Method X: Determination of Metal 

Concentrations in Emissions from Stationary 

Sources 

(Instrumental Analyzer Procedure) 

DRAFT 

June 7, 2005

Submitted to: 

The Environmental Protection Agency 

Research Triangle Park, NC 

Prepared by: 

Cooper Environmental Services, LLC 

10180 SW Nimbus Blvd Suite J6 

Portland, Oregon 97223 
 

Method X: Determination of Metal 

Concentrations in Emissions from Stationary 

Sources 

(Instrumental Analyzer Procedure) 

DRAFT

June 7, 2005

Prepared by: 

J.A. Cooper, K. Petterson, B.E. Johnsen, 

C. A. Yanca, M. Nakanishi, D. Barth 

Cooper Environmental Services, LLC 

10180 SW Nimbus Blvd Suite J6 

Portland, Oregon 97223 
 

Method X: Determination of Metal 

Concentrations in Emissions from Stationary 

Sources 

(Instrumental Analyzer Procedure) 

Prepared by:___________________________________ Date:_________

 Krag A. Petterson, Environmental Scientist 

Reviewed by: ___________________________________ Date:_________ 

 Cay A. Yanca, Environmental Scientist 

Reviewed by: ___________________________________ Date:_________ 

 Bruce E. Johnson, QA Manager 

Approved by: ___________________________________ Date:________ 

 John A. Cooper, Director 
Method X: Multi-Metals Instrumental Analyzer Procedure Page i of v 

Executive Summary 

Method X is an instrumental analyzer procedure for the determination of multiple metals 

using x-ray fluorescence as an analytical technique. Method X specifies the criteria for 

accuracy stability and precision that must be met by an x-ray fluorescence based 

instrument analyzer. Method X also describes the emission test procedures associated 

with an x-ray fluorescence based metals measurement system. 
Method X: Multi-Metals Instrumental Analyzer Procedure Page ii of v 

List of Symbols 

Bi = The background concentration of the ith metal as determined by the 

 instrumental metals measurement system 

CDi = X-ray fluorescence calibration drift for the ith metal 

L Ci = Value of the emission limit for the ith metal 

RB CFi = Relative bias correction factor for the ith metal 

di = Difference between paired alternative reference method or reference 

 aerosol and instrumental metals measurement system concentrations for 

the ith metal 

i d = Average difference in concentration between the instrumental 

measurement system and the alternative reference method or aerosol 

0 Li = Zero reference value for the ith element at the last calibration 

IA Li = Concentration reported by the instrumental metals measurement system 

for the ith metal 

IAC Li = Value of the standard reported by the x-ray fluorescence module for the ith

metal 

IAU Li = Response to the ith element in the upscale reference 

IAZ Li = Instrumental metals measurement system response for the ith metal to the 

zero reference 

std Li = Calibrated value of the calibration test standard for the ith element 

u Li = Calibrated value of ith element on the upscale reference 

n = Number of data points 

PRB = Percent i relative bias for the ith metal 

RM Ri = The concentration of the ith metal in the alternative EPA reference 

method data set or reference aerosol concentration 

RM Ri = Average concentration of the ith metal in the alternative EPA reference 

method data set or reference aerosol concentration 

PRSDi = Percent relative standard deviation of the ith metal 

SDi = Standard deviation of differences for the ith metal 

UDi = Upscale drift of the ith metal of an instrumental metals 

 measurement system in percent 

VA = Volume or flow measurement accuracy 

Vc = Volume or flow reported by the instrumental metals measurement 

system’s volume check device 

VD = Volume or flow drift 

VIA = Volume or flow reported by the instrumental measurement system’s 

 volume or flow sample measurement device 

Vr = Sample gas volume measured by the independent calibrated 

 reference device
Method X: Multi-Metals Instrumental Analyzer Procedure Page iii of v 

xi = Value of the ith measurement 

ZDi = Zero drift of ith metal on an instrumental metals measurement system 
Method X: Multi-Metals Instrumental Analyzer Procedure Page iv of v 

Table of Contents 

Executive Summary............................................................................................................. i

1.0 Purpose and Applicability....................................................................................... 1 

1.1 Purpose................................................................................................................ 1 

1.2 Applicability ....................................................................................................... 1 

2.0 Method Summary.................................................................................................... 1 

2.1 Principle .............................................................................................................. 1 

3.0 Range and Sensitivity ............................................................................................. 1 

3.1 Analytical range.................................................................................................. 1 

3.2 Sensitivity ........................................................................................................... 1 

4.0 Definitions............................................................................................................... 2

5.0 Apparatus and Reagents.......................................................................................... 3 

5.1 Measurement system........................................................................................... 3 

5.2 Quality assurance and control materials ............................................................. 4 

5.3 Metals generator.................................................................................................. 5 

5.4 Alternative EPA Reference method.................................................................... 5 

6.0 Measurement System Performance Specifications................................................. 5 

6.1 Zero drift ............................................................................................................. 5 

6.2 Upscale drift........................................................................................................ 5 

6.3 Volume drift........................................................................................................ 6 

6.4 X-ray fluorescence module calibration drift check............................................ 6 

6.5 Volume measurement calibration check............................................................. 6 

6.6 Percent relative bias ............................................................................................ 6 

6.7 Interference Check.............................................................................................. 6 

6.8 Reporting requirements....................................................................................... 6 

7.0 Measurement System Performance Test Procedures.............................................. 6 

7.1 Measurement system preparation ....................................................................... 6 

7.2 Zero drift check................................................................................................... 6 

7.3 Upscale drift check ............................................................................................. 7 

7.4 Volume drift check ............................................................................................. 7 

7.5 X-ray fluorescence calibration drift check.......................................................... 7 

7.6 Volume or flow calibration check....................................................................... 7 

7.7 Relative bias test ................................................................................................. 8 

7.8 Interference check............................................................................................... 9 

8.0 Emissions Test Procedure..................................................................................... 10 

8.1 Performance tests prior to emissions testing..................................................... 10 

8.2 Selection of sampling point .............................................................................. 10 

8.3 Sample collection.............................................................................................. 10 

9.0 Calculations........................................................................................................... 11 

9.1 Arithmetic mean ( x )......................................................................................... 11 

9.2 Zero drift ( ZDi ) ................................................................................................ 11 

9.3 Upscale drift (UDi )........................................................................................... 12 

9.4 Volume drift (VD) ............................................................................................ 12 
Method X: Multi-Metals Instrumental Analyzer Procedure Page v of v 

9.5 X-ray Fluorescence calibration drift (CDi ) ...................................................... 12 

9.6 Volume or flow calibration drift (VA).............................................................. 13 

9.7 Relative bias ( RBi ) ........................................................................................... 13 

9.8 Standard deviation (of differences) ( SDi )........................................................ 14 

9.9 Percent relative standard deviation ( RSDi ) ...................................................... 14 

9.10 Correction factor for relative bias ( RB CFi ) ....................................................... 15 

10.0 Safety .................................................................................................................... 15 

11.0 Tables, Figures for Method X............................................................................... 15 

12.0 References............................................................................................................. 20 
Method X: Multi-Metals Instrumental Analyzer Procedure Page 1 of 1 

1.0 Purpose and Applicability 

1.1 Purpose 

The purpose of Method X is to define the emission test procedures that must be followed 

when using an instrumental metals measurement system that reports metal concentrations 

in emissions from stationary sources using x-ray fluorescence as an analytical technique. 

These criteria and emission test procedures are in place to assure the accuracy and 

reliability of the data produced by the system. 

1.2 Applicability 

This method is applicable to the determination of metal concentrations in emissions from 

stationary sources using an x-ray fluorescence based instrumental metals measurement 

system. 

2.0 Method Summary 

2.1 Principle 

A sample of gas is acquired isokinetically from a stack or duct. A portion of that sample 

source gas is then pulled through a capturing medium where metal analytes are removed 

from the effluent stream and concentrated. The metal analyte sample is then presented to 

the x-ray fluorescence module after enough time has elapsed to allow the metal analytes 

to concentrate sufficiently to be detectable. The masses of metal analytes reported by the 

x-ray fluorescence module is divided by the volume of stack effluent sampled to obtain 

the analyte concentration in the source. 

3.0 Range and Sensitivity 

3.1 Analytical range 

The instrumental metals monitoring system must be able to measure metal concentrations 

in a range from 20% to 400% of the allowed emission limit for each metal as 

demonstrated by laboratory or field trials. 

3.2 Sensitivity 

The minimum detectable limit of the instrumental analyzer depends on the analytical 

range, the signal-to-noise ratio of the measurement system and the presence of 

interferences. The minimum detectable limit must be less than 10% of the applicable 

emission standard. 
Method X: Multi-Metals Instrumental Analyzer Procedure Page 2 of 2 

4.0 Definitions 

Analytical range: The range of metal concentrations the instrument can reliably 

measure.

Diluent analyzer: The portion of the instrumental metals measurement system that 

detects the diluent. The diluent may be detected by the x-ray fluorescence module or by 

another device or technique.

Emission limit: The emission limit for a single metal is equal to the maximum amount 

allowed under the applicable regulation for its category assuming all of the other metals 

in its category were not present. 

Element of opportunity: An element that happens to be present in stack or duct effluent 

that can be used to determine relative bias. 

EPA reference method: A method recognized by the United States Environmental 

Protection Agency as appropriate for the measurement of a pollutant or pollutants in 

source emissions. 

Instrumental metals analyzer: The portion of the instrumental metals measurement 

system containing the components necessary for the measurement of metal 

concentrations, including the sampling module, the x-ray fluorescence module, and the 

volume measurement module. 

Instrumental metals measurement system: All of the equipment required for 

determining metal concentrations using an x-ray fluorescence based approach. An 

instrumental metals measurement system may consist of several modules including, but 

not limited to the following: the sample interface, the x-ray fluorescence module, the 

diluent analyzer, the sampling module, the volume measurement module, and the data 

recorder

Non-quantitative spiking: The process of introducing an unknown concentration of 

metal or metals into a gas stream.

Quantitative spiking: The process of introducing a known concentration of metal or 

metals into a gas stream.

Sample conditioning system: The portion of the sample interface that conditions the 

stack or duct gas to prevent concentration loss and or damage to the x-ray fluorescence 

module. Examples of sample conditioning include heaters and dilutent gas to prevent the 

condensation of water vapor.

Sample interface: The portion of the instrumental metals measurement system that is 

used for extracting a sample from the stack or duct. The sample interface may include 

some or all of the following systems; a sample probe, sample transport system, and 

sample conditioning systems.
Method X: Multi-Metals Instrumental Analyzer Procedure Page 3 of 3 

Sampling module: The portion of the instrumental metals measurement system that 

traps the metals and delivers them to the x-ray fluorescence module. 

Sample probe: The portion of the sample interface that extracts the gas from the stack 

or duct.

Sample transport system: The portion of the sample interface which transports the 

sample stack or duct gas from the downstream end of the sample probe to the sampling 

module. 

Volume drift: The difference in the reading between the sample volume or flow 

measurement device and an independently calibrated volume or flow measurement 

device.

Volume measurement module: The portion of an instrumental measurement system 

that determines sample volume. 

Upscale drift: The difference in the reading for the upscale reference from the calibrated 

value after some period of time during which no maintenance or adjustment took place. 

X-ray fluorescence module: The portion of the instrumental metals measurement 

system that uses x-ray fluorescence as analytical technique to identify metals and to 

determine metal concentrations.

XRF: x-ray fluorescence.

Zero drift: The difference in the reading for zero input from the calibrated value after 

some period of time during which no maintenance or adjustment took place. 

5.0 Apparatus and Reagents 

5.1 Measurement system 

5.1.1 Sample interface 

The sample interface must collect a sample of source effluent isokinetically and 

then transport that effluent to the sampling module. The sample interface must at 

least include the following two elements. 

1. Sample probe The sample probe may be made of glass, stainless steel, 

Teflon-coated steel or other material that will prevent loss or 

contamination of analyte metal or metals. The sample probe may also be 

heated to prevent the condensation of water vapor. 

2. Sample transport lines Lines made from any material that will transport 

the analyte metal with minimal particle loss. The transport lines may be 

heated or allow for the addition of diluent gas to prevent the condensation 

of water vapor. 
Method X: Multi-Metals Instrumental Analyzer Procedure Page 4 of 4 

5.1.2 Sampling module 

The sampling module must include a method for capturing the metal analytes of 

interest and presenting them to the x-ray fluorescence module. The sampling 

module may capture the metals from the entire volume of the sample interface or it 

may extract a sub-sample of source effluent. 

5.1.3 X-ray fluorescence module 

The x-ray fluorescence module uses x-ray fluorescence as an analytical technique 

to identify and determine the mass of metal analytes on the capturing medium. 

5.1.4 Data recorder 

The data recorder should be able to record metals concentrations and instrument 

status signals (flags) that indicate whether the metals measurement system is 

performing appropriately. 

5.1.5 Volume measurement module 

This module must accurately measure the volume of effluent drawn through the 

capture media on a dry basis. 

5.2 Quality assurance and control materials 

5.2.1 Zero drift reference 

An instrumental metals monitoring system must include a means to measure zero 

drift. If feasible this reference should produce an instrumental response indicating 

the absence of metals. If this is not feasible the zero reference should produce a 

value between zero and 20% of the emission limit for at least two of the metals 

measured by the system. 

5.2.2 Upscale drift reference 

An x-ray based instrumental metals monitoring system must include an upscale 

drift reference to measure the upscale drift. The upscale drift reference must 

contain an element measured by each energy condition of the XRF analysis. 

The mass of each metal in the reference must generate an instrumental response 

between 80 and 200 percent of the applicable emission limit. 

5.2.3 Volume or flow drift check device 

An instrumental metals measurement system must include a means of checking the 

sample volume drift or flow drift against another internal measurement device. 

5.2.4 Volume or flow calibration check device 

An instrumental metals measurement system must include a means of checking the 

calibration of the volume or flow measurement device against an externally 

calibrated measurement device. 
Method X: Multi-Metals Instrumental Analyzer Procedure Page 5 of 5 

5.2.5 X-ray fluorescence calibration check standards 

An instrumental metals measurement system must also include a means of 

checking the calibration for every metal it measures for compliance purposes. 

NIST traceable thin film standards are an example of a suitable calibration check 

standard. 

5.3 Metals generator 

A method of metals generation is necessary to determine the relative bias of the metals 

measurement system and is required for the interference check if it is performed. The 

following are optional sources of metals that may be used for this purpose. 

5.3.1 Quantitative aerosol generator 

A quantitative aerosol generator produces known metals concentrations in a gas 

stream The known concentrations of the analytes are compared with the 

values reported by the instrumental metals measurement system. 

5.3.2 Non-quantitative aerosol generator 

A non-quantitative aerosol generator produces metals at unknown concentrations in 

a gas stream. To use this approach the concentrations of metals produced by the 

non-quantitative aerosol generator must be measured using an independent 

alternative EPA reference method. The concentration from the alternative 

reference method can then be compared to the concentration reported by the 

instrumental measurement system to determine percent relative bias. 

5.3.3 Source operation 

The metal used during the relative bias test can also be produced by operating the 

source. The metal or metals produced in routine operation can then be measured by 

an appropriate alternative EPA reference method. The concentration, as 

determined by the alternative reference method is then compared with the 

concentration from the instrumental metals measurement system. The metal used 

as the analyte for this test is called an element of opportunity. 

5.4 Alternative EPA Reference method 

Some of the procedures to determine percent relative bias require the use of an alternative 

EPA reference method. The alternative reference method must be able to accurately 

measure the concentration of the metal used during the bias test. 

6.0 Measurement System Performance Specifications 

6.1 Zero drift 

The zero drift, calculated using Equation 3, must be less than 20% of the applicable 

emission limit for each element and each measurement. 

6.2 Upscale drift 

The upscale drift, calculated using Equation 4, must be less than 15% of the value 

determined immediately after calibration for each metal on the upscale reference. 
Method X: Multi-Metals Instrumental Analyzer Procedure Page 6 of 6 

6.3 Volume drift 

The volume or flow drift, calculated using Equation 5, must be less than 10% of the full 

scale value of the flow or volume measurement device. 

6.4 X-ray fluorescence module calibration drift check 

The x-ray fluorescence calibration drift, calculated using Equation 6, must be less than 

10% of the known value of the standard for each metal measured by the instrumental 

analyzer for reporting purposes. 

6.5 Volume measurement calibration check 

The volume or flow measurement made by the instrumental system shall be less than 

10% (calculated using Equation 7) of the volume or flow measurement made by the 

externally calibrated volume or flow measurement device. 

6.6 Percent relative bias 

If the percent relative bias (calculated using Equation 8) is less than 15% and the relative 

standard deviation (calculated using Equation 11) is less than 10% no correction is 

required. If the relative percent bias exceeds 15% and the relative standard deviation is 

less than 10% then a correction factor must be applied to the data using Equation 12. If 

the relative percent standard deviation exceeds 10% a correction factor cannot be applied 

and the instrumental metals measurement system must be adjusted or repaired before it 

can be used. 

6.7 Interference Check 

The average percent relative bias must be less than 15% and the relative standard 

deviation must be less than 10%. 

6.8 Reporting requirements 

An instrumental metals measurement system must report a concentration in the units of 

the applicable standard or in units that can be converted to the applicable standard. 

7.0 Measurement System Performance Test Procedures 

The following procedures must be performed prior to emissions testing. 

7.1 Measurement system preparation 

Assemble the measurement system following the manufacturer’s instructions. Adjust all 

flow rates and heaters to the settings that will be used during sampling. The following 

tests are required after the measurement system has been assembled. 

7.2 Zero drift check 

A zero drift check must be performed before and after each day of emissions testing. The 

zero drift check must be performed according to the procedures provided by the 

instrumental system’s manufacturer. If the instrumental metals measurement system fails 

the zero drift check it must be repaired or recalibrated and all the emission test runs 

performed since the last successful zero drift check shall be considered invalid. After 
Method X: Multi-Metals Instrumental Analyzer Procedure Page 7 of 7 

appropriate repairs have been made the system must pass a zero drift check before testing 

can resume. If changes are made to the calibration of the x-ray fluorescence module the 

measurement system must also pass an x-ray fluorescence calibration drift check. 

7.3 Upscale drift check 

An upscale drift check must be performed before and after each day of emissions testing 

according to the procedures provided by the manufacturer. If the instrumental metals 

measurement system fails the upscale drift check it must be repaired or recalibrated and 

all emission test results acquired since the last successful upscale drift check shall be 

considered invalid. After appropriate repairs have been made to the system, it must pass 

an upscale drift check before emissions testing can resume. If changes are made to the 

calibration of the x-ray fluorescence module the measurement system must also pass an 

x-ray fluorescence calibration drift check. 

7.4 Volume or flow drift check 

A volume drift check must be performed before and after each day of emissions testing 

according to the procedures provided by the instrumental manufacturer. This is an 

internal check of the volume or flow measurement against another flow or volume 

measurement device. If the instrumental metals measurement system fails the volume or 

flow drift check the volume module must be repaired or adjusted and all emissions test 

results acquired since the last successful volume or flow drift check shall be considered 

invalid. The measurement system must successful pass a volume or flow drift check and 

a volume or flow calibration drift check before emissions testing can resume. 

7.5 X-ray fluorescence calibration drift check 

The x-ray fluorescence module calibration drift check must be performed before the start 

of sample measurement and is only performed once per visit to a site. A calibration drift 

check should also be performed if the x-ray fluorescence module is recalibrated for any 

reason during the emissions test. 

During a calibration drift check the x-ray fluorescence analyzer is challenged with NIST 

traceable standards. The calibration of every element that will be measured during the 

emission test must be checked. Each standard must only to be checked once. If the 

calibration drift exceeds plus or minus 10% of the standard’s value the instrument must 

be recalibrated and retested for that element. 

7.6 Volume or flow calibration check 

If the instrumental metals measurement system determines volume or flow as part of its 

metals concentration measurement, a volume or flow calibration check must be 

performed. This check must be performed at least once per site visit prior to the start of 

emissions testing. The check must also be executed if adjustments are made during 

emissions testing to the flow or volume measurement devices. 

If the instrumental metals measurement system determines volume, as opposed to flow, 

the value reported by the system during one sample run must be compared to the value 

reported by an independently calibrated standard such as a dry gas meter. The sampling 
Method X: Multi-Metals Instrumental Analyzer Procedure Page 8 of 8 

time during the volume measurement must be equivalent to the sampling time that will be 

used during emissions testing. 

If the instrumental metals measurement system measures flow and totalizes that flow to 

produce a volume, a flow calibration check may be performed in lieu of a volume 

calibration check. For this calibration check, the flow reported by the instrumental 

metals measurement system is compared with an independently calibrated flow 

measurement device such as a NIST traceable Dry Cal® at 3 to 5 points throughout a 

single sampling period. The error of each measurement is calculated and the average 

error computed. 

If the instrumental metals measurement system fails a volume or flow calibration drift 

check the volume measurement module may need repair. The system must pass another 

volume or flow calibration drift check before emissions testing can resume. 

7.7 Relative bias test 

The percent relative bias must be determined using at least one metal which may be an 

analyte measured for compliance purposes or a surrogate metal (e.g., iron) that can be 

measured by the instrumental metals measurement system. At least three measurements 

are required to establish the average relative bias. If the instrumental metals 

measurement system is being compared to an alternative EPA reference method, at least 

three simultaneous measurements with the alternative reference method are necessary. 

The requirements for the relative bias test associated with the three possible metals 

generation requirements are outlined below. 

7.7.1 Option 1: Quantitative spiking 

In this approach to determining bias, an aerosol of known concentration produced 

according to the specifications laid out in PS-QRAG1

 is spiked into the sample 

transport line as close as possible to the sample probe. This concentration should 

be between 80 and 120 percent of the emission limit. (If a surrogate metal is spiked 

then the concentration should be at 80 to 120 percent of the emission limit for the 

analyte metal with the highest emission limit). The concentration reported by the 

instrumental metals measurement system is compared with the known 

concentration of the spiked aerosol and the percent relative bias and the percent 

relative standard deviation are calculated. 

7.7.2 Option 2: Elements of opportunity 

In this approach the instrumental metals measurement system may be used to 

determine if an element of opportunity is present in the source. If one is present, 

the concentration of that metal must be determined using an alternative EPA 

reference method sampling from the stack or from a point in the transport line as 

close as possible to the sample probe. The alternative reference method 

concentration is compared with the concentration reported by the instrumental 

metals monitoring system. The element of opportunity should be present at 

concentrations well above method detection limits to be used in the relative bias 

test. 
Method X: Multi-Metals Instrumental Analyzer Procedure Page 9 of 9 

7.7.3 Option 3: Non-quantitative spiking 

An aerosol at a concentration level between 80 and 120 percent of the emission 

limit is spiked either into the source or into the sample interface as close as possible 

to the probe. The metal concentration may be determined using a suitable 

alternative EPA reference method. The alternative reference method concentration 

is compared with the measurement made by the instrumental metals measurement 

system. If the metal is spiked into the source the alternative reference method may 

be located either directly in the source or in the transport line as close as possible to 

the sample probe. If the metal is spiked into the transport line then the reference 

method measurements must be made as close as possible to the spiking location. 

7.8 Interference check 

An interference check tests for interferents in the source emissions that inhibit or prevent 

the measurement of analyte metals. For this reason, the instrumental analyzer must 

sample flue gas during the interference check. This check must be performed for each 

model of x-ray fluorescence instrumental metals analyzer the first time that model is used 

on a particular source category. The results of this test must then be retained and 

submitted along with the emissions test results whenever the instrumental metals analyzer 

is used on that particular source category. If an instrumental metals measurement system 

fails an interference test it may not be used for emissions test on that particular source 

category until it does pass an interference check. 

The procedures for the interference test are very similar to the sample interface relative 

bias test. For each test the relative bias and relative percent standard deviation are 

calculated. As with the relative bias test there are three options for performing (only one 

of the options must be executed) the interference check based on the type of metals 

generation performed: 1) Option A. Quantitative spiking, 2) Option B. Element of 

opportunity, and 3) Option C. Non-quantitative spiking. The inference check, however, 

is testing for bias resulting from problems with the capture of metal analytes in the 

sampling module or problems with the x-ray fluorescence, while the relative bias test 

determines the instrumental metals measurement system bias primarily resulting from the 

sample interface. 

7.8.1 Option A: Interference check with quantitative spiking 

For the interference check the quantitative spike injection point should be located 

as close as possible to the sampling module. Only one metal, either an analyte that 

will be measured or a surrogate must be spiked. The concentration level of the 

analyte or surrogate metal in the background should be checked using the 

instrument analyzer. It is recommended that the spiked metal not be present at 

detectable concentrations in the stack. If it is present, the bias may be calculated by 

subtracting the average background concentration using equation 9. At least nine 

sampling periods of 15 minutes or longer are required. The known concentration 

of the spiked metal is compared with the concentration reported by the instrumental 

analyzer to determine percent relative bias. 
Method X: Multi-Metals Instrumental Analyzer Procedure Page 10 of 10 

7.8.2 Option B: Interference check with an element of opportunity 

The element of opportunity may be any metal present in the stack gas that can be 

measured by the instrumental metals analyzer and by an alternative EPA reference 

method and is present at high enough concentrations to be used. The alternative 

reference method must placed as close as possible to the sampling module and 

concentration reported by the method is compared with that reported by the 

instrumental metals analyzer. Nine simultaneous runs of both the alternative 

reference method and the instrumental analyzer are required. 

7.8.3 Option C: Interference check using non-quantitative spiking. 

For option C the non-quantitative spike injection point may be anywhere upstream 

of the sampling module. An alternative EPA reference method is required to use 

Option C and it must be located as close as possible to the sampling module. Only 

one metal, either an analyte that will be measured during the emissions test or a 

surrogate such as iron, must be spiked. As for the element of opportunity nine 

simultaneous runs of the alternative reference method and the instrumental analyzer 

are required. 

8.0 Emissions Test Procedure 

8.1 Performance tests prior to emissions testing 

The appropriate measurement system performance tests must be completed according the 

procedures in sections 7.1 to 7.8 prior to the start of emissions testing. 

8.2 Selection of sampling point 

It is recommended that the sampling location be at least two equivalent diameters 

downstream of any control devices, point of pollution generation, bend or other point at 

which a change in pollution concentration or flow disturbance may occur and be at least 

two equivalent diameters upstream of the exhaust. The equivalent diameter is calculated 

according 40 CFR Part 60, Appendix A, Method 1, Section 2.1.2 

8.3 Sample collection 

8.3.1 Traverses 

An instrumental metals measurement system must sample at the appropriate 

traverse points as outlined in Method 12

 or another EPA approved alternative for 

the selection of sampling points. A sampling run consists of sampling all required 

traverse points over a period of 15 minutes to one third the applicable regulation, 

depending on source conditions and metal concentrations. If feasible all traverse 

points must be sampled for approximately equal lengths of time. 

8.3.2 Isokinetics 

An instrumental metals measurement system must acquire a representative sample 

of source effluent by either sampling at a flow rate that is plus or minus10% of 

isokinetic or by using another means approved by the EPA. Velocity 
Method X: Multi-Metals Instrumental Analyzer Procedure Page 11 of 11 

measurements to determine the percent of isokinetic must be performed according 

to EPA approved procedures such as those outlined in Method 2.3 

8.3.3 Possible additional measurements 

Additional measurements may be required to report the results in units of the 

applicable standard. Among these are source moisture content and percent oxygen 

content. 

9.0 Calculations 

9.1 Arithmetic mean ( x )

= ∑xi

n

x

1 Equation 1 

Where : 

 n = Number of data points 

xi = Value of the ith measurement 

9.1.1 Arithmetic mean of a difference. To calculate the arithmetic mean of 

difference use the above equation substitute di for xi. The

i i di = x − y Equation 2 

Where x and y are paired data points from the instrumental metals measurement 

system and either the reference aerosol or the alternative reference method. 

9.2 Zero drift ( ZDi )

100

0

× − = L

i

i

IAZ

i

i C

L L

ZD Equation 3 

Where: 

ZDi = Zero drift of ith metal on the instrumental metals 

measurement system in percent 
Method X: Multi-Metals Instrumental Analyzer Procedure Page 12 of 12 

IAZ Li = Instrumental metals measurement system response for the ith 

metal to the zero reference 

0 Li = Zero reference value for the ith element at the last calibration 

L Ci L R i

 = Value of the emission limit for the ith metal 

9.3 Upscale drift (UDi )

×100 − = u

i

u

i

IAU

i

i L

L L

UD Equation 4

Where: 

 UDi = Upscale drift of the ith metal of an instrumental metals 

 measurement system in percent. 

IAU Li = Response to the ith element in the upscale reference 

u Li = Calibrated value of ith element on the upscale reference 

9.4 Volume drift (VD)

×100 − = FS

V V

VD IA c

Equation 5

 VD = Volume or flow drift 

 Vc = Volume or flow reported by the instrumental metals 

measurement system’s volume check device 

 VIA = Volume or flow reported by the instrumental measurement 

system’s volume or flow sample measurement device 

 FS = The full scale value of the volume or flow measurement device 

9.5 X-ray Fluorescence calibration drift (CDi )
Method X: Multi-Metals Instrumental Analyzer Procedure Page 13 of 13 

×100 − = std

i

std

i

IAC

i

i L

L L

CD Equation 6

Where: 

CDi = x-ray fluorescence module drift for the ith metal 

IAC Li = Value of the standard reported by the x-ray fluorescence 

module for the ith metal 

std Li = Calibrated value of the calibration test standard for the ith

element 

9.6 Volume or flow calibration drift (VA)

×100 − =

r

r IA

V

V V VA Equation 7

Where: 

VA = Volume (or flow) measurement accuracy 

 Vr = Sample gas volume (or flow) measured by the independent 

calibrated reference device 

 VIA = Sample gas volume (or flow) reported by the instrumental 

metals measurement system 

9.7 Relative bias ( RBi )

= ×100

RM

i

i

i

R

d

PRB Equation 8 

 Where: 

PRB = i Percent Relative Bias for the ith metal 

i d = Average difference between the instrumental metals 

measurement system and the alternative reference method or aerosol 
Method X: Multi-Metals Instrumental Analyzer Procedure Page 14 of 14 

9.7.1 For option A: interference check using quantitative spiking 

Substitute the following equation for di when using quantitative spiking in the 

presence of a significant and stable background concentration of the spiked metal

 RM

i i

IA di = Li − B − R Equation 9 

 Where: 

IA Li = Concentration reported by the instrumental metals 

measurement system for the ith metal 

Bi = The background concentration of the ith metal as determined by 

the instrumental metals measurement system 

RM Ri = Concentration of reference aerosol or concentration reported by 

the alternative EPA reference method for the ith metal 

9.8 Standard deviation (of differences) ( SDi )

1

1 2 2

−

∑ ∑ −

=

⎟

⎠

⎞ ⎜

⎝

⎛

n

d

n

d

SD

i i

i Equation 10 

 Where: 

SDi = Standard deviation of differences for the ith metal 

 di = Difference between paired alternative reference method or 

reference aerosol and the instrumental metals measurement system 

concentrations for the ith metal 

9.9 Percent relative standard deviation ( RSDi )

= ×100

RM

i

i

i

R

SD PRSD Equation 11 

Where: 

PRSD i = Percent relative standard deviation of the ith element 
Method X: Multi-Metals Instrumental Analyzer Procedure Page 15 of 15 

RM Ri = Average concentration of the ith metal in the alternative EPA 

reference method data set or reference aerosol concentration 

SD = i Standard deviation of the instrumental measurement system 

concentrations for the ith metal 

9.10 Correction factor for relative bias ( RB CFi )

IA

i

RM

i

RM

i

i

RB

i

L

R

R

d

CF =

+

=

1

1 Equation 12 

 Where: 

RB CFi = Relative bias correction factor for the ith metal 

RM Ri = Average of the alternative reference method data set or the 

reference aerosol concentration for the ith metal 

d i = The average difference between the instrumental measurement 

system and the alternative reference method or reference aerosol for the ith

metal (where di is calculated according to the following equation) 

RM

i

IA di = Li − R Equation 13 

 

 Where: 

IA L = i Concentration reported by the instrumental metals 

measurement system for the ith metal 

RM Ri = Concentration of reference aerosol or concentration reported by 

the alternative EPA reference method for the ith metal 

10.0 Safety 

People using method X may be exposed to hazardous materials, operational hazards and 

dangerous site conditions. Method X does not purport to address all of the safety issues 

associated with its use. Consult the instrumental metals measurement system 

manufacturer for safety procedures related to its use. Confer with the site safety 

manager concerning safety procedures particular to the emission test site and review all 

appropriate material safety data sheets when working with chemical hazards. 

11.0 Tables, Figures for Method X 
Method X: Multi-Metals Instrumental Analyzer Procedure Page 16 of 16 

Table 1. Performance Test Procedures and Passing Criteria For Metals IAP 

Test Procedure Criteria Frequency 

Zero drift Run zero standard at least 2 

times per sampling day 

<20% drift Before and after each day 

of sampling 

Upscale drift Run upscale standard at least 2 

times per sampling day 

<15% drift from original 

calib. 

Before and after each day 

of sampling 

Volume Drift Run volume drift check at least 

2 times per sampling day 

<20% drift from 

independent flow device. 

Before and after each day 

of sampling 

X-ray Fluorescence 

Calibration Drift 

Check 

Run a standard for each metal 

measured for compliance 

purposes 

<10% for each element Once each time the 

instrument is set up in a 

particular location 

Volume 

Measurement 

Calibration Check 

• 1 sampling period 

• For flow 3 to 5 

measurements of flow during 

a sampling cycle 

• Calculate difference or for 

flow average difference 

<10% Once each time the 

instrument is set up at a 

particular location 

Option 1 

Quantitative spiking at stack 

• 3 measurements of 

instrumental metals 

measurement system 

• Only one metal must be 

spiked 

• RB<15% 

• %RSD<10% 

• If RB criteria not met 

apply a correction 

Option 2

Element of opportunity 

• Determine identity of 

element of opportunity 

• Run the instrumental method 

and the alt. reference method 

simultaneously 

• Analyze alt. reference 

method and compare results 

• RB<15% 

• %RSD<10% 

• If RB criteria not met 

apply a correction 

Sample Interface 

Relative Bias Option 3

Non-quantitative spike 

• Spike into stack or transport 

line 

• Run the instrumental method 

and the alt. reference method 

simultaneously 

• At least three cycles of the 

instrumental metals 

measurement system 

• At least three alt. reference 

method measurements 

• Analyze alt. reference 

method and compare 

• Only one metal must be 

spiked 

• RB<15% 

• %RSD<10% 

• If RB criteria not met 

apply a correction 

Once each time instrument 

is set up at particular 

location 

Interference Check 

See table 3 for Interference 

check options and procedures • Relative Bias<15% 

• %RSD<10% 

• No correction factor 

allowed. 

Once per instrument model 

on each source category 
Method X: Multi-Metals Instrumental Analyzer Procedure Page 17 of 17 

Table 2. Spiking and Alternative EPA Reference Method Options for Sampling 

Bias Tests 

Source of Metals for Bias 

Test 

Location of Spike 

(if applicable) 

Location of Alternative 

EPA Reference Method (if 

applicable) 

Quantitative Spike In transport line as close as 

possible to sample probe. 

N/A 

Option A

In stack 

In stack 

-orIn transport line as close as 

possible to the sample probe

Non-Quantitative Spike 

Option B

In transport line as close as 

possible to the sample probe

In transport line 

immediately downstream of 

spike location 

Option A

In stack 

Element of Opportunity N/A 

Option B

In transport line as close as 

possible to the sample probe

Table 3. Spiking and Alternative EPA Reference Method Locations for Interference 

Checks 

Metals Generation 

Options 

Spiking Location (if 

applicable) 

Location of Alternative 

EPA Reference Method (if 

applicable) 

Option A: Quantitative 

spiking 

As close as possible to the 

sampling module 

N/A 

Option B: Element of 

opportunity 

N/A As close as possible to the 

sampling module 

Option C: Non-quantitative 

spiking 

Anywhere upstream of the 

alternative EPA reference 

method 

As close as possible to the 

sampling module 
Method X: Multi-Metals Instrumental Analyzer Procedure Page 18 of 18 

Figure 1 Alternative Reference Method or Spiking Location for the Relative Bias 

Test with (1) Quantitative Spiking , with (2) Non-Quantitative Spiking into the 

source and using the Alternative Reference Method in the Transport Line, or with 

(3) an Element of Opportunity using the Alternative Reference Method in the 

Transport Line. 
Method X: Multi-Metals Instrumental Analyzer Procedure Page 19 of 19 

Figure 2. Using Non-Quantitative Spiking into the Transport Line During the 

Relative Bias Test 

Figure 3. Using Non-Quantitative Spiking or an Element of Opportunity with the 

Alternative Reference Method in the Source During the Relative Bias Test. 
Method X: Multi-Metals Instrumental Analyzer Procedure Page 20 of 20 

12.0 References 

1 Performance Specification XX. Performance Specifications for A Quantitative 

 Reference Aerosol Generator. 2005 

2 United States. Environmental Protection Agency [EPA]. Technology Transfer 

Network. Emission Measurement Center. Promulgated Methods. Method 1: 

Sample and Velocity Traverses for Stationary Sources. Washington, DC: EPA; 

2004. Available: http://www.epa.gov/ttn/emc/promgate/m-01.pdf via the Internet. 

Accessed May 8, 2005. 

3 United States. Environmental Protection Agency [EPA]. Technology Transfer 

 Network. Emissions Measurement Center. Promulgated Methods. Method 2. 

Determination of Stack Gas Velocity and Volumetric Flow Rate (Type S Pitot 

Tube). Washington, DC. EPA, 2004. Available: 

http://www.epa.gov/ttn/emc/promgate/m-02.pdf via the internet. Accessed June 6, 

2005.