Procedure Z: Quality Assurance Requirements for 

X-Ray-Fluorescence Based Multi-Metals 

Continuous Emission Monitoring Systems at 

Stationary Sources 

DRAFT 

June 9, 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
Procedure Z: Quality Assurance Requirements for 

X-Ray-Fluorescence Based Multi-Metals 

Continuous Emission Monitoring Systems at 

Stationary Sources 

DRAFT 

June 9, 2005

Prepared by: 

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

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

Prepared by: 

Cooper Environmental Services, LLC 

10180 SW Nimbus Blvd Suite J6 

Portland, Oregon 97223
Procedure Z: Quality Assurance Requirements for 

X-Ray-Fluorescence Based Multi-Metals 

Continuous Emission Monitoring Systems at 

Stationary Sources 

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 
Quality Assurance for XRF Based Multi-Metals CEMS (Procedure Z) Page i of iv 

Executive Summary 

 Procedure Z outlines the continuing quality control and quality assurance 

requirements for an x-ray fluorescence based multi-metal CEMS. Procedure Z requires daily 

checks of the upscale, zero and volume measurement drift. It also specifies quarterly checks 

of the x-ray fluorescence calibration and of the volume measurement calibration. Finally 

procedure Z requires that the entire XRF multi metal CEMS accuracy be verified on an 

annual basis. 
Quality Assurance for XRF Based Multi-Metals CEMS (Procedure Z) Page ii of iv 

List of Symbols 

bo = The y intercept of the best fit line 

b1 = The slope of the best fit line 

CAi = X-ray fluorescence calibration accuracy 

C Ci = Corrected CEMS concentration for the ith element 

CEMS Ci = The concentration of the ith element as reported by the CEMS 

CEM Ci = The average reported concentration of the CEMS for the ith element 

PT CFi = Correction factor for percent transport for the ith element 

RB CFi = The relative bias correction factor for the ith element 

L Ci = The emission limit of the ith element 

S Ci = Concentration of the ith element at the stack 

sm Ci = Concentration of the ith element at the sampling module or as reported by the 

XRF multi-metals CEMS. 

di = Difference between two paired measurements 

d = Arithmetic mean of differences 

FS = Full scale value of your CEMS volume (or flow) measurement device 

0 Li = The calibrated value of the ith element on the zero standard 

cem Li = The value of the standard reported by your CEMS 

cemo Li = The measured CEMS response to the zero standard for the ith element 

cemu Li = The measured CEMS response to the ith element in the upscale standard

std Li = The known value of the XRF calibration check standard 

u Li = The value of the ith element of the upscale standard

n = Number of data points 

PTi = The percent transport of the ith element
Quality Assurance for XRF Based Multi-Metals CEMS (Procedure Z) Page iii of iv 

PT i = Average percent transport for the ith element 

PRBi = Percent relative Bias of the ith element 

RM Ri = The average of the reference method measurements for the ith metal 

PRSDi = The relative percent standard deviation for the ith metal 

r = The correlation coefficient 

SDi = The standard deviation of differences for the ith element 

Vcemr = Sample gas volume (or flow) as measured by the CEMS volume check device 

VD = Volume drift 

Vm = Volume (or flow) reported by your multi-metals CEMS 

UDi = The upscale drift of the ith element on your CEMS in percent. 

x = Arithmetic mean

xi = Value of each data point 

yi = CEMS reported concentration for the ith element 

ZDi = The zero drift of the ith element on your CEMS in percent
Quality Assurance for XRF Based Multi-Metals CEMS (Procedure Z) Page iv of iv 

Table of Contents 

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

List of Symbols......................................................................................................................... ii 

Table of Contents..................................................................................................................... iv 

1.0 Using Procedure Z ........................................................................................................... 1 

1.1 What is the purpose and applicability of Procedure Z?............................................. 1 

1.2 What are the basic requirements of Procedure Z?..................................................... 1 

1.3 What special definitions apply to procedure Z? ........................................................ 1 

2.0 Interferences, Safety, and Equipment Requirements....................................................... 2 

2.1 What interferences are associated with procedure Z? ............................................... 2 

2.2 What do I need to know to ensure the safety of persons using Procedure Z? ........... 2 

2.3 What equipment and supplies do I need? .................................................................. 3 

2.4 What reagents and standards do I need?.................................................................... 3 

2.5 What sample collection, preservation, storage, and transport procedures are relevant 

to Procedure Z? ............................................................................................................... 4

3.0 Quality Control, Calibration, and Standardization .......................................................... 4 

3.1 What quality control measures are required by this procedure for my multi-metal 

CEMS? ............................................................................................................................ 4 

3.2 What calibration checks and audit procedures must I perform for my multi-metal 

CEMS? ............................................................................................................................ 4 

4.0 Calculations ..................................................................................................................... 7 

4.1 What calculations and data analysis must I perform?................................................ 7 

4.2 What waste management procedures are required for procedure Z?....................... 13 

5.0 Other Requirements and Information ............................................................................ 13 

5.1 What pollution prevention measures must I take when using procedure Z?........... 13 

5.2 What criteria are necessary for my XRF multi-metal CEMS to be in control and 

what do I do if it is out of control?................................................................................ 13 

5.3 What tables, diagrams and flow charts are relevant to Procedure Z?...................... 16 

5.4 What references are relevant to Procedure Z? ......................................................... 18 

 
Quality Assurance for XRF –Based Multi-Metal CEMS (Procedure Z) Page 1 of 1 

1.0 Using Procedure Z 

1.1 What is the purpose and applicability of Procedure Z? 

The purpose of Procedure Z is to establish the minimum requirements for quality control 

(QC) and quality assurance (QA) procedures for x-ray fluorescence (XRF) based multimetals CEMS. These quality control and quality assurance procedures are in place to ensure 

the accuracy and validity of the data reported by your multi-metal CEMS for emission 

compliance purposes. You must meet these minimum requirements if you plan to use your 

multi-metal CEMS for reporting purposes, however, we encourage you to develop a more 

extensive QA program or to continue with such programs where they already exist. Any 

XRF multi-metals CEMS used to report to us, the state, or a local enforcement agency must 

comply with procedure Z immediately after the completion of the initial performance 

specification test outlined in Performance Specification YY1. 

1.2 What are the basic requirements of Procedure Z?

Procedure Z requires you to perform several drift checks and audits which ensure the 

accuracy of the data reported by your XRF multi-metals CEMS. You are required to, on a 

daily basis, record and calculate zero drift, upscale drift, and, a sample volume drift. On a 

quarterly basis you are required to perform an XRF calibration audit (XFCA) and a sample 

volume audit (SVA). On an annual basis you are required to execute either a linearity audit 

(LA) or a relative bias audit (RBA) and, if applicable, a transport efficiency audit (TEA). 

The criteria for passing these audits and drift checks are outlined in procedure Z. Procedure 

Z also summarizes the requirements for when and if your CEMS fails an audit or drift test. 

Finally, Procedure Z also covers the requirements for and timelines associated with periods 

when your XRF multi-metals CEMS is out of control. 

1.3 What special definitions apply to procedure Z? 

Linearity Audit: (LA) An assessment of the validity of the original linear correlation of 

your CEMS. 

Reference material: A material of known value used to check the calibration drift of your 

XRF multi-metal CEMS. 

Relative Bias: The difference between a reference method or aerosol concentration and the 

concentration recorded by your CEMS divided by the concentration of the reference 

measurement. 

Relative Bias Audit: (RBA) An assessment of the bias in your CEMS. 

Sample Interface: The portion of the CEMS used for one or more of the following: sample 

acquisition from the stack or duct effluent, sample transport, sample conditioning, or 

protection of the monitor from the effects of stack gas. 
Quality Assurance for XRF Based Multi-Metals CEMS (Procedure Z) Page 2 of 2 

Sample Module: The portion of the XRF multi-metal CEMS that traps the metals and 

delivers them to the x-ray fluorescence module. 

Standard Volume Audit: (SVA) This is an evaluation of your XRF multi-metals CEMS 

sample volume measurement system. This is required if your CEMS uses a volume 

measurement to report metal concentrations and is accomplished by comparing the volume 

measured by your CEMS with the volume measured by an independently calibrated device. 

Transport Efficiency Audit: (TEA) An assessment of the transport efficiency of the sample 

interface of your multi-metals CEMS. This audit applies to your XRF multi-metals CEMS if 

either the RBA or LA challenged only the sampling and XRF modules. 

Transport System: The portion of the CEMS that transports a representative sample of 

source effluent from the sample probe to the sample module. 

X-Ray Fluorescence Calibration Audit: (XFCA) This is an evaluation of how well the xray fluorescence portion of your multi-metals CEMS has maintained its original calibration. 

This is accomplished by challenging the XRF module with a standard of known 

concentration for each metal measured by your CEMS for compliance. The analyzer 

response is compared with the known concentration of the standard. 

X-Ray Fluorescence Module: The portion of an XRF based multi-metal CEMS which 

identifies and measures metal masses or concentrations using x-ray fluorescence. 

XRF Multi-Metals Continuous Emission Monitor (CEMS): All of the equipment required 

for determining metal concentrations using x-ray fluorescence as an analytical technique. 

The system may consist of several major subsystems including the sample interface, the xray fluorescence module, the volume measurement module, diluent analyzer, data recorder, 

and sampling module. 

2.0 Interferences, Safety, and Equipment Requirements 

2.1 What interferences are associated with procedure Z? 

There may be interferences arising from the x-ray fluorescence, the trapping media, or from 

condensation in the effluent gas. Check with your multi-metal CEMS manufacturer to find 

out more about potential interferences. 

2.2 What do I need to know to ensure the safety of persons using Procedure Z? 

Persons using procedure Z may be exposed to hazardous materials, equipment, and 

operations. Procedure Z does not purport to address all of the safety issues associated with 

its use. It is your responsibility to establish appropriate safety and health practices before 

using this procedure. You may consult with your CEMS manual and/or manufacturer for 

precautions specific to your multi-metal CEMS. If standard reference methods are used then 

you may also consult the appropriate reference methods to address safety concerns. 
Quality Assurance for XRF Based Multi-Metals CEMS (Procedure Z) Page 3 of 3 

2.3 What equipment and supplies do I need? 

[reserved] 

2.4 What reagents and standards do I need? 

Reference materials for the zero and upscale drifts along with a reference measurement 

device for the sample volume check. 

2.4.1 Zero drift reference 

Every XRF multi-metals CEMS must be equipped with a zero reference that can be 

checked on a daily basis. This reference should produce a CEMS response indicating 

the absence of metals. If this is not feasible this standard should produce a value 

between zero and 20% of the emission limit for at least two elements measured by your 

XRF multi-metals CEMS when the instrument is operating appropriately. 

2.4.2 Upscale drift reference 

The reference for the upscale drift check should generate a response for at least one 

metal from each condition used in the XRF analysis. This response must be at least 80 

percent of the emission limit. 

2.4.3 Sample volume or flow check 

If your XRF multi-metals CEMS makes volume or flow measurements it must be 

equipped to perform a daily sample volume check. 

2.4.4 Sample volume audit standard 

If your XRF multi-metals CEMS makes volume or flow measurements, periodic 

standard volume or flow audits must be performed. An independently calibrated 

volume or flow measurement device or standard such as a Dry Cal® is required for 

these audits. The standard must be able to acquire a volume or flow measurement at 

sampling rates typical of your XRF multi-metals CEMS. 

2.4.5 X-ray Fluorescence Calibration Check Standards 

Your XRF multi-metals CEMS must include a means of checking the x-ray 

fluorescence calibration against an external standard. NIST traceable thin film 

standards are an example of a suitable x-ray fluorescence calibration check standard. 

2.4.6 Reagents and standards for the Linearity Audits and Relative Bias Audits 

You will need other reagents and standards for the linearity audit or relative bias audit. 

The regents and standards required will differ depending on how these audits are 

performed. 
Quality Assurance for XRF Based Multi-Metals CEMS (Procedure Z) Page 4 of 4 

2.4.7 Regents and standards for the Transport Efficiency Audit 

The regents and standards for the transport efficiency audit also depend upon how the 

audit is performed. 

2.5 What sample collection, preservation, storage, and transport procedures are relevant 

to Procedure Z? 

[reserved] 

3.0 Quality Control, Calibration, and Standardization 

3.1 What quality control measures are required by this procedure for my multi-metal 

CEMS? 

You must develop and implement a quality control program that, at a minimum includes 

detailed written procedures for all of the following activities. 

1. Procedures for performing drift checks on a daily basis, including but not limited 

to, zero drift, upscale drift, and sample volume measurement drift. 

2. Procedures and methods of adjusting your multi-metal CEMS in response to the 

results of the drift checks. 

3. Preventative maintenance of your XRF multi-metals CEMS. 

4. Data recording, calculations, and reporting. 

5. Procedures for required audits, including transport efficiency audits (if necessary), 

linearity audits, and relative bias audits. 

6. Procedures for adjusting your CEMS based on audit results. 

7. A program of corrective action and stack operation procedures in case of a CEMS 

malfunction and an out of control period. 

You are required to keep written documentation of your QA/QC procedures on record 

and available for inspection for the life of the CEMS or until you are no longer subject to 

the requirements of this procedure. If you fail two consecutive audits you must revise 

your QA/QC procedures. 

3.2 What calibration checks and audit procedures must I perform for my multi-metal 

CEMS? 

3.2.1 Daily drift check procedures 

Your XRF multi-metals CEMS must have the capacity to perform each of the following 

checks on at least a daily basis. 
Quality Assurance for XRF Based Multi-Metals CEMS (Procedure Z) Page 5 of 5 

• Zero drift: You must check the zero drift to ensure the stability of your CEMS 

response to the zero drift reference. The zero drift must be less than plus or 

minus 20% of the emission limit each day. Follow your CEMS manufacturer’s 

instructions for proper zero drift check procedures. 

• Upscale drift: You must check the upscale drift to ensure the stability of your 

XRF multi-metal CEMS response to the upscale standard. The daily upscale 

drift must be less than 15% of the upscale reference value determined 

immediately after the x-ray fluorescence module has been calibrated. Follow 

your CEMS manufacturer’s instructions for proper upscale drift check 

procedures. 

• Daily volume or flow check: You must check the sample volume or flow 

measurement to verify the accuracy of the volume measurement on your 

CEMS. This volume check must be done at the normal sampling rate for the 

CEMS. Your CEMS is out of control if the one day value exceeds 20% of the 

full scale of the volume or flow measurement device. Follow your CEMS 

manufacturer’s instructions for proper volume or flow check procedures. 

3.2.2 Audit procedures 

Audit procedures and criteria are listed below. These requirements are also 

summarized in Table 1 in section 5.3. 

1. X-Ray Fluorescence Calibration Audit (XFCA): You must perform an 

XFCA once each quarter. To perform an XFCA you must challenge the x-ray 

fluorescence module of your multi-metal CEMS with a standard of known 

concentration for each metal measured by your CEMS for compliance purposes 

and compare the value reported by the CEMS with the known value of the 

standard. If you wish you may make only one measurement of a standard for 

each element. If your multi-metal CEMS fails on the initial measurement you 

may make two more measurements of each standard and average all three 

measurements. If the average CEMS response over the three measurements 

deviates by less than 10% from the known standard the CEMS has passed the 

XFCA. If the average exceeds 10% your CEMS has failed the XFCA and is 

out-of-control. You must follow the procedures outlined in Section 5.2. An 

XFCA is required once per quarter. The minimum allowed time between each 

audit is two months and the maximum allowed time is four months. 

2. Sample volume (or flow) audit (SVA): You must perform a sample volume 

audit of your XRF multi-metals CEMS at least once per quarter and prior to any 

linearity or relative accuracy audit. To perform an SVA you must 

independently measure the volume of sample gas extracted from the stack or 

duct over the sampling period. You may make this measurement either at the 

inlet or outlet of your CEMS. You must make volume measurements during 

three different sampling cycles and the measurements must be able to make 

corrections for moisture content if necessary. 
Quality Assurance for XRF Based Multi-Metals CEMS (Procedure Z) Page 6 of 6 

If your CEMS measures flow and totalizes that flow to determine volume you 

may perform a flow audit instead. You must make flow measurements during 

three different sampling cycles and for each sampling cycle you must make at 

least 3 to 5 simultaneous measurements of flow on your CEMS and on the 

independent flow measurement device. You must calculate the error from each 

set of measurements according to equation 6 and then calculate the average 

error in the flow during each sampling period. Finally you must calculate the 

average error from all three sampling periods and this average must be less than 

10% of the independent flow or volume measurement device. 

A sample volume audit is required on a quarterly basis. The minimum required 

time between each SVA is at least two months while the maximum allowed 

time between audits is four months. 

Accuracy Audits: As outlined in Performance Specification YY it is 

acceptable during the initial performance specification test to assess the 

accuracy and precision of the XRF and sampling modules of your XRF multimetal CEMS separately from the sample interface. You may also do this 

during the Linearity or Relative Bias Audits that are required for Procedure Z. 

If you choose to challenge the sampling module and XRF systems separately 

from the sampling interface you must also perform a Transport Efficiency 

Audit (TEA). If you challenge the entire XRF multi-metals CEMS during the 

Linearity and Relative Bias Audits you are not required to perform an 

independent check of the CEMS transport efficiency. For the purposes of 

Procedure Z you are required to perform either a linearity audit or a relative 

bias audit, but not both. You are also not required to perform the same kind of 

tests for the audit as were performed during the initial performance 

specification test. For example, if a linearity test was performed during the 

initial accuracy tests, either a relative bias audit or a linearity audit is 

acceptable. 

There are four different options available for the accuracy audits depending on 

whether or not a linearity or relative bias audit is performed and depending on 

whether or not the entire CEMS is challenged by the audit. The audit 

requirements are listed below. 

Linearity Audits

Option A 

In this option a linearity audit is performed on the entire CEMS. The types of 

metals generation and their associated requirements are identical to those for 

Option A in performance specification YY section 3.1.4.1

 If you do not meet 

the linearity criteria you must apply a correction according to the procedures 

outlined in performance specification YY.1

Option B

In this option a linearity audit is performed on the sampling and XRF modules 

of the CEMS separately from the sample interface. The types of metals 

generation and their associated requirements are identical to those for Option B 
Quality Assurance for XRF Based Multi-Metals CEMS (Procedure Z) Page 7 of 7 

in performance specification YY section 3.1.4.1

 A transport efficiency audit 

must also be completed. 

Relative Bias Audit 

Option C 

In this option a relative bias audit is performed on the entire CEMS. The types 

of metals generation and their associated requirements are identical to those for 

Option C in performance specification YY section 3.1.4.1

 If your CEMS fails 

to meet the criteria you must apply a correction factor according to the 

procedures in performance specification YY.1 

Option D 

In this option a relative bias audit is performed on the sampling and XRF 

modules of the CEMS separately from the sample interface. The types of 

metals generation and their associated requirements are identical to those for 

Option D in performance specification YY section 3.1.4.1 A transport 

efficiency audit must also be completed. 

An accuracy audit is required on an annual basis. The minimum time between 

successive accuracy audits is 9 months while the maximum allowed time is 15 

months. 

3. Transport Efficiency Audit (TEA): You are required to perform a TEA only 

if you choose to challenge the sampling and XRF modules of your XRF multimetals CEMS separately from the sampling interface. The procedures for 

performing a TEA are the same as those for determining the transport efficiency 

during the initial performance specification test and are outlined in Performance 

Specification YY1. If the transport efficiency of your CEMS is between 90 and 

110 percent no correction is necessary. If your transport efficiency is less than 

90 percent or greater than 110 percent then you must establish a correction 

factor according to the procedures outlined in section 3.1.7 of Performance 

Specification YY1. The minimum time between successive transport efficiency 

tests is 9 months while the maximum allowed time is 15 months. 

4.0 Calculations 

4.1 What calculations and data analysis must I perform? 

4.1.1 Arithmetic Mean 

Calculate the arithmetic mean of a data set as follows 

= ∑xi

n

x

1 Equation 1 

Where : 

x = Arithmetic mean 

n = Number of data points 
Quality Assurance for XRF Based Multi-Metals CEMS (Procedure Z) Page 8 of 8 

xi = Value of each data point 

4.1.2 Arithmetic Mean of Difference 

To calculate the arithmetic mean of difference use the above equation substitute d for x. 

Then 

di = xi − yi

 Equation 2 

Where x and y are paired data points from the CEMS and either the reference 

aerosol or the reference method. 

4.1.3 Daily Zero Drift 

100

0

× − = L

i

i

cemo

i

i C

L L

ZD Equation 3 

Where: 

ZDi = The zero drift of the ith element on your CEMS in percent 

cemo Li = The measured CEMS response to the zero standard for the ith element 

0 Li = The calibrated value of the ith element on the zero standard 

L Ci = The emission limit of the ith element 

4.1.4 Daily Upscale Drift 

×100 − = u

i

u

i

cemu

i

i L

L L

UD Equation 4 

Where: 

UDi = The upscale drift of the ith element on your CEMS in percent. 

cemu Li = The measured CEMS response to the ith element in the upscale 

standard 

u Li = The calibrated value of the ith element of the upscale standard 

4.1.5 Daily Sample Volume Check 

×100 − = FS

V V

VD cemr m Equation 5 

Where: 
Quality Assurance for Batch Multi-Metals CEMS (Procedure Z) Page 9 of 9 

VD = Volume drift 

Vcemr = Sample gas volume or flow measured by the CEMS volume or 

flow check measurement device 

Vm = Sample gas volume or flow reported by your multi-metal CEMS 

FS = Full scale value of the CEMS volume measurement device 

4.1.6 Sample Volume Audit Accuracy 

×100 − =

r

r m

V

V V

VA Equation 6 

Where: 

VA = Volume or flow measurement accuracy 

Vr = Sample gas volume or flow measured by the independent 

calibrated reference device 

Vm = Sample gas volume or flow reported by your multi-metal 

CEMS 

4.1.7 X-Ray Fluorescence Calibration Audit Calibration

×100 − = std

i

std

i

cem

i

i L

L L

CA Equation 7 

Where: 

CAi = X-ray fluorescence calibration accuracy 

cem Li = The value of the standard reported by your CEMS 

std Li = The known value of the standard 

4.1.8 Relative Bias 

= ×100

RM

i

i

i

R

d

PRB Equation 8 

Where d i is the mean difference, RM Ri is the average of the reference method 

set or reference aerosol concentration for the ith element, and PRBi is the 

relative bias for the ith element 

4.1.9 Transport Efficiency 
Quality Assurance for XRF –Based Multi-Metals CEMS (Procedure Z) Page 10 of 18 

= ×100 S

i

sm

i

i C

C PT Equation 9 

Where: 

S Ci = Concentration of the ith element at the stack 

sm Ci = Concentration of the ith element at the sampling module or as 

reported by the XRF multi-metals CEMS. 

PTi = The percent transport of the ith element 

Report the average percent transport ( PT ) of all measurements for each 

element that was tested (only one element is required though more can be 

tested). 

4.1.10 Linearity Audit – Least Squares Linear Regression 

Calculate the linear correlation equation given below. 

y b b x o 1 ˆ = + Equation 10 

Where: 

bo = The y intercept 

b1 = The slope 

The intercept is calculated according to the following equation. 

b y b x o = − 1 Equation 11 

Where: 

∑=

=

n

i

i x

n

x

1

1 

∑=

=

n

i

i y

n

y

1

1 

The slope of the line is calculated according to equation below. 

∑

∑

=

=

−

− −

= n

i 1

2

i

n

i 1

i i

1

( x x )

( x x )( y y )

b Equation 12 

The linear correlation coefficient is calculated according to the following equation. 
Specifications for Batch Multi-Metals CEMS (PS-YY) Page 11 of 18 

∑ ∑

∑

= =

=

− −

− −

= n

i

i

n

i

i

n

i

i i

x x y y

x x y y

r

1

2

1

2

1

( ) ( )

( )( )

 Equation 13 

4.1.11 Standard Deviation (of differences) 

1

1 2 2

−

∑ ∑ −

=

⎟

⎠

⎞ ⎜

⎝

⎛

n

d

n

d

SD

i i

i Equation 14 

Where: 

SDi = The standard deviation of differences for the ith element 

n = The number of data points 

di = The difference between the concentration measured by the 

reference method or the concentration of the reference aerosol and the CEMS 

reported concentration. 

4.1.12 Percent standard deviation 

= ×100

RM

i

i

i

R

SD PRSD Equation 15 

Where: 

RM Ri = The average of the reference method data set for the ith element 

PRSDi = The relative percent standard deviation for the ith metal 

4.1.13 Linearity Test Correction Factors (Applicable only when the linearity test 

challenges the entire CEMS) 

1. Correction equation if CEMS does not meet either the slope or the intercept 

criteria. 

1

0

b

y b CC i

i

− = 

 

Equation 16 

Where:
Quality Assurance for XRF Based Multi-Metals CEMS (Procedure Z) Page 12 of 18 

C Ci = Corrected CEMS concentration for the ith element 

 yi = CEMS reported concentration for the ith element 

 b0 = The intercept of the least squares linear regression line 

 b1 = The slope of the least squares linear regression line 

2. Correction factor if CEMS meets intercept criteria, but does not meet the 

slope criteria.

b0 C yi

C

i = − 

 

Equation 17 

3. Correction factor if CEMS meets slope criteria but does not meet intercept 

criteria.

1 b

y CC i

i = Equation 18 

4.1.14 Relative Bias Correction Factors 

CEM

i

RM

i

RM

i

i

RB

i

C

R

R

d

CF =

+

=

1

1 

Equation 19 

Where: 

RB CFi = The relative bias correction factor for the ith element 

CEM Ci = The average reported concentration of the CEMS for the ith

element 

RM Ri = The average of the reference method measurements for the ith

metal

4.1.15 Percent transport correction factor

i

PT

i

PT

CF 1 = Equation 20 

Where 

PT CFi = Correction factor for percent transport for the ith element 

PT i = Average percent transport for the ith element 
Quality Assurance for XRF Based Multi-Metals CEMS (Procedure Z) Page 13 of 13 

4.2 What waste management procedures are required for procedure Z? 

All chemicals used to produce a reference aerosol or in performing standard methods need to 

be disposed of properly. Please consult the appropriate reference methods. 

5.0 Other Requirements and Information 

5.1 What pollution prevention measures must I take when using procedure Z? 

[reserved] 

5.2 What criteria are necessary for my XRF multi-metal CEMS to be in control and what 

do I do if it is out of control? 

5.2.1 Required Corrective Action for Drift Checks and Audits 

• Daily Zero Drift: If the one day drift exceeds 20% you are required to rerun 

your zero drift reference. If the XRF multi-metal CEMS meets the criteria 

during the second test you may continue to operate. If the CEMS fails to meet 

the zero drift criteria again then it is out of control. It is recommended that you 

examine the zero drift standard for defects. After repairs to the CEMS are 

completed you are required to perform at least five successful zero drift checks 

within a 24 hour period. After the five checks have been successfully 

completed then you CEMS is in control. If the repairs were made to the XRF 

module of the multi-metals CEMS you are also required to complete an x-ray 

fluorescence calibration audit (XFCA) to verify the accuracy of your x-ray 

fluorescence calibration. 

• Daily Upscale Drift: If the one day drift exceeds 15% you are required to retest 

the upscale drift reference. If the XRF multi-metals CEMS meets the criteria 

during the second test you may continue to operate, however, if the CEMS fails 

the second upscale drift check it is out of control. It is recommended that you 

examine the upscale drift standard for defects. After repairs to the CEMS are 

completed you are required to perform at least five successful upscale drift 

checks within a 24 hour period. After the five drift checks are successfully 

completed the CEMS is back in control. Again, if repairs were made to the 

XRF module of the multi-metal CEMS you are also required to successfully 

complete an x-ray fluorescence calibration audit (XFCA) to verify the accuracy 

of the calibration. 

• Daily Sample Volume Check: If your sample volume or flow drift exceeds 

20% it has failed the daily volume check and you must perform another daily 

volume check. If the CEMS passes the second check you may continue to 

operate. If your CEMS fails the second test it is out of control and your CEMS 

must be repaired. After repairs have been made the CEMS must successfully 

complete five sample volume checks within a 24 hour period. Upon successful 

completion of the five checks your CEMS is back in control. If the repairs 
Quality Assurance for XRF Based Multi-Metals CEMS (Procedure Z) Page 14 of 14 

were made to a volume or flow measurement device you are also required to 

successfully complete a sample volume audit (SVA). 

• Quarterly Sample Volume Audit (SVA): Your XRF multi metals CEMS is 

out of control if volume (or flow) measured by your CEMS differs from that 

measured by the independent standard by more than 10% percent. A failure of 

this audit may indicate that repairs need to be made to the volume measurement 

system. Upon completion of these repairs you must perform and pass another 

SVA. 

• Quarterly X-Ray Fluorescence Calibration Audit (XFCA): The response of 

your XRF multi-metals CEMS must be within 10% of the standard’s value for 

each metal measured for compliance purposes by your CEMS. If your CEMS 

fails the XFCA initially, rerun each standard two more times and take the 

average of the three measurements. If the average CEMS response meets the 

XFCA criteria you may continue to operate, however, if the CEMS fails to meet 

the criteria then it is out of control. After the CEMS has been repaired you 

must complete another XFCA. Upon successful completion of the XFCA the 

CEMS is back in control. 

• Annual CEMS Accuracy Tests

Linearity Audit

Option A (Linearity audit of the entire CEMS). 

If you challenge the entire CEMS system (including sampling interface and the 

sampling and XRF modules) with a linearity audit you do not need to apply a 

correction factor to your CEMS data if it meets the following criteria: 

1. a slope between 0.85 and 1.15 

2. the correlation coefficient equal to 0.90 or more 

3. an intercept of less than 20 percent of the emission limit 

If your CEMS does not meet the slope or intercept criteria you must apply a 

correction factor according to the procedures described in Performance 

Specification YY Section 4.2.12.1

 Your CEMS, however, must still meet the 

correlation criteria. 

If your CEMS fails the linearity test it is out of control. After the necessary 

repairs are made it must pass a linearity or relative bias test to be considered 

back in control. 

Option B (Linearity audit of the sampling module and XRF module only 

followed by a TEA) 

If you challenge the sampling and XRF modules separately from the sample 

interface, your XRF multi-metal CEMS is out of control if the linear least 

squares regression analysis of your audit data does not meet the following 

criteria for each of the metals measured by your CEMS for compliance 

purposes: 
Quality Assurance for XRF Based Multi-Metals CEMS (Procedure Z) Page 15 of 15 

1. a slope between 0.85 and 1.15 

2. the correlation coefficient equal to 0.90 or more 

3. an intercept of less than 20 percent of the emission limit 

If your XRF multi-metals CEMS fails a linearity audit you must make the 

necessary repairs to your CEMS and successfully complete either a relative bias 

audit or a linearity audit before it is considered to be back in control. 

You must also complete a transport efficiency audit (TEA) along with your 

linearity audit. 

Relative Bias Audit 

Option C (Relative bias test of the entire CEMS) 

If your CEMS meets the following criteria it has passed the relative bias audit 

and you do not need to apply a correction factor to your CEMS. 

1. the percent relative bias (PRB) exceeds 15% 

2. the percent relative standard deviation(PRSD) exceeds 10% 

3. the correlation coefficient (r) for linearity portion of the relative bias audit is 

less than 0.90 

If your XRF multi-metals CEMS fails to meet the relative bias criteria you may 

apply a correction factor according the procedures described in performance 

specification YY Section 4.2.131

. However, if your CEMS fails to meet either 

the percent relative standard deviation criteria or the correlation coefficient 

criteria it is out of control. If your XRF multi-metal CEMS fails a relative bias 

audit it must successfully compete another linearity or relative bias audit to be 

considered in control. 

Option D (Perform a relative bias test on the sampling and XRF modules) 

Your XRF multi-metals CEMS is out of control if: 

1. the percent relative bias (PRB) exceeds 15% 

2. the percent relative standard deviation(PRSD) exceeds 10% 

3. the correlation coefficient (r) for linearity portion of the relative bias audit is 

less than 0.90 

You must successfully complete another RBA or a linearity audit before your 

CEMS is considered to be in control. You must also successfully complete a 

transport efficiency audit along with the relative bias audit. 

Transport Efficiency Audit (TEA): A TEA is only required if you challenge 

your sampling XRF modules separately from your sample interface (Options B 

and D). If the percent transport is between 90 and 110 percent no correction 

factor is necessary, however, if the percent transport is less than 90 percent or 

greater than 110 percent then you must apply a correction factor to the results 

reported by your multi metal CEMS. The procedures for applying a correction 

factor using the equation in Section 4.1.15. 
Quality Assurance for XRF Based Multi-Metals CEMS (Procedure Z) Page 16 of 16 

5.2.2 General out of control guidelines 

• Out of control period: The out of control period begins immediately after the 

failed drift test or audit and is over immediately following the successful 

completion of required procedures associated with the failure of the audit test. 

During the out of control period you may not use the data generated by your 

XRF multi-metal CEMS for compliance purposes. 

• Reporting guidelines: You must include in your report to us, the state, or local 

enforcement agency the results of the failed audit or drift check, the corrective 

action that was taken, and the results of the successful audit or drift check. 

• Rules governing auditing time periods: The X-Ray Fluorescence Calibration 

Audit (XFCA) and the Sample Volume Audit (SVA) are required once a 

quarter. Two months must pass between successive quarterly audits and no 

more than four months may pass.. The Linearity Audit (LA) and the Relative 

Bias Audit (RBA) are required on an annual basis. Successive LAs and RBAs 

must be separated by at least nine months and no more than 15 months. 

5.3 What tables, diagrams and flow charts are relevant to Procedure Z? 
Quality Assurance for XRF Based Multi-Metals CEMS (Procedure Z) Page 17 of 17 

Table 1: Continuing QA Procedures for XRF Multi-Metals CEMS 

Test 

Frequency 

Test Test Procedures Passing Criteria 

Zero Drift Check zero standard and calculate drift < 20% drift each day 

Daily Upscale Drift Check upscale standard and calculate drift < 15% drift each day 

Volume or Flow Drift Check flow drift and calculate drift < 20% drift each day 

X-Ray Fluorescence 

Calibration Audit 

Test a standard for each element measured for 

compliance by your CEMS (1 time per 

standard) 

• < 10% difference for every 

element measured for 

compliance by your CEMS 

• If criteria not initially met you 

may take the average of 3 

measurements 

Quarterly 

Sample Volume 

(or Flow) Audit 

Volume

• Compare CEMS volume against a standard 

during 3 sampling cycles 

• Average all three 

Flow

• 3 to 5 flow measurements with standard 

and CEMS per sample cycle 

• Measure in 3 CEMS sample cycles 

• Calculate average difference between 

CEMS and standards over all 

measurements 

<10% difference from the standard 

Option A

Perform a linearity test on 

entire CEMS 

• At least one metal from each category 

• Need at least 3 concentration levels which 

include a 2 fold conc. change and the 

emission limit 

• If spiking, spike into source, or spike into 

transport line as close as possible to the 

probe 

• Slope = 0.85 to 1.15 

• r > 0.90 

• intercept < 20% of emission 

limit 

• if above criteria is met then no 

correction 

• if not met apply a correction 

Option B

• Perform a linearity test 

on sampling and XRF 

modules only 

• Determine transport 

efficiency separately 

• At least one metal from each category 

• Need at least 3 concentration levels which 

include a 2 fold conc. change and the 

emission limit 

• Spike or measure concentrations with 

reference method as close as possible to the 

sampling module 

Linearity Criteria

• Slope = 0.85 to 1.15 

• r > 0.90 

• intercept < 20% of emission 

limit 

• the linearity criteria must be met 

Percent Transport Criteria

• 90<PT<110 

• If percent transport criteria are 

not met apply a correction 

factor 

Option C

Perform a relative bias test 

on entire CEMS 

• At least one metal from each category at 80 

to 120 percent of emission limit 

• One other metal at 3 conc. levels which 

include a 2 fold conc. change and the 

emission limit 

• If spiking, spike into source or spike into 

transport line as close as possible to the 

probe 

• Percent relative Bias 

• RB< 15% 

• %RSD < 10% 

• r > 0.90 for metal with three 

fold conc. change 

• If Criteria not met apply a 

correction factor (correlation 

coefficient criteria must be met 

Annually

Option D

• Perform a relative bias 

test on sampling and 

XRF modules only 

• Determine transport 

efficiency separately 

• At least one metal from each category at 80 

to 120 percent of emission limit 

• One other metal at 3 conc. levels which 

include a 2 fold conc. change and the 

emission limit 

• Spike or measure concentrations with 

reference method as close as possible to the 

sampling module 

Percent Relative Bias Criteria

• RB< 15% 

• %RSD < 10% 

• r > 0.90 for metal with three 

fold conc. change 

Percent Transport Criteria

• 90<PT<110 

• If percent transport criteria are 

not met apply a correction 
Quality Assurance for XRF Based Multi-Metals CEMS (Procedure Z) Page 18 of 18 

5.4 What references are relevant to Procedure Z? 

1. Performance Specification YY: Specifications and Test Procedures for Batch MultiMetals Continuous Emission Monitoring Systems at Stationary Sources. 2005.