### This isthe 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 Hgfrom Feed (From Fed RegTable 3) o/oYanance 

### contribution from Limestone 

### of 

### kiln ith. 

### Number istaken 

### from Table 3 Proposed Rule. %Feed¡ Table 

### 3,page 

### of (EPA 2009a)

41 Percent Hgfrom Coal (From Fed RegTable 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 Hgfrom Other (From Fed RegTable 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 .th I 

### t12

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

46 Var Coal Variance 

### from Coal 

### ofkiln ith 

### t12

## * o/oCo

### 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 equalsvariance.

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/oFeed

### = 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 theWithin Group Variance 

### of 

### kiln ith Vo', 1u*on"R€vis€d) +

### V*i çoa

### x*rra¡+Vtri ç,na'¡= trarraut = Vi 1øthi, group¡ Variances areadditive.

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 freedomwithin group 

## : Total number of observations from all kilns - Number of kilns Page351 

### of (Kleinbaum, Kupper et

### al. 1987) Page64 

### of (Roberts and Russo 1999): 

### "totalwithin group 

### variance..., also calledMean 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 

### SSro,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 Autocorrelation64

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 rsdtotal 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 RTIVar (No Autocorrelation. m=1) 

# Xp+O-",rrffi

last equation on section 7

### of 

### RTI doc Section 7

### of (Munoz2010), MCI has been unableto locate this equation 

### in any other literature sources79 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, etal. (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 

### toAnalysis 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
mfufure values 

### ¡/ 

# n:zn, i=l



### ll8.3l Page 

### l8-9 of(EPA 2009b)



# (

# Co^,\t'ut., 

# I

# À")

UTLfrom EPA Unified Guidance Equation 17- 16with 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)