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W.0 EVALUATION OF RCA DATA

W.1 WHAT IS THE PURPOSE OF AN RCA?

A response correlation audit (RCA) is a periodic evaluation of PM CEMS responses to determine

if the responses are consistent with the correlation equation developed for the PM CEMS. RCAs

are used to evaluate the long-term stability of the correlation. If the PM CEMS satisfies the

performance criteria for an RCA, it can be assumed that the correlation equation is still valid. If

the PM CEMS fails an RCA, that indicates that the correlation cannot be used to provide an

accurate measurement of PM emissions. RCA failures can result from changes in emission

characteristics or changes in the operation of the emission source, control device, or PM CEMS. 

In the case of an RCA failure, the correlation equation must be revised. Other corrective actions

may also be necessary.

W.2 HOW DO I PERFORM AN RCA?

The procedure for conducting an RCA is the same as the procedure used to conduct an initial

correlation test for a PM CEMS. The only difference between an RCA and a correlation test is

that a minimum of 12 test runs must be performed for an RCA, instead of the 15 runs required

for the correlation test. Refer to Sections 10.3(8) and 10.4(5) of Procedure 2 for the general

procedures and performance criteria for RCAs. For details on the testing requirements for RCAs,

refer to Section 8.6 of PS-11, which specifies the procedures for performing correlation tests. 

The main requirements for conducting an RCA include

# Recording PM CEMS responses simultaneously with sampling for PM using the

reference method specified in the applicable regulation (use of paired reference

method sampling trains is recommended);

# Coordinating process operations, reference method sampling, and PM CEMS

operation; and

# Performing a minimum of 12 test runs.

Section 8.6(3) of PS-11 allows you to discard the results of up to five test runs without

explanation. You can reject additional test runs if the basis for rejecting them is specified in the

test method, PS-11, or the QA plan for the source. Also note that it is not necessary to conduct

the RCA over the three levels of PM concentration described in Section 8.6(4) of PS-11.
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W.3 WHAT ARE THE PERFORMANCE CRITERIA FOR AN RCA?

Section 10.4(5) of Procedure 2 specifies three performance criteria for an RCA. First, the PM

CEMS response value for any RCA test run can be no greater than the greatest PM CEMS

response value used to develop the correlation. For example, if the correlation equation is based

on PM CEMS responses that ranged from 5.1 mA to 35.7 mA, the maximum allowable PM

CEMS response for an RCA is 35.7 mA. If the PM CEMS response exceeds 35.7 mA for any

RCA test run, the results of that run must be discarded.

The second criterion, which is specified in Section 10.4(5)(ii), is that nine of the 12 PM CEMS

responses must be within the range of response values used to develop the correlation. For the

example cited above, this means that the PM CEMS response for up nine of the 12 test runs must

be within the range of 5.1 mA to 35.7 mA. Otherwise, additional RCA test runs must be

conducted.

The final criterion, which is specified in Section 10.4(5)(iii), is that the measured PM

concentrations for at least 75 percent of the test runs for an RCA must be within a band defined

by the PM concentration calculated from the correlation equation, plus or minus 25 percent of the

numerical emission limit. For any test run, this criterion can be expressed as follows:

í - 0.25EL # yRCA # í + 0.25EL (Equation W-1)

where

í = PM concentration calculated from the correlation equation using the PM CEMS

response (x value) recorded during the RCA test run

EL = value of emission limit (concentration)

yRCA

= PM concentration (y value) measured during the RCA test run.

For example, assume that the emission limit is 34 mg/dscm, and the correlation equation

developed for a PM CEMS is 

í = 1.14x + 2.68

where

x = PM CEMS response.

Substituting the emission limit and correlation equation into Equation W-1, each test run of the

RCA must then satisfy the following expression:

1.14x + 2.68 - (0.25 × 34) # yRCA # 1.14x + 2.68 + (0.25 × 34)

This expression can be simplified to the following:

1.14x + 2.68 - 8.5 # yRCA #1.14x + 2.68 + 8.5
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1.14x - 5.82 # yRCA #1.14x + 11.18

If the PM CEMS response value (x) during an RCA run was 18.2 mA, the PM concentration

would have to fall within the following range for the RCA run to be counted toward the

75 percent criterion:

(1.14 × 18.2) - 5.82 # yRCA # (1.14 × 18.2) + 11.18

20.75 - 5.82 # yRCA # 20.75 + 11.18

14.9 # yRCA # 31.9

For this example, yRCA, the PM concentration for the RCA test run, would have to be within the

range of 14.9 mg/dscm to 31.9 mg/dscm for the run to be counted toward the criterion that

75 percent of the test run values fall within the band defined by the correlation equation plus or

minus 25 percent of the emission limit.

W.4 EXAMPLE PROBLEM: HOW DO I EVALUATE THE RESULTS OF AN RCA?

The correlation equation developed during the initial correlation test for a PM CEMS installation

is linear and is expressed as follows:

í = 0.65x - 1.00

The PM CEMS response data used to develop the correlation equation ranged from 4.9 mA to

32.2 mA. The emission limit is 22.6 mg/dscm. To demonstrate that the installation meets the

criteria for the RCA, 13 test runs were performed. The RCA test data are summarized in

Table W-1.

The first step in determining if the test results satisfy the RCA criteria is to compare the PM

CEMS response values to the maximum response value used to develop the correlation. In this

example, the maximum allowable PM CEMS response value is 32.2 mA. A review of the data

indicates that the PM CEMS response for Run 7 was 33.6 mA, which exceeds the maximum

allowable value. Therefore, Run 7 must be discarded. All other runs satisfy the criterion for

maximum PM CEMS response.

The next step is to determine if the PM CEMS response values for at least nine test runs fall

within the range of values used to determine the correlation, which is 4.9 mA to 32.2 mA for this

example. After discarding Run 7, the PM CEMS responses for the remaining 12 runs range from

7.2 to 31.9 mA and satisfy this criterion.
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Table W-1. Results of RCA Test Runs

Run

PM CEMS

response, mA

Measured PM

Concentration, mg/dscm

1 7.2 7.6

2 10.9 7.4

3 10.2 2.8

4 26.8 23.5

5 27.7 14.2

6 31.9 22.7

7 33.6 25.1

8 12.6 8.0

9 16.8 8.5

10 17.3 6.2

11 19.2 14.6

12 23.3 10.9

13 28.4 18.1

The third step is to determine the number of test runs for which the measured PM concentrations

are within the band defined by the correlation equation plus or minus 25 percent of the numerical

emission limit, as shown by Equation W-1. Substituting the emission limit and correlation

equation, Equation W-1 can be simplified as follows:

0.65x - 1.00 - (0.25 × 22.6) # yRCA # 0.65x - 1.00 + (0.25 × 22.6)

0.65x - 6.65 # yRCA # 0.65x + 4.65

Substituting the PM CEMS response values for x, the allowable range for each test run can be

calculated and compared to the PM concentration for that run. The results of these calculations

are summarized in Table W-2 and illustrated graphically in Figure W-1.

Table W-2. Comparison of PM Concentration to Allowable Concentrations for RCA

Run No.a

PM CEMS response

value (x), mA

Measured PM

concentration (yRCA),

mg/dscm

Allowable range for yRCA Is yRCA within

Minimum Maximum range?

1 7.2 7.6 -1.97 9.33 Yes

2 10.9 7.4 0.44 11.74 Yes

3 10.2 2.8 -0.02 11.28 Yes

4 26.8 23.5 10.77 22.07 No
Table W-2. (continued)

Run No.a

PM CEMS response

value (x), mA

Measured PM

concentration (yRCA),

mg/dscm

Allowable range for yRCA Is yRCA within

Minimum Maximum range?

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5 27.7 14.2 11.36 22.66 Yes

6 31.9 22.7 14.09 25.39 Yes

8 12.6 8 1.54 12.84 Yes

9 16.8 8.5 4.27 15.57 Yes

10 17.3 6.2 4.6 15.9 Yes

11 19.2 14.6 5.83 17.13 Yes

12 23.3 10.9 8.5 19.8 Yes

13 28.4 18.1 11.81 23.11 Yes

a Note that Run 7 has been discarded because it failed criterion 1.

As indicated in Table W-2, of the remaining 12 RCA test runs (following removal of Run 7), all

but Run 4 meet the criterion that the measured PM concentration is within the band defined by

the correlation equation plus or minus 25 percent of the emission limit. For Run 4, the measured

PM concentration was 23.5 mg/dscm, and the allowable range is 10.77 mg/dscm to

22.07 mg/dscm. In Figure W-1, the correlation equation is represented by the solid line, and the

dashed lines represent the ± 25 percent band. Run 4 (26.8 mA and 23.5 mg/dscm) lies outside of

this band. 

Figure W-1. Graphical representation of example RCA test results.

+25%EL

!25%EL

" = RCA data point
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In summary, 11 of the 12 test runs (or 91.7 percent of the runs) were within the band defined by

the correlation equation plus or minus 25 percent of the emission limit. Because more than

75 percent of the test runs were within the allowable range, the third criterion has been satisfied.

Therefore, the PM CEMS satisfied the three RCA performance criteria, and no changes to the

correlation equation are required. 

W.5 WHAT MUST I DO IF I FAIL AN RCA?

Section 10.6 of Procedure 2 specifies a series of corrective actions that must be taken following

the failure of an RCA. The first step following a failed RCA, as noted in Section 10.6(1), is to

combine the RCA data with the data used to develop the current correlation and develop a new

correlation equation using the combined data (original correlation test data plus RCA data). The

new correlation equation must be developed using the procedures specified in Section 12.3 of

PS-11. If the correlation equation developed from the combined data meets the criteria specified

in Section 13.2 of PS-11, the revised correlation equation should be used. No further testing or

corrective action is needed.

If the combined data do not meet the criteria specified in Section 12.3 of PS-11, a revised

correlation equation must be developed using only the results from the RCA. If this revised

correlation equation meets the criteria specified in Section 13.2 of PS-11, the revised correlation

equation should be used, and additional testing or corrective action is unnecessary. However, it

is still advisable to investigate why the correlation changed. One possible explanation for such a

shift in the correlation is a change in control device or process operation. For example, a

difference in fuel properties could change the characteristics of the exhaust stream, thereby

altering how the PM CEMS responds to sampled emissions. In such cases, it may be more

appropriate to develop and use separate correlations for the different operating conditions and

calculate emissions based on the correlation that corresponds to the specific operating conditions.

If neither the correlation equation developed from the combined data nor the correlation equation

developed from only the RCA data satisfies Section 13.2 of PS-11, other corrective actions must

be taken. First, the PM CEMS must be inspected and repaired as needed. If this inspection

indicates that the PM CEMS is operating properly, it may be necessary to relocate the PM CEMS

and perform a new correlation test. An alternative to relocating the PM CEMS is to install a new

PM CEMS that uses a measurement technology that is more appropriate for the source operating

parameters and emissions characteristics. As explained above, it is also possible that a single

correlation is inadequate for characterizing different source or control device operating

conditions, and it may be necessary to develop multiple correlations. If none of these measures

corrects the problem, the final option is to petition the permitting authority for alternative

monitoring.

W.6 EXAMPLE PROBLEM: HOW DO I DEVELOP A NEW CORRELATION

FOLLOWING A FAILED RCA?

A successful correlation test is performed on a hazardous waste incinerator. The incinerator must

meet an emission limit of 22.6 mg/dscm. The correlation test consisted of 15 runs. Table W-3
W-7

Figure W-2. Initial correlation test data and resulting

correlation equation.

summarizes the data from the correlation test. Figure W-2 shows a plot of the correlation test

data. The correlation coefficient for the data is 0.93, and the linear correlation equation is 

í = 0.792x - 2.01

Table W-3. Summary of Initial Correlation Test Results

Run No.

PM CEMS 

Response, mA

Measured PM

Concentration, mg/dscm

1 5.2 3.2

2 7.8 2.9

3 8.2 6.1

4 10.4 5.2

5 14.8 6.8

6 14.1 12.6

7 19.2 9.2

8 20.3 18.8

9 19.5 12.1

10 26.4 15.1

11 21.9 16.4

12 28.7 17.8

13 29.3 23.2

14 33.5 23.9

15 31.8 27.2
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A year after the PM CEMS is brought on line, an RCA is performed. The RCA consisted of

12 test runs. The results of the RCA are summarized in Table W-4. The PM CEMS response

values for the RCA range from 7.2 to 31.9 mA. All of these values fall within the range of PM

CEMS values used to develop the correlation (5.2 to 33.5 mA). Therefore, the RCA data meet

the first two criteria specified in Section 10.4(5)(i) and (ii) for the allowable data range.

Table W-4. Results of RCA

Run

PM CEMS

response

Measured PM

concentration, mg/dscm

Allowable range for yRCA,

mg/dscm Is yRCA within

allowable

x yRCA Minimum Maximum range?

RCA-1 7.2 5.7 -1.95 9.35 Yes

RCA-2 10.9 6.2 0.98 12.28 Yes

RCA-3 10.2 2.4 0.42 11.72 Yes

RCA-4 26.8 12.5 13.57 24.87 No

RCA-5 27.7 11.9 14.29 25.59 No

RCA-6 31.9 14.8 17.61 28.91 No

RCA-7 28.2 9.9 14.68 25.98 No

RCA-8 12.6 6.7 2.32 13.62 Yes

RCA-9 16.8 7.1 5.65 16.95 Yes

RCA-10 17.3 5.2 6.05 17.35 No

RCA-11 19.2 8.7 7.55 18.85 Yes

RCA-12 23.3 9.2 10.8 22.1 No

To determine if the RCA meets the requirements of Section 10.4(5)(iii) of Procedure 2, the band

defined by the correlation line plus or minus 25 percent of the emission limit can be simplified to

the following:

0.792x - 7.66 # yRCA # 0.792x + 3.64

Table W-4 shows the applicable range for each run of the RCA based on the above expression. 

When the values for the PM CEMS responses for the RCA are compared to these ranges, only 6

of the 12 runs (50 percent) fall within the acceptable band. Figure W-3 shows a plot of the

correlation line and the lines that define the plus or minus 25 percent band around the correlation

line. As indicated in the figure, six of the data points for the RCA (indicated by the  symbols)

fall below the band.

As specified in Section 10.6(1) of Procedure 2, the next step is to combine the data used to

develop the correlation and the RCA data and determine if the resulting correlation satisfies the

criteria of Section 13.2 of PS-11. A plot of the combined data is shown in Figure W-4.
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Figure W-4. Plot of combined correlation test data and RCA data.

Figure W-3. Results of RCA.

!25%EL

+25%EL

" = RCA data point
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Figure W-5. Plot of correlation curve for RCA data only.

When the correlation is performed using the combined data, none of the five correlation models

meet the criteria of PS-11. The correlation coefficients are all less than 0.85, and three of the five

models fail to meet the criterion for a tolerance interval half range of 25 percent. Table W-5

shows the outcome of the correlation analysis for the five models.

Table W-5. Results of Correlation Analysis for Combined Correlation Test and RCA Data

Model Equation

Correlation

coefficient

Confidence 

interval 

half range

Tolerance

interval 

half range

Acceptance Criteria for PS-11 $0.85 #10% #25%

Linear í = 0.638x - 1.22 0.813 6.81 % 26.3 %

Polynomial í = 0.0135x

2

 + 0.111x + 2.94 0.816 9.11 % 26.6 %

Logarithmic í = 9.92Ln(x) -17.12 0.765 7.54 % 29.1 %

Exponential í = 2.70e0.0636x0.844 5.63 % 22.7 %

Power í = 0.477x

1.042 0.838 5.72 % 23.1 %

When the correlations developed from the combined data do not meet the criteria specified in

PS-11, Section 10.6(2) of Procedure 2 requires developing a new correlation using only the data

from the RCA test runs. A plot of the RCA data and the new linear correlation equation

developed from these data are shown in Figure W-5. The results of the analysis for the five

correlation models are summarized in Table W-6. The linear and polynomial correlation models

both satisfy the correlation criteria of PS-11 and either equation can be used to determine

compliance with the emission limit.
W-11

Table W-6. Results of Correlation Analysis for RCA Data Only

Model Equation

Correlation

coefficient

Confidence 

interval 

half range

Tolerance

interval 

half range

Acceptance Criteria for PS-11 $0.85 #10% #25%

Linear í = 0.889x + 0.386 0.888 4.61 % 13.6 %

Polynomial í = 0.0131x

2

 - 0.123x + 5.06 0.900 5.96 % 13.5 %

Logarithmic í = 6.24Ln(x) - 9.53 0.826 5.64 % 16.6 %

Exponential í = 2.92e0.0496x0.809 6.25 % 19.3 %

Power í = 0.726x

0.819 0.772 6.77 % 21.0 %