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MEMORANDUM

SUBJECT: Use of the Upper Prediction Limit for Calculating MACT Floors

DATE: December 12, 2014

FROM: Toni Jones Office of Air Quality Planning and Standards

TO: Docket ID No. EPA-HQ-OAR-2003-0119

This document explains EPA’s use of the UPL, which is the statistical methodology EPA uses as the primary tool to account for emissions variability whe n setting emissions standards under these sections, and explains how the UPL is used to calc ulate the average emissions limitation achieved over time by the best performing source or sources

.

I. Emissions Standards under Section 112 and 129

For major stationary sources of hazardous air pollutants (HAP) under section 112 and for sources regulated under section 129, 1 the CAA requires emission standards that represent the maximum achievable control technology, or “MACT” level of contr ol. The MACT standard setting process is a two-step process that starts with the agency determ ining the level of control that is currently achieved by the best-controlled similar source (for new s ource standards) or the average of the best-performing sources (for existing source standards). Tha t level of control is the minimum level of control required by the CAA regardless of cost or feasibility, and it is commonly called

the “MACT floor.” This document focuses on that first step in the MACT standard setting process, as it is in that step that the agency uses th e UPL to both evaluate average emissions performance and estimate variability to determine the lev el of control sources currently achieve. 2

For new sources located at facilities that are major sources of HAP, section 112 of the CAA requires EPA to establish standards that are no less str ingent than the emissions control that is achieved in practice by the best controlled similar source . The statute does not define “achieved in practice” nor does it dictate the manner in which th e agency determines which source is the best controlled similar source, instead leaving it to the agency’s discretion to make those

1 A “major source” is a stationary source or group of sta tionary sources at a single location and under common control that emits or has the potential to emit ten tons per year or more of any hazardous air pollutant or 25 ton s per year or more of any combination of hazardous air polluta nts. Any stationary source that is not a major source is an

“area source.” CAA § 112(a). For area sources of HAP, EPA has the discreti on to set emissions standards under section 112(d)(5) based on generally available control te chnology in lieu of MACT standards.

2 The second step in the MACT standard-setting process is the evaluation of whether beyond-the-floor controls ar e appropriate, as provided in section 112(d)(2) of the Act. Thi s second step is not addressed in this document.Page 2 of 15

determinations. For existing sources located at facilitie s that are major sources of HAP, standards must be no less stringent than the average emissions l imitation achieved by the best performing sources for which EPA has emissions information. Again, the CAA leaves to EPA’s discretion the manner in which to calculate “the average emissions l imitation achieved” by the best performing sources. Under section 112, the CAA recognizes tha t source categories and subcategories have differing numbers of sources and provides category size-specific instructions on determining standard stringency for existing sources. Speci fically, standards for categories or subcategories with fewer than 30 sources must be based on t he average emissions limitation achieved by the best performing 5 sources, and standards for ca tegories or subcategories with 30 or more sources must be based on the average emission limitation achieved by the best performing 12 percent of sources for which EPA has emissions information. Section 129 requires

EPA to establish standards for new sources that are no less stringent than the emissions control that is achieved in practice by the best controlled simi lar source for nine specified criteria and hazardous air pollutants, and standards for existing sources that are no less stringent than the average emission limitation achieved by the best perform ing 12 percent of sources in the category or subcategory for the same nine pollutants. 3

II. Background

EPA promulgated rules covering major source industrial, co mmercial, and institutional boilers and commercial and industrial solid waste incinerators (CI SWI) rule on March 21, 2011, and subsequently made certain revisions to the rules on January 31, 2012. On August 20, 2013, the D.C. Circuit Court of Appeals issued its decision in Nati onal Assn. of Clean Water Agencies v.

EPA , which involved challenges to EPA’s MACT standards for se wage sludge incinerators,

issued under section 129 of the Act. See 734 F.3d 1115. In the NA CWA decision, the D.C. Circuit remanded certain aspects of the rule for furthe r explanation, including the question of how the UPL represents the MACT floor for new and exis ting units, as required by the CAA. The sewage sludge incinerator rule was issued on the same day as the boilers and CISWI rules, and used the same general methodology for calculating the MACT floors. For this reason, EPA requested an opportunity to supplement the record in pending ch allenges to the boilers and CISWI rules, to provide the explanation of the agency’ s analysis of variability in setting the

MACT floor standards that the court believed was needed i n the record for the sewage sludge incinerator rule. The court granted EPA’s motion for a re mand of the record on May 15, 2014. This document provides that additional explanation, which al so applies to MACT standards that are part of the rulemaking for the CISWI source category

.
There are several key points, addressed in more detail bel ow, that underlie EPA’s methodology for calculating MACT floor standards through the use of t he UPL. First, the floor standards reasonably account for variability in the emissions of the sources used to calculate the standards. This variability occurs due to a number of factors, including measurement variability (both sampling and analysis) and short term fluctuations in th e emission levels that result from shortterm changes in fuels, processes, combustion condition s, and controls. Second, because the

emissions data available to EPA is in the form of sho rt-term stack tests and the standards must be

3 Unlike section 112(d)(3)(A), section 129(a)(2) does not direct the agency to base the standards on 12% of the sources for which the agency has data, and the EPA has interpreted this to mean that the incinerator standards require the standards to be based on 12% of the sources i n the category whether or not the agency has data on a ll the sources in the category.Page 3 of 15

complied with at all times, the agency uses the UPL to estimate the average emissions performance of the units used to establish the MACT floor standards at times other than when the stack tests were conducted. Thus, the UPL results in a limit that represents the average emissions limitation achieved by the best performing sour ces over time, accounting for variability in emissions performance.

III. Overview of MACT Floor Methodology

In establishing MACT floors, we use the available informa tion to determine the average performance of the best performing sources (for existing source floors) and the average performance of the best-controlled similar source (for new source floors). Each MACT standard

is based on limited data from sources whose emissions a re expected to vary over their long term performance. For this reason, and because sources must co mply with the MACT standards at all times, consideration of variability is a key factor in establishing these standards. This variability in emissions is due to numerous factors, including operation of control technologies, variation in combustion materials and combustion conditions, vari ation in operation of the unit itself, and

variation associated with the emission measurement te chniques. In order to account for variability that is reflected in the available data tha t we use to calculate MACT floors, we use the

UPL.

The NACWA court recognized that EPA has significant discr etion in establishing the MACT floors, including how to account for variability. See NA CWA v. 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 of the statute .”) However, the court expressed concern about the interpretation it believed EPA was taking of t he “average” emissions performance of the best performing sources. Specifically, the court aske d for further clarification of how “’average’ means the average of a future 3-run compliance test.” Id . at 1143. As explained below, EPA does 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 over time, based on both the calculated average of all emissions test data from the best performing source or sources and the available information regarding the variability of emiss ions. The UPL, which EPA uses to account for variability among the best performing sources, reflects an upper limit for the

emissions of those sources at times other than when the emissions tests occurred. This not only is a prediction of the emissions performance of those source s in tests conducted in the future, but is also an indication of the range of current average emi ssions performance of those units.

In calculating MACT floors, EPA analyzes all availabl e emissions information and then uses the emissions information for the best performing source or sources to calculate a value that represents the level achieved in practice by the best co ntrolled similar source for the new source MACT floor and a value that represents the average emi ssion limitation achieved by the best performing twelve percent of sources for the existing source MACT floor. EPA must establish

the MACT floor standards based on the emissions inform ation before the agency, and the standards must be met at all times by sources subject to t hem. The available emissions data are generally in the form of short term, three-run stack te sts, with each test run lasting for between 1 and 4 hours. Those short term tests cannot encompass t he emissions performance of a source over time. EPA interprets “emissions performance,” as us ed in section 112(d)(3) to mean the emissions of a source over the long term, rather than just during a short-term stack test. This is a reasonable interpretation of the statutory directive that the MACT standard be no less stringentPage 4 of 15

than the average emissions limitation “achieved by” the b est performing sources, since the emissions level of a 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 other than when stack testing was conduct ed. This enables EPA to calculate the average emissions performance of the best performing sources over time. Therefore, the

MACT floor calculation takes into account the inherent variability in emissions performance to more accurately reflect the range of the best performi ng sources’ emissions over time. The remainder of this discussion focuses on why the statistic al methodology that we used - the UPL - provides results that reasonably represent the level achi eved in practice by the best-controlled similar source for new sources, and the average emissio ns limitation achieved by the best performing emissions units for existing sources.

IV. Use of the Upper Prediction Limit

The UPL is a value derived from widely accepted and commonl y used statistical principles, and represents the upper end of a prediction interval. 4 The UPL is used in a wide variety of industries and professions, such as manufacturing, finance, healthcar e and others. 5 The UPL is calculated using one of several equations that must be selected bas ed on certain characteristics of each dataset. The most important parameters in the UPL calc ulation are the mean (average) performance of the unit or units, the distribution of the dataset, the variance in the measured emission values (that is, the individual data points), and the sample size. The equations that are used to calculate the UPL are explained in more detail be low.

In the context of development of MACT floors, the UP L is a value, calculated from a dataset, that identifies the average emissions level that a sour ce or group of sources is meeting and would be expected to meet a specified percent of the time that the source is operating. That percent of time is based on the confidence level used in the UPL equat ion, 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 emissio ns tests conducted in the past, present, and future, based on the short term stack test da ta available for that source. It is important to note that the UPL does not represent the worst emissions performance of the best performing units at any time, but rather the average level expected to have been achieved over time, as the first element of the UPL equation is the average of the short-term emissions test data from the best performing units. In other words, the 99 percent UPL is the level of emissions that we are 99 percent confident is achieved by the average sourc e represented in a dataset over a long-term period based on its previous, measured performance history as reflected in short term

stack test data.

In sum, the UPL predicts the level of emissions 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

4 National Institute of Standards and Technology, NIST/SEMATECH e-Handbook of Statistical Methods

, < http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar /predlimi.htm >.

5 See, e.g., Gibbons, Robert D. and Coleman, David E. (2001). Statistical Methods for Detection and Quantification of Environmental Contamination , New York: Wiley, pp 21-31, and Luko, S.N. and D.V. Neubauer, Statistical

Intervals Part 2. Standardization News , October/November 2011. <http:www.astm.org/standardization -news/datapoints/statistical-intervals-part-2-so11.html>.Page 5 of 15

emissions variability and the uncertainty that exists i n the determination of emissions variability given the available, short-term data. EPA did not have e missions information from sources at all times each source was operating, and therefore determined it was necessary to apply a methodology that addressed the fact that the data were n ot complete. Statistical tools are commonly used in science and industry because they permit pr edictions to be made based on the available data. As explained in more detail below, the U PL equations include a term that adjusts the average emission level of the units to account for b oth the emissions variability observed in the data and the uncertainty that exists in that estima te of variability for a sample of the given size, to estimate the performance of the units over ti me. As shown by the t- and z-statistics incorporated into the UPL equations, the uncertainty regardin g 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 in practice by the best controlled similar source and the average emission limitation currently achieved by the best performing 12 percent of sources by estimating the level achi eved by the best source (for new sources) or by the average of the best sources (for exist ing sources) ninety-nine percent of the time the sources are operating. It is reasonable to interpret the statutory requirement that the

MACT floor level reflect the “emission control that is achieved in practice” by the best controlled similar source and the “average emission lim itation achieved by” the best performing 12 percent of sources as a level that the average level t he best performers are meeting on a consistent basis over time, not just at the single point in time during which emissions test data were collected. If EPA were to simply take the average of the stack test data from the best performing source or sources, the MACT floor would not repr esent the levels of emissions achieved in practice over time because the 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 othe r factors that affect unit performance over time. This is demonstrated by the fact that even single three run tests, which are performed over a short period of time, typically show different emis sions levels during each individual test run.

It would not be reasonable to establish a MACT floor standa rd that the best performing sources would exceed routinely. But neither would it generally be r easonable to establish a standard that all the best performing 12 percent of existing sources can me et without any modification because the statute requires the agency to establish the standard a t the average level of performance of the best 12 percent of sources. If EPA simply calculate d the average (mean) of the emissions data from the best performing 12 percent of sources, that w ould only lead to a limit that can be met by all the existing sources in the floor at all tim es in the unlikely hypothetical situation

where all the sources have identical emissions test dat a and controls and operate in exactly the

same manner– i.e. the sources would have to be essential ly identical and use identical fuels or other material inputs. Since that situation does not represe nt real-world source categories, the agency takes the available data and applies a statistical formula to account for variability in emissions of the best performing source or sources.Page 6 of 15

V. Establishment of MACT Floors

At first glance, developing a HAP emissions limit in ac cordance with the statutory requirements seems a straightforward task, requiring simply that EPA c ollect all available valid data from all the sources in a specific category or subcategory, rank th e data to select the best performing twelve percent of the category or subcategory, and calcula te the average emission level achieved by that group of sources for a particular pollutant. Howeve r, multiple factors complicate these calculations. First, emission test results taken during a three-run stack test, as is the case with virtually all the HAP emission data available to EPA, r epresent three “snapshots” of a source’s operations during the test period and those results generall y will not represent a source’s full range of normal operations or emissions levels. However, because there are three separate runs in a test, a single test will in most cases show some of a particular source’s variability over the short period of time during which testing was conducted. Further, EP A generally has limited data with which to establish MACT standards, primarily because the da ta needed 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 regulat ed under section 129). The

collection of such data is a time- and resource-intensi ve effort, as emissions tests can take more than a week to perform, analyses of samples from the tests can take more than a month, preparation of test reports typically takes several mo nths, and costs range up to $40,000 per test per pollutant. For example, during our data collection eff orts for the boiler and CISWI rules we required hundreds of facilities to conduct emissions testi ng, and we estimated an average cost of about $90,000 for each facility that was required to conduct tes ting.

As explained above, EPA establishes MACT floor standards under sections 112 and 129 as limits that reflect the level achieved in practice by t he best controlled similar source, or the average emissions limitation achieved by the best perfor ming 12 percent of sources over time, but we necessarily must do that based on the emissions information that is available. In this case, that information consisted of emissions test dat a that represents the specific instances in the sources’ operations when testing was conducted. The UPL i s a common statistical technique that

allows EPA to use emissions test data and the data charac teristics, such as the distribution and sample size, along with the intrinsic variability ass ociated with those data, 6 to calculate an emissions limit based on a specified level of confidence such that an average best performing existing source would not be expected to exceed the limit a specified number of times. For instance, if an emission limit were set at the 50 percen t UPL, we would expect the average unit to have emissions above the level of the standard 50 perce nt of the time.

This section explains how EPA applied the UPL to the emis sions data from the best performing

source or sources to calculate MACT floor limits tha t represent the average emissions performance of those sources, while accounting for vari ation in those sources’ emissions over

time.

A. Ranking Sources and Establishing the Distribution of Da ta

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

6 Gibbons, p 30.Page 7 of 15

UPL equation that is used to account for variability and ca lculate the MACT floor standard depends on the distribution of the data. Typical data dis tributions are normal and lognormal, as shown in Figures 1 and 2. Therefore, the first step in app lying the UPL is to rank sources (based on lowest emissions) to identify the best performing sour ces and then analyze the distribution of the emissions data from those best performing sources. Th e ranking is used to establish which set of units make up the top 12 percent of performers for each po llutant and subcategory and which unit EPA considers the single best-controlled for each pollutant and subcategory. Once these units are identified, EPA determines the data distribution a s discussed below.

In order to select statistical equations (to calculate t he UPL) that are appropriate for each individual dataset, EPA evaluates each individual dataset t o determine the data distribution, as

noted above. The individual datasets that we evaluate include the datasets for the best performing unit for each pollutant and subcategory for the new source M ACT floor standards and the datasets for the best performing 12 percent of units for eac h pollutant and subcategory for the existing source MACT floor standards. To evaluate the dist ribution of the data, EPA checks each dataset for distribution characteristics by applying skewnes s and kurtosis tests. Skewness is a measure of symmetry (or the lack of symmetry) of a dist ribution, and is useful in determining the distribution because normal distributions are symmetric while lognormal distributions are not.

Kurtosis is a measure of whether a dataset has a simil ar, more distinct, or flatter peak than a

standard normal distribution. 7 Figures 1 and 2 show simple examples of normal and lognorm al distributions. In each figure for the purpose of EPA’s a nalyses, the x-axis is the level of emissions and the y-axis represents the probability of a particular value occurring (established

based on the number of occurances in the dataset at ea ch level of emissions). If both the skewness and kurtosis tests suggest the data exhibit a norma l distribution, EPA evaluates the emissions data for the source category using statistical equations for normally distributed data. If the test results are inconsistent regarding normality, o r if both test results suggest non-normality, EPA evaluates the emissions data for the source catego ry using statistical equations for lognormally distributed data.

EPA uses this approach because, absent evidence of a norma l distribution, air emissions data have historically been shown to exhibit lognormal dist ribution characteristics such as 1) run values always above zero; 2) a majority of run values w ill be low; and 3) a few run values will be high but will have a low probability of occurring. 8,9,10 These characteristics yield a left-skewed distribution curve, meaning the distribution has a long ta il to the right.

7 National Institute of Standards and Technology, NIST/SEMATECH e-Handbook of Statistical Methods

, < http://www.itl.nist.gov/div898/handbook/eda/section3/eda35b.htm >.

8 Ott, Wayne R. (1990) A Physical Explanation of the Lognormality of Pollutant Concentrati ons , Journal of the Air & Waste Management Association, 40:10, 1378-383, DOI: 10.1080/10473289.1990. 10466789

. 9 Gilbert, Richard O. (1987), Statistical Methods for Environmental Pollution Monitoring , New York: Van Nostrand Reinhold, p 152.

10 Gibbons, Robert D. and Coleman, David E. (2001), Statistical Methods for Detection and Quantification of

Environmental Contamination , New York: Wiley, p 369.Page 8 of 15

Figure 1. Normal Distribution 11

Figure 2. Lognormal Distribution 12

11 http://www.psychstat.missouristate.edu/introbook/sbk10m.htm.

12 http://math.tutorvista.com/statistics/normal-distribut ion.html.Page 9 of 15

The following example demonstrates the characteristics of a lognormal distribution curve. Consider a dataset obtained from three filterable parti culate matter (PM) emissions tests, each consisting of three test runs, from three independent so urces. The nine runs produced the following values measured in pounds PM per million British Thermal Units (lb PM / 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 an d kurtosis consistent with a lognormal distribution. Figure 3 shows Case A data as solid green squa res plotted on the lognormal

distribution determined from the characteristics of the run data. Based on those characteristics, one would expect 50 percent of all filterable PM values to be less than 0.0039 lb PM / MMBTU. In addition, one would expect about 95% of all filterabl e PM values to be less than 0.0188 lb PM / MMBTU. The long tail to the right, as shown in Figur e 1, is consistent with the expectation that high values can exist, but they have a low probability of occurring – below one percent for values greater than 0.0255 lb PM / MMBTU.

FIGURE 3. Lognormal Data Distribution Example. The smooth curve represents the density function of the lognormal distribution determined from t he characteristics of the 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 b est performing twelve percent of sources and the distribution of each dataset, we calcul ate the UPL, as described below, to identify an emissions limit that represents the level the average unit among the best performingPage 10 of 15

units has met, is meeting, and would be expected to meet in practice w ith a specific confidence

level

. 13 The confidence level, in this case 99 percent, is the pe rcentage of measurements (past, present, and future) that are predicted to fall at or belo w the UPL value. Stated differently, the 99 percent UPL is the level of emissions that we are 99 pe rcent confident is achieved by the average source represented in a dataset over a long-term period b ased on its previous, measured performance history as reflected in short term stack te st data. The UPL value is based on the available emissions data from the best performing single source (for new source standards) or the best performing 12 percent of sources (for existing source s tandards). The UPL incorporates the intrinsic variability of the individual run measurements used to calculate an emission test

average. 14 While the UPL can be calculated at different confidence levels, we selected the 99 percent level in order to provide reasonable assurance that the limit can be met at all times by a source with emissions at the average level achieved by th e best performing source or sources.

C. Applying the UPL Equations

Once the distribution is established and the confidence le vel selected, a UPL value is calculated using six components. Four of these components are derived from the emissions dataset: the average (or mean), the variance of the dataset, the t -statistic or z-statistic (depending on the distribution characteristics), and the number of sampl es, which is associated with the total number of emissions test runs. For example, if there a re results from six emissions tests, there typically are at least 18 emissions test run values (or samples), since an emissions test generally

consists of 3 test runs. 15 The other two components are the number of run values use d to calculate the average and the confidence level.

UPL equations are data-distribution specific, so that the normal distribution UPL equation is different from the lognormal UPL equation. Even though t hey differ due to separate mathematical properties associated with each distributi on, the UPL equations share a common format that is composed of two parts which are added togeth er. Equation 1 shows the UPL equation for a dataset with a normal distribution.

Equation 1.    × = ̅ +   

,   

   

 + 

 

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

confidence level = 100 −   × 100 ;

= average or mean of test run data;

 = t score, the one-tailed t value of the Student’s t distribution for a specific degree of
freedom and level of significance;

13 Gibbons, p 28.

14 Gibbons, pp 30-31.

15 EPA test methods typically require 3 test runs. In case s where a test included fewer than 3 valid test runs, we typically do not include the test as a valid test for t he purpose of MACT floor calculations. However, if lim ited or no other data are available for a particular source and pollutant, we consider the use of such data on a case-by- case basis.Page 11 of 15

 = number of test runs;

  = variance of test run data; and

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

The first part of the UPL equation, ̅ is the average of the best performing sources’ emission measurements. Thus, the average of the emission measure ments from the best performing source or sources is a fundamental element, and is in fact t he starting point, of the UPL calculation. The second part of the equation, i.e., everything to the right of ̅ , is associated with the variance of the run data,   ; the total number of runs in the dataset,  ; the confidence level, calculated from

α ; and the number of run values used to calculate the emiss ions average for each test result, 

.

As shown in Equation 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 varia nce, meaning that as either of these 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 of runs averaged for each emissions test. Therefore, as either of these values increases, the UPL value decreas es and as either of these values decreases, the UPL value increases. A primary reason for this res ult is that the amount of uncertainty associated with the UPL is higher when sample sizes a re smaller. Larger datasets provide better estimates of the average, the standard deviation and the di stribution of the data. A lower boundary for the UPL exists at every significance level . This lower boundary corresponds to what the UPL would be if an infinite number of samples was available because the uncertainty component of the UPL becomes negligible as the sample size increases. In practical terms, this lower boundary represents a value that includes almost no uncertainty when the dataset is large. In other words, even if we had an infinite number of sam ples, the 99 UPL would not be below this lower-bound value. Therefore, the first half of th e UPL equation takes the average emissions value of the sources in the MACT pool and the second half of the equation addresses the variability of that average emissions level based on th e factors identified in the variables in that portion of the equation.

Equation 2 shows the UPL equation for a dataset with a lo gnormal distribution.

Equation 2.

 × = !"# $" %

 + & 

 '

 !"#$" % ( $" % − 1 ) +   !"#$" % * +, 

 + +, -

2   − 1 /

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

confidence level = 100 −   × 100 ;

= base of the natural logarithm ( ≈ 2.718282);

0̂ = mean of the log transformed run data (= 

 ∑ ln	 5  56 );Page 12 of 15

+,  = variance of the log transformed run data (= 

 ∑  ln	 5 − 0̂   56 );

& = z score, the one-tailed z value of the z distributio n for a specific level of significance;

 = number of run values used to calculate the test avera ge (generally 3); and

 = number of runs.

The widely-accepted statistical procedure for calculating a UPL for log-normally distributed data involves performing a log-transformation of the data. As w ith Equation 1, the first part of the

UPL equation, !"# 7 " %

%
, is associated with the average of the best performing sour ces’ emissions.

The second part of the equation, i.e., everything to the r ight of !"# 7 " %

% , is associated with the variance of the run data, +,  ; the number of runs in the dataset,  ; the confidence level, calculated

from α ; and the number of run values used to calculate the test average, 

.

UPL Equation 2 operates in a manner similar to Equation 1. The first part of UPL Equation 2 is directly related to the emissions average and corresponds to an estimate of the average of the lognormal data. In other words, as the emissions average goes up or down, so does the UPL value. The second part of the UPL equation is directly r elated to confidence level and to the variance of the average of the lognormal data, meaning th at as either of these values go up or down, so does the UPL value. As in the normal case, th e second part of the UPL equation is inversely related to the number of runs in the dataset an d to the number of runs averaged for an emissions test. Therefore, as either of these values increase, the UPL value decreases and as either of these values decrease, the UPL value increa ses.

Consistent with Equation 1, a lower boundary for the UPL exists for Equation 2 at every significance level when an infinite number of samples i s provided. In practical terms, this lower boundary represents the minimum amount of variability a ssociated with a future, past, or present emissions test average. 16 Furthermore, the selection of a higher confidence leve l for a UPL calculation widens the interval of results, meaning th at a higher confidence level increases the UPL value. As with Equation 1, the first half of the UP L equation takes the average emissions value of the sources in the MACT pool and the second half of the equation addresses the variability of that average emissions level based on th e factors identified in the variables in that portion of the equation.

To provide an example of how the UPL calculation is perf ormed, the application of the UPL to a specific set of data from a set of best performing sources in EPA’s sewage sludge incinerator rule is explained below (Case B).

Case B shows how one takes data from the best performi ng sources and translates that into an emissions limit. There are 150 existing units in the multi ple hearth subcategory for sewage sludge 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

16 Gibbons, p 31.Page 13 of 15

testing for the 18 best performing sources (note that we do not always have the same number of test runs for each source).

Run Unit PM Emissions, mg/dscm

1 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 indiv idual run.

Run Unit PM Emissions, mg/dscm

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 indiv idual run.

Using Excel software, the characteristics of the best performers from this source category are as

follows:

= mean of test run data = 41.33;

 = number of test runs = 90;

  = variance of test run data = 736.24;

kurtosis = -0.31; and

skewness = 0.47.

As the kurtosis and skewness results are both near zero , we conclude that the data exhibit a normal distribution. Given a normal distribution, we use Equation 1 to calculate the UPL.Page 14 of 15

Because we are using a confidence level of 99, the signific ance level,  , calculated using the confidence level is 0.01 (1-0.99). With 90 run values, the  value as determined from Excel software is 2.37 (   8

,  . = 2.37 ). Since emission test averages, such as those used to demonstrate compliance with the UPL-based limits, includ e 3 individual test runs, the value of m is set at 3. The 99 percent UPL is calculated from the b est performers’ dataset for a normal

distribution as follows:

   × = ̅ +   

,   '

  < 1

 + 1

 =

   .× = 41.33 +   8

,  . ' 736.24 < 1

3 + 1

90 =

 88 = 41.33 + 2.37√253.59

 88 = 41.33 + 37.74 = 79.07.

As mentioned earlier, this 99 percent UPL is composed of two parts: the first part which is directly related to the emissions average of the dataset (41.33) and the second part which is related to the variance, level of confidence, number of r uns, and number of runs that constitute an emissions test (37.74). Thus, the equation includes both the average emissions level achieved by the best performing sources, and also a consideration o f the variability of those emissions, including the variability associated with conducting an emiss ions test at other times. The calculation shows that the best performing sources would be expected to have an emissions test value that would not exceed 79.07 mg PM/dscm, based on the aver age of the best performing 12 percent of sources’ emissions data and the consideration of variability within the data.

Most, but not all, of the emissions test data from the best performing twelve percent of sources is below this value. As shown in Figure 4, values of individua l test run data from these sources vary, with 10 values above the 99 percent UPL. The range o f individual unit values is related to an individual unit’s variability. Individual run values abo ve the 99 percent UPL demonstrate that even units among the best performers may need to apply so me combination of additional control devices, modified process operations, or modified raw materi als in order to be able to meet an emissions limit set at the 99 percent UPL. This is to be expected, and further demonstrates that

EPA’s use of the UPL to calculate the MACT floor is r easonable, since the MACT floor represents the average emission level achieved by the best performing sources, not the worst emission level achieved by those sources. For instance, unit s 15, 16, 17, and 18 (the “bottom 4” out of 18 units in the top 12 percent in this example) all h ave at least one test run value above the 99 percent UPL for the entire dataset, but no source amon g the best performing 12 percent of sources had an overall average above the 99 percent UPL, although several sources had an average that is close to the UPL and one source had a 3 -run test average above the UPL.Page 15 of 15

FIGURE 3. Filterable PM data from 18 multiple hearth sewa ge sludge incineration units. Individual run data shown as open red diamonds, unit average e missions test data shown as solid pink squares, the average of all runs shown as the dashe d green line, and the 99 percent UPL is

shown as the solid blue line.

VI. Conclusion

In conclusion, EPA’s methodology for establishing the MACT floors is reasonable and represents the average emissions achieved by the best perfo rming sources with consideration of the variability in the emissions of those sources. Th e methodology first identifies the best performing sources by ranking sources from lowest to highest emissions. Next, the distribution of the data is evaluated in order to identify which UPL equa tion to apply. After that, the average

of all the short-term stack test data from all the be st performing sources (or the single bestcontrolled source, for new sources) is calculated. Final ly, the UPL is applied to that calculated average value to account for variability such that the MA CT floor standard can be met by a unit with emissions at the average level of the best perform ing source or sources.