To: Rochelle Boyd, U.S. Environmental Protection Agency, OAQPS

From: Mark Bahner, RTI International

Date: August 23, 2012

Subject: Clean Charge Cycles Statistical Analysis

1.0 BACKGROUND/EXECUTIVE SUMMARY

The proposed Secondary Aluminum NESHAP revisions published in the Federal Register on 

February 14, 2012 required that furnaces melting other than clean charge use “one or more” 

cycles of clean charge before being able to switch the furnace designation. The Aluminum 

Association and Alcoa commented that using one or more cycles of clean charge was not 

necessary because test data indicated that the first cycle of clean charge has emissions 

comparable to the second and third cycle of clean charge. This memorandum reports on the 

results of a statistical analysis of the data.

Based on a statistical analysis of the data, the Aluminum Association and Alcoa comment that 

there is no need to wait one or more cycles before switching furnace designations appears valid. 

There was not a statistically significant difference between mean or median emissions of the first 

cycle, second cycle, and third cycle.

All tables are presented at the end of this memorandum.

2.0 TEST DATA

Test data were provided by the Aluminum Association and Alcoa in their comments in April 

2012, which were placed in the Secondary Aluminum NESHAP docket (EPA Docket ID No. 

EPA-HQ-OAR-2010-0544). These data included the first cycle emissions results and the average 

emissions for the first three runs. The data are shown in Table 1.

More detailed data were obtained fom Alcoa in July 2012. These data included not just the first 

cycle emissions and the average emissions for the first three runs, but also the emissions for the 

second cycle (run) and third cycle (run). The data are summarized in Table 2.
Page 2 of 5

3.0 STATISTICAL ANALYSIS

Statistical tests were performed comparing mean and median values for the cycles, as shown in 

Table 3. 

Means were compared using a paired t-test. The null hypothesis is that there is no difference in 

the mean difference. The paired t-test first takes the difference of, for example, the first and 

second cycle, and calculates the mean of the differences, and tests if the mean of the differences 

is zero. The interpretation of the results is that a p-value <= 0.05 provides statistical evidence 

that the average of one cycle is different from the average of the other cycle. A p-value >= 0.05 

does not provide evidence against the null hypothesis that the average of both cycles is the same. 

Based on the results in Table 2, there is no evidence that the averages of the cycles are different.

The paired t-test is based on a normality assumption:

For PM (lb/ton): The Shapiro-Wilk test was used to evaluate normality; p-values were 0.9388 

(first cycle), 0.2385 (second cycle), and 0.3212 (third cycle). All values suggest that the first, 

second, and third cycle has a normal distribution.

For HCl (lb/ton): The Shapiro-Wilk test was used to evaluate normality; p-values were 0.022

(first cycle), 0.1572 (second cycle), and 1.061E-07 (third cycle). Results suggest that first cycle 

and third cycle data are not normal. For conclusions about the difference between these cycles 

the Wicoxon test should be used. Caution should be used given the small sample size.

The Wilcoxon signed rank test was used to evaluate the difference in the medians. This test is 

preferred if the assumption of normality doesn’t hold. The same interpretation as described 

previously holds for p-values. 

Based on the results described above, there is no evidence that the means or medians of the 

cycles are different. 
Page 3 of 5

Table 1. Data Provided by the Aluminum Association and Alcoa in April 2012

(Docket ID No. EPA-HQ-OAR-2010-0544)
Table 2. Additional Data Provided by Alcoa

Furnace Test Date Pollutant

Emissions -

First Cycle 

After Dirty 

Charge

Emissions -

Second 

Cycle After

Dirty Charge

Emissions -

Third Cycle 

After Dirty 

Charge

Emissions -

Average of 

3 Test Runs

Group 1 

Furnace

Emission 

Limit

Emissions -

1st Cycle 

After Dirty 

Charge

Emissions -

2nd Cycle 

After Dirty 

Charge

Emissions -

3rd Cycle 

After Dirty 

Charge Average Note

Melter #7 2001 PM (lb/ton) 0.006 0.006 0.040 0.017 0.4 0.005770 0.006280 0.040160 0.01740

Melter #7 2001 HCl (lb/ton) 0.001 0.001 0.001 0.001 0.4 0.000484 0.000595 0.000506 0.00053 Yellow highlight indicates rounding error

Melter #7 2001 D/F (ug/Mg) 0.004 0.003 0.096 0.034 15 0.0038 0.0034 0.0956 0.03427

Melter #7 2006 PM (lb/ton) 0.042 0.043 0.012 0.032 0.4 0.0416 0.0433 0.0122 0.0324

Melter #7 2006 HCl (lb/ton) 0.002 0.002 0.001 0.002 0.4 0.00162 0.00151 0.00126 0.00146 Yellow highlight indicates rounding error

Melter #7 2006 D/F (ug/Mg) 0.017 0.006 0.001 0.008 15 0.0170 0.0055 0.0014 0.0079

Melter #7 2011 PM (lb/ton) 0.023 0.011 0.017 0.017 0.4 0.0228 0.0110 0.0174 0.0171

Melter #7 2011 HCl (lb/ton) 0.083 0.012 0.009 0.010 0.4 0.0832 0.01175 0.00886 0.00964

Melter #7 2011 D/F (ug/Mg) 0.062 0.094 0.086 0.081 15 0.0620 0.0942 0.0862 0.0808

Unit #3 2007 PM (lb/ton) 0.263 0.258 0.200 0.240 0.4 0.2629 0.2581 0.2001 0.2404

Unit #3 2007 HCl (lb/ton) 0.208 0.197 0.234 0.213 0.4 0.2081 0.1968 0.2343 0.2131

Unit #3 2007 D/F (ug/Mg) 3.14 19.060 8.600 10.3 15 3.14 19.06 8.60 10.27

Rounded to 3 sig figs Unrounded Test Report Data
Table 3. Additional Data Provided by the Aluminum Association and Alcoa 

Pollutant

Comparing the Mean (p-values) Comparing the Median (p-values)

First Cycle 

vs Second 

Cycle

First Cycle 

vs

Third Cycle

Second 

Cycle vs 

Third Cycle

First Cycle 

vs Second 

Cycle

First 

Cycle vs

Third 

Cycle

Second 

Cycle vs 

Third Cycle

PM (lb/ton) 0.473 0.975 0.888 1 1 0.75

HCl (lb/ton) 0.43 0.422 0.27 1 0.5 0.371

D/F (lb/ton) 0.659 0.401 0.506 1 0.5 1