# Instructions

**Determine how many sources (N) nationwide Determine number of sources in MA** **CT floor sample set For solid waste incineration sources follow CA**  **A Section 129(a)(2) guidance:**  Take 12 percent of units in the category, and round up to next whole number for MACT floor sample set **For all other sources follow CA A**  **Section 112(d)(3):** N nationwide ≥30, take top 12% of sources with data, and round up to next whole number for MACT floor sample N nationwide <30, take top 5 sources with data for MACT floor sample set **Rank sources to Determine the MA CT floor sample set**  Calculate the UPL for each source using a confidence interval of 99% and rank the sources by the UPL to determine the best performing 12 percent (existing source MACT) and best performing source (new source **Identify the distribution of sample set** Statistical tests of the kurtosis and skewness are used to evaluate the normality assumption. For data sets with greater than 3 runs (n>3) use the "n>3Distribution" tab to determine the distribution. E nter run values for each source in the Raw Data section. For data sets with 3 runs (n=3) use the "n=3Distribution" tab to determine the distribution. Enter run values for each source in the Raw Data section. The skewness, kurtosis, standard error of skewness, and standard error of kurtosis will be calculated for the raw data and the logtransformed data. For n>3 data sets, if the Result Raw Data says "Normal" the data can be considered normally distributed, use

" **UPL Pooled Template** " for n>3 data sets, if the Result Log Data says "Normal" the data can be considered lognormally distributed, use

"**Lognormal Template** " For n>3 data sets, if the Result Ray Data says "Non Normal" and the Result Log Data says "Non Normal" than the data have an unknown/skewed distribution, use " **Template_skewed** " For n=3 data sets, the distribution will be specified as normal or lognormal in row 24. **Templates** Plug the sources' raw run data into the appropriate template based on distribution. Determine the confidence interval % to use fot the t-statistic and z-statistic based on "n" number of runs. 99% is the default in all the templates. For " **UPL Pooled Template** " the UPL will be calculated in cell F107. For "**Lognormal Template** ", use the "lognormal z-stat " worksheet to find the z-statistic at the specified confidentce interval. The UPL will be calculated in cell D165 For the " **Template_skewed** " Template: Cell E173 of the " **Template_skewed** " tab shows the actual confidence level (1 - 'Calculations for Template skew'!J139) after accounting for the skewness and kurtosis. If the confidence level is larger or lower than specified confidence level % [Default is 99%] then need to adjust the t-statistic.

# To adjust the t-statistic go to the “ Recalculate t-stat skew ” tab. This tab starts with the t-statistic in cell H161 from

the “ **Template_skewed** ” tab. If the confidence level from cell E171 of the " **Template_skewed** " tab was larger or lower than specified confidence level %, need to decrease or increase the t-statistic to get closer to the specified confidence level %. Cell G3 of "Recaltulate t-stat skew " tab has the value of the increase also called "interval", the candidate t-values will be calculated as the t-value in cell H102 plus multiples of the interval. These are calculated automatically for yo u in row 5 after a value is placed in cell G3. The corresponding p-values and confidence levels are also calculated automatically for you. Cell G3 of "Recaltulate t-stat skew" tab, the “interval” can be manipulated. For example, start with 0.1 and notice what the values in row 9 are. If they are not at specified confidence level % keep increasing or decreasing the value in G3 until one of the values in row 9 is the specified confidence level percent %. May have to go out to several significant figures. Calculations are in the tabs: "Recalculations1 skew " through "Recalculations6 skew ". Don’t need to do any thing in them, they

are basically

duplicates of tab “ Calculations_for_Template skew ” and each one use a different value of the candidate t-values in row 5. Som etim es the actual significance level in cell E173 of tab “ **Template_skewed** ” is larger than specified confidence level %, then you have to use a negative interval (meaning that your value in cell G3, tab “Recalculate tstat skew ” has to be negative). Once the adjusted t-value from tab “Recalculate t-stat skew ” is at specified confidence interval %, copy the recalculated t-value and paste special the value into cell E178 in tab “ **Template_skewed** ”. Also paste special the "interval of differences for t-values" from the "Recalculate t-stat skew " tab into cell E176 of " **Template_skewed** ". Note: Cell E173 of " **Template_skewed** " is linked to the " Calculations for Template skew " and Cell B174 of "Template_skewed" is linked to the "Recalculations1 skew" worksheet. In order to use " **Template_skewed** " for mu ltiple data sets of UPL calculations make a copy of the worksheet and rename. Paste special Cell E173 and B174 values to freeze the values and remove reference to other worksheets. The UPL will be calculated in cell E181 of " **Template_skewed** " If the new source UPL is greater in value (less stringent) than the existing source UPL, run the t-test to determine if there is statistical difference between the existing source MACT floor pool and the best performing source. In the " t-test " tab enter the new source run data into the new source column and enter the existing source run data into the existing source columns. If the results in cell B127 of " t-test " tab say "Means are not different" then can default to the existing source UPL for the new source UPL. If the results say "Means are different", then cannot default to the existing source UPL for the new source UPL. **Other Notes and Terms** Type of data affects m (number of future runs) that will be used in calculation, for example: If using individual test runs (typically three to a test) to determine compliance; m=3 If 30-day averages are used to determine compliance; m=30 If using the average of test runs to determine compliance; m=1 Default m future runs is 3 in each template. Does data set have non-detect issues, if so take extra step to do UPL v. 3xRDL comparison. N = total num ber of sources n = num ber of individual runs df = degrees of freedom = n - 1 X = mean of data

# s 2

# = pooled variance of data

m = number of future runs tdf 

# = t-statistic: t-distribution with df degrees of freedom at 99% [Default] confidence level Templates can hold up to 30 sources (N); if data set has more than 30 sources, need to expand template. Templates can hold up to 35 runs (n) for each source (N), if data set has more than 35 runs of data per source, need to expand template.Raw Data Runs **SPPD_FAC_04 SPPD_FAC_01**  **SPPD_FAC_02 SPPD_FAC_06**  1 5.89E-01 1.15E+00 4.09E-01 2.38E-01 2 6.06E-01 7.16E-01 7.75E-01 7.32E-01 3 5.06E-01 7.48E-01 8.35E-01 6.80E-01 4 4.71E-01 8.92E-01 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
KURTOSIS CALCULATIONS FOR SAMPLE SETS W ITH n > 3 ONLY Testing Normality Raw Data Logtransformed Sample Size 14.00 14.00 Kurtosis 0.82 2.03 

### http://www.spcforexcel.com/are-skewness-and-kurtosis-useful-statistics SE Kurtosis 1.24 1.24 

### note: cannot use this equation when n=3 because the denominator in second component is not defined (the term n-3 in denominator of second component is zero). Result Kurtosis normal normal Skewness 0.18 -1.09 SE Skewness 0.60 0.60 Result Skewness normal normal


### Result Raw Data Result Log Data Normal NormalLogtransformed **SPPD_FAC_ SPPD_FA**  **SPPD_FA SPPD_FA**  -5.30E-01 1.41E-01 -8.94E-01 -1.43E+00 -5.01E-01 -3.34E-01 -2.55E-01 -3.12E-01 -6.81E-01 -2.90E-01 -1.80E-01 -3.86E-01 -7.53E-01 -1.14E-01



### note: cannot use this equation when n=3 because the denominator in second component is not defined (the term n-3 in denominator of second component is zero).Raw Data Runs SPPD_FAC_04 SPPD_FAC_01 SPPD_FAC_02 SPPD_FAC_06 1 5.89E-01 1.15E+00 4.09E-01 2.38E-01 2 6.06E-01 7.16E-01 7.75E-01 7.32E-01 3 5.06E-01 7.48E-01 8.35E-01 6.80E-01 4 4.71E-01 8.92E-01 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
Testing Normality Raw Data Sample Size 14.00 Kurtosis 0.82 SE Kurtosis 1.24 Result Kurtosis normal Skewness 0.18 SE Skewness 0.60 Result Raw Data Result Skewness normal normal

ni = number test runs = 4 4 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total Number of sources = 4

n =Total # test runs = 14

13

This step is for QC only:

means 5.43E-01 8.77E-01 6.73E-01 5.50E-01 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

6.68E-01 Mean =

Pooled Variance = 5.11E-02

m= number future runs = 3

Term1 4.05E-01

Term2 2.07E-02

Squared root Term2 1.44E-01
NOTE: the pvalue for the t-statistic is calculated as: 2*alpha, where 1-alpha is desired confidence, so if 99% confidence is desired then alpha=0.01 and 2*alpha=2*(0.01)

t-statistic = quantile t-distribution with df degrees of freedom at .99 confidence level = 2.650308838

UPL POOLED VARIANCE = 1.05 Use for large sample sets and small sample sets that are Normal.



###   2 2 1 1 1 n i i s x X n   

 

###  1 1 1 i n N ij i j X x n    

### 

1 1
n m 

2 1 1 s n m        1 1 N i i df n

  

      

df t 2 1 1

s n m        1 1 i n i i

k k i x x n   

### 1

N i i n

  N

2

, 1 1 df p X t s n m    

   

0900006481946321 UPL Pooled Template 12/8/2014