This is the explanation for the calculations in excel spreadsheet FINAL Hq VARABILITY Calculations_HY_MCl Equation

20100527 1l40.xlsx

EXCEL

ROW

NO.

EXCEL NAME DESCRIPTION EQUATION Reference:

38 Count

Number of

observations of kiln

ith (sample size :

population size for

each kiln)

lt¡ Page346 of (Kleinbaum,

Kupper etal.1987)

39 Observed Average Mean of kiln ith x.

40 Percent Hg from Feed

(From Fed Reg Table 3)

o/oYanance

contribution from

Limestone of kiln

ith. Number is taken

from Table 3

Proposed Rule.

%Feed¡ Table 3,page of (EPA

2009a)

41 Percent Hg from Coal

(From Fed Reg Table 3)

o/oYanance

contribution from

Fuel of kiln ith .

Number is taken

from Table 3

Proposed Rule.

%oCoal¡ Table 3, page of (EPA

2009a)

42 Percent Hg from Other

(From Fed Reg Table 3)

%Contribution

from Other of kiln

ith . Number is

taken from Table 3

Proposed Rule.

o/oOther; Table 3, page of (EPA

2009a)

43 Observed Stdev Standard deviation s,
ofobservations of

kiln ilh

44 Observed Variance

Variance of

observations of kiln

.th

I

sr2 Terms already defìned

45 Var Limestone

Variance from

Limestone of kiln

.thI

t12 * o/oFeedr= tra{.1ri,n.rton.¡ Terms already defined

46 Var Coal Variance from Coal

ofkiln ith t 12 * o/oC 

o al, = Vdr¡ (coat) Terms already defined

47 Var Other Variance from

Other of kiln ith s12 x o/oOth€t¡ =Var¡(ot¡",t Terms already dehned

48 RSD lntraquarry

Relative standard

deviation of

Intraquary of kiln .th -' .

r I nrs numoer ls

a constant

0.45

49 Var lntraquarry Variance of

Intraquary (oto,,,,."nuo,ry x

a

\, *r) =Var.

¡ (lntraquarry)

Making use of relation ship of

Relative standard deviation times

the mean equals the standard

deviation for that contribution.

And standard deviation square

equals variance.

s0 Var Limestone Revised

Variance of

Limestone revised

by including

Variance from

Intraquarry of kiln

ith

(V o', rrr^"rron"¡ + V ar i 1tno.q uur.y) ) x o/o F e e d = V a\ 

ltirn"ston e Revi sed)

5l Stdev Coal(regional

coal mines)

Standard deviation

of coal from Stdev..i(regional coal mines)
Regional Coal

Mines of kiln ith

52 Var Coal Revised

Variance of Coal

revised by

including Variance

Regional Coal

Mines of kiln ith

Varr 

lcoat¡ 

* (Sta"'r rngional coal .in"l ) = Vart 

lcoutRevised)

53 Var Total

Totalvariance of

Limestone revised

variance and Coal

revised Variance and

Other Variance of

kiln ith. This is also

the Within Group

Variance of kiln ith

Vo', 1u*on"R€vis€d) + V*i 

çoa x*rra¡ +Vtri ç,na'¡ = trarraut = Vi 

1øthi, group¡ Variances are additive.

54 ProportionalVar

Proportional Within

Group Variance of

kiln iû lror

unbalanced design)

(',r.ur*r*uo, * ",)tfrn,= 4@¡,t íngroup)

)4 : Total number of obserr¡ations from all kilns

Page 350 of (Kleinbaum,

Kupper et al. 1987), "MSE:

..." using n¡ (for population)

instead of n, -l (for sample

from a population)

55 MSE (mean square

error = pooled variance)

TotalWithin Group

Variance of all kilns

(for unbalance

design)

N

Z,N=VW j=l

Page 350 of (Kleinbaum,

Kupper et al. 1987), "MSE:

..." using n¡(for population)

instead of n, - I (for sample

from a population)

56

SE (sum sc¡uare error) =

MSE " degree of

freedom

Sum Square Errors

Vw *df-= SS,

df* =Zr, - N: Degree of freedom within group

: Total number of observations from all kilns - Number of kilns

Page 351 of (Kleinbaum,

Kupper et al. 1987)

Page64 of (Roberts and

Russo 1999): "total within

group variance..., also called
Mean Square Error"

Page 477 of (Montgomery

and Runger 2003) : "the

square root of MSE is pooled

StDev..."

57 Count*(Mean-Grand

mean)^2

ft¡x

X:

/\- l;-r, I -P [^, 'i(benveen group)

Grand mean

Page 351 of (Kleinbaum,

Kupper et al. 1987): "MST

58 STr (sum square

treatment)

Sum Square

Treatment 14 pr*ren group)= SSz"

Page 351 of (Kleinbaum,

Kupper et al. 1987): "MST

59 ST (sum sguare total) =

SE + STr

Sum Square Total =

Sum Square Error +

Sum Square

Treatment

,SSu*SS., =SSro,nt

Page 45 of (Roberts and

Russo 1999\

Page 351 of (Kleinbaum,

Kupper et al. 1987): "TSS

60 Totalvariance

(ST/degree of freedom)

TotalVariance,

including Wíthin

Group and Between

Group Variances =

Sum Square

Total/Degree of

Freedom total

SS ro,ot / df,o,ot =VQTro,ol

df**,: Degree of freedom total

: Total number of observations from all kilns - I

Page 43,44 of (Roberts and

Russo 1999): "general

equation is always the

same..., variance:..."

61 Total stdev = total

variance ^0.5

TotalStandard

Deviation

62 RSD Relative Total

Standard Deviation RSDro,ot = Stdevro,n,/ X

63

SAS Proc Reg 1st Order

Autocorrelation
64

65

Grand mean

Grand mean

X

Also symbolized as =

X or Y in (Kleinbaum,

Kupper et al. 1987) or y.. in

(Montgomery and Runger

2003)

66 MCI rsd total relative

Var Same as row 62 Same as row 62

67 MClsdev Same as row 63 Same as row 63

68

69 usinq RTlVar

70

71

72 usino MClVar

IJ

74

75 using MCI Var with

autocorrelation

76

77

78 UPL using RTI's

Equation with RTI Mean

and RTI Var (No

Autocorrelation. m=1)

Xp+O-",rrffi

last equation on section 7 of RTI doc

Section 7 of (Munoz2010),

MCI has been unable to

locate this equation in any

other literature sources
79 UPL using RTI's

Equation with MCI

grand mean and MCI

Var (No Autocorrelation,

m=1)

To+tr*,rrm

','=V%rroro,

Section 8 of (Munoz2010),

MCI has been unable to

locate this equation in any

other literature sources

80 UPL using RTI's

Equation with MCI

grand mean and MCI

Var (With SAS 1st Order

Autocorrelation. m=1)

T p+r-",*

last equation on section 8 of RTI doc

,,t =Varroro,

Section 8 of (Munoz2}l}),

MCI has been unable to

locate this equation in any

other literature sources

81 UPL from EPA Unified

Guidance Equation 18.7

(p=t, ePR called p as

m) (same as Boiler

MACT when m=1) with

MCI Var

PL = T + tr-o.,-rStdevro,r, ffi,

foruntransformeddata

assumed normal distributed

mean of p future values

/V

n=zn,

i=l

Page l8-14 of(EPA 2009b)

Page 80 of(EPA 2010)
TL=x*"(r,y,I-a).s ll7.l6l

Actual99th Percentile

Reference:

EPA (2009a). Federal Register, National Emission Standards forHazardous Air Pollutants From the Portland Cement Manufacturing

Industry: Proposed Rule. p.

EPA (2009b). Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities Unified Guidance. V/ashington DC, Office of

Resource Conservation and Recovery, Program Implementation and Information Division, US EPA.

EPA (2010). Proposed rules for National Emission Standards for Hazardous Air Pollutants for Major Sources: Industrial,

Commericial, and Institutional Boilers and Process Heaters, Environmental Protection Agency (EPA).

Kleinbaum, D. G., L. L. Kupper, et al. (1987). Applied Reeression Analysis and Other Multivariable Methods.Second, Belmont, CA,

Duxbury Press.

Montgomery, D. C. and G. C. Runger (2003). Applied Statistics and Probabilit]¡ for Eneineers.Third, New York, NY, John Wiley &

Sons, Inc.

Munoz, B. (2010). Constructing the UPL for the aveÍage of "m" new test runs, RTI International.

Roberts, M. J. and R. Russo (1999). A Student's zuide to Analysis of VarianceNew York, NY, Rouledge.
lts I

to,,r,- I

\f*b^ 

)

nC^À å"ìa

PL=i+t_*.*,s

ll

-+-

UPL from EPA Unified

Guidance Equation l8-3

with MClGrand mean

and MClVar

PL = X + tr-o, 

^.n-rStderr",", @r)

for untransformed data

assumed normally distributed

m fufure values

¡/

n:zn,

i=l

ll8.3l

Page l8-9 of(EPA 2009b)

( Co^,\t'ut., I À")

UTL from EPA Unified

Guidance Equation 17-

16 with MCI Grand

mean and MClVar

TL = mean+ rc(n,y,l-a).Stdevro,o,

for untransformed data N

n:zr,

i=l

rc(n,y,l-ø): one sided normal tolerance factor

y i cov erage coefficient

1- ø: confidence level

Page 17-17 of (EPA 2009b)