, and C3) regulate the total dilution flow

rate for the candidate standard, the purge gas flow rate, and the reference standard flow rate. These gas

flow controllers may be needle valves, capillary tubes, thermal mass flow controllers, or other suitable

devices. The flow rates should be controlled to within 1.0 percent variation during the assay. The

dilution flow rates for the reference and candidate standards is measured by a single, common flowmeter

(i.e., M1). The reference standard and purge gas flow rates may be measured at the vent port of valve V2

or by flowmeters M2 and M3 that are mounted in the two gas streams.

When the candidate standard is being measured, valve V1 directs a portion of the total dilution

flow through the candidate standard chamber. This sweep flow rate is regulated by gas flow controller C1

and is measured by gas flowmeter M2. This flowmeter need not be accurately calibrated because only the

total dilution flow rate, measured by flowmeter M1, is used in the dilution calculations. When the

reference standard is being measured, valve V1 directs the purge gas through the candidate standard

chamber. The purge gas prevents the buildup of high pollutant concentrations in the chamber. It is vented

through valve V2 and is not measured by flowmeter M1.

The assay apparatus illustrated in Figure 3-2 may be modified by the addition of multiple

candidate standard chambers. These chambers may be set to different temperatures. 

If it is necessary to use different dilution flow rates for the reference standard and the

candidate standard (see Subsection 3.2.6), separate flow controllers for the two dilution flow rates may

be used. However, the same flowmeter should be used to measure both dilution flow rates to help reduce

systematic flow measurement errors.

The mixing chamber combines the gas streams and should be designed to provide turbulence in the

flow to ensure thorough mixing of the two gas streams. The diluted gas mixtures are routed to the analyzer

through a union tee tube fitting, which vents excess gas flow. Normally, the excess gas is vented to the

atmosphere without any obstructions in the tubing and the gas entering the analyzer is at near-atmospheric

pressure. However, the excess gas can be routed through an uncalibrated rotameter by rotation of a threeway valve (i.e., V4). The rotameter is used to demonstrate that the total gas flow rate exceeds the sample

flow rate of the analyzer and that no room air is being drawn in through the vent line (also see Subsection

3.1.4). Check the apparatus carefully for leaks and correct all leaks before use.

The mean temperature of the candidate standard chamber must be controlled to within 0.05 EC of the

setpoint with a temperature stability of ±0.05 EC. This temperature must be measured with a NISTtraceable thermometer having a measurement uncertainty of not more than 0.05 EC.

3.3.4 Pollutant Gas Analyzer

See Subsection 2.3.4. The pollutant gas analyzer must have a well-characterized calibration

curve and a range capable of measuring the diluted concentrations of both the candidate and reference

standards. It must have good resolution, good precision, a stable response, and low output signal noise.

In addition, the analyzer must have good specificity for the pollutant of interest so that it has no

detectable response to any contaminant that may be contained in the standards. A suitable analyzer with

acceptable performance specifications may be selected from the list of EPA-designated reference and

equivalent method analyzers. If the balance gas of the reference standard must be different from the zero

17

gas used for dilution (e.g., air versus nitrogen or different proportions of oxygen), either a high

dilution ratio (i.e., at least 50 parts zero gas to 1 part standard) should be used, or the analyzer must

be proven to be not sensitive to differences in the balance gas composition. The latter may be
Relative Difference ' 100 Mean Analyzer Response & Predicted Response

Predicted Response

.

3-18

demonstrated by showing no difference in an analyzer's response when measuring a calibration standard that

has been diluted with identical flow rates of the different balance gases.

The analyzer should be connected to a high-precision data acquisition system (e.g., a strip chart

recorder) which must produce an electronic or paper record of the analyzer response during the assay.

Additionally, a digital panel meter with four-digit resolution, a digital voltmeter, data logger, or other

data acquisition system must be used to obtain numerical values of the analyzer's response. More precise

values will be obtained if these instruments have some data averaging capability. The assay record must

be maintained for 3 years after the standard’s certification date.

If the analyzer has not been in continuous operation, turn it on and allow it to stabilize (e.g.,

for at least 12 hours) before beginning any measurements.

3.3.5 Analyzer Calibration

3.3.5.1 Multipoint Calibration—

See Subsections 2.1.7.2 and 2.1.7.4. Following completion of the multipoint calibration, the

accuracy of the assay apparatus must be checked to verify that the error associated with the dilution is

not excessive. This accuracy check involves the measurement of an undiluted or diluted check standard.

The check standard must be a NIST SRM, an SRM-equivalent PRM, an NTRM, or a GMIS as specified in Subsection

2.1.2. It must have a certified concentration that is different from that of the reference standard used

in the multipoint calibration. Information concerning this standard (e.g., cylinder identification

number, certified concentration) must be recorded in the laboratory's records.

If an undiluted check standard is used, its concentration must fall in the well-characterized

region of the calibration curve. If a diluted check standard is used, the diluted concentration must fall

in the well-characterized region.

Make three or more discrete measurements of the undiluted or diluted check standard. "Discrete"

means that the analyst must change the gas mixture being sampled by the analyzer between measurements.

For example, the analyst might alternate between measurements of the check standard and the zero gas.

Record these measurements in the laboratory's records.

Next the analyst must verify that the dilution error is not excessive. For the check standard

measurements, calculate the relative difference (in percent) between the mean analyzer response and the

corresponding response that is predicted from the multipoint calibration regression equation and the

undiluted or diluted check standard concentration. That is,

If the relative difference is >1.0 percent, the dilution error is considered to be excessive. The analyst

must investigate why the relative difference is excessive. The program may be due to errors in the

referencestandard and check standard concentrations, errors in assay apparatus or to some other source.

Assays may not be conducted until the relative difference for a subsequent accuracy check is 1.0 percent.

3.3.5.2 Analyzer Range—

See Subsection 2.3.5.2.

3.3.5.3 Linearity—

See Subsection 2.3.5.3.
3-19

3.3.5.4 Zero and Span Gas Checks—

See Subsection 2.3.5.4.

3.3.6 Selection of Gas Dilution Flow Rates

The dilution flow rates used for the reference standard and the candidate standard should be

selected carefully to provide diluted concentrations for both standards that fall in the wellcharacterized region of the analyzer's calibration curve. Potential errors in the assayed permeation rate

due to dilution flow rate measurement error will be reduced if the same dilution flow rates can be used for

both the reference and candidate standards. This should be feasible by appropriate selection of the

reference standard flow rate. Select a combination of reference standard flow rate and dilution flow rate

that produces approximately equal diluted reference standard and candidate standard concentrations that

fall in the well-characterized region of the analyzer's calibration curve. Additionally, the magnitude

ofthe 95-percent confidence limits for the estimated concentration of the diluted candidate standard must

be ±1 percent of the concentration of the diluted reference standard.

3.3.7 Flowmeter Type and Flowmeter Calibration

Flowmeters M1 and M3, shown in Figure 3-2, measure in-line flow rates and do not operate at

atmospheric pressure because of backpressure from downstream components. Also, this backpressure is

variable, depending on the total dilution and reference standard flow rates. Thus, the flowmeters must

compensate for the variable in-line pressure. Thermal mass flowmeters do not need to be corrected for

pressure effects. Measurements from pressure-sensitive flowmeters such as rotameters or wet test meters

must be carefully corrected for the actual in-line pressure during the flow rate measurements. 

Alternatively, the flow rates can be measured at the outlet of the dilution apparatus, with the

excess gas flow vent temporarily plugged. In this case, a volume-type meter such as a wet test meter or

a soap film flowmeter can be used, and flow measurements may be conveniently referenced to atmospheric

pressure. Each flow rate must be measured independently while the other flow rate is set to zero. Great

care must be exercised to ensure that each measured flow rate remains constant when combined with the other

flow rate and between the time of measurement and the time of the assay.

The flowmeters used should be stable, repeatable, linear, and have good resolution. The

flowmeters must not contaminate or react with the gas mixture passing through them. If possible, select

flow rates or flowmeter ranges such that the measured flow rates fall in the upper half of the flowmeters'

ranges. The flowmeters should be carefully calibrated at several flow rates to prove linearity. The

calibration of the zero gas flowmeter should be accurate to ±1.0 percent, referenced to an accurate flow

or volume standard traceable to a NIST primary standard (see Subsection 3.1.2). This flowmeter

calibration should be checked and recertified on a regular schedule (e.g., yearly). The recertification

frequency is to be determined from stability information such as a chronological control chart of

calibration data.

It is desirable to measure both dilution flow rates with the same flowmeter (i.e., M1). This

practice reduces measurement errors associated with the use of multiple flowmeters. Note that the impact

of any flow measurement error is reduced if the same dilution ratio can be used for both candidate standard

and reference standard measurements.

Allvolumetric flow-rate measurements must be corrected or referenced to the same temperature and

pressure conditions, such as EPA-standard conditions (i.e., 760 millimeters of mercury (mm Hg) and 25 EC)

or the ambient temperature and pressure conditions prevailing in the laboratory during the assay.

Measurements using wet test meters and soap bubble flowmeters also must be corrected for the saturation
Flow Rate '

Volume

Time

PM& PWV

PS

TS

TM

3-20

of the gas stream with water vapor in the moist interiors of these flowmeters. The equation to correct the

flow rate for temperature, pressure, and humidity effects is given below:

where

PM = measured barometric pressure (mm Hg);

PWV = partial pressure of water vapor (mm Hg);

P = standard pressure (mm Hg); S

TS = standard temperature (298.2 K); and

TM = measured ambient temperature (273.2 + EC). 

3.3.8 Candidate Standard

See Subsections 3.1.7 and 3.2.2. Follow the manufacturer's instructions for equilibration and

for use of the candidate standard and for selecting the temperature at which it is to be assayed and

certified. The candidate standard should be assayed at the same temperature at which it will be

subsequently used. The mean operating temperature of the candidate standard chamber must be controlled

to within 0.05 EC of the setpoint with a temperature stability of ±0.05 EC. This temperature must be

measured with a NIST-traceable thermometer with a measurement uncertainty ±0.05 EC or less (see Subsection

3.1.2).

3.3.9 Reference Standard

See Subsections 2.1.2, 2.1.6.4, 2.3.2, 2.3.6, and 3.1.2.

3.3.10 Zero Gas

See Subsection 2.1.8. If possible, the zero gas should be the same as the balance gas of the

reference standard.

3.3.11 Assay Procedure

1. Verify that the assay apparatus is properly configured as shown in Figure 3-2 and described

in Subsection 3.3.3. Inspect the analyzer to verify that it appears to be operating normally

and that all controls are set to their expected values. Record these control values in the

laboratory's records.

2. Determine and establish the operating temperature for the candidate standard in its

temperature-controlled chamber. Install the candidate standard, start the purge gas flow,

and allow ample time for the device to equilibrate (see Subsection 3.1.7.2). Record the

temperature in the laboratory's records.

3. Verify that the flowmeters are properly calibrated (see Subsection 3.3.7).

4. Verify that a multipoint calibration of the analyzer has been performed within 1 month prior

to the assay date (see Subsections 2.1.7.2, 2.1.7.5, and 2.3.4). Additionally, verify that
Diluted

Standard

Conc.

'

(Undiluted Standard Conc.) (Standard Flow Rate)

(Standard Flow Rate % Zero Gas Flow Rate)

.

Diluted Standard Conc. '

10&3 MV

MW

Permeation Rate

Dilution Flow Rate

3-21

the zero and span gas checks indicate that the analyzer is in calibration (see Subsection

2.3.5.4).

5. Determine and establish the reference standard flow rate and the dilution flow rates and

diluted concentrations for the reference standard and the candidate standard that will be

used for the assay (see Subsections 2.3.5.2 and 3.3.6). Ensure that the diluted reference

standard and diluted candidate standards concentrations are within the well-characterized

region of the analyzer's calibration curve (see Subsection 2.3.2). Also check that both

dilution flow rates will provide enough flow for the analyzer, with sufficient excess to

ensure that no ambient air will be drawn into the vent line. If possible, use the same

dilution flow rate for both the reference standard and the candidate standard. Also adjust

the flow rate of the portion of the dilution flow that passes over the candidate standard

(i.e., flow controller C3), and adjust the purge flow rate (i.e., flow controller C2) to

approximately the same value.

Calculate the diluted reference standard concentration using the following equation:

Calculate the diluted candidate standard concentration (in ppm) using the following

equation:

where

MV = Molar volume of the dilution gas (liters/mole);

= (0.08206) Tm

MW = Molecular weight of the dilution gas (grams/mole); permeation rate is given in

nanograms/minute; and dilution flow rate is given in liters/minute.

Use an estimated permeation rate for the candidate standard in this calculation.

Record the measured flow rates and the undiluted and diluted reference standard

concentrations in the laboratory's records.

6. In succession, measure the zero gas, the diluted reference standard and the diluted candidate

standard using the analyzer. Use valves V1, V2, and V3 to select each of the three gas

mixtures for measurement. For each measurement, adjust the flow rates, if necessary, to those

determined in step 5, and allow ample time for the analyzer to achieve a stable reading. If

the reading for each measurement is not stable, the precision of the measurements will

decline and the candidate standard might not be certifiable under this protocol. Record the

analyzer response for each measurement, using the same response units (e.g., volts,

millivolts, percent of scale, etc.) as was used for the multipoint calibration. At this

point, do not convert the data into concentration values using the calibration equation. Do
3-22

not perform any mathematical transformations of the data. These steps will be done later.

Do not make any zero control, span control, or other adjustments to the analyzer during this

set of measurements. Record these analyzer responses in the laboratory's records.

The analyst may assay multiple candidate standards during the same assay session. For

example, a single set of measurements may involve a zero gas, a diluted reference standard,

and three diluted candidate standards. Criteria that apply to the assay of one candidate

standard apply to the assay of multiple candidate standards. The analyst should be aware that

the effect of any short-term calibration drift will be greater when multiple candidate

standards are assayed. This greater effect is due to the longer period of time between

reference standard measurements. Unacceptable uncertainties of the estimated

concentrations for the diluted candidate standards may occur as a result of the longer assay

session.

7. Conduct at least two additional sets of measurements, as described in step 6 above. However,

for these subsequent sets of measurements, change the order of the three measurements (e.g.,

measure the reference standard, zero gas, and candidate standard for the second set and

measure the zero gas, candidate standard, and reference standard for the third set, etc.).

Changing the order that the gas mixtures are measured helps the analyst to discover any effect

that one measurement has on subsequent measurements. The number of sets of measurements will

have been determined during the analysis of the multipoint calibration data such that the 95-

percent uncertainty of the regression-predicted concentration of the candidate standard 1

percent of the concentration of the reference standard.

8. If any one or more of the measurements of a set of measurements is invalid or abnormal for any

reason, discard all three measurements and repeat the set of measurements. Such measurements

may be discarded if the analyst can demonstrate that the experimental conditions were

inappropriate during these measurements. Data cannot be discarded just because they appear

to be outliers, but may be discarded if they satisfy statistical criteria for testing

outliers. The analyst must record any discarded data and a brief explanation about why the

16

data were discarded in the laboratory's records.

9. The spreadsheet described in Appendix A or equivalent statistical techniques must be used to

calculate an estimated concentration and a 95-percent uncertainty for the diluted candidate

standard based on data from the assay measurements and from the multipoint calibration. The

use of both sets of data in the statistical analysis produces an estimated concentration with

smaller uncertainty while correcting for any minor calibration drift that may have occurred

since the multipoint calibration. Record the estimated concentration and the 95-percent

uncertainty in the laboratory’s records.

The spreadsheet also calculated the percentage of the uncertainty that is due to the

multipoint calibration. This percentage is needed for the total uncertainty calculations

when two or more assays fall under the same multipoint calibration. Record this value in the

laboratory’s records.

The analyst should investigate any of the measurements that appear to be outliers. Such data

may be discarded if the analyst can demonstrate that the experimental conditions were

inappropriate during these measurements. Data cannot be discarded just because they appear

to be outliers, but may be discarded if they satisfy statistical criteria for testing

outliers. The analyst must record any discarded as well as a brief summary of the

investigation in the laboratory’s records.
Certified Permeation Rate '

103 MW

MV

Diluted Standard

Conc.

Dilution Flow

Rate .

Uncertainty of Permeation Rate '

103 MW

MV

95&Percent

Uncertainty

Dilution Flow

Rate .

3-23

10. If the multipoint calibration data and the assay data underwent any mathematical

transformations before their statistical analysis, the analyst must perform to reverse

transformations for the estimated concentration and the 95-percent uncertainty. Record the

transformed values in the laboratory’s records.

11. Finally, calculate the certified permeation rate (in nanograms/minute) and uncertainty for

the candidate standard using the equations below:

3.3.12 Equilibration Test for Newly Prepared Permeation Devices

A permeation device that has not been previously assayed must be tested for a stable permeation

rate as follows: Reassay the permeation rate at least 24 hours after the first assay and compare the two

assayed concentrations. The spreadsheet described in Appendix C or equivalent statistical techniques must

be used to evaluate the stability of the permeation rate by comparison of the confidence limits from the

two assays. If the confidence intervals overlap, the permeation rate can be considered to be stable and

the candidate standard may be certified for use. Otherwise, equilibrate the device longer at the

operating temperature and repeat the test, using the second and third assays as if they were the first and

second. This process may be repeated until the rate stabilizes. Permeation devices that are not stable

may not be used for calibration or audit purposes. Candidate standards that fail the initial and the

repeat stability tests are unstable and are disqualified for further use under this protocol.

3.3.13 Certification Documentation

See Subsections 3.1.5 and 3.1.6.

3.3.14 Recertification Requirements

See Subsection 3.1.7.3.

3.4 PROCEDURE P3: ASSAY AND CERTIFICATION OF PERMEATION DEVICE

CALIBRATION STANDARDS REFERENCED TO A MASS REFERENCE STANDARD

3.4.1 Applicability

This procedure may be used to assay the permeation rate of a candidate SO2 or NO2 permeation device

calibration standard based on mass reference standards, and to certify that the assayed permeation rate

is traceable to the reference standard. The procedure employs an analytical balance to measure the weight

loss in the candidate standard. It may be used for the assay of multiple candidate standards during the

same assay session. Criteria that apply to the assay of one candidate standard apply to the assay of
3-24

multiple candidate standards. This procedure may be used by permeation device producers, standard users,

or other analytical laboratories.

3.4.2 Limitations

1. This procedure is intended only for the assay of candidate standards containing SO or NO . 2 2

These liquid compounds must be anhydrous grade (minimum purity 99.99 percent) or phosphorous

pentoxide-dried commercial purity grade (minimum purity 99.5 percent).

2. An accurate analytical balance with a NIST-traceable calibration is required to weigh the

candidate standard.

3. A temperature-controlled chamber for maintaining the candidate standard at a constant, NISTtraceable temperature between weight measurements is required.

4. A source of clean, dry zero gas is required.

3.4.3 Assay Apparatus

3.4.3.1 Analytical Balance—

Choose a balance with adequate vibration-stabilization control and appropriate specifications

for total weighing capacity, accuracy, precision, and readability. The balance should be chosen such that

the manufacturer's specified uncertainty (i.e., three times the standard deviation or "reproducibility")

of the balance divided by the weight of the candidate standard does not exceed 0.001. The balance must be

calibrated annually using NIST-traceable mass reference standards by the manufacturer or a manufacturer's

representative (see Subsection 3.1.2).

If possible, locate the balance in a climate-controlled, draft-free room, preferably dedicated

to the use of balances. If this is not possible, the general guidelines listed below should be followed

to control environmental factors that may affect balance performance:

! Locate the balance away from potential sources of drafts such as doors, windows, aisles with

frequent traffic, ventilation ducts, and equipment with fans or moving parts.

! Locate the balance out of direct sunlight and away from local heating or cooling sources such

as open flames, hot plates, water baths, ventilation ducts, windows, and heat-producing

lamps.

! Locate the balance on a sturdy base (ideally, a stone weighing table) and away from any

equipment that produces vibrations. If this is not possible, isolate the balance from such

equipment by placing a stabilizing slab under the balance or composite damping-pads under the

balance legs.

! Ensure that the balance-support is sufficiently level to permit leveling of the balance

according to the manufacturer's instructions.

3.4.3.2 Temperature-Controlled Chamber—

A temperature-controlled chamber is required for storing the candidate standard between

weighings. One possible design for the chamber is depicted in Figure 3-3. Clean, dry zero gas enters

23

the chamber at the bottom after passing through the heat exchanger tubing (i.e., several turns of copper

tubing). The zero gas' flow rate must be sufficient to purge the chamber thoroughly. The chamber and the

heat exchanger are immersed in a thermostatted bath to the level shown in the figure. The bath must
3-25

control the mean temperature of the chamber to within 0.05 EC of the setpoint with a temperature stability

of ±0.05 EC. The temperature of the bath or the chamber must be measured and recorded in the laboratory's

records on at least a daily basis. A NIST-traceable, liquid-in-glass thermometer or a temperature-sensing

device must be used for this measurement (see Subsection 3.1.2). A temperature-sensing device must be

calibrated annually using NIST-traceable temperature reference standards and must have an uncertainty

similar to that of these reference standards. The output of a temperature-sensing device may be recorded

by a strip chart recorder, data logger, or other data acquisition system.
3-26

Figure 3-3. Chamber for maintaining permeation tubes at constant temperature.23
Minimum

Weighing

Interval

'

100 (Readability)

(Expected Permeation Rate )

3-27

3.4.3.3 Electrostatic Charge Neutralization—

Electrostatic charge buildup will prevent an analytical balance from operating properly. Static

charge is the accumulation of electrical charges on the surface of a nonconductive material, which could

be the permeation device or part of the analytical balance. Common symptoms of this problem include noisy

readout, drift, and sudden readout shifts.

To reduce static charge within the balance, it may be necessary to place a radioactive antistatic

strip containing a very small amount (i.e., 500 picocuries) of Polonium-210 (Po ) in the weighing 210

chamber. It may also be necessary to put each permeation device on an antistatic strip before it is

weighed. Po antistatic strips are used to reduce electrostatic buildup in the analytical balance's 210

weighing chamber and on individual permeation devices by charge neutralization. They will neutralize

electrostatic charges on items placed within an inch of them. These antistatic strips are safe, commonly

available, and very inexpensive. Po has a half-life of 138 days. Change the antistatic strips

210

semiannually and dispose of the old strips according to the manufacturer's recommendations.

Antistatic solutions are available for coating (and recoating at appropriate and relatively

infrequent intervals) the interior and exterior nonmetallic surfaces of the chamber. This coating

facilitates the draining of electrostatic charges from these surfaces to a common electrical ground to

which the metallic conductive surfaces are connected. Earth-grounded conductive mats placed on the

weighing table surface and under the analyst's shoes are used to reduce electrostatic charge buildup. Do

not assume that the electrical grounding of the analytical balance eliminates all electrostatic buildup

because the ground may not be perfect.

Even though a permeation device's weight might stabilize within 60 seconds and no weight drift

is observed during that period, the balance may still be influenced by electrostatic charge buildup. It

may still be necessary to repeat the neutralization procedure and to use antistatic strips inside the

weighing chamber. One may reduce the effect of electrostatic buildup on permeation devices by putting

them in an aluminum foil boat on the balance pan during weighings.

Charge neutralization times may need to be longer than 60 seconds. Electrostatic charge buildup

becomes greater as the air becomes drier. A 60-second neutralization may work sufficiently in ambient

indoor air conditioned to 37 percent relative humidity and 23EC, but not in zero nitrogen. This latter

environment may require that the permeation device sit for more time on the antistatic strip. The longer

neutralization period may have to be done inside the weighing chamber or a second small chamber, which is

used just for charge neutralization.

3.4.4 Weighing Interval

The minimum time period between weighings of the candidate standard is a function of the expected

permeation rate, the specified uncertainty for the rate, and the analytical balance's readability (i.e.,

the smallest scale division). The following equation is based on a ±1 percent uncertainty specification

for the permeation rate:

where the weighing interval is in minutes; the readability is in grams; and the expected permeation rate

is in grams per minute.
Relative

Difference '

100 (Measured Weight & Certified Weight)

(Certified Weight)

.

3-28

3.4.5 Assay Procedure

1. Turn on the balance and allow it to warm up for the period specified in the operator's manual.

To ensure maximum stability, it is recommended to keep the balance turned on at all times.

This procedure enables the balance to be operational at all times and eliminates the need for

a warmup period before analyses. Newer balances are always turned on (except for their

displays) when they are plugged in.

2. Check the balance level and, if necessary, adjust the level according to the manufacturer's

instructions.

3. Ensure that the balance room temperature is within 15 to 30 EC or, if given, within the

balance manufacturer's specifications and that the balance and mass reference standards are

equilibrated to the balance room temperature. Record the temperature in the laboratory's

records.

4. Zero (i.e., tare) and calibrate the balance according to the manufacturer’s directions.

Record the tare reading in the laboratory’s records. Many newer balances calibrate

themselves automatically or only require a key to be touched to calibrate themselves.

5. On each day that the candidate standard is to be assayed, verify the balance's calibration

using at least two NIST-traceable mass reference standards. Use smooth, nonmetallic forceps

to handle the standards. This standard must have a mass that is similar to that of the

candidate standard. Record the date, balance identification, standards identification,

certified weight of the standard, and the measured weight of the standard in the laboratory's

records. Calculate the relative difference (in percent) between the certified and measured

weights as follows:

Record the relative difference in the laboratory's records. If the relative difference is

>0.1 percent, the balance cannot be used under this protocol until it has been recalibrated

or repaired and until a subsequent verification has a relative difference of 0.1 percent.

6. Review the recorded bath or chamber temperature readings since the most recent weighing of

the candidate standard, or since the standard was first put into the temperature-controlled

chamber. Record the minimum and maximum temperatures in the laboratory's records. The

minimum and maximum temperatures must not have deviated from the setpoint by more than

0.1 EC. If these temperatures deviate by more than this amount, the current assay and all

previous assays are invalidated.

7. Record the current bath or chamber temperature in the laboratory's records.

8. Verify that the candidate standard has been in the temperature-controlled chamber for a long

enough time for its permeation rate to have stabilized.

9. Remove the candidate standard from the temperature-controlled chamber and place it on the

balance's pan using stainless steel forceps or a similar noncontaminating device. Note that

Teflon permeation tubes may have an electrostatic charge buildup due to the passage of the

®

dry gas over them between weighings. Such charges should be removed from the candidate
Provisional

Permeation

Rate

'

(Previous Weight & Current Weight)

Elapsed Time Between Weighings

3-29

standard before weighing by Po antistatic strips or similar devices. Note that electronic 210

force balances may require that candidate standards be thermally equilibrated before they

can be weighed.

10. Record the date, time and the candidate standard's identification number and current weight

in the laboratory's records.

11. Return the candidate standard to the temperature-controlled chamber. The standard should

be outside the chamber only for a long enough time to weigh it using reasonable laboratory

technique.

3.4.6 Number of Weighings of the Candidate Standard

The candidate standard must be weighed at least six times after its permeation rate has stabilized

at the certification temperature. After the six or more weighings, the analyst may assess the stability

and uncertainty of the permeation rate by using the spreadsheet described in Appendix B or equivalent

statistical or graphic techniques. The analyst may calculate a provisional permeation rate from the

measured weights and the time between weighings using the following equation:

Based on this data analysis, the analyst may perform additional weighings to reduce the uncertainty or to

replace data that are discarded because they were obtained before the permeation rate stabilized.

3.4.7 Calculation of Certified Permeation Rate

The certified permeation rate for the candidate standard is the slope of the least squares

regression line for data from at least six weighings of the candidate standard after the permeation rate

has stabilized. This statistical analysis technique produces permeation rate estimates that are more

precise than those calculated from weight differences between individual weighings. Although the minimum

number of weighings is six, more precise estimates will be obtained for more weighings.

Calculate the certified permeation rate and its uncertainty using the spreadsheet given in

Appendix B or using equivalent statistical techniques (e.g., the worksheet for linear relationships given

in Chapter 5 of Reference 15). Figure 3-4 presents an example of the graphic output of the spreadsheet.

This rate is the slope (b1) of the least squares regression line where the x-values are the elapsed times

from the initial weighing and the y-values are the measured weights of the permeation device. The
upper CL(b1

)&b1(b1)/100 .

b1&lower CL(b1)&b1(b1)/100 .

3-30

Figure 3-4. Example of spreadsheet graphic

output for calculating permeation rates.

spreadsheet also calculates the predicted initial weight (b ) of the permeation device and 95-percent 0

confidence limits for b and b . 0 1

Afterthe data from the six or more weighings have been entered in the spreadsheet, examine the

95-percent confidence limits (CLs) for b0. If the measured weight from the initial weighing falls outside

of these limits, the permeation device may not have been completely equilibrated at the initial weighing.

The analyst may elect to discard the data from the initial weighing to reduce the uncertainty of the

certified permeation rate.

Examine the upper and lower 95-percent CLs for b1. They should differ from b 1 by no more than 1

percent of its value. That is, 

If these two criteria are met, the permeation device can be certified with a permeation rate equal

to b and an uncertainty equal to the larger of the two values. If the criteria are not met, the analyst 1

must make additional weighings of the candidate standard as described in Subsection 3.4.5. 

These additional measurements will be pooled with the previously collected measurements. The pooled data

will be used to obtain new estimates of the b1 and its uncertainty. When an acceptable value for the

uncertainty is obtained, record it and the slope in the laboratory's records. If an acceptable value is

not obtained, the candidate standard cannot be certified under this protocol.
Uncertainty (Total)

Permeation Rate

'

Uncertainty (Slope)

Slope

2

%

Uncertainty (Mass)

Mass

2

1/2

3-31

The analyst should investigate any of the measurements that appear to be outliers. Such data may

be discarded if the analyst can demonstrate that the experimental conditions were inappropriate during

these measurements. Data cannot be discarded just because they appear to be outliers but may be discarded

if they satisfy statistical criteria for testing outliers. The analyst must record any discarded data and

a brief summary of the investigation in the laboratory's records.

3.4.8 Uncertainty of Certified Permeation Rate for Candidate Standard

The total analytical uncertainty of the certified permeation rate includes the uncertainty of

regression slope and the uncertainty of the mass reference standard that was used to verify the balance’s

calibration. The two components are combined using the following equation for the propagation of errors:

3.4.9 Certification Documentation

See Subsections 3.1.5 and 3.1.6.

3.4.10 Recertification Requirements

See Subsection 3.1.7.3.
3-8

Figure 3-1. One possible design of the apparatus for the assay of permeation device calibration

standards referenced to a permeation device reference standard (Procedure P1).
3-16

Figure 3-2. One possible design of the apparatus for the assay of permeation device calibration

standards referenced to a compressed gas reference standard (Procedure P2).
4-1

SECTION 4

REFERENCES

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8. Nederlands Meetinstituut. Gaseous Primary Reference Materials. Delft, The Netherlands, no date.

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4-2

13. S.G. Wechter. "Preparation of Stable Pollution Gas Standards Using Treated Aluminum Cylinders."

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Government Printing Office. Washington, DC. 1963. pp. 5-1 to 5-46.

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Observations. ASTM Standard Practice E 178-80, 1980.

17. U.S. Environmental Protection Agency. List of Designated Reference and Equivalent Methods.

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Monitoring Technology Information Center (AMTIC) at http://www.epa.gov/ttn.

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(ASTM). Standard Specification for Laboratory Weights and Precision Mass Standards. ANSI/ASTM

Standard E 617-91, 1991.

19. W. Kupper. "High Accuracy Mass Measurements, From Micrograms to Tons," Instrument Society of

America Transactions. 29(4). 1990.

20. G. Harris. "Ensuring Accuracy and Traceability of Weighing Instruments," ASTM Standardization

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21. J.A. Wise. NIST Measurement Services: Liquid-in-Glass Thermometer Calibration Service.

National Institute of Standards and Technology Special Publication 250-23. 1988.

22. J.A. Wise. A Procedure for the Effective Recalibration of Liquid-in-Glass Thermometers. National

Institute of Standards and Technology Special Publication 819. 1991.

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183-197.
A-1

APPENDIX A: INSTRUCTIONS FOR CALIBRATION WORKBOOK

1. ReadMe Spreadsheet

Purpose

This worksheet supports linear, quadratic, cubic, and quartic models:

Linear: y = $0 + $1x+ ,

Quadratic: y = $0 + $1x + $2x + ,

2

Cubic: y = $0 + $1x + $2x + $3x + ,

2 3

Quartic: y = $0 + $1x + $2x + $3x + $4x + ,

2 3 4

y = response

x = concentration

The worksheet estimates the coefficients ($s) and the variance of the error term, ,. The

workbook then performs the following functions:

• determine which model (linear, quadratic, etc.) is better

• determine the replication of unknowns needed for uncertainty control

• determine whether zero and span responses are acceptable

• estimate the concentration and 95% uncertainty of candidate standards analyzed on the

same day as the initial calibration or a subsequent day.

Organization

The workbook consists of several worksheets, which are displayed as tabs at the bottom of the

screen. The functions of these worksheets are described below:

ReadMe describes the workbook, explaining how to use the worksheets

Measurement Data allows for user input of calibration and other analytical data and

includes statistical calculations for polynomial regression

Curves 1 displays the calibration data, the best-fit line, and its confidence

bands

Residuals 1 displays the difference between the observed responses and those

estimated by the best-fit calibration line

Curves 2 displays the calibration data, the best-fit quadratic curve, and its

confidence bands

Residuals 2 displays the difference between the observed responses and those

estimated by the quadratic regression line

Curves 3 displays the calibration data, the best-fit cubic curve, and its

confidence bands

Residuals 3 displays the difference between the observed responses and those

estimated by the best fit cubic regression line

Curves 4 displays the calibration data, the best-fit cubic curve, and its

confidence bands

Residuals 4 displays the difference between the observed responses and those

estimated by the best-fit quartic regression line
A-2

Chart Data includes the data used to create the Curves and Residuals charts.

Conventions

The Measurement Data worksheet includes instructions that guide the user through the steps in

its use. The worksheet is also color coded to simplify use. Shaded cells that are bordered in

blue lines are for input of data. These cells are unprotected, but all other cells of the

Measurement Data worksheet are protected. The only other unprotected cell in the workbook is

cell F4 of the Chart Data worksheet. That cell controls the width of the confidence bands plotted

in the Curves 1 and Curves 2 charts. 

Derived values and statements are colored red. These cells contain formulas and are

protected to prevent alteration. 

Spreadsheet background colors indicate the order of the polynomial supported by the

calculations in the area.

Light green is used for the linear model.

Yellow is used for the quadratic model.

Gray is used for the cubic model

Light blue is used for the quartic model.

Use

The Measurement Data worksheet guides the user through six steps.

STEP 1 Enter Calibration Data

In this step, up to 50 calibration points may be entered. Each calibration point has two parts–the

certified concentration of the calibration gas standard and the instrument response when testing

the standard. These values are entered in two columns. The spreadsheet performs

computations in columns I through P (linear), Q through X (quadratic), Y through AZ (cubic), and

BA and above (quartic).

STEP 2 Review the Parameter Estimates

In this step, the user reviews the estimates of the intercepts (b ), slopes (b ) and other 0 1

coefficients (b2, b3, and b4) for the four models, examines their confidence intervals and the

residual error variances (s ). The result of an F test indicates which of the models is best. The 2

linear model is recommended unless the quadratic or higher-order model significantly reduces

the residual error.

STEP 3 Review the Charts

In this step, the user reviews the charts named Curves 1, Residuals 1, Curves 2, Residuals 2,

etc. These charts help the user understand why one model performs better than the other.

STEP 4 Assess Magnitude of Uncertainty

In this step, the user enters the assumed concentration of a candidate standard and selects a
A-3

replication number, r. Based on the calibration results, the worksheet estimates the 95%

uncertainty that would result from measuring such a standard r times. The user can use this as

a guide for deciding whether to proceed with analysis, to produce additional calibration points, or

to take some corrective action.

STEP 5 Assay Candidate Standard on Same Day

In this step, the user enters the responses to a candidate standard that is tested on the same

day as the calibration of STEP 1. The worksheet provides an estimate of the candidate's

concentration and its 95% uncertainty. The worksheet also indicates whether the variability in

responses is larger than expected (unacceptable).

STEP 6 Assay Candidate Standard on Different Day from Initial Calibration

In this step, the user enters the responses to a candidate standard that is tested on a different

day from the calibration of STEP 1. The worksheet first assesses the zero and span responses. 

If the zero and span responses are acceptable, the user proceeds to enter the results from

testing a candidate standard. The results include those for zero and nonzero reference

standards. (The quadratic model requires the use of two different nonzero standards.) 

The spreadsheet determines whether the regression curve has changed since the initial

calibration. The data are corrected for any change and the estimated concentration of the

candidate standard is provided together with its 95% uncertainty. 

The spreadsheet also determines whether the standard error of the mean response is acceptable

(<1% of the mean response). This additional check is meant to guard against hysteresis or other

errors that are not corrected by the spreadsheet's adjustments.

2. Measurement Data Spreadsheet

STEP 1 Enter Calibration Data

Enter the calibration data in the shaded spaces below. The first column (I) simply counts the

calibration points that you enter. The second column (X) is for the certified concentrations of the

calibration gas standards. The third column (Y) is for the instrument responses corresponding to

the calibration standards. The number of points cannot exceed 50.
A-4

I Xi Yi Color Code

1 0.000 0.2194

2 0.500 0.7141 red = derived value (protected)

3 1.000 1.2885

4 1.500 1.9132 blue = entered value (unprotected)

5 2.000 2.5910

6 2.500 3.2866 black = fixed text (protected)

7 3.000 4.1078

8 3.500 4.9446

9 4.000 5.8145

10 4.500 6.7230

11 5.000 7.7284

12 5.500 8.7566

13 6.000 9.8013

14 6.500 10.8818

15 7.000 12.0982

16 7.500 13.3122

17 8.000 14.5840

18 8.500 15.9238

19 9.000 17.3271

STEP 2 Review the Parameter Estimates

Review the estimates of the coefficients (b , (b ,...) for the linear and quadratic models, their 0 1

confidence, and the residual error variances (s ). 2
A-5

 Linear Model 95% Confidence Limits

Parameter Estimate Lower Upper

b0 = -1.0778 -1.7351 -0.4204

b1 = 1.9005 1.7757 2.0253

s = 0.4986 0.2807 1.1205 2

s = 0.7061 0.5298 1.0585

df = 17

t = 2.1098

Quadratic Model 95% Confidence Limits

Parameter Estimate Lower Upper

b0 = 0.1964 0.1960 0.1968

b1 = 1.0011 1.0010 1.0012

b2 = 0.0999 0.0999 0.0999

s = 0.0005 0.0003 0.0011 2

s = 0.0220 0.0164 0.0335

df = 16

t = 2.1199

Comparing the two models:

F ratio = 1027

F = 2.3167 (5% significance level) critical

The quadratic model produces a significantly smaller error variance. The quadratic model

appears to be the better choice.

If cubic or quartic models are supported by compelling scientific theory or data, then review the

following estimates for those models. Otherwise, go to Step 3.
A-6

 Cubic Model 95% Confidence Limits

Parameter Estimate Lower Upper

b0 = 0.1952 0.1593 0.2310

b1 = 1.0030 0.9676 1.0385

b2 = 0.0994 0.0901 0.1087

b3 = 0.0000 -0.0006 0.0007

s = 0.0005 0.0003 0.0012 2 

s = 0.0227 0.0168 0.0352

df = 15

t = 2.1315

Comparing quadratic and cubic models:

F ratio = 0.9385

F = 2.3849 (5% significance level) critical

The error variances are not significantly different at the 5% level. The quadratic model appears

to be a better choice than cubic.

Quartic Model 95% Confidence Limits

Parameter Estimate Lower Upper

b0 = 0.2206 0.1900 0.2512

b1 = 0.9285 0.8786 0.9783

b2 = 0.1390 0.1156 0.1625

b3 = -0.0069 -0.0109 -0.0030

b4 = 0.0004 0.0002 0.0006

s = 0.0003 0.0001 0.0007 2

s = 0.0165 0.0121 0.0261

df = 14

t = 2.1448

Comparing quadratic and cubic models:
A-7

F ratio = 1.8954

F = 2.4630 (5% significance level) critical

The error variances are not significantly different at the 5% level. The cubic model appears to be

a better choice than quartic.

STEP 3 Review the Charts

View the charts named Curves 1 and Residuals 1. Curves 1 shows confidence bands for the

estimated regression. Compare these bands with those of the quadratic regression, Curves 2. 

(Note: You can change the width of the confidence band interval by changing the "p-value" in cell

F4 of the worksheet named Chart Data.) Residuals 1 shows how the calibration points deviated

from the calibration line. Look for a simple pattern (such as a quadratic curve) in the chart. If

such a pattern appears, the quadratic model may be better. View Residual 2, the deviations

from the best- fit quadratic curve. If Residual 2 effectively removes the simple pattern observed

in Residual 1 and if the magnitude of the deviations has been significantly reduced (as

evidenced by a reduction in the estimate s ), then the quadratic model is superior. An F-test can 2

be run to determine if the two error variances are significantly different.

F = 1026.764 Prob. of greater F = 4.51E-21

The quadratic model produces a significantly smaller error variance. The quadratic model

appears to be the better choice.

STEP 4 Assess Magnitude of Uncertainty

Enter the concentration at which you would like to evaluate the uncertainty of estimation and

prediction. Also enter r, the number of assays to be performed. Increasing r tends to reduce the

prediction uncertainty, but with diminishing effect. 

Concentration = 6

r = 3

Review the estimated mean response (estimate that only takes into account the calibration

uncertainty), and the confidence intervals. Review the predicted mean response and its

confidence intervals. To satisfy the EPA protocol requirements, the 95% confidence limits for the

concentration should be #±1% of the concentration.

Estimates below are based on the quadratic model. Tab-Right to view estimates based on the

other model.
A-8

95% Confidence Limits

Estimate Lower Upper

Instrument Response = 9.8006 9.7858 9.8155

95% Confidence Limits

Prediction Lower Upper

Instrument Response = 9.8006 9.7698 9.8314

Concentration = 6.0000 5.9860 6.0140

95% uncertainty in prediction = 0.23%

STEP 5 Assay Candidate Standard on Same Day

Proceed with the analysis of candidate standards if their 95% uncertainties, as estimated above,

are <1%. Enter the responses from the repeated analyses of an individual candidate standard in

the spaces provided below. 

Note: This step applies only to candidate standards that are assayed on the same day as the

calibration. 

Enter the instrument responses for up to 10 repeated analyses of a single candidate standard

below.
A-9

Analysis Estimated

Number Response Concentration

1 4.500 3.2466

2 4.501 3.2473 NOTE: For Cubic

and Quartic Model

estimates, view the

Calculations in the

spreadsheet’s

shaded regions.

3 4.499 3.2460

4

5

6

7

8

9

10

mean = 3.2466

standard deviation = 0.0006

df = 2

F = 0.0008

F sig? = FALSE (The sample

variance is acceptable.)

Pr(>F) = 0.9992

95% Uncertainty = 0.58%

23.97% = portion of uncertainty2

due to calibration

STEP 6 Assay Candidate Standard on Different Day from Initial Calibration

This step applies to candidate standards that are assayed on a different day than the initial

calibration. Before candidate standards are run, the measurement system is challenged with

zero and span checks. Three or more discrete checks of the zero gas and three or more checks

of the span gas are made. Enter the results below:
A-10

Response to Zero gas Span conc. to Span

Response

0.000 9.000 16.010

0.001 9.000 16.000

-0.001 9.000 15.990

n = 3 n = 3

mean = 0.000 mean = 16.000

s = 0.001 s = 0.010

Cal. Resp.= 0.196 Cal. Response = 17.301

Zero Gas Results Span Gas Results

Std. Error = s/sqrt(n) = 0.0006 0.0058

Rrs/100= 0.1600 0.1600

Std. Error is okay Std. Error is okay

Relative Difference (RD) = 1.14% -7.52%

RD is okay RD is excessive

Following successful completion of the zero and span checks, the candidate standard is

measured together with reference standards. While the candidate standard is normally

interspersed with the reference standards, the analysis conducted in this sheet requires that the

results be entered separately. There are two ways to do this. One way is to enter an analysis set

(one candidate standard response and the responses from its zero and nonzero standard

analyses) below. Another approach is to enter all of the responses (multiple sets) below. Enter

zero and reference standard responses in the area to the left and enter the responses to a single

candidate standard in the are to the right, below. 

More than one nonzero reference standard is needed for the quadratic and higher-order

models.

Estimates below are based on the quadratic model. Tab-Right to view estimates based on the

other model.
A-11

Reference Standards (Enter 0 for 

Zero Concentraton) Candidate Standard

Conc. Response Conc. Conc. Conc. Response Conc. 2 3 4

Observed Estimated

0.000 0.218 0.000 0.000 0.000 4.010 2.9437

0.000 0.219 0.000 0.000 0.000 4.000 2.9374

0.000 1.220 0.000 0.000 0.000 3.990 2.9311

4.500 6.693 20.250 91.125 410.063

4.500 6.723 20.250 91.125 410.063 nnn = 3

4.500 6.773 20.250 91.125 410.063 mean = 4.000 2.9374

9.000 17.317 81.000 729.000 6561.000 stdev = 0.0063

9.000 17.327 81.000 729.000 6561.000 std error = 0.12%

9.000 17.337 81.000 729.000 6561.000 df = 2

F = 0.1128

F sig? = FALSE

Pr{>F} 0.8938

nn= 9 The standard error is okay.

Coefficient are not significantly different.

Consider including thenew data as part of original calibration (Step 1).

Estimated Concentration of Candidate Standard 

2.9374

95% Uncertainty Portion of uncertainty due to calibration uncertainty 2

 0.66% 45.68%

95% Confidence Limits for Candidate Standard Concentration

Lower Upper

2.9181 2.9567

These upper and lower limits are compared with the corresponding limits estimated on different

assay dates to establish that the candidate standard has not drifted.
B-1

APPENDIX B: INSTRUCTION FOR PERMEATION RATE WORKBOOK

1. ReadMe Spreadsheet

What this Workbook Is All About

This workbook enables the user to estimate the rate at which the weight of a permeation tube

decreases. A linear relationship between the tube's weight and elapsed time is established. If

the estimated weight at time zero is significantly different from the actual weight at time zero,

then at least the earliest data pair should be removed from the analysis. Uncertainty of the slope

estimate (the rate of weight loss or drift) will be determined. The traceability protocol requires

that this estimate have a relative uncertainty of less than 1%.

How the Workbook Is Organized

The workbook consists of several worksheets, which are displayed as tabs on the bottom of the

screen. Each worksheet performs a distinct function as described below.

ReadMe describes the workbook and explains how to use the worksheets

Data allows for user input of the calibration data (elapsed time and

weight)

ANOVA performs analysis of variance and determines whether the

intercept term is needed

Calibration Results calculates the drift and its uncertainty

Curve graphically displays the drift line together with its confidence bands

Residual graphically displays the vertical difference between the observed

and estimated weights

Report summarizes the assay results for a permeation device

Chart Data includes the data used to create the curve and residual charts.

How the Worksheets Are Set up

Each worksheet contains instructions that guide the user through the steps in using

the worksheet. The worksheets are also color-coded to simplify use. Shaded cells that are

bordered in blue lines are cells whose contents you can change (i.e., enter data). In other sheets

you can change the following variables:

Sheet Variable Location Current Value

Data Unit of Time H22 m

Data Unit of Weight H24 g

Report Device ID F5 test data

Chart Data significance level D2 1.00E-05

Derived values are colored red. These cells contain formulas that should not be changed. The

cells are protected to prevent alteration.
B-2

How to Use the Worksheets

Step 1: Enter the elapsed times (all in the same units) and corresponding tube weights in

the Data worksheet. The worksheet will compute the total weight loss for each

observation.

Step 2: Select the significance level (alpha) to be used in producing confidence limits for

the estimated slope and intercept. Then review the results of the F-test and t-test

to determine whether the intercept term is needed. If the intercept term is

significant, then determine which of the early data points should be removed. 

Removing those data, and correcting the elapsed times, repeat Steps 1 and 2.

Step 3: Examine the corresponding Curve chart. You may need to adjust the chart's axis

scaling. The points should appear to fall virtually on top of the black line. The

black line should be very close to its confidence bands (colored red and blue).

Step 4: Examine the corresponding Residual worksheet. The residuals should appear to

be random in both magnitude and direction. If they appear to follow a regular

pattern, then the simple linear model is not appropriate. The device does not

have a constant rate of weight loss. More time may be required to establish and

measure a linear relationship. Observations taken before the linear relationship is

established should be discarded and not used in the statistical analysis.

Step 5: Print the one-page report provided in the Report sheet. The report summarizes

the assay data and indicates the uncertainty of the estimate.
B-3

2. Data Entry Worksheet

Data Entry Worksheet

Elapsed

Time Weight Enter the data in the blue-bordered spaces. The first

column (X) is for the elapsed time. The time of the

first entry should be zero. The second column (Y) is

I Xi Yi for the tube weights.

0 0 4.354206

1 8641 4.33745 n = number of weighing. This can’t exceed 50.

2 18722 4.316766 n = 7

3 40322 4.273494

4 64802 4.224514

5 74882 4.20378

6 84962 4.18439 No data entry is required for derived values, which are

colored red, such as n and I. These values are

tabulated automatically and their cells are protected

from alteration. 

Multiple weighings at a single point in time requires

multiple entries in each column. Reenter the time in

column X and enter the corresponding weight in

column Y.

Enter the time and weight units in the spaces below:

Unit of Time = m

Unit of Weight = g

This sheet derives the regression equation in the form: y = b0 + b1 x + ,. The intercept and

slope are estimated. The sheet determines whether the intercept (weight estimated for time

zero) is significantly different from the observed weight at time zero. It also estimates the

uncertainty in the slope estimate and compares this uncertainty with EPA's 1% limit.

STEP 1

Review the estimates of the intercept (b0), slope of the regression line (b1), and their confidence

limits along with the estimates of variance-covariance matrix (V) and the residual error variance

(Var).

Derivation of the estimated intercept (b0) and slope (b1) of the regression line
B-4

X'X = 7 292331 Y'Y = 127.6972 95% Confidence Limits

292331 1.91E+10 df = 5 b0

 lower limit = 4.353872

(X'X) = b upper limit = -1 0.396793 -6.1E-06 t(0.95, df) = 2.570578 0 4.354935

-6.1E-06 1.46E-10

det(X'X) = 4.81E+10 b0 = 4.354403 b1 lower limit = -2E-06

X'Y = 29.8946 b1 = -2E-06 b1 lower limit = -2E-06

1234673

Derivation of the error variance (Var) and variance-covariance matrix (V)

b'X'Y = 127.6972 SS(model), 2df

b'X'Y - sum(Y) / n = 0.027619 SS(regression) 1df 2

(Y'Y - b'X'Y) = 5.38E-07 SS(residual)

Var = (Y'Y - b'X'Y) / df = 1.08E-07 MS(residual), n-2 df

V = Var * (X'X) = 4.27E-08 -6.5E-13 -1

-6.5E-13 1.57E-17

STEP 2

Examine the upper and lower limits for the intercept, b .0

b0 lower limit = 4.353872

b0 upper limit = 4.354935

 y = 4.354206 Conclusion: y is within the confidence limits for the 0 0

intercept

If y is within the confidence limits for the intercept, proceed to STEP 3. Otherwise, consider 1

removing the first observed weight from the analysis. Re-enter the times and weights. 

Remember that the first time (X ) should be zero. This will require adjustment of the other 0

elapsed times. After entering the data, return to STEP 1, above.

STEP 3

Examine the upper and lower limits for the slope, b1. The limits should differ from the estimate

by no more than ±1% of the estimated slope.

(b upper - b ) / |b | = 0.51% Conclusion: Uncertainty is acceptable. 1 1 1

(b1 lower - b1) / |b1| = -0.51%

If the uncertainty is unacceptable, consider collecting additional data. Also, view the Curve and

Residual plots. They may reveal a nonlinear relationship for a portion of the data. The initial

measurements may not align with subsequent measurements if the device was in the process of

stabilizing or equilibrating during those times. If this is the case, the initial points of the Residual

chart would appear to be outliers. The residuals with the same sign (all positive or all negative)
B-5

and their magnitude will likely be greater than the magnitude of subsequent residuals. If this is

the case, consider removing the initial points from the computations and re-enter the remaining

times and weights with the times adjusted so the first entry has time zero.

If the uncertainty is acceptable, print the Report spreadsheet and include it with the

certification documentation.

3. Assay Results For Permeation Device

This sheet provides calibration information and assay results, including uncertainty estimates for

a permeation device identified as: test data

Test Results

Intercept (b0), slope (b1), and their confidence limits

X'X = 7 292331 Y'Y = 127.6972 95% Confidence Limits

292331 1.91E+10 df = 5 b0

 lower limit = 4.353872

(X'X) = b upper limit = -1 0.396793 -6.1E-06 t(0.95, df) = 2.570578 0 4.354935

-6.1E-06 1.46E-10

det(X'X) = 4.81E+10 b0 = 4.354403 b1 lower limit = -2E-06

X'Y = 29.8946 b1 = -2E-06 b1 lower limit = -2E-06

1234673

Error variance (Var) and variance-covariance matrix (V).

b'X'Y = 127.6972 SS(model), 2df

b'X'Y - sum(Y) / n = 0.027619 SS(regression) 1df 2

(Y'Y - b'X'Y) = 5.38E-07 SS(residual)

Var = (Y'Y - b'X'Y) / df = 1.08E-07 MS(residual), n-2 df

V = Var * (X'X) = 4.27E-08 -6.5451E-13 -1

-6.5E-13 1.56725E-17

Upper and lower limits for the intercept, b :0

b0 lower limit = 4.3538722

b0 upper limit = 4.3549347

 y0 = 4.354206

Upper and lower limits for the slope, b : 1

(b1 upper - b1) / |b1| = 0.51%

(b1 lower - b1) / |b1| = -0.51%

Estimated rate of weight loss, b1 = 2.005E-06 g/m
B-6
C-1

APPENDIX C: CALCULATION OF TOTAL ANALYTICAL UNCERTAINTY

ASSAY RESULTS

In this sheet the results of two or three Assays are entered. Calibration dates are entered

so Assays having the same calibration uncertainty may be treated correctly. (Assays having

a common calibration share the same calibration uncertainty.)

Enter the results for up to three separate assays in chronological order below.

ASSAY 1

500 = estimated concentration

0.005 = 95% uncertainty (expressed as percentage of estimated concentration)

0.5 = portion of 95% uncertainty2 due to calibration

35551 = date of prior calibration 

ASSAY 2

500 = estimated concentration

0.005 = 95% uncertainty (expressed as percentage of estimated concentration)

0.5 = portion of 95% uncertainty2 due to calibration

35582 = date of prior calibration 

ASSAY 3 (if applicable)

500 = estimated concentration

0.005 = 95% uncertainty (expressed as percentage of estimated concentration)

0.5 = portion of 95% uncertainty2 due to calibration

35582 = date of prior calibration 

Number of different calibrations represented by the above data:

N = 2 (If this value seems to be incorrect, check the dates

entered for the three assays. The earliest data should

be for Assay 1. Trailing spaces may cause N's formula

to interpret identical dates as different.)
C-2

COMPARISONS

Upper Confidence Limits Variance Components

Calibration Assay Limits 502.5 502.5 502.5 Calibration Imprecision

Lower

Confidence Assay 1 Assay 2 Assay 3

1 1 497.5 --- True True 3.125 3.125

2 2 497.5 True --- True 3.125 3.125

2 3 497.5 True True --- 3.125 3.125

"FALSE" indicates an inconsistency such as an upper confidence limit for one assay that

is lower than a lower confidence limit for another (non-overlapping intervals). "FALSE" will

appear for Assay 3 if no data have been entered for Assay 3.

OVERALL ESTIMATE

Note: Calibration Case = 15

Case Cal. No. Cal. No. Cal. No.

4* = 1 1 ---

6* = 1 2 ---

9 = 1 1 1

12 = 1 1 2

15 = 1 2 2

18 = 1 2 3

*4 and 6 are cases where there is no 3rd assay. In

case 4, the two assays share a common calibration. In

case 6, the two assays have different calibrations.

The standard error of the estimate produced in an assay is equal to approximately 1⁄2 of

the "95% uncertainty." The inverse of the square of the standard error is the (raw)

weighting factor used in producing an overall estimate of the concentration. The raw

weights are adjusted (Adj. Wt.) so their sum is 1.00.

Calibration Estimate Uncert. Raw Wt. Adj. Wt. *Est.

95% Wt. *Conc. of Wt.

Variance

1 500 0.005 40000 0.4285714 214.28571 1.1479592
C-3

2 500 0.0043301 53333.333 0.5714286 285.71429 1.5306122

0 0 0 0

500 = overall estimate of the candidate standard's concentration

1.6366342 = 95% uncertainty (concentration units)

0.0032733 = 95% relative uncertainty

The standard error and 95% uncertainty displayed above do not account for uncertainty

in the reference standards used to calibrate the analytical instrument. In the space below,

enter the 95% uncertainty (typically 2 times the standard error) of the reference standards.

If different calibration standards had different uncertainties, enter the largest.

Example: If NIST SRMs were used in the calibration and their certified concentrations 

were 100 +/- 1 ppm, 200 +/- 1 ppm, 300 +/- 2 ppm, 400 +/- 3 ppm and 500 +/- 4 ppm,

then the largest 95% uncertainty is for the 100 ppm standard: 1/100 = 0.01 or 1%. 

(SRM uncertainties are expressed as two-sigma limits which are 95% confidence

intervals.)

0.005 = 95% uncertainty (2 times the standard error) of the reference standard

0.0059761 = 95% uncertainty of the candidate standard (including the contribution of the

reference standard)
D-1

APPENDIX D: MATRIX NOTATION

1. Matrix Notation

Matrix notation is used to simplify the presentation of calculations that are performed in the linear

regression. A matrix is a rectangular array of numbers. Boldface capital letters represent

matrices, and lower case letters with subscripts represent individual numbers in the matrices. X,

below, is a 10 by 3 matrix. It has 11 rows and 3 columns. The rows are numbered 0, 1, 2,...10

and columns are numbered 0, 1, and 2. (Other texts may begin numbering with 1.)

1 1.002 1.0040

1 0.902 0.8136

1 0.802 0.6432

1 0.701 0.4914

X = 1 0.601 0.3612

1 0.501 0.2510

1 0.401 0.1608

1 0.301 0.0906

1 0.200 0.0400

1 0.100 0.0100

1 0.000 0.0000

Xi,j denotes the number that is found in the ith row and the jth column. X0,1 = 1.002. The first row

and column are numbered zero.

A matrix that has only one column is called a column vector, and a matrix that has only one row

is called a row vector. 

0.999

0.915

0.828

0.738

y = 0.644 is a column vector.

0.549

0.448

0.346

0.237

0.122

0.001

Subscripts following vector names denote the row or column of the vector. For example, y1 is

the number in the second row of y, 0.915. (Remember that we begin counting rows with zero.)
D-2

Matrix operations that come into play for calibration include multiplication, transposition, and

inversion. The rules for these operations can be found in any introduction to matrices. We will

use the following notation for these operations:

X' denotes the transpose of X (the ith column of X becomes the ith row of X')

For the matrices X and Y above, 

1 1 1 1 . . . 1

X' = 1.002 0.902 0.802 0.701 . . . 0.000

1.0040 0.8136 0.6432 0.4914 . . . 0.0000

X'Y denotes multiplication of matrices X' and Y. X' must have the same number of columns as Y

has rows. For the matrix X above,

11 5.511 3.8658 5.827

X'X = 5.511 3.8658 3.0438 and X'Y = 4.0132

3.8658 3.0438 2.5544 3.1272

det(X'X) = 1.0521 (the determinant of X'X)

(X'X) denotes the inverse of the product of X' and X

-1

0.5800 -2.1962 1.7392

(X'X) = 

-1 -2.196 12.5026 -11.5744

1.7392 -11.5744 11.5513

2. Calibration by Linear Regression Using Matrix Notation - Example

The linear regression approach is illustrated below for the simple quadratic curve. 

The starting point for regression analysis will be a matrix named X. This matrix will have 3

columns (one for each coefficient to be determined). The number of rows will be the same as

the number of calibration measurements that are performed by the measurement system. The

first column is a vector of 1s. The second column contains the certified concentrations of the

calibration standards. The third column contains the squares of the values appearing in the

second column. When this matrix is multiplied by the vector of coefficients [b , b , b ], the result 0 1 2

is a vector of responses, so that:

responsei = 1 * b0 + concentrationi * b1 + concentrationi * b2

2

or, letting y represent response and x represent concentration,
D-3

yi = b0 + b1 xi + b2 xi

2

Now, we're interested in estimating the the coefficients b0, b1, and b2, and we're also interested in

computing how much error is involved when we use the information to estimate the concentration

in an "unknown."

3. Determining the Calibration Equation

The coefficients of the calibration equation or curve are found by matrix multiplication and

inversion:

b = (X'X) X'Y = [b , b , b ]

-1

0 1 2

Example

1 1.002 1.0040 0.999 0.9967

1 0.902 0.8136 0.915 0.9151

1 0.802 0.6432 0.828 0.8297

1 0.701 0.4914 0.738 0.7394

X =1 0.601 0.3612 y = 0.644 b'x = 0.6462

1 0.501 0.2510 0.549 0.5491

1 0.401 0.1608 0.448 0.4482

1 0.301 0.0906 0.346 0.3434

1 0.200 0.0400 0.237 0.2336

1 0.100 0.0100 0.122 0.1210

1 0.000 0.0000 0.001 0.0046

 0.0046

b = 1.1837 b' = 0.0046 1.1837 -0.1932

-0.1932

The quadratic calibration curve is: response = 0.0046 + 1.1837 C + -0.1932 * C2
D-4

4. Determining the Estimation and Prediction Error

One assumption that underlies the regression approach is that random error is constant across

the measurement range. Sometimes it may be necessary to apply a transformation in order to

achieve this characteristic, called homogeneity of variance. An estimate of this variance is

obtained using matrix operations:

Var = residual sum of squares / degrees of freedom = Y'Y - b'X'Y / df

This estimate's "degrees of freedom" (df) is the number of calibration points less the number

of coefficients estimated for the calibration equation.

Another important output of the regression analysis is the "variance-covariance" matrix, V:

V = Var * (X'X)

-1

The variance of each coefficient is found in the principal diagonal of V. For example, the

variance of b is V . Covariances are found as off-diagonal elements of V. 0 0,0

Hypothesis tests can be performed and confidence intervals can be estimated for each

coefficient using the coefficient's estimate, the coefficient's variance (contained in V), and the

degrees of freedom, df.

Continuing our example

Var = (Y'Y - b'X'Y) / df = 5.91E-06

3.43E-06 -1.3E-05 1.03E-05

V = -1.3E-05 7.39E-05 -6.8E-05 df = 8

1.03E-05 -6.8E-05 6.83E-05 (df = degrees of freedom)

95% Confidence Interval for b = b +/- t(0.05,df) * sqrt(V ) 0 0 0,0

95% CI for b0 = 0.000324 to 0.008865

t(0.05, df) = 2.306006

95% Confidence Interval for b = b +/- t(0.05,df) * sqrt(V ) 1 1 1,1

95% CI for b1 = 1.163855 to 1.203512

95% Confidence Interval for b = b +/- t(0.975,df) * sqrt(V ) 2 2 2,2

95% CI for b2 = -0.21224 to -0.17413
D-5

Another use of V is in computing the uncertainty in a regression predicted concentration of an 

individual unknown. The analyzer is subjected to the unknown, and a mean response, R, is

produced. A solution for C is found. This is the estimated concentration of the unknown. 

Deriving the confidence intervals for this estimate requires finding two alternative concentrations,

one higher and one lower than the estimate, such that the probability of having produced a lesser

or greater average response is sufficiently small. For a 95% confidence interval, the lower bound

is a concentration whose response would be less than the observed response with 97.5%

probability; the upper bound is a concentration whose response would be less than the observed

response with 97.5% probability.

Unfortunately, for quadratic curves, this derivation is not so simple. 

R measurements of an unknown produce an average response resp:

 R = 6

 resp = 0.601

The estimated concentration is found by solving the following quadratic equation:

0.601 = b0 + b1 C + b2 C2

(b0 - 0.601) + b1 C + b2 C = 0 2

The potential solutions are found using the quadratic formula:

C = 0.553935 and 5.573267 (only the first of these is reasonable)

Now, if the concentration really had been at this value, the 95% confidence interval for

the mean response of six measurements would be symmetric about the observed response:

As above, t = 2.306006

x = 1 0.553935 0.306843 = [1, resp, resp ]

2

xb = 0.601 (check)

var(predicted mean response for x) = [var/R + x' V x]

x'V = -6.09E-07 6.97E-06 -6.7E-06

x'Vx = 1.2E-06

var/6 = 9.86E-07

var(predicted mean response for x) = 2.19E-06

95% confidence interval for predicted response = 0.597588 to 0.604412

This is the observed response -/+: 0.003412 and 0.003412

Solving for concentration, the interval is no longer perfectly symmetric:

0.550418 to 0.557456
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This is the estimated concentration -/+: 0.003516 and 0.003521

As a percentage of the concentration, this is -/+: 0.006348 and 0.0063569

Fortunately, even with the quadratic calibration curve, with good precision, the confidence

intervals will be within a small enough region that the curve is close to linear and the interval will

be very nearly symmetric. The uncertainty criterion for multipoint calibration requires the 95%

confidence interval's half-width to be less than 1%. The calibrated range of the analyzer extends

across all concentrations for which the criterion is satisfied.

Continuing our example

Concentration Response for response concentration concentration

Estimated 95% conf. interval 95% conf. interval for % error for

1.002 0.9967 0.9924 1.0010 0.9966 1.0074 -0.53 0.54

0.902 0.9151 0.9121 0.9181 0.8985 0.9055 -0.39 0.39

0.802 0.8297 0.8273 0.8320 0.7993 0.8047 -0.33 0.33

0.701 0.7394 0.7371 0.7417 0.6985 0.7035 -0.36 0.36

0.601 0.6462 0.6437 0.6487 0.5984 0.6036 -0.43 0.43

0.501 0.5491 0.5466 0.5517 0.4984 0.5036 -0.51 0.52

0.401 0.4482 0.4457 0.4507 0.3986 0.4034 -0.60 0.60

0.301 0.3434 0.3411 0.3457 0.2988 0.3032 -0.72 0.72

0.200 0.2336 0.2313 0.2359 0.1979 0.2021 -1.06 1.06

0.100 0.1210 0.1181 0.1240 0.0974 0.1026 -2.58 2.59

0.000 0.0046 0.0003 0.0089 -0.0036 0.0036 --- ---

0.210 0.2446 0.2423 0.2469 0.2079 0.2121 -0.9996 1.0004

The calibration curve's uncertainty is acceptable for concentrations above 0.21 ppm.

5. Stability Test

As discussed in Subsection 2.1.6.2, the stability test requires at least three initial measurements

of the candidate standard plus at least three additional measurements following a period of 7

days or more. The standard's concentration must be in the calibrated range of the analyzer per

Subsection 2.1.7.2.

Concentrations are estimated using the calibration curve, producing at least three estimates for

the initial concentration and at least three estimates for the concentration following the holding

time. A student's t-test is applied as follows:

Initial Data Final Data (after holding time)
D-7

C1 C4

C2 C5

C3 C6

s1 = standard deviation of (C1, C2, C3) x1 = (C1 + C2 + C3) / 3

s2 = standard deviation of (C4, C5, C6) x2 = (C4 + C5 + C6) / 3

alpha = significance level of the test = 0.05

t(1-alpha/2,df) = value of student's t for which the distribution function value is 0.975

 and degrees of freedom = number of observations - 2

s = sqrt(s + s ) 1 2

2 2

If |x1 - x2| / s > t(1-alpha/2,df) then the difference is statistically significant and the candidate

standard has failed the initial stability test. The test can be repeated after an additional 

7 days or more, using the second and third sets of results in the calculations, as above. If

another significant difference is found, then the candidate standard is unusable and is 

disqualified for further use.

Example:

Initial Data Final Data (after 7-day holding time)

0.995 ppm 0.989 ppm

0.996 ppm 0.989 ppm

0.992 ppm 0.982 ppm

s1 = 0.0020817 ppm x1 = 0.9943333 ppm

s2 = 0.0040415 ppm x2 = 0.9866667 ppm

s = 0.004546 ppm % difference = 0.77% ppm

|x1 - x2| / s = 1.686442

t(1-alpha/2,df) = 2.7764509

The difference is not statistically significant, so the standard can be certified as stable.

6. Recertification

Per Subsection 2.1.6.3, a standard can be recertified if, after the certification period has elapsed,

the mean concentration of at least three assay results is within 1.0 percent of the original certified

concentration. Additionally, the difference between the estimated mean and the certified

concentration must not be statistically significant at the 1% level. 

To determine whether the concentration of the standard has changed since the initial

certification, new measurements are made using a measurement system that has been

calibrated according to Subsection 2.1.7.5. Original certification data are used to provide an

initial estimates of mean (x1) and standard deviation (s1). New data are used to estimate a

second mean (x ) and standard deviation (s ). These are used in a t-test that is similar to that 2 2

used in the stability test. A critical value for t is based on a significance level of 1% (alpha) and

degrees of freedom equal to the number of initial and recertification data minus 2. A pooled
D-8

estimate of the standard deviation (s) is derived from s1 and s2. If the difference between x1 and

x2, divided by s, is greater (in absolute value) than the critical value for t, then the initial and new

concentrations are significantly different and the standard cannot be recertified.

Example:

Initial Data Recertification Data

0.995 ppm 0.989 ppm

0.996 ppm 0.99 ppm

0.992 ppm 0.994 ppm

0.999 ppm

0.999 ppm

0.993 ppm

s1 = 0.0029439 ppm x1 = 0.9956667 ppm

s2 = 0.0026458 ppm x2 = 0.991 ppm

s = 0.0028619 ppm % difference = 0.47%

 |x1 - x2| / s = 1.6306179

t(1-alpha/2,df) = 2.7764509

The % difference is less than the 1% specification, and the difference in means is not found

to be statistically significant. The standard may be recertified. The certified concentration of the

standard is the grand mean of the combined data set.

Certified Concentration = mean (initial data + recertification data) = 0.994 ppm