MACT New UPL for Mercury Using Pooled Variance, Corrected for Temporal Autocorrelation with Intraquarry Variability

Runs 1 2 3 4 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

ni = number runs =

ni-1= sum of (ni-1) 29

means

Mean 8.48

n to be used with 1 source= ni 30 m= number future runs = 30

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

Assuming Correlated variables

correlation =correl(data-last,data - first obs)

Stdev= 1.70801395 Variance data = 2.91731166 adjustment for temporal correlation= 3.47252932 intra quarry variance= 23.633803 adjustment for temporal correlation= 31.7662533 total variance 35.2387826 *** defined as variance of data + intra quarry variance *** if the data in columns Oto Q are the intraquarry data, we can calculate the temporal correlation there and use it for the adjustment of the intraquarry variance *** defined as sdev^2 *** defined as before variance* (1+corr) *** defined as (RSD*Mean)^2Variance = Variance pooled, intraquarry data adjusted for temporal correlation 35.239
SQRT(Variance*(1/n+1/m)) 1.533

UPL-- source mean and variance pooled data, including intraquarry variability **12.25**

Recall the formula for the variance is N is the number of sampling units used in the sample: in this case the number of data points

Calculated limits in concentration basis: 3.63 Rounded-up limit in concentration basis: 3.7 2

### 1 1 sN m       MACT New UPL for Mercury Using Pooled Variance, Corrected for Temporal Autocorrelation with Intraquarry Variability

MACT NewKiln 1589 0.29 7.96 8.88 8.44 9.33 8.69 8.44 10.71 8.44 8.44 8.44 8.44 8.44 10.43 8.44 8.66 8.46 8.44 8.44 8.44 8.44 8.44 8.48 9.76 10.90 8.44 8.44 8.44 8.30 8.45

30

29 Emissions (lb/ton feed)8.48

#source mean = mean of source means

= quantile t-distribution with df degrees of freedom at .99 confidence level = 2.46202135 =tinv((1-.99)*2,df)

0.19031825 Revised 3 quarry, intraquarry variability RSD= 0.57

*** defined as variance of data + intra quarry variance *** if the data in columns Oto Q are the intraquarry data, we can calculate the temporal correlation there and use it for the adjustment of the intraquarry variance *** defined as sdev^2 *** defined as before variance* (1+corr) *** defined as (RSD*Mean)^2lb/MM tons feed

N is the number of sampling units used in the sample: in this case the number of data points

ug/dscm**Kiln ID # 1239** **1248 1376**  0.0795 0.0265 0.0233 0.02 0.0197 0.02960.0212 0.0214 0.0245 0.02 0.0326 0.020.0225 0.0225 0.0495 0.02 0.02 0.0462 0.02 0.0337 0.03150.0263 0.0365 0.0264 0.02 0.0344 0.0294 0.02 0.0313 0.0263 0.02 0.0312 0.0242 0.02 0.028 0.0407 0.02 0.0317 0.03090.0256 0.0207 0.0235 0.02 0.0274 0.02950.0206 0.0263 0.0673 0.02 0.0211 0.0625 0.02 0.0177 0.0624 0.02 0.0318 0.0899 0.02 0.0246 0.0835 0.02 0.0289 0.122 0.02 0.0232 0.0998 0.02 0.0292 0.09910.0237 0.0302 0.1090.0269 0.036 0.13 0.02 0.0291 0.104 0.02 0.0296 0.0589 0.02 0.0265 0.0729 0.02 0.0257 0.0856 0.02 0.0255 **Daily Mercury Concentrations (ppm) in Limestone by Quarry**Avg 0.05940.021 0.0270.036 Stdev 0.021 RSD 0.573303

correlation 0.8052-0.0011 0.22820.3441

=tinv((1-.99)*2,df)

*** if the data in columns Oto Q are the intraquarry data, we can calculate the temporal correlation there and use it for the adjustment of the intraquarry varianceMACT Existing UPL for Mercury Using Pooled Variance, Corrected for Temporal Autocorrelation with Intraquarry Variability

Emissions (lb/ton feed) Runs Kiln ID 1248Kiln ID 1559 1 0.32 15.62 2 15.53 40.66 3 17.43 16.20 4 16.57 31.05 5 18.30 25.67 6 17.06 29.44 7 16.57 28.05 8 21.00 55.73 9 16.57 53.74 10 16.57 25.80 11 16.57 14.91 12 16.57 13.23 13 16.57 22.05 14 20.45 32.64 15 16.57 30.95 16 16.99 30.88 17 16.60 29.73 18 16.57 23.10 19 16.57 26.32 20 16.57 23.67 21 16.57 27.93 22 16.57 12.36 23 16.65 23.96 24 19.14 12.20 25 21.37 22.80 26 16.57 21.37 27 16.57 42.21 28 16.57 24.92 29 16.30 23.07 30 16.58 2.12 31 32 33 34 35

ni = number runs = 30 30

ni-1 29 29

= sum of (ni-1) 87means 16.63 26.08

Mean 17.06

N = Number sources= 3

m= number future runs = 30

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

Assuming Correlated variables

correlation =correl(data-last,data - first obs)

correlation of each kiln = 0.20273792 0.23987665 Pooled stdev= 4.89546605 Variance data = 23.9655879 adjustment for temporal correlation= 29.0217903 intra quarry variance= 95.6875363 adjustment for temporal correlation= 128.613855 total variance 157.635645 *** if the data in columns Oto Q are the intraquarry data, we can calculate the temporal correlation there and use it for the adjustment of the intraquarry variance *** defined as sdev^2 *** defined as before variance* (1+corr) *** defined as (RSD*Mean)^2Variance = Variance pooled, intraquarry data adjusted for temporal correlation 157.635645
SQRT(Variance*(1/n+1/m)) 7.6026138

UPL-- source mean and variance pooled data, including intraquarry variability **35.0805634**

Calculated limits in concentration basis: 10.40 Rounded-up limit in concentration basis: 11MACT Existing UPL for Mercury Using Pooled Variance, Corrected for Temporal Autocorrelation with Intraquarry Variability

Kiln ID 1589 0.29 7.96 8.88 8.44 9.33 8.69 8.44 10.71 8.44 8.44 8.44 8.44 8.44 10.43 8.44 8.66 8.46 8.44 8.44 8.44 8.44 8.44 8.48 9.76 10.90 8.44 8.44 8.44 8.30 8.45

30

298.48

#source mean = mean of source means

#because UPL is based on source means

= quantile t-distribution with df degrees of freedom at .99 confidence level = 2.36997675 =tinv((1-.99)*2,df)

0.19031825 Revised 3 quarry, intraquarry variability RSD= 0.57

*** if the data in columns Oto Q are the intraquarry data, we can calculate the temporal correlation there and use it for the adjustment of the intraquarry variance *** defined as sdev^2 *** defined as before variance* (1+corr) *** defined as (RSD*Mean)^2#calculated as variance*(1+average(temporal correlation))

lb/MM tons feed

ug/dscm**Kiln ID # 1239** **1248 1376**  0.0795 0.0265 0.0233 0.02 0.0197 0.02960.0212 0.0214 0.0245 0.02 0.0326 0.020.0225 0.0225 0.0495 0.02 0.02 0.0462 0.02 0.0337 0.03150.0263 0.0365 0.0264 0.02 0.0344 0.0294 0.02 0.0313 0.0263 0.02 0.0312 0.0242 0.02 0.028 0.0407 0.02 0.0317 0.03090.0256 0.0207 0.0235 0.02 0.0274 0.02950.0206 0.0263 0.0673 0.02 0.0211 0.0625 0.02 0.0177 0.0624 0.02 0.0318 0.0899 0.02 0.0246 0.0835 0.02 0.0289 0.122 0.02 0.0232 0.0998 0.02 0.0292 0.09910.0237 0.0302 0.1090.0269 0.036 0.13 0.02 0.0291 0.104 0.02 0.0296 0.0589 0.02 0.0265 0.0729 0.02 0.0257 0.0856 0.02 0.0255 **Daily Mercury Concentrations (ppm) in Limestone by Quarry**Avg 0.05940.021 0.0270.036 Stdev 0.021 RSD 0.573303

correlation 0.8052-0.0011 0.22820.3441

=tinv((1-.99)*2,df)

*** if the data in columns Oto Q are the intraquarry data, we can calculate the temporal correlation there and use it for the adjustment of the intraquarry variance