MEMORANDUM

DATE: July 30, 2014
SUBJECT: Use ofthe Upper Prediction Limit for Calculating MACTFloors
FROM: Phil Mulrine, EPA OAQPA/SPPD/MICG
TO: Docket ID No. EPA-HQ-OAR-2010-0895
This document explains EPA's use ofthe UPL, which is the statistical methodology EPA uses as the primary tool to account for emissions variability when setting emissions standards under these sections, and explains howthe UPL is used to calculate the average emissions limitation achieved overtime bythe bestperforming source or sources. I. Emissions Standards under Section 112 and 129 Formajor stationary sources ofhazardous air pollutants (HAP) under section 112 and for sources regulated under section 129, 1the CAA requires emission standards thatrepresent the maximum achievable control technology, or "MACT" level ofcontrol. The MACT standard settingprocess is a two-step process that starts with the agency determining the level ofcontrol that is currently achieved by the best-controlled similar source (for new source standards) or the average ofthe best-performing sources (for existing source standards). That level ofcontrol is the minimum level ofcontrol required by the CAA regardless ofcost orfeasibility, and it is commonly called the "MACTfloor." This document focuses on that first step inthe MACT standard setting process, as it is in that step thatthe agency uses the UPL to both evaluate average emissions performance and estimate variability to determine the level ofcontrol sources currently achieve. 2 Fornew sources located at facilities that are major sources ofHAP, section 112 ofthe CAA requires EPA to establish standards that are no less stringentthanthe emissions control that is achieved in practice by the best controlled similar source. The statute does not define "achieved inpractice" nor does it dictate the manner in whichthe agency determines which source is the best controlled similar source, instead leaving itto the agency's discretion to make those determinations. For existing sources located at facilities that are major sources ofHAP, standards must be no less stringent thanthe average emissions limitation achieved by the best performing

1A "major source" is a stationary source or group ofstationary sources at a single location and under common control that emits or has the potential to emit ten tons per year ormore ofany hazardous airpollutant or 25 tons per year or more ofany combination ofhazardous air pollutants. Any stationary source that is not a major source is an "area source." CAA § 112(a). For area sources ofHAP, EPA has the discretion to set emissions standards under section 112(d)(5) based on generally available control technology in lieu ofMACT standards.

2 The second step in the MACT standard-setting process is the evaluation ofwhether beyond-the-floor controls are appropriate, as provided in section 112(d)(2) ofthe Act. This second step is not addressed in this document. Page 1 oflSsources for which EPAhas emissions information. Again, the CAA leaves to EPA's discretion the matmer in which to calculate "the average emissions limitation achieved" by the best performing sources. Under section 112, the CAA recognizes that source categories and subcategories have differing numbers ofsources andprovides category size-specific instructions on determining standard stringency for existing sources. Specifically, standards for categories or subcategories with fewer than 30 sources mustbe based onthe average emissions limitation achieved bythe best performing 5 sources, and standards for categories or subcategories with 30 or more sources must be based on the average emission limitation achieved by the best performing 12 percent ofsources for which EPA has emissions information. Section 129 requires EPAto establish standards for new sources that are no less stringent than the emissions control that is achieved in practice by the best controlled similar source for nine specified criteria and hazardous air pollutants, and standards for existing sources that are no less stringentthanthe average emission limitation achieved by the bestperforming 12 percent ofsources in the category or subcategory for the same nine pollutants. II. Background EPApromulgatedrules covering major source industrial, commercial, and institutional boilers and commercial and industrial solid waste incinerators (CISWI) rule onMarch 21, 2011, and subsequently made certain revisions to the rules on January 31, 2012. On August 20, 2013, the D.C. Circuit Court ofAppeals issued its decision inNational Assn. ofClean Water Agencies v. EPA, which involved challenges to EPA's MACT standards for sewage sludge incinerators, issued under section 129 ofthe Act. See 734 F.3d 1115. In the NACWA decision, the D.C. Circuit remanded certain aspects ofthe rule for further explanation, including the question of howthe UPL represents the MACTfloor for new and existing units, as required by the CAA. The sewage sludge incineratorrule was issued on the same day as the boilers and CISWI rules, and used the same general methodology for calculating the MACT floors. Forthis reason, EPA requested an opportunity to supplementthe record in pending challenges to the boilers and CISWI rules,to provide the explanation ofthe agency's analysis ofvariability in setting the MACT floor standards thatthe court believed was needed in the record for the sewage sludge incineratorrule. The court granted EPA's motion for a remand ofthe record on May 15,2014. This documentprovides that additional explanation, which also applies to MACT standards that are part ofthe rulemaking for the Ferroalloys Production source category. There are several key points, addressed in more detail below, that underlie EPA's methodology for calculating MACT floor standards through the use ofthe UPL. First, the floor standards reasonably account for variability in the emissions ofthe sources used to calculate the standards. This variability occurs due to a number offactors, including measurement variability (both sampling and analysis) and shortterm fluctuations in the emission levels that result from shortterm changes in fuels, processes, combustion conditions, and controls. Second, because the emissions data available to EPA is in the form ofshort-term stacktests and the standards must be complied with at all times, the agency uses the UPL to estimate the average emissions performance ofthe units used to establishthe MACT floor standards at times otherthan when the stacktests were conducted. Thus, the UPL results in a limitthat represents the average emissions limitation achieved bythe bestperforming sources over time, accounting for variability in emissions performance. · III. Overview ofMACT Floor Methodology Page 2 of15In establishing MACT floors, we use the available information to determine the average performance ofthe best performing sources (for existing source floors) and the average performance ofthe best-controlled similar source (for new source floors). Each MACT standard is based onlimited data from sources whose emissions are expected to vary overtheir long term performance. For this reason, and because sources must comply with the MACT standards at all times, consideration ofvariability is a key factor in establishing these standards. This variability in emissions is due to numerous factors, including operation ofcontrol technologies,'variation in combustionmaterials and combustion conditions, variation in operation ofthe unit itself, and variation associated withthe emissionmeasurement techniques. In orderto account for variability that is reflected in the available datathat we use to calculate MACT floors, we use the UPL. The NACW A court recognized that EPAhas significant discretion in establishing the MACT floors, including how to account for variability. See NACWAv. EPA, 734 F.3d at 1142-43 ("EPA can decide what value the MACT floors are supposed to represent, as long as that decision is a reasonable interpretation ofthe statute.") However, the court expressed concern about the interpretation it believed EPA was taking ofthe "average" emissions performance of the bestperforming sources. Specifically, the court asked for further clarification ofhow '"average' means the average ofa future 3-run compliance test." Id. at 1143. As explained below, EPAdoes not interpret the term "average" as used in section 112(d)(3) in this manner. Rather, EPA interprets the average to mean the average emissions overtime, based on boththe calculated average ofall emissions test data from the best performing source or sources and the available information regarding the variability ofemissions. The UPL, which EPA uses to account for variability among the bestperforming sources, reflects an upper limit for the emissions ofthose sources at times otherthan whenthe emissions tests occurred. This not only is a prediction ofthe emissions performance ofthose sources intests conducted inthe future, but is also an indication ofthe range ofcurrent average emissions performance ofthose units. In calculating MACT floors, EPA analyzes all available emissions information and then uses the emissions information for the bestperforming source or sources to calculate a value that represents the level achieved in practice by the best controlled similar source for the new source MACT floor and a value that represents the average emission limitation achieved by the best performing twelve percent ofsources for the existing source MACT floor. EPA must establish the MACTfloor standards based on the emissions information before the agency, and the standards must be met at all times by sources subject to them. The available emissions data are generally inthe form ofshortterm, three-run stack tests, with eachtest run lasting for between 1 and 4 hours. Those short term tests cannot encompass the emissions performance ofa source over time. EPA interprets "emissions performance," as used in section 112(d)(3) to meanthe emissions ofa source over the long term, rather thanjustduring a short-term stack test. This is a reasonable interpretation ofthe statutory directive that the MACT standard be no less stringent than the average emissions limitation "achieved by" the bestperforming sources, since the emissions level ofa source is not expected to always be the same as it is during stack testing. Therefore, EPA applies a methodology that predicts the actual emissions levels the source is achieving at times otherthan when stacktesting was conducted. This enables EPA to calculate the average emissions performance ofthe bestperforming sources over time. Therefore, the MACT floor calculation takes into account the inherent variability in emissions performance to Page 3 of15more accurately reflect the range ofthe bestperforming sources' emissions over time. The remainder ofthis discussion focuses onwhy the statistical methodology that we used

- the UPL

- provides results thatreasonably represent the level achieved inpractice by the best-controlled similar source for new sources, and the average emissions limitation achieved by the best performing emissions units for existing sources. IV. Use ofthe Upper Prediction Limit The UPL is a value derived from widely accepted and commonly used statistical principles, and represents the upper end ofa prediction interval.3 The UPL is used in a wide variety ofindustries and professions, such as manufacturing, finance, healthcare and others.4 The UPL is calculated using one ofseveral equations thatmust be selected based on certain characteristics ofeach dataset. The most importantparameters inthe UPL calculation are the mean (average) performance ofthe unit or units, the distribution ofthe dataset, the variance inthe measured emission values (that is, the individual datapoints), and the sample size. The equations that are usedto calculate the UPL are explained in more detail below. Inthe context ofdevelopment ofMACT floors, the UPL is a value, calculated from a dataset, that identifies the average emissions level that a source or group ofsources is meeting and would be expected to meet a specified percent ofthe time that the source is operating. Thatpercent of time is based on the confidence level used in the UPL equation, as explained in more detail below. For a single best controlled emission source that serves as the basis for a new source MACT floor, the 99 percent UPL is the emissions level that the source would be predicted to be below during 99 out of 100 performance tests, including emissions tests conducted in the past, present, and future, based onthe short term stack test data available for that source. Itis important to note that the UPL does not represent the worst emissions performance ofthe best performing units at any time, butrather the average level expected to have been achieved over time, as the first element ofthe UPL equation is the average ofthe short-term emissions test data from the bestperforming units. In other words, the 99 percent UPL is the level ofemissions that we are 99 percent confident is achieved bythe average source represented in a dataset over a long-term periodbased onits previous, measured performance history as reflected in short term stacktest data. In sum, the UPL predicts the level ofemissions that the sources upon which the floor is based are expected to meet over time, considering both the average emissions level achieved as well as emissions variability and the uncertainty that exists in the determination ofemissions variability given the available, short-term data. EPA did not have emissions information from sources at all times each source was operating, and therefore determined it was necessary to apply a methodologythat addressed the fact that the data were not complete. Statistical tools are commonly used in science and industry because they permitpredictions to be made based on the available data. As explained in more detail below, the UPL equations include a term that adjusts the average emission level ofthe units to account for boththe emissions variability observed in

3 National Institute ofStandards and Technology, NISTISEMATECH e-Handbook of StatisticalMethods, <http://www.itl.nist.gov/div898/ oftware/dataplot/refman 1 /auxillar /predlimi.htm>. 4 See, e.g., Gibbons, Robert D. and Coleman, David E. (2001). StatisticalMethods for Detection and Quantification of

Environmental Contamination, New York: Wiley, pp 21-31, and Luko, S.N. and D.V. Neubauer, Statistical Intervals Part2. StandardizationNews, October/November 2011. <http:www.astm.org/standardization-news/datapoints/statistical-intervals-part-2-so11.html>. Page 4 of15the data andthe uncertainty that exists inthat estimate ofvariability for a sample ofthe given size, to estimate the performance ofthe units overtime. As shownby the t- and z-statistics incorporated into the UPL equations, the uncertainty regarding emissions variability is higher in small samples and is lower in large samples, but it is always accounted for in UPL. The 99 percent UPL value reasonably estimates the level currently achieved inpractice by the best controlled similar source and the average emission limitation currently achieved by the best performing 12 percent ofsources by estimating the level achieved by the best source (for new sources) orby the average ofthe best sources (for existing sources) ninety-nine percent ofthe time the sources are operating. Itis reasonable to interpret the statutory requirement that the MACT floor level reflect the "emission control that is achieved inpractice" by the best controlled similar source and the "average emission limitation achieved by" the bestperforming 12 percent ofsources as a level thatthe average level the bestperformers are meeting on a consistent basis overtime, notjust atthe single point in time during which emissions test data were collected. IfEPA were to simply take the average ofthe stacktest data from the best performing source or sources, the MACT floor would not represent the levels ofemissions achieved inpractice over time becausethe MACT floors would not reflect variations in material inputs (e.g., fuels), control device performance, operating unit performance (e.g., changes in combustion conditions that impact emissions), and other factors that affect unitperformance over time. This is demonstrated by the fact that even single three runtests, which are performed over a short period oftime, typically show different emissions levels during each individual testrun. Itwould notbe reasonable to establish a MACT floor standard that the best performing sources would exceed routinely. Butneither would it generallybe reasonable to establish a standardthat all the bestperforming 12 percent ofexisting sources can meet without any modification because the statute requires the agency to establish the standard at the average level ofperformance of the best 12 percent ofsources. IfEPA simply calculated the average (mean) ofthe emissions datafrom the bestperforming 12 percent ofsources, that would only lead to a limit that can be met by all the existing sources in the floor at all times in the unlikely hypothetical situation where all the sources have identical emissions test data and controls and operate in exactly the same manner- i.e. the sources would have to be essentially identical and use identical fuels or other material inputs. Since that situation does not represent real-world source categories, the agency takes the available data and applies a statistical formula to account for variability in emissions ofthe bestperforming source or sources.

Page 5 of15V. Establishment ofMACTFloors At first glance, developing a HAP emissions limit in accordance with the statutory requirements seems a straightforward task, requiring simplythat EPA collect all available valid data from all the sources in a specific category or subcategory, rank the data to select the best performing twelve percent ofthe category or subcategory, and calculate the average emission level achieved by that group ofsources for a particularpollutant. However, multiple factors complicate these calculations. First, emissiontestresults taken during a three-run stack test, as is the case with virtually all the HAP emission data available to EPA, represent three "snapshots" ofa source's operations during the test period and those results generally will not represent a source's full range ofnormal operations or emissions levels. However, because there are three separate runs in a test, a single test will inmost cases show some ofa particular source's variability overthe short period oftime during which testing was conducted. Further, EPA generally has limited datawith which to establish MACT standards, primarilybecause the dataneeded are not generally collected by sources prior to regulation (particularly for HAP, but also for other pollutants such as nitrogen oxides, sulfur dioxide, and carbon monoxide regulated under section 129). The collection ofsuch data is a time- and resource-intensive effort, as emissions tests cantake more than a week to·perform, analyses ofsamples from the tests cantake more than a month, preparation oftest reports typically takes several months, and costs range up to $40,000 pertest perpollutant. For example, during our data collection efforts for the boiler and CISWI rules we required hundreds offacilities to conduct emissions testing, and we estimated an average cost of about $90,000 for each facility that was required to conduct testing. As explained above, EPA establishes MACT floor standards under sections 112 and 129 as limits that reflect the level achieved inpracticeby the best controlled similar source, orthe average emissions limitation achieved by the bestperforming 12 percent ofsources overtime, but we necessarily must do thatbased onthe emissions information that is available. Inthis case, that information consisted ofemissions test data thatrepresents the specific instances inthe sources' operations when testing was conducted. The UPL is a common statistical technique that allows EPA to use emissions test data and the data characteristics, such as the distribution and sample size, along with the intrinsic variability associated with those data,5 to calculate an emissions limit based on a specified level ofconfidence suchthat an average best performing existing source would not be expected to exceed the limit a specified number oftimes. For instance, ifan emission limit were set at the 50 percent UPL, we would expect the average unit to have emissions above the level ofthe standard 50 percent ofthe time.
This section explains how EPA applied the UPL to the emissions data from the bestperforming source or sources to calculate MACTfloor limits thatrepresentthe average emissions performance ofthose sources, while accounting for variation inthose sources' emissions over time.
A. Ranking Sources and Establishing the Distribution ofData
After collecting emissions data, EPA analyzes the data both to identify and rank the best performing sources and to evaluate the data distribution. This evaluation is necessary because the

5 Gibbons, p 30. Page 6 of15UPL equation that is used to account for variability and calculate the MACT floor standard depends onthe distribution ofthe data. Typical data distributions are normal and lognormal, as shown in Figures 1 and 2. Therefore, the first step in applying the UPL is to rank sources (based on lowest emissions) to identify the best performing sources and then analyze the distribution of the emissions data from those bestperforming sources. The ranking is used to establish which set ofunits make up the top 12 percent ofperformers for eachpollutant and subcategory and whicli unit EPA considers the single best-controlled for eachpollutant and subcategory. Once these units are identified, EPA determines the data distribution as discussed below.
In order to select statistical equations (to calculate the UPL) that are appropriate for each individual dataset, EPA evaluates each individual dataset to determine the data distribution, as noted above. The individual datasets that we evaluate include the datasets for the bestperforming unit for eachpollutant and subcategory for the new source MACT floor standards and the datasets for the best performing 12 percent ofunits for eachpollutant and subcategory for the existing source MACT floor standards. To evaluate the distribution ofthe data, EPA checks each dataset for distribution characteristics by applying skewness andkurtosis tests. Skewness is a measure ofsymmetry (or the lack ofsymmetry) ofa distribution, and is useful in determining the distribution because normal distributions are symmetric while lognormal distributions are not. Kurtosis is a measure ofwhether a dataset has a similar, more distinct, or flatter peakthan a standard normal distribution.6 Figures 1 and 2 show simple examples ofnormal and lognormal distributions. In each figure for the purpose ofEPA's analyses, the x-axis is the level of emissions and the y-axis represents the probability ofa particular value occurring (established based onthe number ofoccurances inthe dataset at each level ofemissions). Ifboththe skewness and kurtosis tests suggest the data exhibit a normal distribution, EPA evaluates the emissions datafor the source category using statistical equations for normally distributed data. If the test results are inconsistent regarding normality, orifboth testresults suggestnon-normality, EPA evaluates the emissions data for the source category using statistical equations for lognormally distributed data.
EPAuses this approach because, absent evidence ofa normal distribution, air emissions data have historically been shown to exhibit lognormal distribution characteristics such as 1) run values always above zero; 2) a majority ofrun values will be low; and 3) a few run values will be high but will have a lowprobability ofoccurring.7•8• 9 These characteristics yield a left-skewed distribution curve, meaning the distribution has a long tail to the right.

6National Institute ofStandards and Technology, NIST/SEMATECHe-Handbook of StatisticalMethods, <http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm>. 7 Ott, Wayne R. (1990)A PhysicalExplanation of the Lognormality of Pollutant Concentrations, Journal ofthe Air & Waste Management Association, 40:10, 1378-383, DOl: 10

. 1080/10473289.1990.10466789. 8 Gilbert, Richard 0. (1987), StatisticalMethodsfor EnvironmentalPollution Monitoring, New York: Van Nostrand Reinhold, p 152. 9 Gibbons, Robert D. and Coleman, David E. (2001), StatisticalMethodsfor Detection andQuantification of Environmental Contamination, New York: Wiley, p 369.
Page 7 of15Figure 1. Normal Distribution 10



### X

Figure2. Lognormal Distribution11

10 http://www.psychstat.missouristate.edu/introbook/sbkIOm

. btrn

. 11 http://math.tutorvista.com/statistics/normal-distribution.htmI

. Page 8of15The following example demonstrates the characteristics ofa lognormal distribution curve. Consider a dataset obtained from three filterable particulate matter (PM) emissions tests, each consisting ofthree test runs, from three independent sources. The nine runs produced the following values measured inpounds PM per million British Thermal Units (lb PM 

### I MMBTU): 0.00134,0.00139,0.00153,0.00319,0.00387,0.00417,0.00970,0.0128, and 0.0243. This dataset, referred to as Case A, yields both skewness and kurtosis consistent with a lognormal distribution. Figure 3 shows Case A data as solid green squares plotted on the lognormal distribution determined from the characteristics ofthe run data. Based onthose characteristics, one would expect 50 percent ofall filterable PM values to be less than 0.0039 lb PM 

### I MMBTU. In addition, one would expect about 95% ofall filterable PM values to be less than 0.0188 lb PM 

### I MMBTU. The long tail to the right, as shown in Figure 1, is consistent with the expectationthat high values can exist, butthey have a low probability ofoccurring- below one percent for values greaterthan 0.0255 lb PM 

### I MMBTU.


### Lognormal Data Distribution for Case A


# I



# - ::J 120

..... 

### t m ::!: 2 

# _I



# - ::!:



### ------ D. .Q 

### eo ::::. 

# -**~** 

### :a cu .Q 0

.... 40 D.
·---



# . .



### - 

# -,----
1--

- - 00 0.005 0.01 0

.015 0.02 0

.025 lb PM I MMBTU FIGURE 3. Lognormal Data Distribution Example. The smooth curve represents the density function ofthe lognormal distribution determined from the characteristics ofthe filterable PM emissions test data (shown as squares) from Case A.
B. Calculating the MACT Floor
Once EPA identifies the best performing single source or best performing twelve percent of sources and the distribution ofeach dataset, we calculate the UPL, as described below, to identify an emissions limit that represents the level the average unit among the bestperforming Page 9 oflSunits has met, is meeting, and would be expected to meet inpractice with a specific confidence level. 12 The confidence level, in this case 99 percent, is the percentage ofmeasurements (past, present, and future) that are predicted to fall at orbelowthe UPL value. Stated differently, the 99 percent UPL is the level ofemissions that we are 99 percent confident is achieved by the average source represented in a dataset over a long-termperiod based on its previous, measured performance history as reflected in shortterm stacktest data. The UPL value is based onthe available emissions data from the bestperforming single source (for new source standards) or the best performing 12 percent ofsources (for existing source standards). The UPL incorporates the intrinsic variability ofthe individual run measurements used to calculate an emission test average. 13 While the UPL can be calculated at different confidence levels, we selected the 99 percentlevel in order to provide reasonable assurance thatthe limit canbe met at all times by a source with emissions at the average level achieved by the bestperforming source or sources. C. Applying the UPL Equations
Once the distribution is established and the confidence level selected, a UPL value is calculated using six components. Four ofthese components are derived from the emissions dataset: the average (or mean), the variance ofthe dataset, the t-statistic or z-statistic (depending on the distribution characteristics), and the number ofsamples, which is associated withthe total number ofemissions test runs. For example, ifthere are results from six emissions tests, there typically are at least 18 emissions test run values (or samples), since an emissions test generally consists of3 test runs. 14 The othertwo components are the number ofrun values used to calculate the average and the confidence level.
UPL equations are data-distribution specific, so that the normal distribution UPL equationis different from the lognormal UPL equation. Eventhough they differ due to separate mathematical properties associated with each distribution, the UPL equations share a common format that is composed oftwo parts which are added together. Equation 1 shows the UPL equation for a dataset with a normal distribution.
Equation 1. 

### UPL1

### oo-(ax1

### oo) = 

### i 

## + tcn- 1),(1

### -a)Js2

# (~ +

# ~) where a= level ofsignificance expressed as a decimal (e.g., 1% significance= 0.01), note that confidence level= 

### 100- (ax 

### 100); 

### :X = average or mean oftest run data;

12 Gibbons, p 28. 13 Gibbons, pp 30-31. 14 EPA test methods typically require 3 testruns. In cases where a test included fewer than 3 valid test runs, we typically do not include the test as a valid test for the purpose ofMACT floor calculations. However, iflimited orno other data are available for a particular source and pollutant, we consider the use ofsuch data on a case-by-case basis. Page 10 of15

### t = t score, the one-tailed t value ofthe Student's t distribution for a specific degree of freedom and level ofsignificance;



### n = number oftest runs;



### s 2 =variance oftestrun data; and



### m =number oftest run values used to calculate the test average (generally 3).

The first part ofthe UPL equation, xisthe average ofthe best performing sources' emission measurements. Thus, the average ofthe emission measurements from the bestperforming source or sources is a fundamental element, and is in fact the startingpoint, ofthe UPL calculation. The second part ofthe equation,**i.~.,** everything to the right of

# x, is associated with the variance of the run data, s 2; the total number ofruns inthe dataset, n; the confidence level, calculated from a; and the number ofrun values used to calculate the emissions average for eachtest result, 

### m. As shown inEquation 1, the UPL is directly related to the sources' emissions average. In other words, as the emissions average goes up or down, so does the UPL value. The UPL also is directly related to the confidence level and to the variance, meaning that as either ofthese values go up or down, so does the UPL value. However, the UPL is inversely related to the number of runs in the dataset and to the number ofruns averaged for each emissions test. Therefore, as either ofthese values increases, the UPL value decreases and as either ofthese values decreases, the UPL value increases. A primary reason for this result is that the amount ofuncertainty associated with the UPL is higher when sample sizes are smaller. Larger datasets provide better estimates ofthe average, the standard deviation and the distribution ofthe data. A lower boundary for the UPL exists at every significance level. This lower boundary correspondsto whatthe UPL would be ifan infinite number ofsamples was available because the uncertainty component ofthe UPL becomes negligible as the sample size increases. In practical terms, this lower boundary represents a value that includes almostno uncertainty when the dataset is large. In other words, even ifwe had an infinite number ofsamples, the 99 UPL would not be below this lower-bound value. Therefore, the first halfofthe UPL equation takes the average emissions value ofthe sources inthe MACTpool and the second halfofthe equation addresses the variability ofthat average emissions level based onthe factors identified in the variables in that portion ofthe equation. Equation 2 shows the UPL equation for a dataset with a lognormal distribution. Equation 2.

-z 11+!!._ Z(l-a) UPLloO-(axlOO) = 

### e 2 

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

### 100- (ax 

### 100);



### e =base ofthe natural logarithm**c~** 2.718282); Page 11 of15{l =mean ofthe log transformed run data(=_.:

## Ii- 1 

### ln(x)i); n - 8 2= variance ofthe log transformed run data(=.,:

## If= 1 On(x)i

- 

### {1.) 2); n


### z = z score, the one-tailed z value ofthe z distribution for a specific level ofsignificance;



### m =number ofrun values used to calculate the test average (generally 3); and



### n = number ofruns. The widely-accepted statistical procedure for calculating a UPL for log-normally distributed data involves performing a log-transformation ofthe data. As with Equation 1, the first part ofthe

- az UPL equation, ell+--z, is associated with the average ofthe best performing sources' emissions.

- &2 The secondpart ofthe equation, i.e., everything to the right ofell+--z, is associated withthe variance ofthe run data, 8 2 ; the number ofruns in the dataset, n; the confidence level, calculated from a; andthe number ofrun values used to calculate the test average, m. UPL Equation 2 operates in a manner similarto Equation 1. The first part ofUPL Equation 2 is directly related to the emissions average and corresponds to an estimate ofthe average ofthe lognormal data. In other words, as the emissions average goes up or down, so does the UPL value. The second part ofthe UPL equation is directly related to confidence level and to the variance ofthe average ofthe lognormal data, meaning that as either ofthese values go up or down, so does the UPL value. As in the normal case, the second part ofthe UPL equation is inversely related to the number ofruns in the dataset and to the number ofruns averaged for an emissions test. Therefore, as either ofthese values increase, the UPL value decreases and as either ofthese values decrease, the UPL value increases.
Consistent with Equation 1, a lowerboundary for the UPL exists for Equation 2 at every significance level when an infinite number ofsamples is provided. Inpractical terms, this lower boundary represents the minimum amount ofvariability associated with a future, past, orpresent emissions test average. 15 Furthermore, the selection ofa higher confidence level for a UPL calculation widens the interval ofresults, meaning that a higher confidence level increases the UPL value. As with Equation 1, the first halfofthe UPL equation takes the average emissions value ofthe sources in the MACTpool and the second halfofthe equation addresses the variability ofthat average emissions level based onthe factors identified in the variables in that portion ofthe equation.
To provide an example ofhowthe UPL calculation is performed, the application ofthe UPL to a specific set ofdata from a set ofbestperforming sources in EPA's sewage sludge incinerator rule is explainedbelow (Case B).
Case B shows how one takes data from the bestperforming sources andtranslates that into an emissions limit. There are 150 existing units in the multiple hearth subcategory for sewage

15 Gibbons, p 3 1. Page 12 ofl5sludge incinerators, so there are 18 units that are best performing sources for Case B since 12 percent of 150 sources is 18 sources. Charts 1 and 2 show PM emissions data for each run of testing for the 18 best performing sources (note that we do not always have the same number of test runs for each source).
Unit PMEmissions, mg/dscm Run I 2 3 4 5 6 7 8 9 1 2.08 1.99 0.82 2.87 16.02 15.25 25.95 41.72 38.90 2 0.50 0.55 5.57 15.42 12.02 18.31 26.90 39.64 30.40 3 1.05 2.73 5.41 8.31 15.84 19.08 20.05 20.40 32.24 4 18.55 28.59 40.18 5 18.82 23.66 40.46 6 2.70 29.56 39.24 7 19.10 8 20.60 9 21.40
Chart 1. PM emissions data, mg/dscm, for Units 1 - 9 by individual run. Unit PM Emissions, mg/dscm Run 10 11 12 13 14 15 16 17 18 1 47.11 33.76 49.65 42.53 48.90 45.99 72.26 80.51 70.31 2 43.86 41.11 34.07 40.52 46.64 124.20 60.89 80.46 88.68 3 27.71 44.49 28.54 37.87 70.58 45.33 78.61 69.49 83.01 4 27.91 56.75 89.06 63.62 73.99 74.90 5 52.90 48.47 28.92 94.64 79.78 69.80 6 37.16 24.03 55.09 63.06 75.36 85.83 7 45.03 81.62 8 32.13 77.11 9 55.30 67.15
Chart 2. PM emissions data, mg/dscm, for Units 10

- 18 by individual run. Using Excel software, the characteristics ofthe best performers from this source category are as follows:
:X= mean oftestrun data= 41.33;



### n**~number** oftestruns = 90;

s 2 =variance oftest run data= 736.24; kurtosis = -0.31; and skewness = 0.47.

Page 13 oflSAs the kurtosis and skewness results are bothnear zero, we conclude that the data exhibit a normal distribution. Given a normal distribution, we use Equation 1to calculate the UPL. Because we are using a confidence level of99, the significance level, 

### a, calculated using the confidence level is 0.01 (1-0.99). With 90 run values, the 

### t value as determined from Excel software is 2.37 (tc90

_ 1),(1 -o.o 1) = 2.37). Since emissiontest averages, such as those usedto demonstrate compliance withthe UPL-based limits, include 3 individual test runs, the value ofm is set at 3. The 99 percent UPL is calculated from the bestperformers' dataset for a normal distribution as follows:

- 2 ( 

# 1 1) UPL100-(aX100) 

### =X+ tcn-1),(1-a) 

### s m 

## +

# n

UPL100-(0.01X100) = 41.33 

## + t(90-1),(1-0.01) 736.24

# (~+9 1 0)



### UPL99 = 41.33 

## + 2.37vf253.59


### UPL99 = 41.33 

### + 37.74 = 79.07.
As mentioned earlier, this 99 percent UPL is composed oftwo parts: the first part which is directly relatedto the emissions average ofthe dataset (41.33) and the second part which is related to the variance, level ofconfidence, number ofruns, and number ofruns that constitute an emissions test (37.74). Thus, the equation includes both the average emissions level achieved by the bestperforming sources, and also a consideration ofthe variability ofthose emissions, including the variability associated with conducting an emissions test at othertimes. The calculation shows that the best performing sources would be expected to have an emissions test value that wouldnot exceed 79.07 mg PM/dscm, based onthe average ofthe bestperforming 12 percent ofsources' emissions data and the consideration ofvariability within the data. Most, but not all, ofthe emissions test data from the best performing twelve percent ofsources is belowthis value. As shown in Figure 4, values ofindividual testrun data from these sources vary, with 10 values above the 99 percent UPL. The range ofindividual unit values is related to an individual unit's variability. Individual run values above the 99 percent UPL demonstrate that even units among the bestperformers may need to apply some combination ofadditional control devices, modifiedprocess operations, ormodified raw materials in orderto be able to meet an emissions limit set atthe 99 percent UPL. This is to be expected, and further demonstrates that EPA's use ofthe UPL to calculate the MACT floor is reasonable, since the MACT floor represents the average emission level achieved by the best performing sources, notthe worst emission level achieved by those sources. Forinstance, units 15, 16, 17, and 18 (the "bottom4" out of 18 units inthe top 12 percent in this example) all have at least one test run value above the 99 percent UPL for the entire dataset, but no source among the bestperforming 12 percent of sources had anoverall average above the 99 percent UPL, although several sources had an average that is close to the UPLand one source had a 3-runtest average above the UPL.

Page 14 oflS20

-- Average 

### I

-- UPL99 

### I**~0** 

### <XX> I <X> 

### I 

### I 00 

# • 0 IS 

### 00 

### I @ 0 

### 0 

### I <X> 

# • 0 00 0**~** 

### 0 0 0

. t:: 

### 0 100 0 c: 10 :J

# ~**~** 

# •**0~** 

### I (:e) 

### I
5 (:II) ' 

### I 0 011 O<> 

### I 

### I I I 

### I
00 20 40 60 eo 100 120 140 Emissions FIGURE 3. Filterable PM data from 18 multiple hearth sewage sludge incineration units. Individual run data shown as openred diamonds, unit average emissions test data shown as solid pink squares, the average ofall runs shown as the dashed green line, and the 99 percent UPL is shown as the solidblue line.
VI. Conclusion
In conclusion, EPA's methodology for establishing the MACT floors is reasonable and represents the average emissions achieved by the best performing sources with consideration of the variability in the emissions ofthose sources. The methodology first identifies the best performing sources by ranking sources from lowest to highest emissions. Next, the distribution ofthe data is evaluated in orderto identify which UPL equation to apply. After that, the average ofall the short-term stack test data from all the best performing sources (or the single bestcontrolled source, for new sources) is calculated. Finally, the UPL is applied to that calculated average value to account for variability suchthat the MACTfloor standard can be met by a unit with emissions at the average level ofthe best performing source or sources.

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