Appendix C to Part 60 - Determination of Emission Rate Change
40:9.0.1.1.1.0.1.1.10 : Appendix C
Appendix C to Part 60 - Determination of Emission Rate Change 1.
Introduction
1.1 The following method shall be used to determine whether a
physical or operational change to an existing facility resulted in
an increase in the emission rate to the atmosphere. The method used
is the Student's t test, commonly used to make inferences
from small samples.
2. Data
2.1 Each emission test shall consist of n runs (usually
three) which produce n emission rates. Thus two sets of
emission rates are generated, one before and one after the change,
the two sets being of equal size.
2.2 When using manual emission tests, except as provided in §
60.8(b) of this part, the reference methods of appendix A to this
part shall be used in accordance with the procedures specified in
the applicable subpart both before and after the change to obtain
the data.
2.3 When using continuous monitors, the facility shall be
operated as if a manual emission test were being performed. Valid
data using the averaging time which would be required if a manual
emission test were being conducted shall be used.
3. Procedure
3.1 Subscripts a and b denote prechange and postchange
respectively.
3.2 Calculate the arithmetic mean emission rate, E, for each set
of data using Equation 1.
Where:
Ei = Emission rate for the
i th run.
n = number of runs.
3.3 Calculate the sample variance, S2, for each set of
data using Equation 2.
3.4 Calculate the pooled estimate, Sp, using Equation
3.
3.5 Calculate the test statistic, t, using Equation
4.
4. Results
4.1 If Eb>,Ea and t>t′, where
t′ is the critical value of t obtained from Table 1,
then with 95% confidence the difference between Eb and
Ea is significant, and an increase in emission rate to the
atmosphere has occurred.
| Degrees of freedom
(na=nb−2) |
t′ (95 percent confidence
level) |
| 2 |
2.920 |
| 3 |
2.353 |
| 4 |
2.132 |
| 5 |
2.015 |
| 6 |
1.943 |
| 7 |
1.895 |
| 8 |
1.860 |
For greater than 8 degrees of freedom, see any standard statistical
handbook or text.
5.1 Assume the two performance tests produced the following set
of data:
| Test a |
Test b |
| Run 1. 100 |
115 |
| Run 2. 95 |
120 |
| Run 3. 110 |
125 |
5.2 Using Equation 1 -
Ea = 100 + 95 + 110/3 = 102
Eb = 115 + 120 + 125/3 =
120
5.3 Using Equation 2 -
Sa2 = (100−102) 2 + (95−102) 2 + (110−102) 2/3−1 = 58.5
Sb2 = (115−120) 2 + (120−120) 2 + (125−120) 2/3−1 = 25
5.4 Using Equation 3 -
Sp = [(3 − 1)(58.5) + (3 + 1)(25) / 3 + 3 − 2] 1/2 = 6.46
5.5 Using Equation 4 -
5.6 Since (n 1 + n 2 − 2) = 4, t′ = 2.132
(from Table 1). Thus since t>t′ the difference in
the values of Ea and Eb is significant, and there has
been an increase in emission rate to the atmosphere.
6. Continuous Monitoring Data
6.1 Hourly averages from continuous monitoring devices, where
available, should be used as data points and the above procedure
followed.
[40 FR 58420, Dec. 16, 1975]