UNITED STATES ENVIRONMENTAL PROTECTION AGENCY RESEARCH TRIANGLE PARK, NC 27711

OFFICE OF AIR QUALITY PLANNING AND STANDARDS MEMORANDUM SUBJECT: Approach for Applying the Upper Prediction Limit to Limited Datasets DATE: September 3, 2014 FROM: BarrettParker and Brian Shrager

# ~p !51.) Office ofAir Quality Planning and slandards TO: Docket ID No. EPA-HQ-OAR-2010-0895 What is Our Approachfor Applyingthe Upper PredictionLimit to Limited Oatasets? The UPL approach addresses variability ofemissions 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 canbe influenced by components such as the number of samples available for developing MACT standards and the number ofsamples that will be collected to assess compliance with the emission limit. The UPL approach has been used in many environmental science applications. 1'2'3'4'5'6As explained in more detail in memorandum entitled "Use ofthe 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 ofthe best performing source or sources to establish MACT floor standards. Sample size (the number ofvalues in aparticular dataset) is an important component ofthe UPL approach. First, the use ofthe UPL approachrequires us to identify the distribution ofthe data, that is, whether aparticular dataset is normally or non-normally distributed (see the memorandum entitled "Use ofthe Upper Prediction Limit for Calculating MACTFloors", which

1Gibbons, R. D. (I987), Statistical Prediction lntervalsfor the Evaluation ofGround-Water Quality. Groundwater, 25: 455-465 and Hart, Barbara F

. and Janet Chaseling, OptimizingLandfill Ground WaterAnalytes

- 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 ofWind Power Generation

.20I4

. IEEE Transactions on Power Systems, ISSN 0885

-8950, 29(3): pp. 1166- 1 I74

. 3 Khosravi, Abbas; Mazloumi, Ehsan; Nahavandi, Saeid; Creighton, Doug; van Lint, J. W. C. Prediction Intervals to Account for Uncertainties in Travel Time Prediction. 20I I

. IEEE Transactions on Intelligent Transp01tation Systems, ISSN I524-9050, 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, JSSN 0262-6667, 57(1 ): 134

- 143

Internet Address (URL) • http://www

.epa.gov Recycled/Recyclable • Printed**w~h** Vegetable Oil Based Inks on Recycled Paper (Minimum 25% Postconsumer) 1is located in the docket for this action). To determinethe distribution ofthe data, we use wellestablished tests (kurtosis and skewness tests), and these tests require at leastthree datapoints. In prior rulemakings, we usedthe kurtosis equationthat is a built-in function in Excel software, but that equationrequires at least 4 values in orderto avoid dividing by zero, whichprecluded its use for datasets of3. However, we recently further reviewed the application ofthe UPL where data are limited, and concludedthat it is appropriate to use another kurtosis estimator7that provides a meaningful result withjust 3 values. The use ofthis estimator is important, as many, ifnot most, ofour new source emissions limits are based on 3 samples collected during an emissions test. Once we determine the data distribution, the appropriate equationto be used inthe UPL approach is selectedbasedonthe data distribution. We recognize that the use ofthe UPL approachfor limited datasets introduces some amount ofuncertainty inthe calculation ofMACT standards, and, therefore, we are taking additional steps, discussed in this document, to ensure that the level ofthe MACT standards is reasonable. We also note that after MACT standards are promulgated, we are required to reviewthose standards periodically, and for suchreviews, we typically have significant additional HAP emissions datafrom the intervening years of compliance with which to further assess the actual performance ofthe various emission sources. Regardless ofthe distribution ofthe data, UPL equations have three well-defined components: an average, the t-score and a measure ofvariability that includes the actual variability ofthe data, the sample size, and the number ofdatapoints that are averaged together to determine compliance with aparticularemissionlimit. At-score is a value that estimates the uncertainty and variability for a certain confidence level associated with a specific number ofdatapoints. For a constant confidence level, t-scores decrease as the number ofsamples increase. This means that, ifthe mean and variance remain constant, UPL values for aparticular confidence level decrease as the number ofsamples increase. Figure 1and Table 1 showthe t-scores for various sample sizes, and demonstrate thatthe t-score is highly variable at the smallest sample sizes and becomes relatively constant once the sample size is largerthan 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 canhave a disproportionate effect, overwhelming the other components ofthe emission limit calculation. In addition, we recognize that for a sample size offewer thanthree datapoints, which has a very large t-score and precludes the appropriate selection ofa distribution, we should not develop emission limits using the UPL. In other words, iffewer than 3 datapoints are available for use in determining an emission limit for aparticular 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 notrely on the UPL.

7 Doric D, Nikolic-DoricE, Jevremovic V and Malisic 1. 2009. On measuring skewness and kurtosis. Qual Quant. 43:481-493. DOl 10.1007/slll35-007-9128-9. 2Q) I.. 0 (.) 

# "' I 1- 

## T-score vs Number of Samples 35r---------------------------------------------------, 78% reduction from 2 to 3 samples 30

### .~--------~~=========-----------~ 

## ' ' 

## • ' 25 '

# ' ' ' 20

15 

### ' 

# • ' • '

## ' 

# • 35% reduction from 3to 4 samples

I 

# I ' ' I I 17% reduction from 4 to 5 samples

/ 10% reduction from 5 to 6 samples 

## ' '

## • 

## / 

# / /**~~------~----~** 10

5

02 

# • • 

# •**~** I



## .. I

---

_ l#

......... I

3 4 5 6 7 

### Number of Samples 7% reduction from 6 to 7 samples

8 9
Figure 1. Sample sizes versus one-sided, 99 percent confidence interval t-scores for normal distributions

Table 1. Degrees ofFreedom, T-Score for a One-Tailed, 99 Percent Confidence Interval, and Percent Difference in T-Score for Each Sample Size Sample Size Degrees ofFreedom (n- t-score (99 Relative Percent (n) 1) percent) Differencea 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 aThe relative percent difference betweenthe t-score and the t-score shown on the precedmg row

3In the case ofa dataset with a normal distribution, the equation to calculate the UPL is as follows:


### UPL = 

## x+

## trcn- 1

## ).c1 -u)J 

### s 2

# (~+

# ~) where 

# x= average or mean oftest run data; 

## trcn- 1),(1 -u)J = t score, the one-tailed t value ofthe Student's t distribution for a specific degree offreedom (n-1) and confidence level (1- a);



### a=level ofsignificance expressed as a decimal (e.g., 1% significance= 0.01), note that confidence level= 100- (a X 100);

s 2 =variance ofthe dataset (test run);



### n =numberofvalues (test runs) in the dataset; and

m =numberofvalues used to calculate the test average (generally 3).

As shownin the equation, the sample size (n) directly affects the UPL calculations intwo ways. First, as mentioned earlier, the t-score is selectedbased on the sample size. Second, the sample size is a separate variable in the equation, and as withthe 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 influencesboth the mean (x) and variance (s2) in that larger sample sizes provide better estimates ofthe populationmean and variance. The confidence level also influences the t-score, and is represented inthe UPL equation by the subscript "1- a." As noted in the memorandum entitled "Use ofth.e Upper Prediction Limitfor Calculating MACT Floors", which is located in the docket for this action, we typically choose the 99 percent UPL, which is another way ofsayingthat 

### a equals 0.01

. Note that the UPL equationfor a lognormal distribution uses a z-score, instead ofat-score.8As with the normal UPL equation, the lognormal UPL equation is affected by sample size and the variance ofthe data, andthe basic concepts outlined inthis discussion apply to datasets regardless ofthe distribution. In summary, sample size is important for UPL calculations, as it is akey component ofthe tscore value and the calculation ofthe mean and variance ofthe sample. Forthe reasons presented above, for datasets below a certain size, further evaluation is warranted to ensure that the results are a valid representation ofthe performance ofthe emission sources whose data are included in the dataset. The remainder ofthis documentprovides our assessment ofwhat constitutes a

8 Bhaumik, D.K

. and Gibbons, R.D. ' 'An Upper Prediction Limit for the Arithmetic Mean ofa Lognmmal Random Variable", Technometrics, 46, 2004, 239-248. 4limited dataset and what additional analyses are appropriate for ensuring that the UPL calculations are valid representations ofthe performance ofunits as reflected in the available data. What is a limited dataset? While there are different options for choosing the number ofsamples that represents a limited dataset (or small sample size), we canuse distinctions based on our observations in Figure 1and Table 1as an aid in defining what constitutes alimited dataset. As discussed earlier, the t-score is an influential parameterthat can have a particularly large influence on an emission limit developed from a limited dataset. As such, the t-score is akey parameterfor identifying what constitutes a limited dataset for purposes ofMACT analyses. As shown in Figure 1and Table 1, above, at the 99 percent confidence level there is a clear distinction betweent-score values for sample sizes of3 and fewer when comparedto t-score values for sample sizes ofmore than 6

.As Figure 1and Table 1show, the t-score changes drastically from sample size equal to 2 to sample size equal to 3. The changes inthe t-score are considerably less dramatic as the sample size approaches 9 datapoints and larger. As noted earlier, we will not use the UPL approach for datasets with fewer than 3 values because ofthe high degree ofunce1iainty that results from the size ofthe dataset and the related t-score. In fact, the t-score (see Figure 1 and table 1) for a dataset of3 is 78 percent lowerthan at-score for a dataset of2, meaning that given an equal variance, the component oftheUPL 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 andfigure also showthat the relative change ofthe tscore for each additional data point decreases as the sample size gets larger. As sample size increases, uncertainty decreases, butthere is always some amount ofuncertainty. The discussion that follows presents our examination ofthe 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 ofthe UPL to ensure that the amount ofuncertainty is within areasonable range. Based on Table 1, the lower bound ofthe sample size where such further evaluation is needed is 3 values, and a reasonable value (where the size ofthe t-statistic has much less influence on the eventual emission limit) lies between4 and 9 values. An additional factor to consider is that, in the context ofMACT analyses, emissiontests typically include 3test runs (independent datapoints), and, therefore, our MACT floor dataset size typically is a multiple of3. For this reason, we first considered sample sizes that are multiples of3 when identifying the size belowwhich further scrutiny is needed. As canbe calculated from the t-scores shown inTable 1, the relative difference between the t-score for 6 datapoints and the t-score for 9 datapoints is about 14 percent ((3.36-2.90)/3.36). The relative difference betweenthe t-scores for 7 and 9 datapoints is about 8percent ((3.14-2.90)/3.14). Given that the test methods that are used to generate the datatypically 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 alarge influence onthe magnitude ofan emission limit. Conversely, comparingthe t-score for 3runs to that for 7 runs, the relative

9 (ReMAP): PHASE I, Precision ofManual Stack Emission Measurements; American Society ofMechanical Engineers, Research Committee on Industrial and Municipal Waste, February 200I. 5difference in the t-score is 55 percent ((6.96-3.14)/6.96), indicating that there is a possibility, especially ifthe variance is high, thatthe t-score for 3test runs may introduce a large amount of uncertainty in an emission limit, and, therefore, additional analysis ofa dataset ofthis size is warranted. We also conductedthe same type ofevaluation on datasets between4 and 6points, and while the change int-score for datasets ofthese sizes could be considered to be sufficiently small, to be conservative, we concludethat a limited dataset, for purposes ofMACTanalyses, is a dataset that includes at least 3test runs and fewer than 7test runs. Because ofthe uncertainty associated with datasets at orbelowthis size, further evaluation is warranted, and the types of additional analyses that we may choose to conduct are explained below. What approach will the EPA follow for MACT floors based on limited datasets? When a MACTfloor for either existing or new sources is based on fewer than 7 data points, we will further evaluate each individual dataset in orderto ensure that the uncertainty associated with a limited datasetdoes not cause the calculated emission limitto be so high that it does not reflect the average performance ofthe units upon which the limit is based after accounting for variability in the emissions ofthose units. The evaluationwill include one or more ofthe following, depending on the specific dataset: confirming thatthe data distribution was selected correctly; after confirmingthe data distribution, ensuringthat we use the most appropriate UPL equation 10; and, as necessary, comparing UPL equation components for the individual unit upon which a new source floor is based withthose ofthe units in the existing source floor to determine ifour identification ofthe best unit is reasonable. Each ofthe additional evaluations are discussed below

. Confirming the data distribution is importantbecause UPL equations and the emission limits derived from those UPL equations depend onthe distribution. Inpriorrulemakings, we had not identified a way ofascertaining 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 ofwhich were based on three samples. However, we have since identified and adopted an established technique that compares the ratio ofskewness to the standard error ofthe skewness for both the raw and log transformed data.·The lower ofthe 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 optionfor the UPL equation given the small sample SIZe. After confirming that we selected the best distributionbased onthe available data and ensuring that we used the correct equation to calculate a MACTfloor 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 oftest runs (i.e., sample size), and number ofruns in each test (i.e., the number ofdatapoints that are averaged together to determine compliance with a particular emission limit). The considerations related to each variable are discussed below.

IO For datasets with lognom1al distributions, we recently determined that the most appropriate UPL equation, which is especially importantfor the smallest datasets that we use, is based on an approach described in Bhaumik,2004, op. cit

. 6The average, which typically is calculated as the mean value ofa dataset, does not require additional consideration. Once it is calculated, it is used to rankthe performance ofunits, and also is the key value upon which each emission limit is based. As such, average values have already been compared within a particular dataset, and additional assessment is not necessary. However, in the overall assessment ofvariables, 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 whichunit is the single bestperformer. 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 importantbecause the t-statistic is multiplied by the variance and a factor that involves the sample size and the number oftestruns used for compliance (i.e., the "m"term in the UPL equation). Forthe smallest datasets (3 datapoints) that we consider underthe UPL approach, a large variance coupled with at-score that is significantly greater thanthe t-score for a dataset of7 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 ofemissions could realistically be expected from the type ofunit, controls, and other relevant factors, and would ensure thatthe emission limit is reasonable. The variance is another key variable that we would evaluate. Generally speaking, ifour evaluation showed a very small amount ofvariability (e.g., a small variance), the emission limit would not contain an unacceptable amount ofuncertainty and variability because a small variance would result in an emission limit that would be reasonably close to the mean ofthe data. With larger datasets, it is more likely that the demonstrated variance is truly representative ofthe variation inthe source's emissions simply becausethere is more evidence ofthe source's emissions overtime

. Onthe otherhand, when a limited dataset includes a large amountof variability (e.g., a large variance), we would need to carefully evaluate the data

.For instance, considerthe case where the pool ofbestperforming 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 ofthe other similarly-controlledbest-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 ofvariance will allowus to better ascertain which unit should be considered the best performer. Another tool that could be used to adjust umeasonable emission limits is the selection ofthe confidence level. In certain instances, we may determine that a limited dataset includes such a high degree ofvariability thatthe 99 percent confidence level results in an emission limit that our experience suggests is higherthanthe 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 of95 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. Underthese conditions, we may choose to acknowledge the better operation by lowering the confidence level (which lowers the emissions limit).

7Establishing and using this approach on a case-by-casebasis for limited datasets will ensure consistent application ofemissions limit developmentprocedures, which will mitigate the additional uncertainty that could otherwise result from calculating MACT floor standards with limited data. 1 1
How did we apply the approach for limited datasets to limited datasets in th £ rroalloys source category? For the ferroalloys source category, we have limited datasets for the following pollutants and subcategories: PAHs for existing and new furnaces producing ferromanganese (FeMn); PAHs for new furnaces producing silicon manganese (SiMn); mercury for new furnaces producing SiMn; mercury for existing and new furnaces producing FeMn; and HCl for newfurnaces producing FeMn or SiMn. Therefore, we evaluated these specific datasets to determine whether it is appropriate to make any modifications to the approach usedto calculate MACT floors for each ofthese datasets. For each dataset, we performedthe steps outlined above, including: ensuring that we selected the data distributionthat bestrepresents each dataset; ensuringthat the correct equation for the distribution was then applied to the data; and comparing individual components ofeach limited dataset to determine ifthe standards based on limited datasets reasonably represent the performance ofthe units included in the dataset. The results ofeach analysis are presented below. The MACT floor dataset for PAHs from existing furnaces producing FeMn includes 6testruns from 2 furnaces. This subcategory includes only two units, and the CAA specifies thatthe existing source MACT floor for subcategories with fewer than 30 sources shall not be less stringent than "the average emission limitation achieved by the best performing 5 sources." However, since there are only 2 units in the subcategory and we have data for both units, the data from both units serve as the basis for the MACT floor. After determining that the dataset is best represented by a normal distribution and ensuringthat we used the correct equation for the distribution, we considered the selection ofa lower confidence level for determining the emission limitby evaluating whetherthe calculated limit reasonably represents the performance ofthe units upon which it is based. Inthis case, where two units make up the pool ofbest performers, the calculated emissionlimit is about twice the short-term average emissions from the best performing sources, indicating that the emission limit is not unreasonable compared to the actual performance ofthe units upon which the limit is based and is within the range that we see when we evaluate larger data sets using our MACT floor calculationprocedures. Therefore, we determined that no changes to our standard floor calculationprocedure are warranted for this

11 We note that in the recent D.C. Cir· cuit Court ofAppeals decision in National Assn

.ofClean 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 cout1 identified the anomalous result is where we did not apply the most appropriate lognormal UPL equation. 8pollutant and subcategory, and we are proposing that the MACT floor is 1,400 

### 11gldscm for PAHs from existing furnaces producing FeMn. The MACT floor dataset for PAHs from new furnaces producing FeMn includes 3 test runs from a single furnace (furnace #12 at Eramet) that we identified as the best performing unit based on average emissions performance. 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 ofthe best performing unit. Our analysis showedthat this unit, which was identified as the best unit based on average emissions, also had the lowest variance. Therefore, we determined that the emission limit would reasonably account for variability and that no changes to the standard floor calculationprocedure were warranted for this pollutant and subcategory, and we are proposing that the MACT floor is 880 11g/dscm for PAHs from new furnaces producing FeMn. The MACTfloor dataset for PAHs initially identified for new furnaces producing SiMn includes 6test runs from a single furnace (furnace #2 at Felman) that we identified as the bestperforming unit based on average emissions. After determining that the dataset is bestrepresented by a normal distribution and ensuring that we used the correct equation for the distribtition, we evaluated the variance ofthis unit (furnace#2 at Felman) and concluded that further consideration ofthe variance was warranted. Inparticular, wenoted that the variance ofthe dataset for this unit was almost twice as large as the variance ofthe dataset for the pool ofbest performing units that was used to calculate the existing source MACT floor. The high degree of variance in the dataset for the unit with the lowest average prompted us to question whether this unit was, in fact, the best performing unit and to evaluate the dataset for the unit with the next lowest average (furnace #7 at Felman). The dataset for furnace #7 includes 3test runs, the furnaces are controlled withthe same type ofadd-on control technology, and the average emissions from furnace #2 are only about 22 percent lowerthanthe average emissions from furnace #7. While we find the average performance ofthese 2 units to be similar, the unit with the higher average has a variance more than 2 orders ofmagnitude lower than that ofthe unit with the loweraverage, thus indicating that the unit with the higher average has a far more consistent level ofperformance. The combination ofcomponents from the unit with the higher average (furnace #7) yields an emissions limitthat is lower than that calculated from the dataset ofthe unit (furnace #2) with the lowest average (71.7 versus 132.8**~-tg/dscm).** For these reasons, we determined that the unit with the lowest average (furnace #2) is not the best performing source for this pollutant and we are instead selecting furnace #7 as the best performing source. After selecting the source upon whichthe new source limit would be based, we next considered whether the selection ofa different confidence level would be appropriate. In this case, we determined that a lower confidence level was not warranted given the small amount ofvariability in the data for the unit that we identified as the best performer. Based on the factors outlined above, we are proposing that the MACT floor is 72 11g/dscm for PAHs from new furnaces producing SiMn. The MACT floor dataset for mercury from existing and newfurnaces producingFeMn includes 6test runs from a single furnace. We first determined that the dataset is best represented by a normal distribution and ensured that we usedthe correct equation for the distribution. Because the floor for both existing and newfurnaces is based onthe performance ofa single unit, our

9evaluation ofthe data was limited to ensuring that the emission limit is a reasonable estimate of the performance ofthe unit based on our knowledge about the process and controls. Accordingly, we compared the calculated emission limit to the highest measured value and the average shortterm emissions from the unit, and found thatthe calculated emission limit is about 2.5 times the short-term average from the unit, which is within the range that we see when we evaluate larger data sets using our MACT floor calculationprocedures. The fairly wide range in mercury emissions shown by the available data for this best performing unit indicate that variability is significant, and we determined that the emission limit is representative ofthe actual performance ofthe unit upon which the limit is based, considering variability. Therefore, we determined that no changes to our standard floor calculationprocedure were warranted for this pollutant and subcategory, and we are proposing that the MACT floor is 170**~tg dscm**  for mercury from existing furnaces producing FeMn. We also note that while we calculated the same MACT floor value for new sources, we are proposing a beyond-the-floor standard for new sources,which is discussed later in this section ofthis preamble

. The MACT floor dataset for mercury from new furnaces producing SiMn includes 3test runs from a single furnace (furnace#7 at Felman)thatwe identified as the best performing unit based on average emissions. After determining that the dataset is bestrepresented by a normal distribution and ensuring thatwe used the correct equation for the distribution, we evaluated the variance ofthis unit. Our analysis showed thatthis unit, identified as the best unit based on average emissions, also had the lowest variance, indicating consistentperformance. Therefore, we determined that the emission limit reasonably accounts for variability and that no changes to the standard floor calculationprocedure were warranted for this pollutant and subcategory, and we are proposing thatthe MACT floor is 4.0**~g/dscm** for Hg from new furnaces producing SiMn. The MACT floor dataset for HCl from new furnaces producing FeMn or SiMn includes 6 test runs from a single furnace (furnace #5 at Felman) that we identified as the best performing unit based onaverage emissions. Afterdetermining that the dataset is best represented by a nonnormal distribution and ensuring that we used the correct equation for the distribution, we evaluated the variance ofthis bestperforming unit. Our analysis showed that this unit, identified as the best unit based on average emission, also had the lowestvariance, indicating consistent performance. Therefore, we determined thatthe emission limit reasonably accounts for variability and that no changes to the standard floor calculationprocedure were warranted for this pollutant and subcategory. We also note that for this standard, the calculated new source floor level was belowthe level that canbe accurately measured (the level that we refer to as "3 times the representative detection level" or 3xRDL). Therefore, we are proposing a new source MACT emission limit of 180 ppm, which is the 3xRDL value for HCl.

10