1 M E M O R ANDU M

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 addresse s 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, wh ich can be influenced by components such as the number of samples available for developing MA CT 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 Ca lculating MACT Floors”, which is located in the docket for this action). To determine the distribu tion of the data, we use well- established tests (kurtosis and skewness tests), and these tests re quire 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 f o r

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 – 1432 However, we recently further reviewed the application of the UPL where data are limited, and concluded that it is appropriate to use another kurtosis estimator 7 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 sample s collected during an emissions test.

Once we determine the data distribution, the appropr iate equation to be used in the UPL approach
is selected based on the data distribution. We re cognize that the use of the UPL approach for
limited datasets introduces some amount of uncer tainty in the calculation of MACT standards, and, therefore, we are taking additional steps, disc ussed 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 period ically, 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 performa nce of the various emission sources.

Regardless of the distribution of the data, UPL eq uations have three well-defined components: an average, the t-score and a measure of variability that includes the actual va riability 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 a ssociated with a specific number of data points. For a constant confidence level, t-scores decrea se 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. Figu re 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/s11135-007-9128-9.3T-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
2 3 4 5 6 7 8 9 

### Number of Samples

Figure 1. Sample sizes versus one-sided, 99 perc ent 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 row4 In the case of a dataset with a normal distribu tion, the equation to calculate the UPL is as
follows:

ܷܲܮ ൌ ݔ ̅ ൅ݐ ሾ ሺ ௡ିଵ ሻ

, ሺ ଵି஑ ሻ ሿ ඨ

ݏ ଶ ൬ 1

݊ ൅ 1

݉ ൰

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

ݐ ሾ ሺ ௡ିଵ ሻ

, ሺ ଵି஑ ሻ ሿ = 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 expr essed as a decimal (e.g., 1% significance = 0.01), note that

confidence level = 100 െ ሺ ߙ ൈ 100 ሻ ;

ݏ ଶ = variance of the dataset (test run);

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

݉ = number of values used to calcula te 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 sele cted based on the sample size. Second, the sample size is a separate variable in th e equation, and as with the t-score, as the sample size gets larger (all other variables being held c onstant), the UPL gets smaller (i.e., approaches the mean value). The sample size also influences both the mean ( x- ) and variance (s 2 ) in that larger sample sizes provide better estimates of the population mean and variance. The confidence level also influences the t-score, and is represente d in the UPL equation by the subscript “1- α .” As noted in the memorandum entitled “Use of the Upper Pr ediction 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 dist ribution 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 ba sic concepts outlined in this discussion apply to datasets regardless of the distribution.

In summary, sample size is important for UPL ca lculations, 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 perf ormance of the emission sources whose data are
included in the dataset. The remainder of th is document provides our assessment of what
constitutes a limited dataset and what additional an alyses 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 th e number of samples th at represents a limited dataset (or small sample size), we can use distin ctions based on our observa tions in Figure 1 and Table 1 as an aid in defining what constitutes a li mited dataset. As discussed earlier, the t-score is an influential parameter that can have a part icularly 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-sc ore values for sample sizes of more than 6. As Figure 1 and Table 1 show, the t-score changes dras tically 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) fo r a dataset of 3 is 78 perc ent lower than a t-score for a dataset of 2, meaning that given an equal variance, the com ponent 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 po int 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 poin ts), and, therefore, our MACT floor dataset size typically is a multiple of 3. For this reas on, 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 fo r 9 data points is about 14 per cent ((3.36-2.90)/3.36). The relative
difference between the t-scores for 7 and 9 da ta points is about 8 percent ((3.14-2.90)/3.14). Given that the test methods that are used to gene rate the data typically are accurate to within 10 to 20 percent 9 , 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-scor e 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-sc ore for 3 test runs may introduce a large amount of uncertainty in an emission limit, and, therefore, ad ditional 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 th ese sizes could be consid ered 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 fe wer than 7 test runs. Because of the uncertainty
associated with datasets at or below this size , further evaluation is wa rranted, and the types of additional analyses that we may choo se 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 so urces is based on fewer than 7 data points, we
will further evaluate each individual datase t in order to ensure that the uncertainty associated
with a limited dataset does not cause the calculated em ission 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. Th e evaluation will include one or more of the following, depending on the specific dataset: confir ming that the data distribution was selected correctly; after confirming the data distribution, ensuring that we use the most appropriate UPL equation 10 ; and, as necessary, comparing UPL equati on 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 di stribution. 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 samp les. However, we have since identified and adopted an established technique that compares th e ratio of skewness to th e 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 se t. 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 dist ribution 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-scor e, 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 li mit is based. As suc h, 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 data set, and additional assess ment is not necessary. However, in the overall assessment of variable s, 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 uni t 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 mu ltiplied by the variance and a factor that involves the sample size and th e number of test runs used fo r 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 creat e a situation where the emission limit includes a large amount of uncertainty. In such cases, we use our technical ex pertise to assess what le vel of emissions could realistically be expected from the type of unit, controls, and other rele vant 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 variab ility (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 wo uld 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 becau se there is more evidence of the source’s emissions over time. On the other hand, when a limited dataset incl udes 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 ma y 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. Care ful consideration of vari ance 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 confid ence 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 fo r variability. In such cases, we may choose to select a confidence level of 95 percent or 90 percen t. As an example, consider a unit identified as the best performing new source with a specifi c 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 device s. Under these conditions, we may choose to acknowledge the better operation of that unit by lo wering 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 the8 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 ca tegory, 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 calc ulate 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 da ta; 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 So u r ces :

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 s ubcategory. We determined that the datasets associated with POM for existing CWPB2 and CWPB3 potlines, PM for existing CWPB2 and CWPB3 potlines, and PCB for ex isting VSS2 potlines were best represented by normal
distributions and that the data set 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 we re each based on the pe rformance 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 tim es the mean of the dataset. Th ese ratio values are within the range that we typically see when we evaluate la rger datasets using our MACT floor calculation procedures. Therefore, we concluded that no ch anges to our standard MACT floor calculation procedure were warranted for these pollutants and subcategories.

Table 3. Ratio of 99 Percent UPL to the Mean fo r 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 1.810 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 mi crograms of toxicity equiva lence 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 us ed 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 So u r ces :

The MACT floor dataset for POM from new pot lines includes 4 test runs from a single potline
that we identified as the best performing unit ba sed on average emissions. After determining that the dataset is best represented by a normal di stribution 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 perf ormer 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 account s 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 fr om a single source and is best represented by a lognormal distributi on. 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 co nsidered the best performer for this pollutant and source category.

The MACT floor dataset for PM from paste produc tion 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 percen t lower than those of the unit with the next lowest average emissions. Therefore, the comparison of variance di d not lead us to conclude that another unit should be considered the best performer. We th en ensured that the calculated emission limit (based on the 99 percent UPL) is a reasonable estim ate 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. Ther efore, 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 al so had the lowest varian ce, indicating consistent performance. We determined that the final emi ssion limit (ultimately ba sed 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 tim es 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 Handli ng 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 perfor mance 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 fo r this pollutant and subcategory.