1

MEMORANDUM

SUBJECT: Approach for Applying the Upper Prediction Limit to Limited Datasets for the 

Final Rule for Primary Aluminum Production Source Category 

DATE: September 08, 2015 

FROM: David Putney 

Office of Air Quality Planning and Standards 

TO: Docket ID No. EPA-HQ-OAR-2011-0797 

I. What is Our Approach for Applying the Upper Prediction Limit to Limited Datasets? 

The Upper Prediction Limit (UPL) approach addresses variability of emissions data from the best 

performing source or sources in setting MACT standards. The UPL also accounts for uncertainty 

associated with emission values in a dataset, which can be influenced by components such as the 

number of samples available for developing MACT standards and the number of samples that will

be collected to assess compliance with the emission limit. The UPL approach has been used in 

many environmental science applications.1,2,3,4,5,6 As explained in more detail in the memorandum 

entitled “Use of the Upper Prediction Limit for Calculating MACT Floors”, which is located in 

the docket for this action, the EPA uses the UPL approach to reasonably estimate the emissions 

performance of the best performing source or sources to establish MACT floor standards. 

Sample size (the number of values in a particular dataset) is an important component of the UPL 

approach. First, the use of the UPL approach requires us to identify the distribution of the data, that 

is, whether a particular dataset is normally or non-normally distributed (see the memorandum 

entitled “Use of the Upper Prediction Limit for Calculating MACT Floors”, which is located in the 

docket for this action). To determine the distribution of the data, we use well- established tests 

(kurtosis and skewness tests), and these tests require at least three data points. In prior 

rulemakings, we used the kurtosis equation that is a built-in function in Excel software, but that 

equation requires at least 4 values in order to avoid dividing by zero, which precluded its use for 

datasets of 3. 

1 Gibbons, R. D. (1987), Statistical Prediction Intervals for the Evaluation of Ground-Water Quality. Groundwater, 

25: 455–465 and Hart, Barbara F. and Janet Chaseling, Optimizing Landfill Ground Water Analytes—New South 

Wales, Australia, Groundwater Monitoring & Remediation, 2003, 23, 2. 

2 Wan, Can; Xu, Zhao; Pinson, Pierre; Dong, Zhao Yang; Wong, Kit Po. Optimal Prediction Intervals of Wind 

Power Generation. 2014. IEEE Transactions on Power Systems, ISSN 0885-8950, 29(3): pp. 1166 – 1174. 

3 Khosravi, Abbas; Mazloumi, Ehsan; Nahavandi, Saeid; Creighton, Doug; van Lint, J. W. C. Prediction Intervals to 

Account for Uncertainties in Travel Time Prediction. 2011. IEEE Transactions on Intelligent Transportation 

Systems, ISSN 1524-9050, 12(2):537 – 547. 

4 Ashkan Zarnani; Petr Musilek; Jana Heckenbergerova. 2014. Clustering numerical weather forecasts to obtain 

statistical prediction intervals. Meteorological Applications, ISSN 1350-4827. 21(3): 605. 

5 Rayer, Stefan; Smith, Stanley K; Tayman, Jeff. 2009. Empirical Prediction Intervals for County Population 

Forecasts. Population Research and Policy Review, 28(6): 773 – 793. 

6 Nicholas A Som; Nicolas P Zegre; Lisa M Ganio; Arne E Skaugset. 2012. Corrected prediction intervals for 

change detection in paired watershed studies. Hydrological Sciences Journal, ISSN 0262-6667, 57(1): 134 – 143 
2

However, we recently further reviewed the application of the UPL where data are limited, and 

concluded that it is appropriate to use another kurtosis estimator7 that provides a meaningful result 

with just 3 values. The use of this estimator is important, as many, if not most, of our new source 

emissions limits are based on 3 samples collected during an emissions test. 

Once we determine the data distribution, the appropriate equation to be used in the UPL approach 

is selected based on the data distribution. We recognize that the use of the UPL approach for 

limited datasets introduces some amount of uncertainty in the calculation of MACT standards, 

and, therefore, we are taking additional steps, discussed in this document, to ensure that the level 

of the MACT standards is reasonable. We also note that after MACT standards are promulgated, 

we are required to review those standards periodically, and for such reviews, we typically have 

significant additional HAP emissions data from the intervening years of compliance with which to

further assess the actual performance of the various emission sources. 

Regardless of the distribution of the data, UPL equations have three well-defined components: an 

average, the t-score and a measure of variability that includes the actual variability of the data, 

the sample size, and the number of data points that are averaged together to determine 

compliance with a particular emission limit. A t-score is a value that estimates the uncertainty 

and variability for a certain confidence level associated with a specific number of data points. 

For a constant confidence level, t-scores decrease as the number of samples increase. This means 

that, if the mean and variance remain constant, UPL values for a particular confidence level 

decrease as the number of samples increase. Figure 1 and Table 1 show the t-scores for various 

sample sizes, and demonstrate that the t-score is highly variable at the smallest sample sizes and 

becomes relatively constant once the sample size is larger than a few data points. Consequently, 

we recognize that we need to take special care when smaller, limited sample sizes are used to 

establish emission limits, as the t-scores can have a disproportionate effect, overwhelming the 

other components of the emission limit calculation. In addition, we recognize that for a sample 

size of fewer than three data points, which has a very large t-score and precludes the appropriate 

selection of a distribution, we should not develop emission limits using the UPL. In other words, 

if fewer than 3 data points are available for use in determining an emission limit for a particular 

source, and no other data from sources in the subcategory are available, we would have to 

establish a different procedure for establishing the MACT floor that does not rely on the UPL. 

7 Doric D, Nikolic-Doric E, Jevremovic V and Malisic J. 2009. On measuring skewness and kurtosis. Qual Quant. 

43:481-493. DOI 10.1007/s11135-007-9128-9. 
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T-score

T-score vs Number of Samples

35

78% reduction from 2 to 3 samples

30

35% reduction from 3 to 4 samples

25 17% reduction from 4 to 5 samples

20 10% reduction from 5 to 6 samples

15

7% reduction from 6 to 7 samples

10

5

5% reduction from 7 to 8 samples 0

2345678 9

Number of Samples

Figure 1. Sample sizes versus one-sided, 99 percent confidence interval t-scores for normal 

distributions 

Table 1. Degrees of Freedom, T-Score for a One-Tailed, 99 Percent Confidence Interval, and 

Percent Difference in T-Score for Each Sample Size 

Sample Size 

(n) 

Degrees of Freedom 

(n-1) 

t-score 

(99 percent) 

Relative Percent 

Difference a

2 1 31.82 

3 2 6.96 78 

4 3 4.54 35 

5 4 3.75 17 

6 5 3.36 10 

7 6 3.14 7 

8 7 3.00 5 

9 8 2.90 3 

a The relative percent difference between the t-score and the t-score shown on the preceding row 
4

In the case of a dataset with a normal distribution, the equation to calculate the UPL is as 

follows: 

ܷܲܮ ൌ ݔ̅ ൅ݐሾሺ௡ିଵሻ,ሺଵି஑ሻሿ

ඨݏଶ ൬

1

݊

൅

1

݉൰

Where: ݔ = average or mean of test run data; 

ݐሾሺ௡ିଵሻ,ሺଵି஑ሻሿ = t score, the one-tailed t value of the Student’s t distribution for a specific 

degree of freedom (n-1) and confidence level (1- α); 

α = level of significance expressed as a decimal (e.g., 1% significance = 0.01), note that 

confidence level = 100 െ ሺߙ ൈ 100ሻ; 

ݏଶ = variance of the dataset (test run); 

݊ = number of values (test runs) in the dataset; and 

݉ = number of values used to calculate the test average (generally 3). 

As shown in the equation, the sample size (n) directly affects the UPL calculations in two ways. 

First, as mentioned earlier, the t-score is selected based on the sample size. Second, the sample 

size is a separate variable in the equation, and as with the t-score, as the sample size gets larger 

(all other variables being held constant), the UPL gets smaller (i.e., approaches the mean value). 

The sample size also influences both the mean (x-) and variance (s2

) in that larger sample sizes 

provide better estimates of the population mean and variance. The confidence level also 

influences the t-score, and is represented in the UPL equation by the subscript “1- α.” As noted in 

the memorandum entitled “Use of the Upper Prediction Limit for Calculating MACT Floors”, 

which is located in the docket for this action, we typically choose the 99 percent UPL, which is 

another way of saying that α equals 0.01. 

Note that the UPL equation for a lognormal distribution uses a z-score, instead of a t-score.8 As 

with the normal UPL equation, the lognormal UPL equation is affected by sample size and the 

variance of the data, and the basic concepts outlined in this discussion apply to datasets 

regardless of the distribution. 

In summary, sample size is important for UPL calculations, as it is a key component of the tscore value and the calculation of the mean and variance of the sample. For the reasons 

presented above, for datasets below a certain size, further evaluation is warranted to ensure that 

the results are a valid representation of the performance of the emission sources whose data are 

included in the dataset. The remainder of this document provides our assessment of what 

constitutes a limited dataset and what additional analyses are appropriate for ensuring that the 

UPL calculations are valid representations of the performance of units as reflected in the 

available data. 

8 Bhaumik, D.K. and Gibbons, R.D.``An Upper Prediction Limit for the Arithmetic Mean of a Lognormal Random 

Variable", Technometrics, 46, 2004, 239-248. 
5

II. What is a limited dataset? 

While there are different options for choosing the number of samples that represents a limited 

dataset (or small sample size), we can use distinctions based on our observations in Figure 1 and 

Table 1 as an aid in defining what constitutes a limited dataset. As discussed earlier, the t-score is 

an influential parameter that can have a particularly large influence on an emission limit 

developed from a limited dataset. As such, the t-score is a key parameter for identifying what 

constitutes a limited dataset for purposes of MACT analyses. As shown in Figure 1 and Table 1, 

above, at the 99 percent confidence level there is a clear distinction between t-score values for 

sample sizes of 3 and fewer when compared to t-score values for sample sizes of more than 6. As 

Figure 1 and Table 1 show, the t-score changes drastically from sample size equal to 2 to sample 

size equal to 3. The changes in the t-score are considerably less dramatic as the sample size 

approaches 9 data points and larger. 

As noted earlier, we will not use the UPL approach for datasets with fewer than 3 values because 

of the high degree of uncertainty that results from the size of the dataset and the related t-score. 

In fact, the t-score (see Figure 1 and Table 1) for a dataset of 3 is 78 percent lower than a t-score 

for a dataset of 2, meaning that given an equal variance, the component of the UPL that includes 

the t-score and variance would be more than 78 percent less when evaluating a 3-point dataset 

compared to a 2-point dataset. The table and figure also show that the relative change of the tscore for each additional data point decreases as the sample size gets larger. As sample size 

increases, uncertainty decreases, but there is always some amount of uncertainty. The discussion 

that follows presents our examination of the t-score at various sample sizes. We rely on this 

examination to help identify a sample size below which we would further evaluate the data and 

the application of the UPL to ensure that the amount of uncertainty is within a reasonable range. 

Based on Table 1, the lower bound of the sample size where such further evaluation is needed is 

3 values, and a reasonable value (where the size of the t-statistic has much less influence on the 

eventual emission limit) lies between 4 and 9 values. 

An additional factor to consider is that, in the context of MACT analyses, emission tests 

typically include 3 test runs (independent data points), and, therefore, our MACT floor dataset 

size typically is a multiple of 3. For this reason, we first considered sample sizes that are 

multiples of 3 when identifying the size below which further scrutiny is needed. As can be 

calculated from the t-scores shown in Table 1, the relative difference between the t-score for 6 

data points and the t-score for 9 data points is about 14 percent ((3.36-2.90)/3.36). The relative 

difference between the t-scores for 7 and 9 data points is about 8 percent ((3.14-2.90)/3.14). 

Given that the test methods that are used to generate the data typically are accurate to within 10 

to 20 percent9 , this difference in t-score (between datasets with 7 and 9 runs) is less than the 

uncertainty in the test methods and would not have a large influence on the magnitude of an 

emission limit. Conversely, comparing the t-score for 3 runs to that for 7 runs, the relative 

difference in the t-score is 55 percent ((6.96-3.14)/6.96), indicating that there is a possibility, 

especially if the variance is high, that the t-score for 3 test runs may introduce a large amount of 

uncertainty in an emission limit, and, therefore, additional analysis of a dataset of this size is 

9 (ReMAP): PHASE 1, Precision of Manual Stack Emission Measurements; American Society of Mechanical 

Engineers, Research Committee on Industrial and Municipal Waste, February 2001. 
6

warranted. We also conducted the same type of evaluation on datasets between 4 and 6 points, 

and while the change in t-score for datasets of these sizes could be considered to be sufficiently 

small, to be conservative, we conclude that a limited dataset, for purposes of MACT analyses, is 

a dataset that includes at least 3 test runs and fewer than 7 test runs. Because of the uncertainty 

associated with datasets at or below this size, further evaluation is warranted, and the types of 

additional analyses that we may choose to conduct are explained below. 

III. What approach will the EPA follow for MACT floors based on limited datasets? 

When a MACT floor for either existing or new sources is based on fewer than 7 data points, we 

will further evaluate each individual dataset in order to ensure that the uncertainty associated 

with a limited dataset does not cause the calculated emission limit to be so high that it does not 

reflect the average performance of the units upon which the limit is based after accounting for 

variability in the emissions of those units. The evaluation will include one or more of the 

following, depending on the specific dataset: confirming that the data distribution was selected 

correctly; after confirming the data distribution, ensuring that we use the most appropriate UPL 

equation10; and, as necessary, comparing UPL equation components for the individual unit upon 

which a new source floor is based with those of the units in the existing source floor to determine 

if our identification of the best unit is reasonable. Each of the additional evaluations is discussed 

below. 

Confirming the data distribution is important because UPL equations and the emission limits 

derived from those UPL equations depend on the distribution. In prior rulemakings, we had not 

identified a way of ascertaining the data distribution for units with three samples, so we either 

assumed a normal or lognormal distribution. This particularly affected new source emissions 

limits, many of which were based on three samples. However, we have since identified and 

adopted an established technique that compares the ratio of skewness to the standard error of the 

skewness for both the raw and log transformed data. The lower of the two ratios identifies the 

data distribution that best represents the sample set. This ability to more precisely ascertain the 

data distribution enables us to select the best option for the UPL equation given the small sample 

size. 

After confirming that we selected the best distribution based on the available data and ensuring 

that we used the correct equation to calculate a MACT floor value, we then examine key 

variables that factor into the calculated floor values. The variables that are factored into the 

emission limit include the following: average, t-score, confidence level, variance, number of test 

runs (i.e., sample size), and number of runs in each test (i.e., the number of data points that are 

averaged together to determine compliance with a particular emission limit). The considerations 

related to each variable are discussed below. 

The average, which typically is calculated as the mean value of a dataset, does not require 

additional consideration. Once it is calculated, it is used to rank the performance of units, and 

also is the key value upon which each emission limit is based. As such, average values have 

10 For datasets with lognormal distributions, we recently determined that the most appropriate UPL equation, which 

is especially important for the smallest datasets that we use, is based on an approach described in Bhaumik, 2004, 

op. cit. 
7

already been compared within a particular dataset, and additional assessment is not necessary. 

However, in the overall assessment of variables, when multiple best performing units have 

emission averages that are similar, we may look to other variables like the variance to help to 

inform our decision as to which unit is the single best performer. 

As discussed earlier, the t-score is dependent on the sample size, and, therefore, we discuss these 

two variables together. As shown earlier in Figure 1, as the sample size decreases, the t-statistic 

increases. This is important because the t-statistic is multiplied by the variance and a factor that 

involves the sample size and the number of test runs used for compliance (i.e., the “m” term in 

the UPL equation). For the smallest datasets (3 data points) that we consider under the UPL 

approach, a large variance coupled with a t-score that is significantly greater than the t-score for 

a dataset of 7 or more can create a situation where the emission limit includes a large amount of 

uncertainty. In such cases, we use our technical expertise to assess what level of emissions could 

realistically be expected from the type of unit, controls, and other relevant factors, and would 

ensure that the emission limit is reasonable. 

The variance is another key variable that we would evaluate. Generally speaking, if our 

evaluation showed a very small amount of variability (e.g., a small variance), the emission limit 

would not contain an unacceptable amount of uncertainty and variability because a small 

variance would result in an emission limit that would be reasonably close to the mean of the data. 

With larger datasets, it is more likely that the demonstrated variance is truly representative of the 

variation in the source’s emissions simply because there is more evidence of the source’s 

emissions over time. On the other hand, when a limited dataset includes a large amount of 

variability (e.g., a large variance), we would need to carefully evaluate the data. For instance, 

consider the case where the pool of best performing units all have similar averages and the unit 

identified as the single best performer (based on average emissions only) has a limited dataset 

and a variance that greatly exceeds the variance of the other similarly-controlled best-performing 

units. In such a case, the MACT floor analysis may yield an emission limit for that unit (i.e., the 

new source MACT floor) that is higher than the existing source MACT floor, which is an 

indicator that further analysis is warranted. Careful consideration of variance will allow us to 

better ascertain which unit should be considered the best performer. 

Another tool that could be used to adjust unreasonable emission limits is the selection of the 

confidence level. In certain instances, we may determine that a limited dataset includes such a 

high degree of variability that the 99 percent confidence level results in an emission limit that our 

experience suggests is higher than the average emissions limitation achieved by the best 

performing source or sources after accounting for variability. In such cases, we may choose to 

select a confidence level of 95 percent or 90 percent. As an example, consider a unit identified as 

the best performing new source with a specific process or control device that has been 

demonstrated to operate far more efficiently (thus having the potential to lower emissions) in 

similar units, processes, or control devices. Under these conditions, we may choose to 

acknowledge the better operation of that unit by lowering the confidence level (which lowers the 

emissions limit). 

Establishing and using this approach on a case-by-case basis for limited datasets will ensure 

consistent application of emissions limit development procedures, which will mitigate the 
8

CWPB2 = Center-worked prebake two; POM = Polycyclic Organic Matter 

CWPB3 = Center-worked prebake three; PM = Particulate Matter 

VSS2 = Vertical stud Soderberg two; Hg = Mercury 

PCB = Polychlorinated Biphenyl 

additional uncertainty that could otherwise result from calculating MACT floor standards with 

limited data.11

IV. How did we apply the approach for limited datasets to limited datasets in the Primary 

Aluminum Production source category? 

For the Primary Aluminum Production source category, we have limited datasets for the 

pollutants and subcategories shown in Table 2. 

Table 2. Limited Datasets Used in Developing MACT Floor Limits for the Primary Aluminum 

Production Source Category 

MACT Standard a Data Points Sources b Distribution 

Existing CWPB2 Potline POM 6 1 Normal 

Existing CWPB3 Potline POM 6 1 Normal 

New Potline POM 4 1 Normal 

Existing CWPB2 Potline PM 6 1 Normal 

Existing CWPB3 Potline PM 6 1 Normal 

Existing VSS2 Potline PM 3 1 Lognormal 

New Potline PM 3 1 Lognormal 

Existing and New VSS2 Potline PCB 3 1 Normal 

New Anode Bake Furnace Hg 6 1 Normal 

New Paste Production Plant PM 3 1 Lognormal 

a 

b The number of emission sources from which the data points represented within the limited dataset were 

drawn. 

Therefore, we evaluated these specific datasets to determine whether it is appropriate to make 

any modifications to the approach used to calculate MACT floors for each of these datasets. For 

each dataset in Table 2, we performed the steps outlined above, including: ensuring that we 

selected the data distribution that best represents each dataset; ensuring that the correct equation 

for the distribution was then applied to the data; and comparing individual components of each 

11 We note that in the recent D.C. Circuit Court of Appeals decision in National Assn. of Clean Water Agencies v. 

EPA (NACWA), which involved challenges to EPA’s MACT standards for sewage sludge incinerators, the court 

identified two instances where we replaced a new source floor value with the existing source value because the new 

source value was less stringent than the existing source value (the “anomalous result”). See 734 F.3d 1115. The 

procedures outlined here would eliminate the anomalous result in both instances in the rule at issue in NACWA. The 

first instance in which the court in the NACWA decision identified the anomalous result is where we established an 

emission limit using the UPL on a dataset that included only 2 data points. The other instance in which the court 

identified the anomalous result is where we did not apply the most appropriate lognormal UPL equation. 
9

limited dataset to determine if the standards based on limited datasets reasonably represent the 

performance of the units included in the dataset. The results of each of these analyses are 

presented below. 

Existing Sources:

In each of the six existing source MACT floor determinations made on the basis of limited 

datasets (shown in Table 2), we had emissions data from only one source within each of the 

subject subcategories (i.e., CWPB2, CWPB3 and VSS2). For each of these subcategories there is 

only one existing source. Therefore, it is clear that the datasets for these subcategories represented 

the best performing source in the associated subcategory. We determined that the datasets 

associated with POM for existing CWPB2 and CWPB3 potlines, PM for existing CWPB2 and 

CWPB3 potlines, and PCB for existing VSS2 potlines were best represented by normal 

distributions and that the dataset associated with PM for existing VSS2 potlines was best 

represented by a lognormal distribution, and then calculated the emission limits (based on the 99 

percent UPL) using the appropriate equation for each dataset. Since the calculated emission limits

for each of these pollutants and subcategories were each based on the performance of a single 

unit, our evaluation of the data was limited to ensuring that each calculated emission limit is a 

reasonable estimate of the actual performance of the associated unit. 

Therefore, we calculated the ratio of each calculated emission limit to the average short-term 

emissions of the associated unit (i.e., the mean for the associated dataset). These ratios for the 

limited datasets are summarized in Table 3, below. We determined that the calculated emission 

limits for the six existing source MACT floor determinations made on the basis of limited 

datasets were between 1.6 and 2.3 times the mean of the dataset. These ratio values are within the 

range that we typically see when we evaluate larger datasets using our MACT floor calculation 

procedures. Therefore, we concluded that no changes to our standard MACT floor calculation 

procedure were warranted for these pollutants and subcategories. 

Table 3. Ratio of 99 Percent UPL to the Mean for the Limited Datasets Used in Developing 

MACT Floor Limits for the Primary Aluminum Production Source Category 

MACT Standard Mean of the 

Dataset a

99 Percent 

UPL a

Ratio of UPL 

to Mean 

Existing CWPB2 Potline POM 5.48 12 2.2 

Existing CWPB3 Potline POM 1.31 2.7 2.1 

Existing CWPB2 Potline PM 4.69 11 2.3 

Existing CWPB3 Potline PM 12.43 20 1.6 

Existing VSS2 Potline PM 12.24 26 2.1 

Existing VSS2 Potline PCB 1.1 2.0 1.8 

New Potline POM 0.55 0.77 1.4 

New Potline PM 2.62 5.39 2.1 

New Paste Production Plant PM 0.002 0.0056 2.8 

New Anode Bake Furnace Hg b 0.81 1.7 2.1 

New VSS2 Potline PCB 1.1 2.0 1.8 
10

a. Units are pounds of pollutant per ton of aluminum produced for potline PM and POM standards, micrograms per 

dry standard cubic meter for bake furnace standards, and micrograms of toxicity equivalence per ton of aluminum 

produced for potline PCB standards. 

b. The UPL for new source Hg standards (1.1 ug/dscm) was less than 3 times the representative detection level 

(RDL) (1.7 ug/dscm). As such, 3 times the RDL is used for the MACT limit based on guidance from the 

following memo, “Data and Procedure for Handling Below Detection Level Data in Analyzing Various Pollutant 

Emissions Databases for MACT and RTR Emissions Limits”, available in the docket (EPA-HQ-OAR-2011-

0797). 

New Sources:

The MACT floor dataset for POM from new potlines includes 4 test runs from a single potline 

that we identified as the best performing unit based on average emissions. After determining that 

the dataset is best represented by a normal distribution and ensuring that we used the correct 

equation for the distribution, we evaluated the variance of this unit. Our analysis showed that this 

unit, identified as the best performer based on average emissions, also had the lowest variance, 

indicating consistent performance. Therefore, we determined that the calculated emission limit 

(based on the 99 percent UPL) reasonably accounts for variability and that no changes to our 

standard MACT floor calculation procedure were warranted for this pollutant and subcategory. 

The MACT floor dataset for PM from new potlines includes 3 test runs from a single source and 

is best represented by a lognormal distribution. The unit in this dataset (Alumax - Mt. Holly 

(CWPB1)) was identified as the best performing unit based on average emissions. After ensuring 

that we used the correct equation for this distribution, we evaluated the variance of this unit. The 

variance of this source was 1.1 times higher than the variance of the unit with the next lowest 

average emissions. The unit with the next lowest average emissions was Alcoa – Intalco (SWPB) 

and there were 12 test runs available for this source. The comparison of variance led us to 

conclude that the Alcoa - Intalco unit should be considered the best performer for this pollutant 

and source category. 

The MACT floor dataset for PM from paste production plants includes 3 test runs from a single 

paste production plant and is best represented by a lognormal distribution. This unit was identified 

as the best performing unit based on average emissions. After ensuring that we used the correct 

equation for this distribution, we evaluated the variance of this unit. Although the paste production 

plant identified as the best performer based on average emissions did not also have the lowest 

variance, the variance was comparable to that of the unit with the next lowest average emissions. 

We note also that the average emissions of the paste production plant identified as the best 

performer were about 15 percent lower than those of the unit with the next lowest average 

emissions. Therefore, the comparison of variance did not lead us to conclude that another unit 

should be considered the best performer. We then ensured that the calculated emission limit 

(based on the 99 percent UPL) is a reasonable estimate of the actual performance of the associated 

unit by calculating the ratio of the calculated emission limit to the average short-term emissions of 

the associated unit (i.e., the mean for the associated dataset). We determined that the calculated 

emission limit for PM from new paste production plants was 2.8 times the mean of the associated 

dataset. This ratio value is within the range that we typically see when we evaluate larger datasets 

using our MACT floor calculation procedures. Therefore, we concluded that no changes to our 

standard MACT floor calculation procedure were warranted for this pollutant and subcategory. 
11

The MACT floor dataset for Hg from new anode bake furnaces includes 6 test runs from a single 

potline that we identified as the best performing unit based on average emissions. After 

determining that the dataset is best represented by a normal distribution and ensuring that we used 

the correct equation for the distribution, we evaluated the variance of this unit. Based on the data 

available, our analysis showed that this unit also had the lowest variance, indicating consistent 

performance. We determined that the final emission limit (ultimately based on 3 times the RDL) 

reasonably accounts for variability and that no changes to our standard MACT floor calculation 

procedure were warranted for this pollutant and subcategory. The 99 percent UPL for this best 

performing source (1.1 ug/dscm) was less than 3 times the RDL (1.7 ug/dscm). As such, 3 times 

the RDL is used for the MACT limit, in lieu of the 99 percent UPL, based on guidance from the 

following memo, “Data and Procedure for Handling Below Detection Level Data in Analyzing 

Various Pollutant Emissions Databases for MACT and RTR Emissions Limits”, available in the 

docket (EPA-HQ-OAR-2011-0797). 

The new source MACT floor determination for PCB from VSS2 potlines was made using 

emissions data from the only source within the subject subcategory. Therefore, it is clear that the 

dataset represented the best performing source in the associated subcategory. We determined that 

this dataset is represented by a normal distribution. Since the calculated emission limit for this 

pollutant and subcategory was based on the performance of a single unit, our evaluation of the 

data was limited to ensuring that the calculated emission limit is a reasonable estimate of the 

actual performance of the associated unit. We determined that the calculated emission limit for 

PCB (based on the 99 percent UPL) was 1.8 times the mean of the dataset. This ratio is within 

the range that we typically see when we evaluate larger datasets using our MACT floor 

calculation procedures. Therefore, we concluded that no changes to our standard MACT floor 

calculation procedure are warranted for this pollutant and subcategory.