**Category Pollutant**  **Source ID Existing Limit**  **Average Existing** 

**Limit Variance**  **n Distribution** **Existing Limit**  **UPL Existing** 

**Limit 3xRDL** **Existing**

**Limit Floor**  Alternate new small tunnel kilnsPM gr/dscf @ 7% O2

[using lb/ton rank] 599, 549, 665 0.00292 1.15E-06 9 Normal 0.0050 0.0050

**Category Pollutant**  **Source ID Average**  **Variance n**  **Distribution UPL**  **3xRDL Floor**  599 0.00231 1.81E-06 3 Lognormal 0.0072 0.0072 665 0.00273 2.17E-07 3 Lognormal 0.0040 0.0040 Alternate new small tunnel kilnsPM gr/dscf @ 7% O2

[using lb/ton rank]**Using for New**

**Limit Floor** No YesRuns PM Small conc 599PM Small

conc 665Example 3Example 4Example 5Example 6Example 7Example 8 1 2.03E-032.39E-03 2 3.77E-032.53E-03 3 1.12E-033.26E-03
Average 2.31E-032.73E-03 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! Standard Deviation1.35E-034.66E-04 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

1 6.30E-151.22E-14 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! 2 4.61E-121.58E-15 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! 3 1.96E-128.01E-14 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!
Testing Normality Raw DataRaw DataRaw DataRaw DataRaw DataRaw DataRaw DataRaw Data Sample Size 3.00 3.00 0.00 0.00 0.00 0.00 0.00 0.00 Kurtosis -2.00 -2.00 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! SE Kurtosis 2.83 2.83 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! Result Kurtosis normal normal #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! Skewness 0.90 1.57 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! SE Skewness 1.22 1.22 0.00 0.00 0.00 0.00 0.00 0.00 Result Skewness normal normal #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

0.734964581.28544651#DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! Distribution LognormalLognormal #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

1 2 3 4 5 6 7 8Example 9Example 10 Example

11 Example

12 Example

13 Example

14 Example

15 Example

16 Example

17 Example

18

#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! #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!

Raw DataRaw DataRaw DataRaw DataRaw DataRaw DataRaw DataRaw DataRaw DataRaw Data 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 #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! #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! 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 #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! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

9 10 11 12 13 14 15 16 17 18Example

19 Example

20 Example 1Example 2Example 3Example 4Example 5Example 6Example 7

-6.20E+00-6.03E+00 #NUM! #NUM! #NUM! #NUM! #NUM! -5.58E+00-5.98E+00 #NUM! #NUM! #NUM! #NUM! #NUM! -6.79E+00-5.73E+00 #NUM! #NUM! #NUM! #NUM! #NUM!

#DIV/0! #DIV/0! -6.19E+00-5.91E+00 #NUM! #NUM! #NUM! #NUM! #NUM! #DIV/0! #DIV/0! 6.06E-01 1.65E-01 #NUM! #NUM! #NUM! #NUM! #NUM!

#DIV/0! #DIV/0! 1.39E-082.13E-04 #NUM! #NUM! #NUM! #NUM! #NUM! #DIV/0! #DIV/0! 1.40E-01 1.98E-05 #NUM! #NUM! #NUM! #NUM! #NUM! #DIV/0! #DIV/0! 1.30E-01 1.24E-03 #NUM! #NUM! #NUM! #NUM! #NUM!

Raw DataRaw Data Log DataLog DataLog DataLog DataLog DataLog DataLog Data 0.00 0.00 3.00 3.00 0.00 0.00 0.00 0.00 0.00 #DIV/0! #DIV/0! -2.00 -2.00 #NUM! #NUM! #NUM! #NUM! #NUM! #DIV/0! #DIV/0! 2.83 2.83 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! normal normal #NUM! #NUM! #NUM! #NUM! #NUM! #DIV/0! #DIV/0! 0.08 1.52 #NUM! #NUM! #NUM! #NUM! #NUM! 0.00 0.00 1.22 1.22 0.00 0.00 0.00 0.00 0.00 #DIV/0! #DIV/0! normal normal #NUM! #NUM! #NUM! #NUM! #NUM!

#DIV/0! #DIV/0! 0.065847241.2445431 #NUM! #NUM! #NUM! #NUM! #NUM! #DIV/0! #DIV/0!

19 20 1 2 3 4 5 6 7Example 8Example 9Example 10 Example

11 Example

12 Example

13 Example

14 Example

15 Example

16 Example

17 #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!

#NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!

#NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!
Log DataLog DataLog DataLog DataLog DataLog DataLog DataLog DataLog DataLog Data 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!

#NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!

8 9 10 11 12 13 14 15 16 17Example

18 Example

19 Example

20 #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!

#NUM! #NUM! #NUM! #NUM! #NUM! #NUM!

#NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM!
Log DataLog DataLog Data 0.00 0.00 0.00 #NUM! #NUM! #NUM! #DIV/0! #DIV/0! #DIV/0! #NUM! #NUM! #NUM! #NUM! #NUM! #NUM! 0.00 0.00 0.00 #NUM! #NUM! #NUM!

#NUM! #NUM! #NUM!

18 19 20Raw Data PM conc (ranked by lb/ton) Runs 599 549 665 1 0.002025429 0.003003086 0.002394258 2 0.003772857 0.004854779 0.002527273 3 0.001123347 0.003321691 0.003258852 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

Testing Normality Raw Data Sample Size 9.00 Kurtosis 0.63 SE Kurtosis 0.98 Result Kurtosis normal Skewness 0.16 SE Skewness 0.72 Result Raw Data Result Skewness normal normal

ni = number test runs = 3 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 0

Total Number of sources = 3

n =Total # test runs = 9

8

This step is for QC only:

means 2.31E-03 3.73E-03 2.73E-03 #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! #DIV/0!

2.92E-03 Mean =

Pooled Variance = 1.15E-06

m= number future runs = 3

Term1 4.44E-01

Term2 5.12E-07

Squared root Term2 7.15E-04

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 = 2.896459448

UPL POOLED VARIANCE = 4.99E-03 Use for large sample sets and small sample sets that are Normal.

2 2

1 11n

i i s xX n

  

 1 1 1 i

n N
ij i j X x n
  

1 1

n m 

21 1 sn m        1 1 N

i i df n

  

      

df t 21 1

sn m        1 1 i n

i i

k k i x x n
 1

N

i in

  N

2

, 1 1 dfp X t s n m    

   

0900006481934216 E-PM-Small-conc 12/1/2014Raw Data Runs 599 PM conc 1 2.03E-03 2 3.77E-03 3 1.12E-03 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

Testing Normality Raw Data Logtransformed Data Sample Size 3.00 3.00 Kurtosis #DIV/0! #DIV/0! SE Kurtosis #DIV/0! #DIV/0! Average of Raw Data 2.31E-03 Result Kurtosis #DIV/0! #DIV/0! Skewness 0.90 0.08 SE Skewness 1.22 1.22 Result Raw Data Result Log Data Result Skewness normal normal #DIV/0! #DIV/0!
1. Take LN( ) of Raw Data Runs 599 PM conc 1 -6.20E+00 2 -5.58E+00 3 -6.79E+00 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

3

3. Calculate -6.19E+00

0.367033652 4. Calculate

5. m= number future runs = 3

6. Calculate Use for small sample sets that are Lognormal.

2. Calculate sample size, n=

1 ˆ n

i

i x

n   

 2

2 1 ˆ 1

n

i i x x

n   



 

### 

222 ˆˆˆ 4 3 2 233 1 3 1 e e e       

  

0900006481934216 N-PM-599 conc 12/1/201413.60669361

0.589934377

25.06475796

7. Calculate 1.323894336

9. substitue the values of in cell D7 and F7 respectively

3.484z value from "z-stat"

a- Calculate 0.002459994

b- Calculate 6.05157E-06

c- Calculate 0.443446493

d-calculate 0.156022976

e- Calculate 0.004068

f- Calculate UPL 7.18E-03 11. In column B, go down the the row number from Step 10. above, and copy the z value.

12. calculate the UPL using the formula a- Numerator first term

b- denominator first term

8. Go to tab distribution for 99 percentile "z-stat"

10. In column AE indentify the value that is the smallest value that is larger than 0.99, note what row number this is. 222 ˆˆˆ 4 3 2 233 e e e  

###  2 2

ˆ1 m e



2z    2 2 ˆ ˆ

1 1 2

z e e

m     



2z

 1z



2
ˆ 2 2 2 2 2 4

ˆ ˆ ˆ ˆ ˆˆ 2 22 .99 ˆ ˆ

( 1) 2(1) z UPLe me e m e

m n n                  

  

2 ˆ 2 ˆ e  

2 ˆ ˆ 2 e  

2 ˆ ( 1) e



2 4 ˆ ˆ 2(1) n n       

  

2 2 2 2 4

ˆ ˆ ˆ ˆˆ 2 22 ˆ ˆ ( 1) 2(1) me e me n n           

 

     2 2 2

ˆ 233 1 3 1 1 z e e e

m

m e      

    



0900006481934216 N-PM-599 conc 12/1/2014∆z z

0.101 25.06476 1.323894

-5=f(a) 416.185 1 -4.899 378.2311 2 -4.798 342.7997 3 -4.697 309.782 4 -4.596 279.0713 5 -4.495 250.5634 6 -4.394 224.1564 7 -4.293 199.7506 8 -4.192 177.2485 9 -4.091 156.5552 10 -3.99 137.5777 11 -3.889 120.2257 12 -3.788 104.411 13 -3.687 90.04759 14 -3.586 77.05193 15 -3.485 65.34269 16 -3.384 54.84089 17 -3.283 45.46979 18 -3.182 37.15498 19 -3.081 29.82435 20 -2.98 23.40806 21 -2.879 17.83859 22 -2.778 13.0507 23 -2.677 8.981463 24 -2.576 5.570227 25 -2.475 2.758651 26 -2.374 0.490686 27 -2.273 -1.28742 28 -2.172 -2.62713 29 -2.071 -3.57759 30 -1.97 -4.18568 31 -1.869 -4.49597 32 -1.768 -4.55072 33 -1.667 -4.38991 34 -1.566 -4.05123 35 -1.465 -3.57005 36 -1.364 -2.97947 37 -1.263 -2.31028 38 -1.162 -1.59097 39 -1.061 -0.84775

#   1 3 

## 1 3 6 24 z

## z z      

     2z  1z



## 40 -0.96 -0.10451

41 -0.859 0.617125 42 -0.758 1.297854 43 -0.657 1.920659 44 -0.556 2.470819 45 -0.455 2.935911 46 -0.354 3.305807 47 -0.253 3.572675 48 -0.152 3.730981 49 -0.051 3.777483 50 0.05 3.71124 51 0.151 3.533604 52 0.252 3.248223 53 0.353 2.861042 54 0.454 2.380302 55 0.555 1.816539 56 0.656 1.182588 57 0.757 0.493577 58 0.858 -0.23307 59 0.959 -0.97763 60 1.06 -1.71809 61 1.161 -2.43013 62 1.262 -3.08714 63 1.363 -3.66022 64 1.464 -4.11817 65 1.565 -4.42749 66 1.666 -4.55238 67 1.767 -4.45476 68 1.868 -4.09424 69 1.969 -3.42814 70 2.07 -2.41148 71 2.171 -0.99698 72 2.272 0.864917 73 2.373 3.226086 74 2.474 6.140687 75 2.575 9.665179 76 2.676 13.85832 77 2.777 18.78115 78 2.878 24.49702 79 2.979 31.07158 80 3.08 38.57276 81 3.181 47.07079 82 3.282 56.63822 83 3.383 67.34986 84 3.484 79.28284 85 3.585 92.51657 86 3.686 107.1328 87 3.787 123.2155 88 3.888 140.850989 3.989 160.1278

90 4.09 181.137 91 4.191 203.9716 92 4.292 228.7273 93 4.393 255.5017 94 4.494 284.3949 95 4.595 315.5094 96 4.696 348.9498 97 4.797 384.823 98 4.898 423.2384 99 4.999 464.3076distribution of Z Normal distribution

1.48672E-06 0.00061875 2.45094E-06 0.000927022 3.9995E-06 0.001371028 6.46025E-06 0.002001268 1.03291E-05 0.002882552 1.63472E-05 0.004096022 2.56093E-05 0.00574048 3.97118E-05 0.007932448 6.09553E-05 0.010804227 9.26132E-05 0.014499072 0.000139285 0.019162512 0.000207351 0.024928892 0.000305546 0.031902354 0.000445674 0.040131863 0.000643469 0.049580535 0.000919619 0.060090387 0.001300942 0.07134482 0.001821704 0.082832487 0.002525035 0.093817614 0.003464389 0.103323142 0.004704958 0.110133936 0.006324913 0.112827533 0.008416337 0.109839129 0.011085658 0.099565434 0.014453386 0.080508648 0.018652949 0.051456981 0.023828414 0.011692272 0.030130931 -0.038791199 0.03771375 -0.099078831 0.046725789 -0.167165893 0.057303789 -0.239855592 0.069563239 -0.312754163 0.083588399 -0.380387341 0.099421884 -0.436453338 0.117054396 -0.474214065 0.136415346 -0.487009838 0.157365126 -0.468864849 0.179689839 -0.41513362 0.203099244 -0.323124977 0.227228529 -0.192632427 

# 

#  

2 4 2

## 336 6 24 z 

## z z   

    

     

#  2 1 3 

### ( ) 1 3 ( )

6 24 z G 

### f z z z z      
      

## ( ) z 0.251644341 -0.026300091 0.275855243 0.170237143 0.299326439 0.388482034 0.321498297 0.61748847 0.341807853 0.844545238 0.359712192 1.056082845 0.37471238 1.238726673 0.386376486 1.380397662 0.394360216 1.471350295 0.398423793 1.505039262 0.398443914 1.478721087 0.394419966 1.393723865 0.386474058 1.255353764 0.374844865 1.072446741 0.359875719 0.856612727 0.34199778 0.621252443 0.32170943 0.380449756 0.299553264 0.147852541 0.276092166 -0.064348664 0.25188591 -0.246251116 0.227469632 -0.390812433 0.203335281 -0.494130352 0.17991684 -0.555428408 0.157579839 -0.576777136 0.136615273 -0.562604983 0.117237788 -0.519068967 0.099587708 -0.45336132 0.083736272 -0.373025154 0.069693339 -0.285341364 0.05741676 -0.19683266 0.046822635 -0.112911738 0.037795734 -0.037681672 0.030199481 0.026120048 0.023885038 0.077055193 0.018699163 0.114825714 0.014490659 0.140054815 0.011115369 0.154040288 0.008439746 0.158508112 0.006343145 0.155388153 0.004718997 0.146626671 0.003475077 0.134043312 0.002533081 0.119234119 0.001827693 0.103517299 0.001305351 0.087915229 0.000922829 0.073164505 0.00064578 0.059745389 0.00044732 0.047922624 0.000306705 0.037790843 0.000208159 0.0293193280.000139842 0.022392556 9.29928E-05 0.016844434 6.12113E-05 0.012485365 3.98826E-05 0.009122237 2.5722E-05 0.006572019 1.64209E-05 0.004670016 1.03767E-05 0.003273935 6.49066E-06 0.002264914 4.01874E-06 0.001546502 2.46298E-06 0.001042426 1.49417E-06 0.000693755Absolute values

0.00061875 3.12469E-05 0.000927022 9.36292E-05 0.001371028 0.000138474 0.002001268 0.000202128 0.002882552 0.000291138 0.004096022 0.000413698 0.00574048 0.000579788 0.007932448 0.000801177 0.010804227 0.001091227 0.014499072 0.001464406 0.019162512 0.001935414 0.024928892 0.002517818 0.031902354 0.003222138 0.040131863 0.004053318 0.049580535 0.005007634 0.060090387 0.006069129 0.07134482 0.007205827 0.082832487 0.008366081 0.093817614 0.009475579 0.103323142 0.010435637 0.110133936 0.011123528 0.112827533 0.011395581 0.109839129 0.011093752 0.099565434 0.010056109 0.080508648 0.008131373 0.051456981 0.005197155 0.011692272 0.001180919 0.038791199 0.003917911 0.099078831 0.010006962 0.167165893 0.016883755 0.239855592 0.024225415 0.312754163 0.03158817 0.380387341 0.038419121 0.436453338 0.044081787 0.474214065 0.047895621 0.487009838 0.049187994 0.468864849 0.04735535 0.41513362 0.041928496 0.323124977 0.032635623 0.192632427 0.019455875 

## 

#  

2 4 2

### 336 ( ) 1 3 ( )

6 24 z 

### z z f z z z z    

      

1 

## ( )2 () () 2 M

i

i 

## xf a f x f b

 

##  

      

# 0.026300091 0.002656309 0.170237143 0.017193951 0.388482034 0.039236685 0.61748847 0.062366335 0.844545238 0.085299069 1.056082845 0.106664367 1.238726673 0.125111394 1.380397662 0.139420164 1.471350295 0.14860638 1.505039262 0.152008965 1.478721087 0.14935083 1.393723865 0.14076611 1.255353764 0.12679073 1.072446741 0.108317121 0.856612727 0.086517885 0.621252443 0.062746497 0.380449756 0.038425425 0.147852541 0.014933107 0.064348664 0.006499215 0.246251116 0.024871363 0.390812433 0.039472056 0.494130352 0.049907166 0.555428408 0.056098269 0.576777136 0.058254491 0.562604983 0.056823103 0.519068967 0.052425966 0.45336132 0.045789493 0.373025154 0.037675541 0.285341364 0.028819478 0.19683266 0.019880099 0.112911738 0.011404086 0.037681672 0.003805849 0.026120048 0.002638125 0.077055193 0.007782575 0.114825714 0.011597397 0.140054815 0.014145536 0.154040288 0.015558069 0.158508112 0.016009319 0.155388153 0.015694203 0.146626671 0.014809294 0.134043312 0.013538375 0.119234119 0.012042646 0.103517299 0.010455247 0.087915229 0.008879438 0.073164505 0.007389615 0.059745389 0.006034284 0.047922624 0.004840185 0.037790843 0.003816875 0.029319328 0.0029612520.022392556 0.002261648 0.016844434 0.001701288 0.012485365 0.001261022 0.009122237 0.000921346 0.006572019 0.000663774 0.004670016 0.000471672 0.003273935 0.000330667 0.002264914 0.000228756 0.001546502 0.000156197 0.001042426 0.000105285 0.000693755 3.50346E-05Cumulativenormalization

3.12469E-05 1.11452E-05 0.000124876 4.4541E-05 0.00026335 9.3932E-05 0.000465478 0.000166027 0.000756616 0.000269871 0.001170314 0.000417429 0.001750102 0.000624229 0.00255128 0.000909994 0.003642507 0.001299214 0.005106913 0.001821541 0.007042327 0.002511867 0.009560145 0.003409926 0.012782283 0.004559202 0.016835601 0.006004945 0.021843235 0.007791075 0.027912364 0.009955821 0.035118191 0.012526005 0.043484272 0.01551003 0.052959851 0.018889793 0.063395488 0.022611991 0.074519016 0.026579546 0.085914597 0.030644137 0.097008349 0.034601072 0.107064457 0.038187899 0.115195831 0.041088209 0.120392986 0.042941937 0.121573905 0.043363149 0.125491816 0.044760595 0.135498778 0.048329892 0.152382533 0.054352013 0.176607948 0.062992768 0.208196119 0.07425968 0.24661524 0.087963066 0.290697027 0.103686219 0.338592648 0.120769695 0.387780642 0.138314137 0.435135991 0.155204909 0.477064487 0.170160023 0.50970011 0.181800542 0.529155985 0.18874009 

## ( )2 () () f a f xf b        0.531812294 0.189687546 0.549006245 0.195820309 0.588242931 0.209815304 0.650609266 0.232060215 0.735908335 0.262484805 0.842572703 0.30053 0.967684096 0.345154905 1.10710426 0.394883483 1.25571064 0.447888612 1.407719606 0.502107381 1.557070435 0.555378042 1.697836546 0.605586694 1.824627276 0.650810587 1.932944397 0.689445288 2.019462282 0.720304607 2.082208779 0.742685115 2.120634204 0.756390749 2.135567311 0.76171711 2.142066526 0.764035259 2.166937889 0.772906411 2.206409944 0.786985359 2.25631711 0.804786316 2.312415379 0.824795524 2.37066987 0.845573817 2.427492973 0.86584156 2.479918939 0.884540926 2.525708432 0.900873186 2.563383973 0.91431135 2.59220345 0.924590721 2.612083549 0.931681583 2.623487635 0.935749208 2.627293483 0.937106683 2.629931608 0.938047653 2.637714183 0.940823553 2.64931158 0.944960128 2.663457116 0.950005578 2.679015185 0.955554851 2.695024505 0.961265078 2.710718708 0.966862908 2.725528002 0.972145107 2.739066376 0.976973993 2.751109022 0.981269381 2.76156427 0.984998573 2.770443708 0.988165704 2.777833323 0.990801442 2.783867607 0.992953759 2.788707792 0.994680162 2.792524667 0.996041571 2.795485919 0.9970977942.797747567 0.997904482 2.799448855 0.9985113 2.800709877 0.998961083 2.801631223 0.99928971 2.802294997 0.999526466 2.802766669 0.999694702 2.803097336 0.999812645 2.803326093 0.999894238 2.803482289 0.999949951 2.803587574 0.999987504 2.803622609 1

140.1275143Raw Data Runs 665 PM conc 1 0.002394258 2 0.002527273 3 0.003258852 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

Testing Normality Raw Data Logtransformed Data Sample Size 3.00 3.00 Kurtosis #DIV/0! #DIV/0! SE Kurtosis #DIV/0! #DIV/0! Average of Raw Data 2.73E-03 Result Kurtosis #DIV/0! #DIV/0! var of raw data 0.00 Skewness 1.57 1.52 SE Skewness 1.22 1.22 Result Raw Data Result Log Data Result Skewness normal normal #DIV/0! #DIV/0!
1. Take LN( ) of Raw Data Runs 665 PM conc 1 -6.03E+00 2 -5.98E+00 3 -5.73E+00 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

3

3. Calculate -5.91E+00

0.027101332 4. Calculate

5. m= number future runs = 3

6. Calculate Use for small sample sets that are Lognormal.

2. Calculate sample size, n=

1 ˆ n

i

i x

n   

 2

2 1 ˆ 1

n

i i x x

n   



 

### 

222 ˆˆˆ 4 3 2 233 1 3 1 e e e       

  

0900006481934216 N-PM-665 conc 12/1/20143.450996165

0.002264118

1526.212152

7. Calculate 0.289710307

9. substitue the values of in cell D7 and F7 respectively

3.484z value from "lognormal distribution 99%"

a- Calculate 0.002738509

b- Calculate 7.49943E-06

c- Calculate 0.027471913

d-calculate 0.009217398

e- Calculate 0.001114

f- Calculate UPL 0.0040 11. In column B, go down the the row number from Step 10. above, and copy the z value.

12. calculate the UPL using the formula a- Numerator first term

b- denominator first term

8. Go to tab distribution for 99 percentile "lognormal distribution 99%"

10. In column AE indentify the value that is the smallest value that is larger than 0.99, note what row number this is. 222 ˆˆˆ 4 3 2 233 e e e  

###  2 2

ˆ1 m e



2z    2 2 ˆ ˆ

1 1 2

z e e

m     



2z

 1z



2
ˆ 2 2 2 2 2 4

ˆ ˆ ˆ ˆ ˆˆ 2 22 .99 ˆ ˆ

( 1) 2(1) z UPLe me e m e

m n n                  

  

2 ˆ 2 ˆ e  

2 ˆ ˆ 2 e  

2 ˆ ( 1) e



2 4 ˆ ˆ 2(1) n n       

  

2 2 2 2 4

ˆ ˆ ˆ ˆˆ 2 22 ˆ ˆ ( 1) 2(1) me e me n n           

 

     2 2 2

ˆ 233 1 3 1 1 z e e e

m

m e      

    



0900006481934216 N-PM-665 conc 12/1/2014∆z z

0.101 1526.212 0.28971

-5=f(a) 30333 1 -4.899 27604.79 2 -4.798 25055.27 3 -4.697 22676.83 4 -4.596 20462.03 5 -4.495 18403.56 6 -4.394 16494.31 7 -4.293 14727.28 8 -4.192 13095.67 9 -4.091 11592.81 10 -3.99 10212.22 11 -3.889 8947.541 12 -3.788 7792.6 13 -3.687 6741.37 14 -3.586 5787.987 15 -3.485 4926.744 16 -3.384 4152.093 17 -3.283 3458.643 18 -3.182 2841.165 19 -3.081 2294.585 20 -2.98 1813.989 21 -2.879 1394.621 22 -2.778 1031.885 23 -2.677 721.3405 24 -2.576 458.7089 25 -2.475 239.868 26 -2.374 60.85472 27 -2.273 -82.1356 28 -2.172 -192.749 29 -2.071 -274.473 30 -1.97 -330.637 31 -1.869 -364.412 32 -1.768 -378.809 33 -1.667 -376.682 34 -1.566 -360.727 35 -1.465 -333.479 36 -1.364 -297.318 37 -1.263 -254.462 38 -1.162 -206.972 39 -1.061 -156.752

#   1 3 

## 1 3 6 24 z

## z z      

     2z  1z



## 40 -0.96 -105.545

41 -0.859 -54.9361 42 -0.758 -6.3534 43 -0.657 38.935 44 -0.556 79.81908 45 -0.455 115.3473 46 -0.354 144.7266 47 -0.253 167.3226 48 -0.152 182.6592 49 -0.051 190.4189 50 0.05 190.4427 51 0.151 182.7301 52 0.252 167.4392 53 0.353 144.8865 54 0.454 115.547 55 0.555 80.05425 56 0.656 39.2003 57 0.757 -6.06431 58 0.858 -54.6305 59 0.959 -105.231 60 1.06 -156.439 61 1.161 -206.671 62 1.262 -254.182 63 1.363 -297.073 64 1.464 -333.282 65 1.565 -360.592 66 1.666 -376.624 67 1.767 -378.843 68 1.868 -364.556 69 1.969 -330.91 70 2.07 -274.892 71 2.171 -193.335 72 2.272 -82.9092 73 2.373 59.87151 74 2.474 238.6523 75 2.575 457.237 76 2.676 719.5875 77 2.777 1029.825 78 2.878 1392.228 79 2.979 1811.234 80 3.08 2291.44 81 3.181 2837.601 82 3.282 3454.629 83 3.383 4147.596 84 3.484 4921.733 85 3.585 5782.428 86 3.686 6735.229 87 3.787 7785.841 88 3.888 8940.12889 3.989 10204.11

90 4.09 11583.98 91 4.191 13086.06 92 4.292 14716.86 93 4.393 16483.04 94 4.494 18391.4 95 4.595 20448.93 96 4.696 22662.76 97 4.797 25040.17 98 4.898 27588.61 99 4.999 30315.7distribution of Z Normal distribution

1.48672E-06 0.045096659 2.45094E-06 0.067657674 3.9995E-06 0.100208621 6.46025E-06 0.146497943 1.03291E-05 0.211354104 1.63472E-05 0.300847609 2.56093E-05 0.422406958 3.97118E-05 0.584846236 6.09553E-05 0.798249687 9.26132E-05 1.073647389 0.000139285 1.422408616 0.000207351 1.855278892 0.000305546 2.380996941 0.000445674 3.004452714 0.000643469 3.724390884 0.000919619 4.530727696 0.001300942 5.401632444 0.001821704 6.30062408 0.002525035 7.174040011 0.003464389 7.949334535 0.004704958 8.534740355 0.006324913 8.820856589 0.008416337 8.684688137 0.011085658 7.996534292 0.014453386 6.629896472 0.018652949 4.474245286 0.023828414 1.450071559 0.030130931 -2.474820921 0.03771375 -7.269287309 0.046725789 -12.82497648 0.057303789 -18.94676824 0.069563239 -25.3496673 0.083588399 -31.66403689 0.099421884 -37.45046632 0.117054396 -42.22467364 0.136415346 -45.4917086 0.157365126 -46.78745442 0.179689839 -45.72418499 0.203099244 -42.03589657 0.227228529 -35.61848185 

# 

#  

2 4 2

## 336 6 24 z 

## z z   

    

     

#  2 1 3 

### ( ) 1 3 ( )

6 24 z G 

### f z z z z      
      

## ( ) z 0.251644341 -26.5596999 0.275855243 -15.15441498 0.299326439 -1.901741465 0.321498297 12.5175372 0.341807853 27.28278696 0.359712192 41.49182753 0.37471238 54.23086266 0.386376486 64.64951757 0.394360216 72.03351075 0.398423793 75.86740485 0.398443914 75.88072339 0.394419966 72.07240687 0.386474058 64.71091479 0.374844865 54.30996184 0.359875719 41.58256008 0.34199778 27.37837594 0.32170943 12.61110477 0.299553264 -1.816584749 0.276092166 -15.0830584 0.25188591 -26.5061459 0.227469632 -35.5851148 0.203335281 -42.02341832 0.17991684 -45.73170907 0.157579839 -46.8127345 0.136615273 -45.53146458 0.117237788 -42.27497249 0.099587708 -37.50711378 0.083736272 -31.7229407 0.069693339 -25.40714093 0.05741676 -18.99975481 0.046822635 -12.87118377 0.037795734 -7.307235751 0.030199481 -2.503814792 0.023885038 1.430033304 0.018699163 4.462599056 0.014490659 6.625665104 0.011115369 7.998481133 0.008439746 8.691459597 0.006343145 8.8311029 0.004718997 8.547208694 0.003475077 7.962932726 0.002533081 7.187872301 0.001827693 6.314002793 0.001305351 5.41407066 0.000922829 4.54191858 0.00064578 3.734179009 0.00044732 3.012802031 0.000306705 2.387959019 0.000208159 1.8609639990.000139842 1.426961175 9.29928E-05 1.077226481 6.12113E-05 0.801014615 3.98826E-05 0.586946691 2.5722E-05 0.423977082 1.64209E-05 0.302003127 1.03767E-05 0.21219171 6.49066E-06 0.14709621 4.01874E-06 0.100629824 2.46298E-06 0.067950063 1.49417E-06 0.045296839Absolute values

0.045096659 0.002277381 0.067657674 0.006833425 0.100208621 0.010121071 0.146497943 0.014796292 0.211354104 0.021346764 0.300847609 0.030385608 0.422406958 0.042663103 0.584846236 0.05906947 0.798249687 0.080623218 1.073647389 0.108438386 1.422408616 0.14366327 1.855278892 0.187383168 2.380996941 0.240480691 3.004452714 0.303449724 3.724390884 0.376163479 4.530727696 0.457603497 5.401632444 0.545564877 6.30062408 0.636363032 7.174040011 0.724578041 7.949334535 0.802882788 8.534740355 0.862008776 8.820856589 0.890906515 8.684688137 0.877153502 7.996534292 0.807649963 6.629896472 0.669619544 4.474245286 0.451898774 1.450071559 0.146457227 2.474820921 0.249956913 7.269287309 0.734198018 12.82497648 1.295322625 18.94676824 1.913623592 25.3496673 2.560316397 31.66403689 3.198067726 37.45046632 3.782497099 42.22467364 4.264692038 45.4917086 4.594662568 46.78745442 4.725532897 45.72418499 4.618142684 42.03589657 4.245625554 35.61848185 3.597466667 

## 

#  

2 4 2

### 336 ( ) 1 3 ( )

6 24 z 

### z z f z z z z    

      

1 

## ( )2 () () 2 M

i

i 

## xf a f x f b

 

##  

      

# 26.5596999 2.68252969 15.15441498 1.530595913 1.901741465 0.192075888 12.5175372 1.264271258 27.28278696 2.755561483 41.49182753 4.190674581 54.23086266 5.477317128 64.64951757 6.529601274 72.03351075 7.275384585 75.86740485 7.66260789 75.88072339 7.663953063 72.07240687 7.279313094 64.71091479 6.535802393 54.30996184 5.485306146 41.58256008 4.199838568 27.37837594 2.76521597 12.61110477 1.273721581 1.816584749 0.18347506 15.0830584 1.523388898 26.5061459 2.677120736 35.5851148 3.594096595 42.02341832 4.244365251 45.73170907 4.618902616 46.8127345 4.728086185 45.53146458 4.598677922 42.27497249 4.269772222 37.50711378 3.788218492 31.7229407 3.20401701 25.40714093 2.566121234 18.99975481 1.918975235 12.87118377 1.299989561 7.307235751 0.738030811 2.503814792 0.252885294 1.430033304 0.144433364 4.462599056 0.450722505 6.625665104 0.669192175 7.998481133 0.807846594 8.691459597 0.877837419 8.8311029 0.891941393 8.547208694 0.863268078 7.962932726 0.804256205 7.187872301 0.725975102 6.314002793 0.637714282 5.41407066 0.546821137 4.54191858 0.458733777 3.734179009 0.37715208 3.012802031 0.304293005 2.387959019 0.241183861 1.860963999 0.1879573641.426961175 0.144123079 1.077226481 0.108799875 0.801014615 0.080902476 0.586946691 0.059281616 0.423977082 0.042821685 0.302003127 0.030502316 0.21219171 0.021431363 0.14709621 0.014856717 0.100629824 0.010163612 0.067950063 0.006862956 0.045296839 0.00228749Cumulativenormalization

0.002277381 1.28114E-05 0.009110806 5.12529E-05 0.019231877 0.000108189 0.034028169 0.000191426 0.055374934 0.000311512 0.085760542 0.000482447 0.128423645 0.000722448 0.187493115 0.001054744 0.268116333 0.00150829 0.376554719 0.002118311 0.52021799 0.00292649 0.707601158 0.003980616 0.948081849 0.005333441 1.251531573 0.0070405 1.627695052 0.009156611 2.08529855 0.011730863 2.630863426 0.014799942 3.267226458 0.018379807 3.9918045 0.022455926 4.794687288 0.026972549 5.656696063 0.031821786 6.547602579 0.036833587 7.424756081 0.041768021 8.232406044 0.046311461 8.902025588 0.050078411 9.353924362 0.052620571 9.500381589 0.053444467 9.750338502 0.054850602 10.48453652 0.058980838 11.77985915 0.066267685 13.69348274 0.077032789 16.25379913 0.091435868 19.45186686 0.109426622 23.23436396 0.130705087 27.499056 0.154696144 32.09371857 0.180543453 36.81925146 0.207126973 41.43739415 0.233106369 45.6830197 0.256990167 49.28048637 0.277227743 

## ( )2 () () f a f xf b        51.96301606 0.292318334 53.49361197 0.300928712 53.68568786 0.302009237 54.94995911 0.309121404 57.7055206 0.324622836 61.89619518 0.348197507 67.37351231 0.379010195 73.90311358 0.415742516 81.17849817 0.456670246 88.84110606 0.499776303 96.50505912 0.542889928 103.7843722 0.583839758 110.3201746 0.620606963 115.8054808 0.651464594 120.0053193 0.675090817 122.7705353 0.69064656 124.0442569 0.69781189 124.2277319 0.698844031 125.7511208 0.707413866 128.4282416 0.722474029 132.0223382 0.742692646 136.2667034 0.766569354 140.885606 0.792553025 145.6136922 0.819150909 150.2123701 0.845020806 154.4821424 0.869040442 158.2703608 0.890351093 161.4743779 0.908375314 164.0404991 0.922811049 165.9594743 0.933606258 167.2594639 0.940919359 167.9974947 0.945071157 168.25038 0.946493765 168.3948134 0.947306276 168.8455359 0.949841819 169.514728 0.953606364 170.3225746 0.958150911 171.2004121 0.963089192 172.0923534 0.968106815 172.9556215 0.972963136 173.7598777 0.977487485 174.4858528 0.981571464 175.1235671 0.98515893 175.6703882 0.988235077 176.129122 0.990815687 176.5062741 0.992937359 176.8105671 0.994649161 177.051751 0.996005943 177.2397083 0.997063298177.3838314 0.997874064 177.4926313 0.998486118 177.5735338 0.998941236 177.6328154 0.999274725 177.6756371 0.999515619 177.7061394 0.99968721 177.7275707 0.999807772 177.7424275 0.999891349 177.7525911 0.999948524 177.759454 0.999987132 177.7617415 1

8975.749282