- Increasing the “conservative” kiln dust metal concentration limit by imposing a stricter PM emissions standard; or
- Increasing the “conservative” kiln dust metal concentration limit by performing a more detailed risk assessment to increase the metal emission limits.
· Meanwhile, the facility shall continue with daily kiln dust metals monitoring (Step 5).
Appendix A to Appendix IX—Statistics
A.1 Determination of Enrichment Factor
After at least 10 initial emissions tests are performed, an enrichment factor for each metal shall be determined. At the 95% confidence level, the enrichment factor, EF95% s, is based on the test results and is statistically determined so there is only a 5% chance that the enrichment factor at any given time will be larger than EF95% . Similarly, at the 99% confidence level, the enrichment factor, EF99% , is statistically determined so there is only a 1% chance that the enrichment factor at any given time will be larger than EF99% .
For a large number of samples (n > 30), EF95% is based on a normal distribution, and is equal to:
EF95% = EF + zc ó (1)
where:
For a 95% confidence level, zc is equal to 1.645.
For a small number of samples (n<30), EF95% is based on the t-distribution and is equal to:
EF95% = EF + tc S (4)
where the standard deviation, S, is defined as:
tc is a function of the number of samples and the confidence level that is desired. It increases in value as the sample size decreases and the confidence level increases. The 95% confidence level is used in this method to calculate the “violation” kiln dust metal concentration limit; and the 99% confidence level is sometimes used to calculate the “conservative” kiln dust metal concentration limit. Values of tc are shown in table A-1 for various degrees of freedom (degrees of freedom = sample size-1) at the 95% and 99% confidence levels. As the sample size approaches infinity, the normal distribution is approached.
A.2 Comparison of Enrichment Factor Groups
To determine if the enrichment factors measured in the quarterly tests are significantly different from the enrichment factors determined in the initial Step 2 tests, the t-test is used. In this test, the value tmeas:
is compared to tcrit at the desired confidence level. The 95% confidence level is used in this method. Values of tcrit are shown in table A-1 for various degrees of freedom (degrees of freedom n1+n2-2) at the 95% and 99% confidence levels. If tmeas is greater then tcrit, it can be concluded with 95% confidence that the 2 groups are not from the same population.
A.3 Rejection of Data
If the concentration of any hazardous metal in the “required” kiln dust sample exceeds the kiln dust metal concentration limit, the “spare” samples are analyzed. If the average of the combined “required” and “spare” values is still above the limit, a statistical test is used to decide if the upper value can be rejected.
The “Q-test” is used to determine if a data point can be rejected. The difference between the questionable result and its neighbor is divided by the spread of the entire data set. The resulting ratio, Qmeas, is then compared with rejection values that are critical for a particular degree of confidence, where Qmeas is:
The 90% confidence level for data rejection is used in this method. Table A-2 provides the values of Qcrit at the 90% confidence level. If Qmeas is larger than Qcrit, the data point can be discarded. Only one data point from a sample group can be rejected using this method.
