[Code of Federal Regulations]
[Title 40, Volume 14]
[Revised as of July 1, 2003]
From the U.S. Government Printing Office via GPO Access
[CITE: 40CFR75.41]

[Page 275-280]
 
                   TITLE 40--PROTECTION OF ENVIRONMENT
 
         CHAPTER I--ENVIRONMENTAL PROTECTION AGENCY (CONTINUED)
 
PART 75--CONTINUOUS EMISSION MONITORING--Table of Contents
 
                Subpart E--Alternative Monitoring Systems
 
Sec. 75.41  Precision criteria.

    (a) Data collection and analysis. To demonstrate precision equal to 
or better than the continuous emission monitoring system, the owner or 
operator shall conduct an F-test, a correlation analysis, and a t-test 
for bias as described in this section. The t-test shall be performed 
only on sample data at the normal operating level and primary fuel 
supply, whereas the F-test and the correlation analysis must be 
performed on each of the data sets required under paragraphs (a)(4) and 
(a)(5) of this section. The owner or operator shall collect and analyze 
data according to the following requirements:
    (1) Data from the alternative monitoring system and the continuous 
emission monitoring system shall be collected and paired in a manner 
that ensures each pair of values applies to hourly average emissions 
during the same hour.
    (2) An alternative monitoring system that directly measures 
emissions shall have probes or other measuring devices in locations that 
are in proximity to the continuous emission monitoring system and shall 
provide data on the same parameters as those measured by the continuous 
emission monitoring system. Data from the alternative monitoring system 
shall meet the statistical tests for precision in paragraph (c) of this 
section and the t-test for bias in appendix A of this part.

[[Page 276]]

    (3) An alternative monitoring system that indirectly quantifies 
emission values by measuring inputs, operating characteristics, or 
outputs and then applying a regression or another quantitative technique 
to estimate emissions, shall meet the statistical tests for precision in 
paragraph (c) of this section and the t-test for bias in appendix A of 
this part.
    (4) For flow monitor alternatives, the alternative monitoring system 
must provide sample data for each of three different exhaust gas 
velocities while the unit or units, if more than one unit exhausts into 
the stack or duct, is burning its primary fuel at:
    (i) A frequently used low operating level, selected within the range 
between the minimum safe and stable operating level and 50 percent of 
the maximum operating level,
    (ii) A frequently used high operating level, selected within the 
range between 80 percent of the maximum operating level and the maximum 
operating level, and
    (iii) The normal operating level, or an evenly spaced intermediary 
level between low and high levels used if the normal operating level is 
within a specified range (10.0 percent of the maximum operating level), 
of either paragraphs (a)(4) (i) or (ii) of this section.
    (5) For pollutant concentration monitor alternatives, the 
alternative monitoring system shall provide sample data for the primary 
fuel supply and for all alternative fuel supplies that have 
significantly different sulfur content.
    (6) For the normal unit operating level and primary fuel supply, 
paired hourly sample data shall be provided for at least 90.0 percent of 
the hours during 720 unit operating hours. For each of the remaining two 
operating levels for flow monitor alternatives, and for each alternative 
fuel supply for pollutant concentration monitor alternatives, paired 
hourly sample data shall be provided for at least 24 successive unit 
operating hours.
    (7) The owner or operator shall not use missing data substitution 
procedures to provide sample data.
    (8) If the collected data meet the requirements of the F-test, the 
correlation test, and the t-test at one or more, but not all, of the 
operating levels or fuel supplies, the owner or operator may elect to 
continue collecting the paired data for up to 1,440 additional operating 
hours and repeat the statistical tests using the data for the entire 30- 
to 90-day period.
    (9) The owner or operator shall provide two separate time series 
data plots for the data at each operating level or fuel supply described 
in paragraphs (a)(4) and (a)(5) of this section. Each data plot shall 
have a horizontal axis that represents the clock hour and calendar date 
of the readings and shall contain a separate data point for every hour 
for the duration of the performance evaluation. The data plots shall 
show the following:
    (i) Percentage difference versus time where the vertical axis 
represents the percentage difference between each paired hourly reading 
generated by the continuous emission monitoring system (or reference 
method) and the alternative emission monitoring system as calculated 
using the following equation:
[GRAPHIC] [TIFF OMITTED] TC01SE92.156


(Eq. 10)

where,

[Delta] e = Percentage difference between the readings generated by the 
alternative monitoring system and the continuous emission monitoring 
system.
ep = Measured value from the alternative monitoring system.
ev = Measured value from the continuous emission monitoring 
system.

    (ii) Alternative monitoring system readings and continuous emission 
monitoring system (or reference method) readings versus time where the 
vertical axis represents hourly pollutant concentrations or volumetric 
flow, as appropriate, and two different symbols are used to represent 
the readings from the alternative monitoring system and the continuous 
emission monitoring system (or reference method), respectively.
    (b) Data screening and calculation adjustments. In preparation for 
conducting the statistical tests described in paragraph (c) of this 
section, the

[[Page 277]]

owner or operator may screen the data for lognormality and time 
dependency autocorrelation. If either is detected, the owner or operator 
shall make the following calculation adjustments:

    (1) Lognormality. The owner or operator shall conduct any screening 
and adjustment for lognormality according to the following procedures.

    (i) Apply the log transformation to each measured value of either 
the certified continuous emissions monitoring system or certified flow 
monitor, using the following equation:

lv=ln ev


(Eq. 11)

where,

ev = Hourly value generated by the certified continuous 
emissions monitoring system or certified flow monitoring system
lv = Hourly lognormalized data values for the certified 
monitoring system

    and to each measured value, ep, of the proposed 
alternative monitoring system, using the following equation to obtain 
the lognormalized data values, lp:

lp=ln ep


(Eq. 12)

where,

ep = Hourly value generated by the proposed alternative 
monitoring system.
lp = Hourly lognormalized data values for the proposed 
alternative monitoring system.

    (ii) Separately test each set of transformed data, lv and 
lp, for normality, using the following:
    (A) Shapiro-Wilk test;
    (B) Histogram of the transformed data; and
    (C) Quantile-Quantile plot of the transformed data.
    (iii) The transformed data in a data set will be considered normally 
distributed if all of the following conditions are satisfied:
    (A) The Shapiro-Wilk test statistic, W, is greater than or equal to 
0.75 or is not statistically significant at [alpha] = 0.05.
    (B) The histogram of the data is unimodal and symmetric.
    (C) The Quantile-Quantile plot is a diagonal straight line.
    (iv) If both of the transformed data sets, lv and 
lp, meet the conditions for normality, specified in 
paragraphs (b)(1)(iii) (A) through (C) of this section, the owner or 
operator may use the transformed data, lv and lp, 
in place of the original measured data values in the statistical tests 
for alternative monitoring systems as described in paragraph (c) of this 
section and in appendix A of this part.
    (v) If the transformed data are used in the statistical tests in 
paragraph (c) of this section and in appendix A of this part, the owner 
or operator shall provide the following:
    (A) Copy of the original measured values and the corresponding 
transformed data in printed and electronic format.
    (B) Printed copy of the test results and plots described in 
paragraphs (b)(1) (i) through (iii) of this section.
    (2) Time dependency (autocorrelation). The screening and adjustment 
for time dependency are conducted according to the following procedures:
    (i) Calculate the degree of autocorrelation of the data on their 
LAG1 values, where the degree of autocorrelation is represented by the 
Pearson autocorrelation coefficient, [rho], computed from an AR(1) 
autoregression model, such that:
[GRAPHIC] [TIFF OMITTED] TC01SE92.101


(Eq. 13)

where,

x'i = The original data value at hour i.
x[dprime]i = The LAG1 data value at hour i.
COV(x'i, x[dprime]i) = The autocovariance of 
x'i and defined by,

[GRAPHIC] [TIFF OMITTED] TC01SE92.102


(Eq. 14)

where,

n = The total number of observations in which both the original value, 
x'i, and the lagged value, x[dprime]i, are 
available in the data set.
s'x i = The standard deviation of the original data 
values, x'i defined by,


[[Page 278]]


[GRAPHIC] [TIFF OMITTED] TC01SE92.103


(Eq. 15)

where,

s[dprime]x i = The standard deviation of the LAG1 data 
values, x[dprime]i, defined by

[GRAPHIC] [TIFF OMITTED] TC01SE92.104


(Eq. 16)

where,

x' = The mean of the original data values, x'i defined by

[GRAPHIC] [TIFF OMITTED] TC01SE92.105


(Eq. 17)

where,

x[dprime] = The mean of the LAG1 data values, x[dprime]i, 
defined by

[GRAPHIC] [TIFF OMITTED] TC01SE92.106


(Eq. 18)


where,

    (ii) The data in a data set will be considered autocorrelated if the 
autocorrelation coefficient, [rho], is significant at the 5 percent 
significance level. To determine if this condition is satisfied, 
calculate Z using the following equation:
[GRAPHIC] [TIFF OMITTED] TC01SE92.107


(Eq. 19)

If Z  1.96, then the autocorrelation coefficient, [rho], is 
    significant at the 5 percent significance level (a = 0.05).

    (iii) If the data in a data set satisfy the conditions for 
autocorrelation, specified in paragraph (b)(2)(ii) of this section, the 
variance of the data, S2, may be adjusted using the following 
equation:

S2adj = VIF x S2

(Eq. 20)

where,

S2 = The original, unadjusted variance of the data set.
VIF = The variance inflation factor, defined by

[GRAPHIC] [TIFF OMITTED] TC01SE92.108


(Eq. 21)

S2adj = The autocorrelation-adjusted variance for the data 
set.

    (iv) The procedures described in paragraphs (b)(2)(i)-(iii) of this 
section may be separately applied to the following data sets in order to 
derive distinct autocorrelation coefficients and variance inflation 
factors for each data set:
    (A) The set of measured hourly values, ev, generated by 
the certified continuous emissions monitoring system or certified flow 
monitoring system.
    (B) The set of hourly values, ep, generated by the 
proposed alternative monitoring system,
    (C) The set of hourly differences, ev-ep, 
between the hourly values, ev, generated by the certified 
continuous emissions monitoring system or certified flow monitoring 
system and the hourly values, ep, generated by the proposed 
alternative monitoring system.
    (v) For any data set, listed in paragraph (b)(2)(iv) of this 
section, that satisfies the conditions for autocorrelation specified in 
paragraph (b)(2)(ii) of this section, the owner or operator may adjust 
the variance of that data set, using equation 20 of this section.
    (A) The adjusted variance may be used in place of the corresponding 
original variance, as calculated using equation 23 of this section, in 
the F-test (Equation 24) of this section.
    (B) In place of the standard error of the mean,

[[Page 279]]

[GRAPHIC] [TIFF OMITTED] TC01SE92.111


in the bias test Equation A-9 of appendix A of this part the following 
adjusted standard error of the mean may be used:
[GRAPHIC] [TIFF OMITTED] TC01SE92.109


(Eq. 22)where
[GRAPHIC] [TIFF OMITTED] TC01SE92.110

    (vi) For each data set in which a variance adjustment is used, the 
owner or operator shall provide the following:
    (A) All values in the data set in printed and electronic format.
    (B) Values of the autocorrelation coefficient, its level of 
significance, the variance inflation factor, and the unadjusted original 
and adjusted values found in equations 20 and 22 of this section.
    (C) Equation and related statistics of the AR(1) autoregression 
model of the data set.
    (D) Printed documentation of the intermediate calculations used to 
derive the autocorrelation coefficient and the Variance Inflation 
Factor.
    (c) Statistical Tests. The owner or operator shall perform the F-
test and correlation analysis as described in this paragraph and the t-
test for bias described in appendix A of this part to demonstrate the 
precision of the alternative monitoring system.
    (1) F-test. The owner or operator shall conduct the F-test according 
to the following procedures.
    (i) Calculate the variance of the certified continuous emission 
monitoring system or certified flow monitor as applicable, 
Sv2, and the proposed method, Sp2, using the 
following equation.
[GRAPHIC] [TIFF OMITTED] TR08AU95.064


(Eq. 23)

where,

ei = Measured values of either the certified continuous 
emission monitoring system or certified flow monitor, as applicable, or 
proposed method.
em = Mean of either the certified continuous emission 
monitoring system or certified flow monitor, as applicable, or proposed 
method values.
n = Total number of paired samples.

    (ii) Determine if the variance of the proposed method is 
significantly different from that of the certified continuous emission 
monitoring system or certified flow monitor, as applicable, by 
calculating the F-value using the following equation.
[GRAPHIC] [TIFF OMITTED] TR08AU95.065


(Eq. 24)


Compare the experimental F-value with the critical value of F at the 95-
percent confidence level with n-1 degrees of freedom. The critical value 
is

[[Page 280]]

obtained from a table for F-distribution. If the calculated F-value is 
greater than the critical value, the proposed method is unacceptable.
    (2) Correlation analysis. The owner or operator shall conduct the 
correlation analysis according to the following procedures.
    (i) Plot each of the paired emissions readings as a separate point 
on a graph where the vertical axis represents the value (pollutant 
concentration or volumetric flow, as appropriate) generated by the 
alternative monitoring system and the horizontal axis represents the 
value (pollutant concentration or volumetric flow, as appropriate) 
generated by the continuous emission monitoring system (or reference 
method). On the graph, draw a horizontal line representing the mean 
value, ep, for the alternative monitoring system and a 
vertical line representing the mean value, ev, for the 
continuous emission monitoring system where,
[GRAPHIC] [TIFF OMITTED] TC01SE92.112


(Eq. 25)
[GRAPHIC] [TIFF OMITTED] TC01SE92.113


(Eq. 26)

where,

ep = Hourly value generated by the alternative monitoring 
system.
ev = Hourly value generated by the continuous emission 
monitoring system.
n = Total number of hours for which data were generated for the tests.


A separate graph shall be produced for the data generated at each of the 
operating levels or fuel supplies described in paragraphs (a)(4) and 
(a)(5) of this section.
    (ii) Use the following equation to calculate the coefficient of 
correlation, r, between the emissions data from the alternative 
monitoring system and the continuous emission monitoring system using 
all hourly data for which paired values were available from both 
monitoring systems.
[GRAPHIC] [TIFF OMITTED] TR12JN02.007


(Eq. 27)

    (iii) If the calculated r-value is less than 0.8, the proposed 
method is unacceptable.

[58 FR 3701, Jan. 11, 1993, as amended at 60 FR 26530, May 17, 1995; 60 
FR 40296, Aug. 8, 1995; 67 FR 40440, June 12, 2002]