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 kilns

PM 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 kilns

PM gr/dscf @ 7% O2 

[using lb/ton rank]
Using for New

Limit Floor

No

Yes
Runs

PM Small 

conc 599

PM Small 

conc 665 Example 3 Example 4 Example 5 Example 6 Example 7 Example 8

1 2.03E-03 2.39E-03

2 3.77E-03 2.53E-03

3 1.12E-03 3.26E-03

Average 2.31E-03 2.73E-03 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

Standard Deviation 1.35E-03 4.66E-04 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

1 6.30E-15 1.22E-14 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

2 4.61E-12 1.58E-15 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

3 1.96E-12 8.01E-14 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

Testing Normality Raw Data Raw Data Raw Data Raw Data Raw Data Raw Data Raw Data Raw 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!

0.73496458 1.28544651 #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

Distribution Lognormal Lognormal #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0! #DIV/0!

1 2 3 4 5 6 7 8
Example 9

Example 

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 Data Raw Data Raw Data Raw Data Raw Data Raw Data Raw Data Raw Data Raw Data Raw 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 18
Example 

19

Example 

20 Example 1 Example 2 Example 3 Example 4 Example 5 Example 6 Example 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-08 2.13E-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 Data Raw Data Log Data Log Data Log Data Log Data Log Data Log Data Log 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! 0.06584724 1.2445431 #NUM! #NUM! #NUM! #NUM! #NUM!

#DIV/0! #DIV/0!

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

Example 

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 Data Log Data Log Data Log Data Log Data Log Data Log Data Log Data Log Data Log 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 17
Example 

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 Data Log Data Log 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 20
Raw 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

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 ik

i k

x x

n 

 

1

N

i

i

n





N

2

,

1 1 X tdf p

s

n m

 

     

0900006481934216 E-PM-Small-conc 12/1/2014
Raw Data

Runs 599 PM conc 1 2.03E-03 2 3.77E-03 3 1.12E-03 456789

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 456789

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 4 3 ˆˆˆ 2

2331

3 1 e e e





  

   

0900006481934216 N-PM-599 conc 12/1/2014
13.60669361

0.589934377

25.06475796

7. Calculate

1.323894336

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

3.484 z 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 4 3 ˆˆˆ 2

e e233 e

 

 

2

2

ˆ m e 1





2z 

 

2 2

ˆ ˆ

1

1 2

z

e e

m

 



 



2z 1z 

2

ˆ 2 2 2

2

2 4

ˆ

.99 2 2 ˆ ˆ ˆ ˆ 2 ˆ

ˆ ˆ ( 1)

2( 1)

z

UPL e me e m e

m n n

       

   

      

  

2

ˆ

2

ˆ

e

 

2

2 ˆ ˆ

e

 

2

ˆ

( 1 e )

 

2 4

ˆ ˆ

n n 2( 1)

      

  

2 2 2

2 4

2 2 ˆ ˆ ˆ ˆ 2 ˆ ˆ ˆ ( 1)

2( 1)

me e m e

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 3.888 140.8509
89 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 4.999 464.3076
distribution 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

24

z

    z z 

 

 



 

1 3

 2

( ) 1 3 

6 24

z

G

f 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 0.029319328
0.000139842 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 0.000693755
Absolute 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

( )

24

z

z z

z z





   





1

( ) 2 ( ) ( )

2

M

i

i

x

f 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 0.002961252
0.022392556 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-05
Cumulative normalization

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

( f x ) ( f 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 0.997097794
2.797747567 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

140.1275143
Raw Data

Runs 665 PM conc 1 0.002394258 2 0.002527273 3 0.003258852 456789

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 456789

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 4 3 ˆˆˆ 2

2331

3 1 e e e





  

   

0900006481934216 N-PM-665 conc 12/1/2014
3.450996165

0.002264118

1526.212152

7. Calculate

0.289710307

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

3.484 z 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 4 3 ˆˆˆ 2

e e233 e

 

 

2

2

ˆ m e 1





2z 

 

2 2

ˆ ˆ

1

1 2

z

e e

m

 



 



2z 1z 

2

ˆ 2 2 2

2

2 4

ˆ

.99 2 2 ˆ ˆ ˆ ˆ 2 ˆ

ˆ ˆ ( 1)

2( 1)

z

UPL e me e m e

m n n

       

   

      

  

2

ˆ

2

ˆ

e

 

2

2 ˆ ˆ

e

 

2

ˆ

( 1 e )

 

2 4

ˆ ˆ

n n 2( 1)

      

  

2 2 2

2 4

2 2 ˆ ˆ ˆ ˆ 2 ˆ ˆ ˆ ( 1)

2( 1)

me e m e

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 8940.128
89 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 30315.7
distribution 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

24

z

    z z 

 

 



 

1 3

 2

( ) 1 3 

6 24

z

G

f 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 1.860963999
0.000139842 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 0.045296839
Absolute 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

( )

24

z

z z

z z





   





1

( ) 2 ( ) ( )

2

M

i

i

x

f 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 0.187957364
1.426961175 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 0.00228749
Cumulative normalization

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

( f x ) ( f 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 0.997063298
177.3838314 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