Runs

Captital 

Cement, San 

Antonio, TX

Alamo, San 

Antonio, TX

Holcim, 

Portland 

CO

1 <0.34 0.54

2 <0.34 0.66

3 <0.34 0.78

4 <0.34 0.25

5 <0.34 0.25

6 <0.34 0.27

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

Em

1

N

i

i

n





N

22

23

24

25

26

27

28

29

30

31

32

33

34

35

ni = number test runs = 660 0 0

Total Number of sources = 3

n =Total # test runs = 12

1

N

i

i

n





N
11

This step is for QC only:

means 0.34 0.46

0.40

Mean =

Pooled Variance = 0.0286  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 

        

2 1 1

s

n m

      

1

1 i n

i ik

i k

x x

n 

 

1

N

i

i

n





m= number future runs = 30

Term1 0.1167

Term2 0.0033

Squared root Term2 0.0577707

NOTE: the pvalue for the t-statistic is calculated as: 2*alpha, where 1-alpha is desired confidence, so if

 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 

        

2 1 1

s

n m

      

1

1 i n

i ik

i k

x x

n 

 

1

N

i

i

n




t‐statistic = quantile t‐distribution with df degrees of freedom at .99 confidence

UPL  POOLED VARIANCE = 0.56

df t

2

,

1 1 Xt s df p n m

       
missions (ppmvd@7%O2))

0 00 0 0 0
f 99% confidence is desired then alpha=0.01 and 2*alpha=2*(0.01)
level = 2.718079183
UPL Pooled 

Variance=

2

,

1 1 Xt s df p n m

       

2

,

1 1 Xt s df p n m

       
Runs

Captital 

Cement, San 

Antonio, TX

1 <0.34

2 <0.34

Em

1

N

i

i

n





N

3 <0.34

4 <0.34

5 <0.34

6 <0.34

7

8

9

1

N

i

i

n





N

9

10

11

12

13

14

15

1

N

i

i

n





N

16

17

18

19

20

21

22

1

N

i

i

n





N

22

23

24

25

26

27

28

1

N

i

i

n





N

28

29

30

31

32

33

34

35

1

N

i

i

n





N

35

ni = number test runs = 600 0 0

Total Number of sources = 3

1

N

i

i

n





N

n =Total # test runs = 6

1

N

i

i

n





N
5

 2 2

1

1

1

n

i

i

s xX

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 ni

i ik

i k

x x

n 

 

1

N

i

i

n





This step is for QC only:

means 0.34

 2 2

1

1

1

n

i

i

s xX

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 ni

i ik

i k

x x

n 

 

1

N

i

i

n





0.34

Mean =

 2 2

1

1

1

n

i

i

s xX

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 ni

i ik

i k

x x

n 

 

1

N

i

i

n





Pooled Variance = 0.0000  2 2

1

1

1

n

i

i

s xX

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 ni

i ik

i k

x x

n 

 

1

N

i

i

n





m= number future runs = 30

Term1 0.2000

 2 2

1

1

1

n

i

i

s xX

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 ni

i ik

i k

x x

n 

 

1

N

i

i

n





Term2 0.0000

 2 2

1

1

1

n

i

i

s xX

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 ni

i ik

i k

x x

n 

 

1

N

i

i

n





Squared root Term2 0

NOTE: the pvalue for the t-statistic is calculated as: 2*alpha, where 1-alpha is desired confidence, so 

 2 2

1

1

1

n

i

i

s xX

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 ni

i ik

i k

x x

n 

 

1

N

i

i

n





 2 2

1

1

1

n

i

i

s xX

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 ni

i ik

i k

x x

n 

 

1

N

i

i

n




t‐statistic = quantile t‐distribution with df degrees of freedom at .99 confidence

UPL  POOLED VARIANCE = 0.34

df t

2

,

1 1 Xt s df p n m

       

df t

2

,

1 1 Xt s df p n m

       
issions (ppmvd@7%O2))

0 00 0 0 0
if 99% confidence is desired then alpha=0.01 and 2*alpha=2*(0.01)
e level = 3.364929997
UPL Pooled 

Variance=

2

,

1 1 Xt s df p n m

       

2

,

1 1 Xt s df p n m

       

2

,

1 1 Xt s df p n m

       

2

,

1 1 Xt s df p n m

       

2

,

1 1 Xt s df p n m

       

2

,

1 1 Xt s df p n m

       

2

,

1 1 Xt s df p n m

       

2

,

1 1 Xt s df p n m

       