### meet thes e RRA criteria, it is out of control . (i) 

### For all three data points , the PM CEMS response value can be no greater tha n t h e gr e atest PM CEMS response value us ed to develop your corre lation curve. (ii) For two of the three da t a points , the PM CEMS response value must lie within the PM CEMS output range us ed to develop your correlation curve . (iii) At least two of the thr ee sets of PM CEMS and refer ence method m easurements must fall within the same spec i fied area on a graph of the correlation regressio n line as requ ired for t he RCA and described in paragraph (5) (iii) 

### of this section . 10 . 5 What do I do if my PM C E

HS is out of con tro l? If your PM CEMS 

### is out of control , you must take the act ions listed in paragraphs (1) and (2) of this section . (1) You m ust ta k e necessary corrective action to elimi nate the problem and perform tests , as appropriate, to ensure that the corrective action was successful . (i )**Fol l01~i** **ng** 

### corrective action , you must repeat the previously failed audit to confir m t hat your**~ CE** **~S** 

### is operating within the specificat ions . (ii) If your**P~ l**  

### CEMS tailed an RRA , you must take co rrective action until your PM CEMS 

### passes the RRA criteria . If the RRA criteria cannot be achieved, you



## V ES009700

### must perform an RCA . (iii) I f yo u r PM CEMS fai l ed an RCA, you must follow procedures specified in section 10 . 6 of this procedure . ( 2 ) You must re po rt both the aud it sho w i ng your PM CEMS to be out of control and th e results of the audit fol l owing corrective ac t ion show1n9 your PM CEMS to be operat ing wit hin specif i cations . 10 . 6 Wha t do I do if my PM CEMS fail s an RCA? A fter an RCA failure, you must take all app licable actions listed in paragraphs (1) through (3) of this section. (1) Combine RCA data l<ith dat a from the active**P~l** 

### CE M S correlation and perfo rm the mathem atical evaluations defined in PS-11 for development of a PM CEMS correlation, includi ng examination of alternate c orre l at1on models ( i . e . , li near, po l y no mial , logarit hm ic , exponentia l, and po w er} . If the exp anded data base and revised correlation meet PS

- 11 sta t istical criteria, use the revised correla tion. (2} If the crite ri a specifie d in paragraph ( ll of t his section are not ach ieved , you must develop a new PM CEMS correlation based on revised data. The revised data set must consist of the test result s from only the RCA. The new data must me et all requir eme nts of PS

- 11 t o develop a rev i sed PM**CEI~S** 

### correlation , except that t he



### VES009701

### mini mum numbe r of sets of PM CE MS and reference method mebsur e m e nts is 12 

### i ns t ead of t he mi nimum o f 15 

### sets required by PS-11 . Your PM 

## cgMs is considere d to be back i n cont ro l l ed statu s when the re vised cor rel a t ion meet s all of the performan c e cr ite ria specified in s ect ion 13 . 2 

### of PS-1 1 . {3) If t he acti o ns in parag rap hs {1) and (2) of t his secti on d o n ot resu lt in an accep table correla t i on , yo u must ev a luate the c ause(s) and com ply with t he ac ti ons lis ted i n pa ra graphs {3) { i J throu gh (iv) of th is se ction with i n 90 days after the completion o f t he fa ile d R CA. {i) 

### Co m pletely i nspec t your PM CEM S for me c h anical or operational problems . lf you find a mechanical or o perat io na l problem , repa i r your PM CEMS and re peat th e RCA . ( ii ) You may need to re locate your PM CEMS to a m ore app ropriate m easur ement l ocation . If you relocat e yo u r P M CEMS , you must p e rform a new correl ati on test according to the pro ced ures specif ied in P S- 1 1 . (i i i) The chara cter istics of t he P M or ga s in you r sou rce's f l u e gas stream may ha ve changed such that your PM CE MS measu re ment t ec hno lo gy i s no long er app ropriat e . I f t h is is th e cas e, you m use insta l l a P M CE MS w i th measureme nt tec hnol ogy tha t is a pprop riate fo r your



## VES009702

### sou rce's flue gas characteristic s . You must perform a new corre la t i on test according to the procedures specified in PS- 11. ( i v) If 

### t he correcti v e actio ns i n pa ragrap h s ( 3 ) (i ) 

### throug h ( ii i) of this section were not suc cessful , yo u must pe ti t ion us , the State , or lo ca l agency for approval of alternat i ve criteria or an a ltern ative for continuous PM monitoring . 10 . 7 When d oes the ou t- of-control period begin and end? The out-of-control period begi ns im m ediately after the last test run or c heck o f an unsu ccessful RCA , RRA , ACA , SVA, drift check , o r sa mp le v o l ume chec k. T he ou t - of

- con trol period ends imm ed iate l y after the last test run or check of the subsequent successful audi t or drif t chec k. 10 . 8 Can I use the data recorded by my PM CEMS durin g o u t - of

- control per i ods? Duri ng an y period when y o ur PM CEM S is out of co ntrol , you ma y not use your P M GEMS data to calculate e m iss ion co m pl i ance or to meet m

i nim um data a va ila b ility re qui r ements d escribed i n the applic able regulation . 10 . 9 What are the QA/QC reporting requirements for my**~M** 

### CEMS? You must report the accuracy results for your**~M** 

### G EM S , speci fied in section 10 . 4 of this pr ocedure , at



## VE$009703

### the interval specified in th e applicable regu l a t ion. Report the dr ift and accu racy i nforma tio n as a Da ta Assessment Rep or t (DAR), and incl ude one copy of this DAR for each q u art erly a udit wi th t h e rep ort of em is s ions requir e d under the appl ic a bl e reg ulat ion . A n e xample DAR is p rovided in Pr oc e dure 1 , Appendix F of**th~s** 

### pa rt. 10 . 1 0 W hat minimum i nformatio n must I i nc l ude in my DAR? A s a min imum, you mu st inclu de the information list ed in parag rap hs ( 1 ) through (5) of this se c t ion in th e DAR : (1) Your name and address . ( 2 ) I de nti f ic at ion and location o f moni tor s in y our CEMS . ( 3 ) Manufac turer an d mod el nu m b er of ea ch monitor in y our CEMS . (1) Assessment of PM CEMS data accuracy/acceptability, an d date of assessment, as determ i ned by a n RCA , R RA , ACA , or SVA described in sec ti on 10 , i ncluding the acceptability determination f o r the R CA or RRA , th e ac cu racy for the A C

A or SVA , t he refere nce me thod results, t he aud it standa rds, your PM CEM S r es ponses, and the calculation results a s def in ed in section 12 . I f th e ac cura cy audit re s u lt s sho w your PM CEMS to be out of contr o l, you must report bo t h the audit



## VES009704

### results showing your P M CEMS to be 

### ou t of control and the resu l t s of the aud it fo l lowing corre c tive action showi ng your PM CEMS t o be opera tin g within spe cifi cations. (5) Summary of a ll corrective ac tions you t ook when you d etermi ned you r PM CEMS to be out of con trol, as described i n sec tion 10 . 5 , 

### or a fter failing an R C

A, as d es cribed in se ction 10 . 6 . 10.7 

### Where and ho'• long m ust I 

### r etai n the QA 

### data t hat this procedur e requ ires me to re cord for m y PM CEMS? You m ust keep the records required by t h i s proce dure fo r your PM CE MS ons ite and a va i l able for inspectio n by us , the St ate , and/or loca l enfo r cem ent ag ency for a p e r io d of 5 

### years . 11 . 0 Wh at anal yt ical p rocedures apply to this 

### pro cgdt1re? 

### Sample col lectio n and analysis are co ncurrent for this procedur e . You mu st r efer to the appropriate reference met hod for t he sp ecific ana lytical proced ur es . 12 .0 What calculatjons and data ana l ysis must I p erform for mv pM CE;MS? 

### ( 1 ) Hovl do I determine RCA and RRA acceptability? You must plot each of your PM C E

MS and refe rence m eth od data sets from a n RCA or RRA on a grap h base d on your P M C

E

MS correl ation l ine to d etermine i f the crit er ia in paragr a phs 1 0 . 4(5) or (6), respectively , a re met.



## VES009705

### ( 2) Ho w d o 

## r calculate ACA ac curacy? You mu s t u se Equat io n 

### 2

- 1 t o c a lculate ACA accuracy for e a c h of t he three aud it poin ts: ACA 

# !R ca - R v

l Ac curacy= x 

### 100 

### R, 

### (Eq . 2 - 1)



### wh ere : ACA A ccuracy • T he A CA acc uracy a t each audit point , in p ercent , Your PM**CE! ~S**  

### response to the reference standard , an d Th e reference st a ndard va l ue . ( 3) 

### Ho w do I 

### c a lculate daily u p scal e a nd zero dri f t? You mus t calculate the upsca le drift u s ing to Equation 2-2 

### and the zero drift accor ding to Equation 2-3 : 

# I R - R 

# I UD = 0 ' " 0 x 1 00 

### R o 

### (Eq . 2

- 2 )

"'here : UD 

# - The upscal e drift of y o ur P M CEMS , in p e rcen t , You r PM CE M S re sponse to the upscale ch e ck value , and



## V ES009706= 

### The upscale chec k valu e . ( Eq . 2 -3)



### where : ZD = 

### The zero (low-level) drift of your PM CEMS , in percent,**R~** 

### Your PM CEMS response of the zero chec k value , T

h e zero check v a lue , and



# - The upscale check value . (4) How do I ca l culat e SVA accuracy? Y ou mu st use Equat i on 2-4 to calculate the accuracy , in percent, for each of the three SVA tests or th e daily sample volume chec k :**~<here :**  

### (v- v) 

### Accu rac y= " • x 100 FS (E q . 2- 4 )



### Sample gas volume d etermin ed/reported by your PM CEMS (e . g ., dscm} , Sample gas volume measured by the independent calibrated reference device (e.g. , dscm) for the SVA or the reference



## VES009707

### value for the daily sa mple volume check , and FS**~ull-sca le**  

### value . Note : Before calculating SVA ac curacy , you must co r rect the sam ple gas vo l umes measu re d by you r PM**CE~ S**  

### and the independent calibrate d reference device to the same basis o f temperat ure , p ressure, and moisture content . Y

ou must document all data and calculations. 

### 13 . 0 Methqd Performance . (Reserved! 

### 14 . 0 Pqll ption preven tio n . ( Reserved] 15 . 0 

### W ast e Management . (Rese rved] 16 . 0 W hj ch references are 

### rele v ant 

## t o this method? 

### (Reserved ] 17 . 0 What tables. diag rams . flow c harts . and ya lidati qn data are r e l gya nt to t his me jh od? {Reserved)



## V E S009708

# VES009709 . pdf

### Y . O 

### EXAMPLE CALCULATIONS-INITIAL CORRELATION TEST This section presents several exampl es of initial correla tion test calculations. For each of the examples, a brief description of the correlation tes t scenario is 

### pro vi ded , followed by a summary a nd discussion of the results of the calculations . For the fm t example , a ll of the equations used to evaluate the da ta and so me sample ca lcu lation s arc presented. The calcu l ations for a ll of the exumples were pcrfonned using th e Corre l ation 

### Test Ca lcul at i on Spreadsheet, which i s described in Section X. 

### Appendix A includ es the entire spreadsheet o u tput for each of the examples. 

### Y. I EXAMPLE I: HOW DO I DEVELOP AN INITIAL CORRELATION? Y . 1.1 

### Correl ati on Tes t Scenario A correlation te st is performed on a boiler at Facility A . 

### The boiler is e quipped with an in s iru PM CB MS that responds to PM co ncentrations at a crua l condition s. The emission limit, when converted to unit s that 

### are consistent with the PM CEMS sampling conditions, is 20 . 0 

### m gl acm. Twenty-four test 

### runs are performed using a sing le Method 

### 5 sampling train. The facil ity detcnnines that four of the test run s (Runs 

### 7, 8, 9, a nd 

### 18) were s us pect because of problems with the sampling train. Table Y - I 

### summarizes the correlation t es t data. Figure Y-1 sho ws a plot of the data . T ab le Y-1. 

### S u mmary o f Corr elat io n Test Data for F ac ili ty A PM 

### O : MS re spon se. Pl\1 

### conce ntT ation, 

### Ruo no. mA 

### mg/ a cm I 

### 4 . 90 2 . 1 

### 2 7.60 

### 2. 9 3 7 . 80 

### 5. 1 4 9.20 

### 4.8 

# s 10 . 10 

### 2. 9 6 

### 1 1.06 6.3 7 

### 13.40 0 . 2 8 1 6 . 1 0 

### 0 . 6 9 

### 15 . 80 0.3 10 12.00 8.4 (co llfinued) 

### Y-1 

## VES009709Run no.

20 18 E 16 

### X 

## a. 14 E .: 12 0**~** 

### 10 

# t a t! c 

### 6 

# 8 :Iii 

### 4 

## .,_ 2 0 

### 11 

### 1 2 13 1 4 IS 

### 16 17 

### 18 19 20 21 

### 22 23 24



## - -

0 

### T ab le Y-1. (co ntinued) PM**E~f S**  r esponse, PM 

### concen tration, rnA 

### mglacm 1 8.20 8.4 

### 15.70 4 . 9 13.90 6.3 

### 19.70 1 3.0 21.02 9 .1 22.30 13 . 9 24.10 8.7 25 . 90 0.6 24.70 12.6 26 . 40 1 5.9 29.08 16.2 29.30 

### 13 . 5 3 0.50 15. 9 33. 10 18.5



# •

- 

# - -· -- 

# - -- · -- 

# - 

# • • • • 

# • • • • • 

# • 

# • 

# • • • # 

# • 5 10 15 20 

### 25 30 PM CEMS 

### Response , mA 

### Figur e Y -1 . Plot of t be cor r e l ation te s t data for Fa dllty 

### A. Y-2 35



## VES009710

### Mu st I u s e all ofthe te st data to d e velop th e c orre l a tio n ? Section 8.6(3) ofPS -1 1 requires a 

### minimum of 15 valid tes t run s 

### for deve l oping the correlation , and Sec tion 8.6{3 )(i i i) allows you to discard 

### u p to 

### 5**t~t** 

### runs w itho ut exp l anation . Additiona l te s t run s c an 

### be d is carded i f the bas is fo r rej ect ing the 

### runs is speci fi ed i n t he manual test met h od, in PS-1 1, or in the q uali ty assura nce plan t b r th e s o urce. In th is example , an add it i o n a l n i ne te st run s were performed , 

### so it is not necess ary to 

### use a ll of tl1 e te st d a ta . Fiv e of the ru ns can b e d isca rded w i th out ex p lanation . A s i nd i c o ted in Fi gure Y - I, t he results from test Ru n s 7, 8, 9, and 18 ap pear to 

### b e ou tl iers. 

### If the four o utl iers are disc arded , th ere are 20 ru n s remai n i ng, w hich satisfies the minimum requirement of 15 runs for develo p ing the initial corr elation. Note that Sec t ion 8.6(3Xii) of P S- 1 1 stiU req u ires you to 

### report all of the d ata . even fo r those nms tha t 

### a re rejected. 

### How do 

### I de yelop a linear co n · e Jati on curv e 

### fio m the data ? To develo p 

### a linear correlation model , fol l ow th e proced u res de scr i bed i n Sectio n 12 .3(1) of PS

- 11. The form of the linear model is pr ovided in Equation I 1-3 of PS- I I : wher e 

# y = b0 

## + b,x 

## y 

# = t he predict ed PM c once ntratio n 

### b

0 

# = the in tercept for**th~** 

### correlation curve 

### b 1 : 

### the sl ope of the correlation curve 

### x - the P M CEMS 

### response value. T o begin, the mean PM CE M S res p on se 

### (X) a nd 

### mean PM concentra t i o n 

### (y) are c alcu l a te d as follow s: I**~** 

### I 

# x = -**~** 

### x 1 = - 

### 0 ( 4 . 9 + 7.6+ 7.8 + ... . 

### + 33. 1 )**~** 

### 18 53 II t• l 

### 2



### I • I 

## .Y= -Ly, = 2 0 (2.1+ 2.9 + 5 .1 + ....**+185)~** 

### 9 . 47 n r- 1 

### The vari a bles S ., and S, ,.. whi ch are presen ted in E q u ation 

### II · 7 of PS

- 11 , nrc calcu lated next a s fo ll o w s: 

## s M = 

# f (x,

- x)' • (( 4.9- 1 K

S 3) ' 

### + (7.6

- 1 H.S3) 2 

### + ... +(33.1

- 1 H.S3) ') 

### = 1,442.2 

### • • • 

### • 

# s. , .**~** 

# L: ( x1 - 

### x)(y , - 

## y ) = 

### (4 . 9 - 1 8.53){ 2 .1

- 9 .47 ) 

### + (7 . 6 - 1 8.53) ( 2.9- 9.47) + ... 

### + I • I (33. 1

- 18.53)(18.5

- 9.47)= 785.2 

### Y-3 

## V ES009711

### The slope o f t he correlat i o n c u rv e (b , ) is d e termin ed by Equ a t i

on 1 1-6 of PS

- 1 1: b

- 

# s,, = 785.2

- 0.544**~** 1,442.2 

### The intet -ce pt of the corre lutio n curve is det e nnin ed using Equati on 1 1

-4 ofPS

- 11 : 

### b. = 

## y- b , . X. 

### 9 .47

- ( 0.544 X 18.53) 

### = 

### - 0.62 1 The 

### res u lting equation for the correlati on curve i s as 

### follows: 

### f = 

### - 0 . 62 1 

### + 0. 5 44x How do I 

### determjne the 

### ljnear correlation coeffici ent ? 

### The linear correl atio n coefficient (r) is calculated usin g the paramet ers 

### Sc and 

### Sy. The parameter 

### Sc i s defined i n Equation 1 1-9 as follow s : S

L 

### = 

# - ' - f ( ;, -y , )' n - 2 ,.. 1 

### To calculat e 

### S v the line ar correlat ion equa t io n mus t be 

### used 

### to determ i ne the pred i c ted 

### PM concenlnltion (j ) 

### for each test run. For exam ple , for Run 3 , the PM CEM S response is 7. 8 and the 

### predi cted PM concentration is 

## y = 

### - 0 . 621 

### + 0.544(7.8) = 

### 3.626 Table Y - 2 

### shows the 

### resul ts ofthe ca l culations of

## y . Usin g these values , the calculation for 

### Sc is 

### as follows : S

L 

### = - 1

- ((2.04 7 - 2. 1 ) 2 

### + (3.5 17- 2.9) 2 

### + (3 .626- 5.1) 2 

### + ... + ( 17.401

- 1 8.5) ' ) 

# = 1.910 2 0

- 2 

### Table Y - 2 . Predicted Pl\1 C oncen tration s (j ) 

### for Line a r Corr e

lati o n PM CUtS Pl\f c onc utrallo n , 

### P redlcted PM Run no . res p onse, mA m glac m concentratio n 

## If)' I 

### 4.9 2 .1 2.047 2 7 . 6 2 . 9 3 . 517 3 

### 7. 8 5 . 1 3. 626 4 9.2 

### 4.8 4.388 5 10.1 2 . 9 

# I 4.878



### - (con t in u ed) Y-4 

## VES009712

### T able Y - 2. (con tin ue d ) PM C EM S PM oo n cc ntra t km , P red i c ted 

### P M Run n o. r es p o n se, rn A 

### m g/ucm co n centra ti o n (j)' 6 

### I 1. 06 

### 6. 3 5.40 1 10 12 8.4 5.913 I I 

### 18 .2 8.4 

### 9 . 289 1 2 15.7 4.9 7.9 2 8 1 3 1 3 .9 6.3 6.947 14 19 .7 1 3 10 . 105 I S 

### 21.02 9.1 10.824 16 2 2.3 1 3.9 11. 52 1 1 7 24. 1 8.7 12.5 01 1 9 24.7 12.6 12 .828 20 26.4 1 5.9 1 3.753 2 1 29.08 16.2 15 . 2 1 3 22 29.3 1 3.5 1 5 . 332 23 

### 30. 5 1 5.9 1 5 . 986 

### 2

4 33 . 1 18.5 17.4 01 • Calcu lated usi ng the correlation equatio n:**.r ~**  

### ..0.62 I 

### + O . S44.r. 

### Tbe parameter 

### S , i s calculat ed using Equation 1 I-15 of PS

- I 

### J as loll o ws: 

# f (y ,- y)' 

# s = 

### 1 1-"'""''

- - - =



### · " n - l 

### ( 2.1

- 9.47)' 

### + (2. 9- 9.47 )' 

### + ( 5.1

- 9 . 4 7)' + ... 

### +( 185 - 9 . 47 )' 20

- I 

### = 5

· 095 

### With t h

e values for**~,** 

### and S " the correlation coeffi cient i s calculated us ing Equation 1 1

- 1

4 as follows: ·

The correl ation coefficient (0 .927) 

### is 

### greater than 0 .&5 and, ther e f

ore , sati s fies PS

- 1 1. Note: For dam se t s that show l itt le to no correlation, the value for S L can be greater t h a n S, . In 

### suc h cases, the correlat i on coefficient (r) calculated us ing Eq uation I I - I 4 is undefined because it e ot<til s determining the 

### s qu are root of a neg a tive number. Even though the correlation coefficient cannot be determined , it c an be assumed t hat the value f o r r does not meet the c riterion of 0 . 85 spec ified by 

### PS

- 1 1. Y - 5 

### VES009713

### How do I calculate the confidence interval half range percentage for the ljnear correlation? 

### The half range for the 

### 95 percent confidence interva l (CI) for the predic ted PM coocemrntion at tlte 

### mean valu e of x is determined using Equation 11

- 8 ofPS-11: 

### Cl • t 4f.•-·;: · 

### S ,- 

# Jf

The variable t .... ••• 

### is obtained 

### fTOm n table of !

- statistic values. 

### The degrees of freedom (dl) equals n- 2 , and the value for the t 

### statistic for this example is 2 . 10 I. With thi s value and the value fo r 

### S, calculated above, C l is calculated as follows: 

## a= 2.JOI ( L9t)Ho 

### = 0.897 The emission limit io this example is 20.0 mglacm. To d e termine Cl as a percentage of the emission limit, Equation Il-l 0 is used as follows: 

### Cl 0.897 

### CJ% 

### = EL x 

### 100% 

### = 2 0 .0 x 

### 1000/o 

# = 4.49% The resulting value for CI % is 4.49 percent Because this value is less than 10 percent, the correlation satisfies the criter i on fo r confidence i n terval h alf range. How do I calculate tbe tolerance interval half range percentage for the linear C!>rrelation ? Equation 11-11 of PS-11 

### is used to calculated tbe tolerance interval half mngc (Tl) 

### at the mean value ofx: 

### The parameter k 1 

### is determined using Eq uatio n 11-1 2 of PS -11 :

The parameters u,. an d v., are detennined from Table I of PS-I I. In this example, n ' is the number of test runs used for the co rr e l

ation (20), 

### u, . • l. l 77, and v« equals 1 .384 for n-2 degrees of freedom. With these values. k 1 

### and 

## n 3rc 

### calculated as follow s: 

### k T = 

### u 11 , • 

### v df : 1.177( 1.384) = 1.629 

### Tl 

# = k , · S , = 1.629(1.91 ) = 3.111 With a n emission limit of20.0 mg/acm, the toleranc e interval as a percentage of the emis sion limit is determined using Equation 

### J 1-13 as follows: 

### Y-6 

## VES009714

### TT 3.1 1 1 T

l %= 

### -x 1 0 0% = - x 

### 100%= 156% 

### EL 20.0 . The resulting 

### value for Tl% is 15.6 

### pe:rcenL B ecause litis value is less than 25 percent, the correlation satisfies the criterion for to lerance interval half range. In summa ry, the linear c on-el ati on deve l oped trorn the data satisfies all of t he criteria specified in PS- 11 . H ow do I 

### develo p a OOIVI19rnial correlation curve from the 

### data? A 

### polynomial correla t ion curve can 

### be expressed 

### by the fo ll owi n g:

The 

### procedures for deve l oping a polynomia l correlation curve are 

### de scribed in Section 12.3(2) or PS

- 1 1. T h e first s tep i s to de t ermine the val u es 

### for t he parameters 

### S , through S , , 

### a s**defin e~**  

### in Equat i o n s 11 -1 7 a nd 11 -18 of PS

- 11. The.se calcula t io ns are summarized as fo llows: 

## • S, = 

# I;(x , ) = (4.9+ 7 .6 + 7 .8 + ... 

### + 33.1 ),.. 370.7 i= l s l 

# = 

# :f;(x / ) = (4.9 2 

### + 7.67 

### + 7.8 2 

### + ... +33. 1 2 

# ) = 8,312 

# ,., • S, = 

# I;{x /) = (4.9 3 

## + 7.6 3 

### + 7.8 3 

### +.. .+ 33.1 ')= 208,377 

# ,. , " S, a 

# L (x,') = (4 .9' 

### + 7.6 4 

### + 7 .8' 

### + ... 

## +

33.1 4 

## ) + 5,574,977 i.s.l 

### • 

# s

, = 

# I: ( y,) = c2.1 

### + 2.9 

### + 

### s.It ...

## + t 8.5 l = 189 . 4 I• I 

## • S 6 

# = 

# L (x ,y, ) 

# = ((4.9)(2.1 ) 

### + ( 7.6)(2.9) 

### + (7.8)( 5 .l) t ... +(33 .1X l 85)) 

# = 4,295 i =- 1 

# s, = 

# :f: ( x

,' 

# r,) . ((4.9'X2.1 ) 

### + (7 . 6 'X2ol 

### + (7.s ' Xs.I)+ ... 

### + (33.l')( ls.s J) 

## = 1os,s61 

# ,_, Nex t, the parameter d et A must 

### be calculated using Equation I 1-22 ofPS.-11. For this exampl e, the calculation is as 

### follows: dct 

### A = 

### n · 

### S , · S, - S, · S , · S , 

### + S , · 

### S, · S , - S , · S, · n . 

### + 

# s, · S, · S, - S, · S , · S , = 

## (2 ol(s.mXs ,s 74,977)

- (s, 312Xs.312Xs .3 12) + 

## 37o .7(20 s . mXs.312)

- (2o s .mX 2 os.J77)(2o) + (8 ,312X370.7)( 208 .377)- (5,574,977X370 .7 )(370.7) 

### = 2.120x 

## to • T h e v a lues for the correla ti on curve p n r runeters b., b 1 • 

### and b , ca n n ow be dete nn incd us ing Eq ua tions 1 1

- 19 to 11 -2 1 ofPS -1 1: Y - 7 

## VES0097 15

# (s,. s , . s , + 

# s ,. s ,. s , + 

# s ,. s• . s, - 

# s , . s

, . s , - 

# s, . s ,. s ,- 

# s • .s • . s ,) b

o = det A 

# = 2 

### .t 2

# ~ 10• f( l s9J (s,312X s,s74,977)+ ( 37o .7)(2os,mX Jo s,s67) + (zos ,377 X4,29s)(2os ,m)- (tos,s67Xs,mXs .3 12)

- (2oS,377X2os . mXls9)

- (s,s74 ,97 7)(4.295X370 .7)J

= 

### 0. 420

(n · S,·S, t 

### S ,·S,·S, t S 2 

### · S 1 

### · S,

- 

### S, ·S. · S ,- S, · S ,· n - S, ·S, 

### ·S, )**,=~~~ --~** **~~~~ ~~~** **~-- ~~~~**  

### del A

= 

### 2 2 1 o • [ {2o )(

4 , 295X s,s7 4,977) + ( I 89)( 2os,m Xs.J 1 2) + (& ,3 t 2X3 70.7 l (l os , s67)

- .I X 

### I 

### (s, 3t2X4 ,295X8.3 1 2)- (tos,s61X2os ,m) 2oJ

- (s,s74 ,977)37o .7X ts9 l l

= 

### 0 .406 b, 

# = 

# (n · 

# s , · s , + 

# s , · S 6 • 

# s , + 

# s , ·s , ·s , - s , · s , ·

# s , - s , · 

# s •. , - s , . s,. s,) • detA

= I • 

### [{ 20 ) (8,312Xl08.567)+ ( 3 70 .7)(4,295X8,312)+ ( 189){370.7)( 208,377)

- 2.12 X 

### 10 (s,mXs.J12Xts9 )

- (20S.J77X4.295X2o}

- ( 1 os.s67X37o.7 ){37 o.7} J

= 

### 0.00 368 The resulting correlation curve is as fo llows : j = 

### 0. 4 20 

### + 0 .4 06. t 

### + 0.0036&x> How do I determine t he polynomial correlation coefficient? The polynom ial C<lrrelation coefficien t (r) is calculat e d using the paranteters S, and 

# s . . The par dmcter s, i s defined in Eq u atio n 1 1

- 26 as follow s: · 

# I I • ' 

# sp = 

# "n - 3 

# L (Ji , - 

# yJ y , ., 

### To calculates •• the pr edicted PM concent rat ion s must be 

### detennined by s ubstituting the PM CEMS response values int o th e corr elation curve . Fo r example , the predicted PM concentration for Run 10 

### is 

### Y - 8 

## YES009716

# y = 0 . 420 + 0.406( 1 2)+ 0 . 00 3 68(12) 2 

### = 5 .819 Ta bl e Y ·3 sho ws the predicted PM concentra tions for all ofthe 20 test runs used to develop the correlation . Substitute the se v alues into Equation 

### I 1-26 to calculate the value for 

# s.:



# s, = 

### 20

# ~ 3 ((2.497

- 2 .1 ) 2 

### + (3.7 1 7- 2.9f 

### + 

### (3.8 09

- 5.1) 2 

### + ... +( 1 7.88 4- 185)') = 

### 1. 951

Tab le Y - 3. P red i cted P M Conc entration s (9) for Po l yno mial Corr e l

a tion 

### Pllf CEM S PM 

### concentration, P redi cted P M Run no. 

### response , rnA 

### m&f ocm eoncen trolion (!) ' 

### 1 4 .9 2. 1 2 . 497 2 7 . 6 

### 2.9 3.717 3 7.8 S . l 

### 3.809 4 

### 9.2 4 . 8 4.465 5 

### 10 . 1 2.9 4.894 6 11.06 6.3 5 . 358 

### 10 12 8.4 5.81 9 II 

### 18.2 8.4 9.024



### - 12 15 . 7 

### 4 .9 7.698 13 13.9 6.3 6 . 77 1 14 1 9 .7 13 9.842 1 5 

### 21.02 9 . 1 10 .576 16 

### 22 .3 13 . 9 11.299 1 7 24 .1 8.7 12.337 

### 19 24. 7 12.6 12 .6 88 20 26.4 15.9 13.698 21 29.08 16 .2 15 . 33 3 22 

### 29.3 13.5 1 5. 46 9 23 30.5 

### 15.9 16.22 1 24 33 . 1 18 . 5 1 7 . 884 

### • Calculated usmg the correlauon equanon: j • 

### 0.420 

### + 0 . 406x + 

### 0.00368..-' . The parame terS , was determined previously to be 5.095. As shown below, substituting S, and S, into Eq ua tion 1 1-3 3 r es ults 

### in a correla ti on coe fficient of 0 . 9 24 , which satislie s the minimum v alue of0.85 specified 

### by I 'S-1 

### I. 

### I - ( 1. 

### 9 S l )'

- 0.924 ( 5 .o95) ' 

### Y-9 

### VES0097 1 7

### How do 1 ca lcu l ate the 

### confidence i n tezyal half range oorcentage for the nolynomjal correlation? The half range for the 95 

### percent CI for the predicted PM concentration must be determined at the mioim1m1 valu e of the parameter delta (Am ; . ). The 

### expression for calcu lating A is 

### provided in Equatio n 1 1- 25 

### of PS- 1 1:6 = 

## C 0 

### + 2C 1 .t 

### + (2C, 

### + 

## c, )x' + 

## 2C,x' + 

## C. ', x' Before cal c u l ating A , it is first 

### nec es sary to calculat e tb e parameters 

## C. to 

## Cs, whlcb are defined i n Equation 1 1-23 

### ofPS

- 11 

### as f ollows: 

# (S2 

# ·S , - S , ') Co = 

### D 

### C, = 

# (s, · S 2 - 

# S , · S,) D 

## c, = 

# s, . s , - s ,>

- D 

# (ns, - 

# S / ) 

# c, = 

### D 

# (s ,. s ,- ns , ) C, = 

### D 

# (ns ,- 

# s , ' ) 

# c

, = 

### D 

### The v ariable Din the 

### denominator of these expres s ion s is determined u s ing Equation 11

- 24. 

### For this example , this calculation 

### is as follows: D= 

# n(s, ·S,- 

# s, ' ) + s , (s , · S , - 

# S ,· S,) + 

# s,(s, . s , - s ,' )

=

## 2~ (s,312X5,574,977)

- (208,377)') 

### + 370.7( (208,377)(8,312)

- (370.7)( 5.574,577) ) 

### + 8,3 t 2((37o . 7X208,377)

- (8 , 312) ' ) 

# =2.120 x 

### 10• 

### Substituting the values fo r D and for the variables S 1 

### to S, , whlch were 

### defoned previous ly, y ou find 

### the following coefficients for determining 

### A : ((s,m Xs,s 7 4,977)

- (20 8 , 377Y) _ 

### Co 2 .1 

### 2 x l0 • -1 375

Y-10 

## VES009718

### ((zos. m Xs,3r2)

- (370 . 7)(s.s7 4,9 77)) 

# c

, • 2 2 0 • 

# =- 0.1578 .I 

### xl ((310.7)(208,377)- (8,312)') 

### C2 

# = 2 .1 

### 2 x 

### 10• = o.003846 ( (2 o)(s,s74 , 977)

- (s.mY) C, : 

### 2. l 2 X J0 9 - 

### 0 . 02001 (( 370.7)(8,3 1 2)

- (20}{208,377)) C,= 2 .1 

### 2 

# x r o• = - 0.0005126 ((20)(8 ,3 1 2)

- (370.7)')

- s 

### C, 

# = 9 

### 1360x 10 2J2 X 

### 10 

### When these va lue s are substitut ed , Equa t ion l l

-25 

### becomes the following: A = 

### 1.375 + 2(

- 0.1578 ).<+ ((2)( 

### 0 .

003846) 

### + 0.02001)x' 

### + 2(

- 0.0005 1 26)x' 

### + 1 .36 x 

### W ' 

### x' = 

### 1.3 

### 75

- 03155.<+ 0.0277 

## x ' - 0.00 I025x 3 

### + 136 x 

### I 

# o -s .< 4 

### Table Y-4 su m m

ari zes the res u l ts wb en the PM CEMS res po nse 

### values fo r each test mn are s ub stitut ed i nto the above equa ti on. Tabl e Y-4. V alues for 6. Run 

### P MCEMS P M c oo c ent ral io n , 

### no. res poJUe, mA 

### m gl acm 

# r x> x ' 6. I 

### 4.9 2.1 24.01 118 

### 576 0.3817 2 

### 7.6 2.9 57.76 439 3,336 0. 1 72 7 3 7.8 5 .1 60.84 475 3,702 0.1634 4 9.2 4 .8 84 . 64 779 7, 164 0 . 1162 5 

### 1 0.1 2.9 102 . 01 1,0 30 10,406 0.0995 6 

### 11.06 6.3 122.32 1 , 353 1 4,963 0.0906 10 1 2 . 0 8 .4 144.00 1, 728 2 0,736 0 .0884 II 

### 18 .2 8.4 

### 331.24 6 , 029 109 .720 0.1202 12 1 5.7 4.9 246 . 4 9 3,8 7 0 60, 757 0.1084 13 13.9 6.3 193.21 2,686 37,330 0.0960 14 19.7 13 . 0 388.09 7,645 150,6 1 4 0 .1204 15 

### 21.02 9 . 1 441.84 9 , 287 195,223 0.1162 16 22 . 3 13 .9 497.29 11,090 

### 247,29 7 0.1092 (continued)



### Y-1 1 

## VES009719

### T a b le Y-4. (continu ed) 

### R a. n P l\lCEM S PM cooctntr.ltion, 

### no. response, mA 

### mgl ac m 

## x ' 

## x> x' 4 17 24.1 

### 8.7 580. 81 13 ,9 98 337 ,340 0 . 0985 19 24. 7 12.6 610,09 1 5 ,069 372,21 0 

### 0 . 0959



# - - 20 26.4 1 5.9 696.96 18 , 400 48 5,753 0.0960 2 1 29. 08 16 .2 845.65 24,591 7 15,118 0. 1 417 22 29.3 13.5 858.49 25 , 154 737,005 0 . 1492 23 

### 30 .5 15 .9 930 . 25 28 ,373 865,365 0 . 2046 24 

### 33.1 18.5 1 , 09 5. 61 36,265 I 200,36 1 0.4 3 12 

### The minimum value for 

### 11 is 0.0884 and corresponds to Run 

### I 0. Using I 

### his value for 

### 11 ... " the value l b r 

### S, ca l cul ated previously , and th e 1 

### statisti c with 

### n-3 degrees of freedom, you can calculale the confidence in terval half range us ing Equation 11

- 27. 

# ct = , ., . 

# s ,.Jt. ... = (2. 11 X

### 19SI**)~ o.o884**  = 

### 1. 223 

### The confidence interval ha l f range 

### as a percentage 

### of the emission limi1 i s calculated u sing Equation 

### I I- 28 as follows : 

### CI 1 . • 22 4 

### Cl% 

### = - x 

### 100" /o 

# = - -x 

### 100"/o 

# = 612% 

### EL 

### 20 . T h e rcs ulling value for 

### Cl% is 6.12 percent Because this value is 

### l ess than 

### I0 percenl, 

### the correlalion s atisfies the c rilcrion for confidence i nlerval h a l f range. Ho w do I deteonine the tol erance interval half 

### range percentage for 

### the oolynomial correl ation ? To calculate the tolerance interval halfrange , tbe parameter n ' 

### mUSt 

### be calculated using Equation 

### I I -31 of PS- II . 

### I I n' ; 

## --= - -= 11.31 

### "' ""' 0.0884 With n ' rounded to the nearest inleger (II), the va lue s for the variables 

## u,. . and v« with 

### n-3 degree s of freedom are taken from Table I ofPS-1 1 

### and substitute d into Equation 11 -3 0 to determine kr: 

### k,=**.- ·v~r**  = 

### (1.195)(1.400) = 1. 673 Using this value for k r and the value fo r 

### S , calculated previously , the tolerance interval half range is calculated using Equation 11-29 

### as follows: Y - 1 2 

## VES009720

### TI= k r ·S , • 

### ( 1 .6 73 )( 1. 951)= 3.263 F

inally, to dete rmine t he tolerance imerval a s a percentage ofthe emi ss ion limit (TI %), Equation I I - 32 i s us ed a s foUows : T

l 

### 3.263 

### TI% 

# = - X 

### I000 /o 

# = - - X 

### I 000 /o 

# =I 

### 6.3 % 

### EL 2 0 . 0 The resultin g valu e for TI % is 1 6.3 percent Bec ause thi s value is les s th an 2 5 percen t, the c01relatio n sati s fi e s tile criterion for tolerance iJnerval half range . In summary , Ote polynomia l correlation developed ltom the data satisfies all of the criteria specified in PS

- 11 . How do I de velop a log ari thmic correlation c urv e from the data? A logarithmi c correl ati on c urve i s expre ssed as fo llow s : 

## y = b 

### 0 

### + b 

### 1 /11 ( x) 

# = b 0 

### + b , x ' 

### Developing a l ogarithmi c correlation entails following the same procedure s us ed to develop a linear correlation . However, instead of using the PM CEMS respon se (x) values , the natural logari t hm ofOte 

### PM CEMS values (x ' values) ar e us ed in the ca lculation s. Table Y-5 summarize s the tes t d a ta, including the correspon ding valu es ofx' . Tabl e Y-S. D ata for D evelop i n g Loga ri thmJc Correlatlon 

### Loga rithm of PM PM CEMS 

### CO t S r '"'ponse PM ooncentrallon, 

### Run no. response, rnA s' • In (x) 

### mg/a cm l 4 .9 

### 1. 589 2 . 1 2 

### 7.6 2 .0 2 8 

### 2. 9 

### 3 7 . 8 2 . 05 4 5 . 1 4 9 . 2 2 . 2 19 4 . 8 5 

### 10.1 2 . 3 1 3 2. 9 

### 6 11.06 2. 4 03 

### 6. 3 l O 

### 1 2 

### 2.48 5 8.4 ll 

### 1 8. 2 2 . 90 1 8 . 4 12 15.7 2 . 754 4 . 9 13 

### 13.9 2. 632 6 .3 1 4 

### 19.7 2. 98 1 1 3 15 2 1.02 3 . 04 5 9 . 1 (co lllilrued)



### Y - 1 3 

## VES00972 1

### Tab le 

### Y-5. (co n tinu ed ) Logaritbm o f PM PM C EM S CE M S r esp on se P M tonc cntntion , Run no. res p o n se, mA x' • In (x) mg/a c nt 

### 16 22 .3 3 . 105 1 3.9 17 24 . 1 3.182 

### 8 . 7 19 24. 7 3.207 12. 6 

### 20 26.4 

### 3 . 273 1 5.9 21 

### 29.08 3.37 0 1 6.2 

### 22 29.3 3.378 1 3.S 23 

### 30.S 3.418 15 . 9 24 

### 33 . 1 3.500 18 . 5 

### Following the sa me proc edure s described previously for develop i ng a li near corre l a tion c u rve, yo u ca n calcu late values for the parameters 

## x' and 

## y, usi n g Equation 1 1 -5 ; 

### S ,.,. a nd S ,.Y , usi ng Equ ati on I J - 7; b 1, 

### using Equation 1 1-6; 

### aod b 0 , 

### us ing Equat i o n 1 1 -4 : 

### I 

## x' 

# = 20 ( L5 8 9 + 2 . 028 + 2 . 0 5 4 + ... + 3.500) = 

### 2.79 

### I 

## y = 2 0 ( 2 .1 

### + 29 .. 5.1 + ... + 18.5) " 9. 4 7 

# s

•.•. = 

### ( L589

- 2.79) 2 

### + (2.02 8

- 2 .7 9) 2 

### + (2 . 054

- 2 . 79) ' 

### + ... +( 3.50

- 2.79) 2 • 

### 5.7 4 

# s

...... = 

### (1 .5 89- 2 . 79)(2 .1

- 9.47) 

### + ( 2.028

- 2.79)(2. 9 - 9.47 )+ ... 

### + ( 3.50

- 2.79 )( 18.5

- 9 . 4 7) = 

### 4 7 .8 47.8 b, 

# = 5 .74 = 

### 8.323 b . " 

### 9 . 47

- ( 8 . 32 3)(2.79) 

# =- 13.77 The resulting eq uat i o n for the 

### lo ga rithmi c correlation curve is 

## y • - 13.8 + 8.32· ltr(x ) H ow do I determine the l ogarit hm ic correlat i on coefficien t? Determining the logarithmic correlation coefficient requ ires calculating th e predicted PM concentration (Y) 

### for each test ron , the param ete r St, and the parameters , following the same p rocedure used 10 calculate the linear correlation coefficient. The only difference is th at the predicted PM co ncentra tions are calculated using the logarithmic correlation equation. Table Y-6 

### shows the PM concentrations calculated using the logarithmic correlation coefficient .

Y-14 

## V E S009722

### Table Y-6 . 

### Pr edicted PM 

### Concen tnt i on s for t be 

### Logarithmi c C orrel ation Log arithm or I' M PM CEMS CEMS r es p onse PM co nceolrlltio n, Predlctc d PM Run no. 

### r esjH)n . sc , rnA x ' = In (x) mg/acm concentra tion (j)' I 

### 4 .9 1.589 2.1 

### -0.539 2 7.6 2.028 2.9 3 .114 3 7 .8 2.054 5.1 

### 3 . 330 4 9.2 2 . 219 4.8 4.704 5 

### 10 . 1 2.313 

### 2.9 5 .481 6 11.06 2 .403 6 .3 6.237 10 12 2.485 8 . 4 li . 916 11 

### 18 .2 2.901 8 . 4 10 .3 82 12 15 .7 2.754 4 . 9 9 . 152



## - 13 13 .9 2.632 6.3 8. 139 14 19.7 2.981 13 11.041 

### 1 5 2 1. 02 3 . 045 9.1 11. 581 1 6 22.3 3.10 5 13.9 12 . 073 17 24.1 3. 1 82 8.7 1 2.719 19 24.7 3.207 1 2.6 12 .9 24 20 26.4 3.273 15 . 9 13.478 21 29.0 8 3 .370 16 .2 14 . 283 22 

### 29.3 3.3 7 8 13.5 1 4.345 

### 23 30.5 3.4 1 8 15 . 9 14.679 24 33. 1 3.500 18.5 1 5.360 ' Cnlculatcd using the lo gar ithmic corre l ati on equation: j= 

### - 13.8 

### + 8.32 · /n( x ). 

### With the values f o r 

## y shown 

### in Table 

### Y

### -6 , the calc ulation for 

### S, is as 

### follow s: 

### S L : ( 

### 20

# ~ 2) 

# (< - 0539

- 2.1 ) 2 

### + 

### (3 .114

- 2.9) 2 t.. 

### .t ( J5.J6

- 

### 185) 1 ) ; 

### 2.305 

### The value for 

# s , is tbe 

### same as was 

### calculated fo r the linea r corre l ation (5.095). 

### Substituting the values for S, and S, 

### into Equation ll

- 14, the 

### lo garithmic correlation coem c ient is

r 

### = 

### 1

- ( 2 .30S) ' = 

### 0.892 (5.095)' 

### The logarithm ic correla tion 

### coefficient 

### (0.892) is greater 

### than the minimum value 

### specifi ed by 

### PS -1 1 ( 0 . 85) and is acceptable. Y-15 

### VES009723

### How do I determine the confiden ce interval ha l fmnge oerceutage for the logarithmic correlation? The confidence interval half range for the logarithmic correlation is detcnnined using the same procedures used for the linear corre lation . Sub stitu t ing the value for S L calculated above (2.305) and t h e sa m e 

### valu e for the / -sta ti st ic (2.1 01) 

### used for the li ne ar correl ation, Equation**It-~** 

### yie l ds 

### CJ = 

### (2 .l01 )(2J05) , {fa 

# = 1.083 The emission limit in thi s example is 20 .0 mg/ncm . To determine Cl 

### as a percentage of the emission limit, Equation 11-10 is 

### used as follows: 1. 083 

# Tox 1 00"/o 

# = 5.41% The resulting value for C!% is 5.41 percent . Because this value is 

### less than 10 percent, the correlation satisfie s the criterion for co n fidence interva l half range. How do I 

### determ i ne the 10 l ergnce interval half range oecceorage for t h

e logarithmic correl ation? The tolerance interval halfrange for the logari thmic correlation i s dete rmined using the same procedures used fo r the linear correlation. Substituting the value for 

# s .. calculated above (2 . 305) and the 

### same value for the k T



### used for the linear correlation ( 1.629), Equation 11 -1 1 yields 

### TI = 

### (L629)(2.305) = 

### 3.75 The emissio n limit in this exumple is 20.0 mglucm. To d etermine Tl as u 

### percentage o f the emission limit, Equation 1 1- 13 is used as follow s: 3.75

-- x 

### 100 % • 18.8 % 20 .0 The resulting value for Tl% is 18.8 percent . Because this va lue i s l ess than 25 percent, the correlation satisfies t11e 

### c ri te ri on fo r confidence interval half 

### range. How do I 

### develo p 

# an exoonep)jal correlation curve from )he d ata? An exponential correlation curve is expressed as foUows:

To d eve lop a. n exponenti al con-elation curve, fo llow the same procedure s used to deve l op 

### a linear correlation curve. However, ins tead of u si n g the 

### PM CEMS concentrations (y) 

### values, use Y-16 

## VES009724

### t h e natu ral log arithm of the PM CEMS co n centrati o ns (y' value s) to perf o rm th e calcu l a t ions. T a bl e Y-7 summarizes the t es t data, incl udi ng the c orrespondi n g va lu e s ofy'. Tabl e Y - 7. Tran sfor med Daw f or D eve lopi ng Expo nentlal Cor r e

l ati o n Loga rit hm o fl ' M 

### PM C EM S P M concentrati on, C EM S r esponse Run no. r espo n se , rn A mg/acm 

### v ' =In (y) I 4 .9 2 . 1 0 . 74 2 2 7.6 2. 9 1.065



## -- 

# - 3 7.8 5. 1 1.629 4 9 . 2 4 .8 1. 569 5 10 . 1 2.9 1. 065 6 1 1.06 6 .3 1. 84 1 10 12 8 .4 2. 128 I I 1 8.2 8 .4 2. 12 8 

# -· .. 12 15.7 4.9 1.589 13 13.9 6 . 3 1.841 14 19 .7 13 2.56 5 15 2 1. 02 9.1 2 . 208 16 22.3 13 . 9 2.632 17 2 4 .1 8.7 2. 163 19 24.7 12 . 6 2.53 4 20 

### 26 . 4 15 .9 2 .7 6 6 21 29 . 08 1 6.2 

### ' 2 .785 2 2 29 . 3 13 .5 2 .603 23 30.5 15 . 9 2.766 

### 24 33.1 1 8 .5 2.9 1 8 

### Following the same procedures de sc ribed previousl y for d evelop ing a linear correlatio n curve , cal c ulate val ues for the parameters lt 

### and y' , using Equatio n 11-5; 

### S ,.. and S,-, using Equatio n 11- 7; 

### b 1 ', 

### using Equation 11

- 6; 

### nod**b~',** 

### using Eq uation 11-4 : 

## x = ; 0 (4 .947.6+7.8 + .. .+ 3 3 .1) : 1 8.53 I 

## Y' 

# =20 ( 0. 7 42 

### + 1.065 + 1. 629 + ...+2 . 9 18) 

### = 2.077 

## s u 

# = (( 4 . 9 - 1 8 .5 3) ' + (7.6

- 1 8.53) 2 + ... + {33.1

- 1 853 ) ' ) = 1 , 44 22 

# s , .. = 

### ( ( 49- 18 53)(0 . 742

- 2.077) + (7 . 6 - 1 8 .5 3)(1. 065

- 2.077) + ... + ( 33.1

- 1 8 5 3)( 2. 9 1 8

- 2.077) ) " 96 .5 8

Y-17 

## VES009725

### 96.58 b , = 

### 1 4 42.2 = 

### 0.067 0 

## b



## 0 = 

## 2.on- 

## <o.o67o)(Js.s3l 

# = o.s3s7 T he resulting equation is expressed in the following form:

For thi s examp l e, the correla tio n equ a t io n becomes 

## y ' 

# = 0.836 + 0.067 0 x Con verting thi s to the fonoat that yields the pred icted 

### PM concen tra tion i n 

### t he correct units entails ta k ing the exponential of

### each side of the equation , 

### as follows: 

# E.rp{y · ) = &p(O.S357 + 0.0670x) 

# y = 

### 2.3le0 . 0670x In t h e r es u lti ng corre l ation eq uat ion , the cocfficient2.31 

### i s sim ply th e exp o ne ntial o fb

## 0 . Ho w d o 

### I d ete nujnc 

### the exno n ential correl atio n coefficient? Determining the exponential corre lation coefficient requires calculating the predicted 

### PM concentration ()' ') for each test run, the parameter 

### S.., and the parameter 

## s ,.. following the same procedure used to calculate the l inea r correlation coefficient. Table 

### Y-8 s hows the 

### PM concen t rations ca l culated using the l inear form (i.e., 

# r = 

### bo. 

### + b ,'x) ofthe exponent i al correl ation equat i on. Ta ble Y -8 . Pr ed i c ted PM Conce n Crati o n s Us in g E x p o nenti a l C orre l ati o n Equation Logarithm of 

### PM PM C EM S**mpo~** Pl\t r ontenfnltlon, CEMS resp o n se Pr e di cted P M R un n o . 

### ntA m gl orm y' =In (y) <o ncen tration (y')" I 4 .9 2 .1 0.742 1.164 2 7.6 

### 2.9 1.065 1 .345 3 7.8 5. 1 1.629 1.358 4 9 . 2 4.8 1.569 1.452 

### 5 10.1 2.9 1.065 1.51 2 6 11.06 

### 6.3 1. 84 1 1.576 1 0 12 

### 8.4 2. 1 28 1. 639



### . 

### - 1 I 18.2 8.4 2. 1 28 2.055 12 15.7 

### 4 .9 1.589 1.887 (co ntmued) 

### Y-18 

## VES009726

### Tab le Y - 8. (c onti nued ) LogarUtlm ofl'M PM C EM S response, P M eonce nt ratlon, CEMS response P re d icted P l\1 

### Run no. mA 

### m wac m y• • In (y) 

### concen tration 

# cr>· 13 

### 13.9 6 .3 1. 84 1 1.767 1 4 19 . 7 13 2.565 2.155 15 21.02 9 . 1 2 . 208 2.243 16 22 . 3 13 . 9 2.632 2 .329 1 7 24. 1 

### 8.7 2.163 2.4 50 19 2 4 .7 1 2. 6 2.534 2.490 20 26.4 1 5.9 2.766 2.604 21 29.08 16.2 2.785 2. 783 22 

### 29 .3 13.5 2.603 

### 2.798 23 30.5 15 .9 2.766 2.R1R 

### 24 33.1 18 .5 2.9 18 3.052 • Calcula ted 

### u smg the 

### exponenhal correla tron equa t1 0<1: j'**~** 

### 0 . 836 + 0.06 7x. 

### Usi ng the vulucs for 

## 9' s hown in Table Y-8. 

### calcu lat e SL 

### as fo llo w s : S L - 

### (20

# ~ 2) 

### (( 1.164

- 0.742 ) 2 

### + ( 1345- 1.065) 1 t . ..

### +( 3.05 2

- 2.918)') = 0218 

### The value for 

## S,.. is detennined using Equation 11- 15 

### with the values for y ' 

### s ubstituted for the v a lues of y, as follow s: (( 0.742- 2.077) 2 

### + ( 1.065

- 2 .077) 2 

### +...+(2 . 91 8

- 2.077 ) 2 ) 

## s

y



# = (20

- 

### 1) 

# = 0.643 

### S u bstitute the va lues for SL 

### and S Y

. 

### into Equation 11

- 1 4 

### t o calcu l ate the expone ntial corre l atio n coefficien t : 

### (0278) 2 

### I - ( )' = 

### 0 . 902 0.643 r = 

### The exponential con · e lat io n coeffici ent (0.902) 

### i s greater than t h e minimum value spec ified by 

### PS-11 (0.85) a nd is acceptable . How do I d etenn ine t he confidence interva l half ra nge percentage for the ex po neo t jal correlation? The confidence interval halfrang e for the exponentia l correlation is detennined using Equation 11

- 8 , whic h is the same equa ti on used to 

### calcula te the confidence in terval balfrang e Y

- 19 

# ·-

VE$009727

### for linear correlations. Because the confidence interval balf range is calculated on the log scale, it is designated asC I' for the exponential model. Using Equation 11-8, Cl ' 

### is calculated as fo llows: Cf ': 

### t ,lf./ · •

/ > ' s L {f D 

### (2 .I OJ){0 .2 78)Ho = 

### O.JJ07 The lower confidence limit (LCL') and upper confidence li mit (UCL ' ) arc cal c ul ated using Equations 1 1-40 a u d 11-4 1, respective l y' LCL ' 

# =5'' - C l ' 

# = 2.077 • 0. 1 307 

# = 1 . 946 UCL ' 

# = 9' + Cl' 

## = 2.077 

### + 0.1307 = 

### 2.207 Next, the confidence interval half range (C I ) must be 

### calculated on the original PM concentration scale using Equation 11-42 !Tom PS-11 (e <ICL' _ eLCL') 

### (e '·20' _ e'5>6) 

### CI 

### = 

### 2 = 

### 2 "' 1.045 The confidence interval as a percentage of the emiss ion limit is calculated using Equation Il

- l 0 as follows: 1.045 

### CI% 

### =-- X 1 000/o = 

### 5.23% 20 The resulting value for Cl% is 5.23 percent. Because this 

### value i s less tha n 10 percent, the correlation satisfies the criterion for confidence interval halfrange. I low do I detennioe the tolerance interval balfrapge percenta ge for the exnonep(jal correlation? The tolerance i nterval balfrange for the expo n ential correlation also i s ca l cu l ated us ing the same procedure as is used for linear model s. Because it is ca l culated on the l og sca l e, it is denoted here as Tl' . Using Equat ion 11-11 , Tl' 

### is calcu lated as fo llows : Tl' = k 1 • 

### SL 

# = ( I .629)(0.278) = 

### 0.453 The l ower tolerance limit ( LTL') and upper to leran ce limi t (UTL ') are ca l cula ted us i ng Equationsl l-4 3 a n d ll-44, respectively L

TL ' • 

### 'J ' - Tl ' 

## = 2.077 • 0.453 

# = 1.624 UTL '- "/' 

### + Tl' - 

### 2.077 

### + 0.453 

# = 2.530

1 Tbe equations presented i n thi.s section for exponential and power models correspood to lbc amended version of PS .. I t, w h

ich wns n ot yet publisbed ot the tune this was prepared. 

### Y-20 

## VES009728

### Next, the tolerance inteJVal half range (TI) 

### must be calculated on the original PM concentration s cale using Equation I 1 -45 from PS- I I

The t o l

erance interval a s a percentage of the e mission limit is calcu l ated usi ng Equation II - I 3 as follows: 3 . 74 Tl %= --x 

### J OO%= 18.7% 

### 20 The re s ulting value for 

### TJ % i s 18 .7 percent. Because this value is less than 25 percent, the correlation satisfies the criterion for confidence interval half range. In 

### summary, the exponential model satisfies the PS-11 cri t eria for correla t ion coefficient, ronfidence interval halfrdoge percentage , and 

### t olerance inte"• al ha lf rang e percentage. How do I develo p a cowe r correlation curve from the data"! A power correlation curve has the following form: Developing a power correlation req uires tran s forming both the 

### PM CEMS respo nse (x) values, as described previously for a l ogarithmic correlation, and the 

### PM concen t ration ( y) val ues , as was described above for an exponenti a l corre l ation. The procedures used to dev e lop a linear correlation are then followed using the tran s fonned values fo r x and y. Tab le Y -9 shows the test data and transformed v alues that mu st be used .

Run no . I 

### 2 3 

### 4 5 

### I 6 10 J1 

### T able Y-9. S ummary of Test D ata and T ransformed Va lu es fo r Develo p ing P ower Co rrelation

L

ogarilllm of PM Logarithm of PM PM C E MS 

### r espon¥e, CEM S re sp on se PM conc entration, CE M S 

### respo nse D

I A 

### x' • In (x) 

### milia em Y ' • In 

## cY) 4.9 

### 1.589 2.1 0.7 4 2 7.6 2 . 028 

### ' 2 . 9 1.065 

### ' 7 . 8 2 . 054 5.1 1.629 

### 92 2.21 9 

### 4 . 8 l.S69 10. 1 2.313 2 . 9 1.06 5 1 1.06 2. 40 3 6 . 3 1.841 12 

## I 2 .485 

### 8.4 2. 1 28 

### 1 8.2 

## I 2 . 901 8 . 4 2. 1 28 (co ntinued ) Y -21 

## VES009729

### Table Y-9. (continued) Logarit h m or PM Logarithm or PM PM C EM S response , C EM S respon se PM concent r ation, CEM S mponse R un no- mA 

### x' • I n {x) m l!facm y' • Ln (y) 

### 12 15. 7 2.754 4.9 1. 58 9 13 

### 13.9 2.632 6.3 

### 1.84 1 14 

### 1 9 .7 2.981 13 

### 2.565 1 5 2 1.02 3.045 9 . 1 2.208 1 6 22 .3 3. 1 05 13 .9 2.632 1 7 24 . 1 3. 18 2 8 . 7 2.163 19 

### ' 24. 7 

### 3 . 207 12.6 2.53 4 20 26.4 

### 3 . 273 15.9 2.766 21 

### 29.08 3 .370 16.2 

### 2.785 22 29.3 

### 3.378 13.5 2 . 603 23 

### 30.5 3 .41 8 1 5.9 2 . 766 

### 2

4 33.1 3.500 18.5 2.9 1 8 

### Following the same procedur es d e scr ibed prev iously for developing a linear corre lat io n curve, calculate values for the paramet ers l<' 

### and y ' , using Eq uation 1 1 -5; 

### S, ., . and S , y, 

### using Eq u ation 11

- 7; b 1 

### ',using Equation l l

- 6 ; and b u', using Equation ll-4: I 

### X' 

### = 20 ( 1 589 t 

### 2. 0 2R t 

### 2.054 + ...

### +35) = 2.7 92 I 

## Y' 

# = 20 ( 0.742+ 1.065 + 1.629 +... + 2.918)= 2 . 077 

# s

, ... = ((1589

- 2.792 ) 2 

### + (2.028- 2.792)'+ ... +(350- 2.792 ) ')= 5. 74 S ,y = ( 1.588

- 2.792)(0 . 742- 2.077) + ( 2.028- 2 . 792)(1.065

- 2 . 077 )+ ... 

### + (35 0

- 2 .792)(2 .918

- 2.077 ) = 

### 6.22 6.22 

### b, = 5. 74 = 

### 1.0839**b~** = 

### 2.077- ( 1. 0839)( 2.792) . - 0.9492 

### The r e sulting equation is expressed i n the following fonn :

For this example , lhe correla tion equat i on becomes 

## y' 

# = -0.9 4 92 

### + 1.084x ' 

### Converting this to ihe format th at yield s t he predic te d PM concentrati on in the correct units en tail s taking the exponent ial of each side of t he e qu at ion, as foll ows: Y-22 

## VES009730

### Ex p(f) 

# = E.xp(

-0 . 9492 

### + !.084 x' ) 

### j • 0.387 x 1

· "" 

### In thls equation, the coefticient 0. 3 87 i s the exponential of -0.9492 , the value for b 0 ' . 

### How d o 

### I d eterm ine the po wer corr e l at ion coefficienfl To detem1ine t he po wer correlat i on coe ffici e nt , the p r edicted PM concentrat i on 

### (f) mu s t be c alcul ated for each test run . Table 

### Y - I 0 s ho w s the predicted 

### PM concentration s c al c ulated using 

### tbe linear form 

### ( i.e ., 

## y = 

### b0 • 

### + b 1 

### 'x ') o f 

### the p o we r corre l atio n equation . 

### Tabl e Y- 10 . Pr edi cted 

### PM Co n c e.ntmtio n s 

### Using the P ower Correl ation Equation Logarithm 

### of P M P M 

### Loga . ritbm of 

### PM P MCE M S 

### CEM S 

### res pon se concentration, 

### C E. M S respon se P r e dlct•'ll PM Run 

### no . n!$poose, mA x• • In (x) 

### m gl ac m y' • In (y) concentration 

### (Y 1 )• I 

### 4.9 1. 5 89 2.1 0 . 742 0 .773 2 7.6 

### 2. 028 2 . 9 

### \ 1.065 1.249 3 7. 8 2 .054 5. 1 1. 629 1.277 4 9.2 2 . 219 4 . 8 1.569 1. 4 5 6



## . 

# s 10 . 1 2 . 3 13 

### 2 . 9 1. 06 5 1.5 57 6 11.06 2 . 40 3 

### 63 1.84 1 1.65 6 10 1 2 2.4 8 5 8.4 2. 12 8 1. 744 11 

### 18.2 2 . 901 8 .4 2.1 28 2.196 12 15.7 2 . 75 4 

### 4 .9 1.589 2 . 035 1 3 13. 9 2.632 6 .3 

### 1.841 1.903 1 4 19. 7 2.98 1 13 2.565 2.281 15 21.02 3 .04 5 9.1 2. 208 2.352 1 6 22 . 3 3. 10 5 1 3.9 I 

### 2. 63 2 2 . 4 1 6 17 24 . 1 3 . 182 8. 7 2 . 163 2 . 500 19 2 4. 7 3.207 1 2 . 6 2.534 2.52 7 2

0 26 .4 3 . 273 15.9 2 . 766 2.5 99 2 1 29.08 3.37 0 16.2 2 . 785 2 . 7 04 22 29.3 3 . 37R 13 . 5 2. 603 2. 71 2 23 30. 5 3.41 8 15.9 2 .76 6 2.755 24 

### 33 . 1 3 .5 00 18.5 2 . 918 2. 844 • Calcul at ed usmg th e expo n entaa1 c o rrel a tion eq u atton : 

### f' = 

### - 0.9492 

### + 1. 0 84x '



### Y -2 3 

## VES009 7 31

### The para meters. is calc ul a ted using Equ ation 1 1-9 with the predic ted values 

### (9') given in the above table, and th e parameters, . is calcula ted lbllowing the sa me procedure used for the exponentia l correlation coefficient, as follow s: 

# s, =

# (20~ 2) ((0.773- 0.742 ) 2 

### + ( 1.249- 1.065 ) 2 

### +.. .+ ( 2.844- 2.918) 2 ) 

# = 0249 ((0.742

- 2.077) 2 

### + ( 1.065- 2.077)' .f- ... 

### + (2.9 18

- 2.077) 2 ) 

# s,. . = 20

- l 2 

### 0.643 Subs titu ting the values for S L and Sy. into E quation 11-1 4, the power correlation coefficient is (02 49 ) 2 r 

### = I - ( )' 

### = 0.922 0.643 T he corre l ation coefficie nt for the power model (0.922) is greater t han the minimum va l ue specified 

### by PS-I I (0.85) an d is acceptable. How do I dctennine lhe contjdence interva l half range oercentage for the nower correla tion ? The confidence i nterval half range for the power correlatio n is detennined using the same procedure s used fo r the exponentia l correlation . Because the confidence int erva l half range is calculated on the lo g sca le , it is designated as C I ' for the exponential modeL Us ing Equation 11-l! , CJ' is calculated as follows : 

### Cl ' =

# (2.101X0.249)~ = 

### 0 .1 17 Tbe l ower confidence limit 

### (LCL ')and upper confidence 

### limit (UCL') 

### arc calculated using Equations 1 1-40 and 11-41 , respective ly 

### LCL ' 

# =y ' - Cl'

- 2.077-0. 117 

# = 1.96 UC L ' = 

### y ' + Cl ' = 2.077 

### + 0.1 17 

### = 2. 

### I94 Next, the confidence interval half range (CI)**rnu~t** 

### be calc ulated on the origina l PM concentration scale using Equation 11-4 2 from l 'S- 1 1

The confidence i nterval as a percentage ofthe emiss i on limit is calculated u s ing Equation 11

- 10 as foUows: Y-24 

## VES009732

### 0.936 Cl%**~** 

# 2o X 

### 1 00"/o = 

### 4.68% The resulting value for CI% is 4.68 pcrcenl. Because this val u e is less than 10 percent , the correlation satisfies the criterion for confidence in terval half range. How do I determine the tolerance j nteryal half range Percentage fo r the oower correlation'? The to lerance interval h a l f range. for the power correl ation also is ca l culated us ing the same procedure used for the exponential model. Because it is calculated on the Jo g scale, it 

### is denoted here a s Tl ' . Using Equation 11-11 , Tl' i s calculated as follows: 

### TI' = kT · 

### S L = 

### (1.629)(0.249) 

# = 0.406 The lower tolerance limit (LTL') 

### and upper to le rance limit (UTL') are calculated using Equatio nsll-43 and 11-44, respective ly LTL ' = 

## 9'- TI ' , 2.077- 0.406 = 

### 1.671 

### UTL' 

## = y• + Tl' 

# =2.077 

### + 0.406 = 

### 2.483 Next, the tolerance interval h a

lf range (TI) must be calculated on the original PM concentra tion scale us ing Equation 1 1 -45 

### from P S - I 

### I 

### (e un: - 

### e=·) Tl = - 

### 2 The tolerance interval as 

### a percentage of the emission limit is calculated using Equation 11

- 13 

### as follows: 3327 Tl% 

# = 

# 20 X 

### 100" /o 

# = 16.6% The resulting value for Tl% i s 16.6 percent. Because this value is less than 25 percent, the correlation satisfies the criterion for co nJidc u ce interval h alf range. In summary , the power mode . ! satis fies the PS-1 1 criteria for corre l ation coefficient, confidence interval half range pe.rcenlage , and to lerance interval half range percentage. Whjch model is the best fit for the data ? Table Y-1 1 summarizes the results of the analysis for all of the correlation models. As indicated in the table. all five models met the acceptance criteria specified in Section 13.2 ofPS-11. The linear model bad the highest correlation coefficient and would be considered the best lit for the data . However, any of the models could be 

### used to show compliance . The complet e output for the spreads heet for 

### this example is provided in Appendix A . I . Y -25 

## VES009733

### Ta b le Y - U . S umm ary of**e.~ ull** **s** 

### for Facility A Cor r e l ation T es t Co n Odcnce T olera n ce C orrel a tio n ln terv a . l half in ten • al h alf lltodel t ype 

### C orrclation equation coeffic\ea t ( r) ran g e range Acceptance Criteria for PS.Il**~** 0 . 85 

### s I OOh s2 5 % 

### Lin ear 

## y • -0 . 621 

### + 0.544x 0.927 4.49 % I 15.6%



### . P

olyn omial 

## y • 0 . 420 

### + 0.406x + 0.00368 

### x • 0 . 924 

### 6.12% 16.3% Lo ga r i

thm i c 

## y a - 1 3.8 

### + 8.32 Ln (x) 0.892 5.4 1 % 18 . 8 % E

xpo nential 

### 9

- 2 . 3 1 

## e"·""" 0 . 902 5.23% 18 . 7% P

ower 

### Y a 0 . 387x 1-"' 0 . 922 4 .68% 16 . 6% 

### Y.2 EXAMPLE 2: HOW DO I D EVELOP A CORRELA TION WITH PAIRED SAMPLING TRAIN 

### DATA ? Y .2 . 

### I Corre l ation 

### Test Scenari o 

### A corre l atio n t es t is per f onn ed on an i n cin era tor at F ac ili t y B . The incinerato r i s eq uipped with an in situ PM CE! MS th at res pon ds to PM con cen t rations at ac tu al c o n ditions. The emi s sio n limit , wl1en con ve rted to u n

its t hat are cons i s t ent with the PM C E MS sa m p li ng conditi ons, i s 2

4 .3 mg f acm. F iftee n tes t ru n s ar e perf om1 cd us i ng M ethod 5i with paired samp ling trai ns (Train A and Trai n 

### D) . N o p roblems were reported for t he test. 

### Tab le Y-1 2 

### s ummarizes the correla t i on test 

### data. Figure 

### Y - 2 show s 

### a plot 

### of the data . T ab le Y -1 2. 

### S u mmary of C o rre lation T est D ata fo r F a c ilit y B P

M C E

MS P M c o a te n tratio n , 

### mgf oom R un 11(1 . 

### r l'S pons e , m A S a m pling Train A S am p ling Tral n B 

### I 6 .4 

### 1.3 1.2



# - 2 7.5 2 . 3 2 .5 3 11. 2 2 . 5 2.8 4 16.4 7.7 7 . 9 5 29.9 12 .9 12.5 6 222 7. 8 7.3 7 19. 5 5 . & 5.9 

### 8 2 7.4 11 .7 1 2. 0 9 3 2 .8 20.4 2 0 . 9 

### 1 0 26 . 5 20.9 

### 21.3 II 33 .5 22.3 

### 22.6 1 2 28 .1 18 . 4 17 . 58 13 9 . 6 3 .7 3.9 14 5.3 4.2 4 .3 

### IS 18.1 

### 6.8 7.1 

### Y - 26 

## V ES 00 9 7 3425 

# • E 20 

## " 

# • • a. * E 

## c 15 0 

# "' 1': 

# • • 3 10 

### · - c 

# 8 :E 

### 5 

### a.. 

# • 

# • * • • 

# • • 

# • • 0 0 

### 5 10 

### 15 20 2 5 

### 30 35 

### 40 PM CE M S Response , rnA 

### F i

g ure Y - 2. Plo t o f co .-r e latio n t est data f or F aci lity 

# n . Should I averoge the two PM concentrations for each test 

### run? You should nm average the 

### rwo PM concentrations for any of the test runs . Instead , you should treat each PM concentration as a separate data point, as specified in 

### Section 12.3 of PS -1 1 . This means that for each run, the d ata set in cludes two PM concentrat i ons and one PM CE M S resp on se va l ue. In other words, th e correlation should be deve l oped a s i f there were 30 t est runs with o n e PM co n cent rat io n fo r each ru n. Tab l e Y -1 3 shows the data in th e f01111 

### tha t s hou ld be use d for d eveloping tlte correl ation . Before proceed i ng with the corre lation, paired s ampling train d ata shou ld be 

### checked for precision and bias. Guidance on precision and bias is provided separately. For this example, it is assumed that the data meet the criteria of precision and bias and are acceptable.



### Y-27 

## VES009735

### Table V - 13. Paired Sam plin g Train Test Data in 

### Format for Developi n g Correlation P M CEMS R esponse, PM Concentration , Run No. 

### m A mg/acru lA 

### 6.4 1. 3 1B 6 . 4 1.2 2A 7.5 

### 2. 3 2B 7 . 5 2.5 3A 11.2 2.5 38 11. 2 2 .8 4A 16.4 7.7 4B 16 .4 7.9 SA 29 .9 12.9 58 29. 9 12.5 6A 

### \ 22.2 7 . 8 6B 

# ' 22.2 7 . 3 7A 19 . 5 5.8 

### 78 19.5 5. 9 

### S

A 27 .4 I 1.7 88 27 . 4 12.0 

### 9A 32.8 20.4 9B 32 .8 20.9 

### lOA i 26.5 20.9 lOB 26.5 21.3 IIA 33.5 2 2 . 3

. 

### - - ·- liB 33.5 22.6 12A 28 .1 18.4 1 2 8 28.1 17.8 13A 9.6 3 . 7 138 9.6 3 . 9 14A 

## i 5.3 4.2 148 

### 53 4.3 ISA 1 8. 1 6 . 8 1 58 18. 1 7 . 1



### V - 28 

### VES009736

### What are t he results of t he corre l ation analysis? Table Y- 14 sununarizes th e results of the anal ysis. The complete outpu t for t h

e spread sheet for this exam ple is provided in Append i x A.2. Table Y - 1 4 . S umm a ry of Res ults for Facili ty B C orre lation 

### T es t 

# I C onfide n ce 

### T ol en mcc C orre la tion in te rn! h a l f inte r v al h alf Model type C orrel ati o n e qu ati o n coeffici e nt (r) ra n ge r a n ge Ac c eptance Cr i teria fo r PS

- 1 1**~** 0 . 85 s JO % s 25 % Linear j = - 3.24 + 0.672x 0 . 895 4.98% 20 .0% Pol}'ltomial f= 2.85

- 0. 173x + 0.0220 >' ! 0 .9 19 5.9 1 % 18 .0% ' ; Lo g arithm ic 

## y ; -17.7 + 9.81 Ln(x} 0 . 8 22 6.37 % ; 25.6% Exponential f = 1.43e 0

·

0 "' ' 0 . 921 3.80% 15.9% 

### P

ower f=**0.201x 7**  0 . 892**4.41~ -'o**  1 8.7% 

### Which model s h ould I use? 

### All of the model s e xcept the logarithm ic model s atisfy the acceptance criteria for PS

- 11 . The 

### logarithmic mode l fails to meet the 

### minimu m all owable corre l ation coefficient of0 . 85 . 

### In a ddition, the tolerance interval half ra n ge percentage for t he logarithm ic model exceeds dte 

### allowab le percentage of25 percent. Based on the correlation coefficien t , the expo n ential model i s the best fit . However, the linear , polynomial , and power models could a l so be 

### use d . Y.3 EXAMPLE 3 : HOW DO I D E VELOP THE I N ITIA L CORRELATION'? Y . 3 .1 Correlation Test Scenario A correlation test is pe r formed on a hazardous waste incinerator at Fa c ilit y C. The incinerator is equipped with an extractive PM C EMS that extracts and h eats the samples to 121 °C (250 °F) . The inci n erator is subject to 40 CFR 63 , s u bpart BEE , and mus t mee t an e mi ssion limit of 34.0 mg/dscm corrected to 7 percent oxygen. Fi ft

een test runs are perfonu e d us i ng a Meth od 

### 5 sampling trai n. The average stack gas p re ssure , mo i sture content, an d oxygen cont ent during the test were 760 

### mi llimeters of mercury, 12 

### percent moisture, and 10 percent oxy gen , respectively. No probl ems we r e reported for t he tes t, and all data points wi ll be used for the correl ation. Table Y-15 summarizes the correla t ion test data . Figure Y-3 show s a plot of the data .

Y -29 

## VES009737

### Table Y-15. S u mma ry ofCo rr c . la tio o Test D a ta for FacllJty C Ru.o no. PM CEM S rt-spo ns c, mA 

### P M co.o centralio n , mg/ocm I 

### 5.8 3.5 

### 2 7.6 

### 9.0 3 

### 7.8 

### 7.8 4 

### 16 . 4 25.2 

### 5 i 

### ' 10 . 1 16.6 

### 6 1 1.1 

### 14.3 7 12 . 0 19.6 8 

### 13 . 2 20. 1 9 

### 15.7 

### 23.4 10 1 7 . 6 26.7 I I 

### 2 1.7 26 . 8 

### 12 

## ' 21. 0 

### 28.9 1 3 

### I 22 . 3 25.7 14 

### 24 . 1 26 . 2 15 

### 2 4 . 7 26.2

### ------**---------- ----** **---------------- .** 

### ~ 30 

### a, 2 5 E 

# g 20 

# g 15 c 

## 8 c 1 0 

# 8 ::E 

### 5 

# ... • 

# • • • 

# • 

# •• • • 

# • • 

# • •**0+- ----** **r- --~~--~--** **-- ~--** **-- ~----** **~** 0.00 5 .00 10 . 00 15.00 

### 20 . 00 

### 25 . 00 30.00 PM CE M S Re sponse , mA 

### Figure Y -3 . Plot of corre lation tes t d ata f or Facil ity 

### C.

Y - 30 

## VES009738

### Do I need to co n yen the emjs sjop l j mi t to other units for detennining co nmlian ce wjth PS-l l ? As indi cated i n Section 13.2 of PS-ll , yo u mus t couv en the emi ssion limit to units that are 

### consistent with the measuremen t conditions 

### of your 

### PM CE MS. F or thi s ex a mp l e, you Jnust conven the em iss ion limit, which 

### is spec ified in units of mgfdscm a t 7 percent o:>: y gen , to mat c h the condition s u nd er whi c h the PM CEMS i s operat ing. The following calcu lat io ns show thi s conversion :



### where

## ~ T, 

## T

"' p

•d 

## P

, me 

### %0, 

# T. P, ld 1 13.9 

### = 

## Co X 

# I'.rd X 

## P,, X (

# ~-;:) X 

### (z0.9

- 

# % 0z)

= PM concentration at 

### s tandard co nditi ons , corrected to 

### 7 percent oxygen • s tack gas temperatu re at a ctual conditions, ° K 

### •**~tack** 

### gas t emperature at s tandard conditions ; 

### 293 ° K =**s~dc k**  

### gas p ressure at standard condit i ons= 

### 760 mm 

### of 

### Hg • stack gas pressure at actu a l co nd it ions, mm ofHg "' s tack gas moisture content , 

### % • s tack gas oxygen contem , 

### %. ( 1 2 1

### + 273) ( 7 60 ) [ I ] 13.9 34.0 • 

# c . X 

### 29 3 X 

### 760 X 

### 1

- 

# /! X 

### { 20.9

- 10) 34 . 0 

### = 

### 1.95C . 

## c.= 1 7.45 

### The emiss i on limit in units of concentration at the opera t ing conditions of the PM 

### CEMS is 17.45 

### m g!acm . Thi s i s the value that mu st be us ed for d e termining the confidence and tolerance interval ha lf rang e percentages . What are the rqu!t s o f the correlation analy sj s? Table Y 

### -16 summari zes the res ult s of the correlation analys is. Only the l ogarithm i c model satisfies all of the a cceptance criter i a for 

### PS-11 . The correlation coefficient for the exponential m

odel 

### (0.812) f.1il s to meet th e minimum allow a b l

e value of0 . 85 . The co nt idence and tolerance interval ha lf ra nge percentages for t he linear model 

### (11.3 a nd 35 .6 percent, respecti ve l y) exceed the limits of I 0 and 25 percent, respect ively. For the power model. the confidence interval (1 4 .3 p e r cent ) a n d to l erance interval 

### (46.4 percent) halfrange percentages also ex ceed the maximum a llowabl e values .



### Y - 3 1 

## VES009739

### Table Y - 1 6. Su mm a. ry of R es ult s f o r Facility C Corrc lutlo n Tes t C onfid enc e Tole r iUice Correlation l n ttr> • a l half interval 

### half Mode l type Corre.Lttion 

### equation coe fficient ( r ) 

### range range 

### Acceptance 

### Criteria for PS.II**~** 

### 0.85**~** 

### 10" /o £ 25 % 

### linear ja 2 . 27 + 1.15x 0. 898 1 1.3 % 35.6%



# - Polynomia l j • -1 8 . 4 + 4 . 30x · 

### O .lOLx' 0.987 

### 5.56% 13.4% 

### Logarithmic**~** -24.4 

### + 16.8Ln(.<) 0.959 7.32% 23.1% 

### Eil<ponentia l j• 

### 5.26e'"'"" 0 . 812 19.9% 66.5% 

### Power 

# v • o .7 47x. '·,. 0.90 8 14 .3% 46.4% 

### The polynomia l model bas the highest correlation c oefficient (0. 987) 

### and meets d1e criteria for confidence a nd tol e r a nce interva l halfrang e percentages. However, Section 12 . 4(3) 

### of PS

- 11 

### specifies that the maximum value for a polynomial correlation curve must occur at a PM 

### CEMS response value that 

### is al least 1 .25 

### times the highest PM CEMS 

### response value 

### used to develop the corre l ation eq ua tion . In 

### this example , the maximum PM CEMS 

### response value is 24.7 rnA , 

### and the maximum val ue for the correlation curve mu s t occur 

### at a PM CEMS 

### response val ue of at l east 32 .4 rnA 

### (24.7 • 1.25**~** 

### 30.88) . 

### However, 

### the maximum value for the polynomial correlation c urve occurs at 21.2 rnA , 

### as i s 

### evident from Figur e Y-4 . 

### Therefore, the polynomial model carUlOt 

### be u sed. 

### The complete 011 tput for 

### the sprea dsheet for 

### tlus ex amp**I~** 

### is provided in A ppe ndix A.3 . P lot of P olynomi a l Reg r ession C u rv e E 35 

# " -;. 30 

### y=.() . 10 tx'• 4296x

- t 8.37t E 25 t! 

## :8 20 

# i 15 

### • 10 

### I! 

# 8 5 :I 0**-!--- ~~~~-** **--.....-~ ~~~~~** **~---~** 

# ... 0.00 5 . 00 10 .00 15 .00 20.00 25 . 00 30.00 PM CEMS Response, rnA 

### F i gure Y - 4 . P lot 

### of polynomi a l c or rel a t io n curve f or F acility C.

Y -3 2 

## VES009740

### Y.4 E X AMPLE 4: WH AT CAN I DO IF MY PM CEM S FAILS THE C ORRE LATION TEST? Y.4.1 Correlat io

n Te s t Scenario 

### A corre la t i on test i s performed on a boiler at Facility 

### D. The boiler is equ i pped with an 

### in situ 

### PM C. 'EMS that respond s to 

### PM concentr a ti ons at actual cond itions. The emission l imit , when converted to units that 

### are consi s tent w ith t he 

### PM CEMS s ampling con ditions , is 1 8.5 mg/ac m . The correlation te st cons ists o f 1 5 test runs using a single Method 

### 5 sampling tra i n . Table Y-17 s u

mmarizes the correlation test 

### data. Figure Y -5 show s 

### a p l o t of the 

### data . T ab l e 

### Y - 1 7. S umm ary of T es t D a ta for 

### Facility D PM CEM S 

### r e spon se, PM 

### con centration , Run no . mA 

### mglacm I 

### 6. 7 3.1 

### 2 7.6 7.4 

### 3 7.8 

### 2. 1 4 9.2 

### 3.7



## ·- - ... 

### -· - 5 10.1 

### 6.1 6 11.1 2 . 8



### - · 

# -- 7 

### 12 .0 

### 4.9 8 1 8.2 8. 3 9 13.7 

### 4.5 10 14.6 

### 8.2 I I 

### 19 .7 13 .0 12 18.0 1 1.1 13 20.3 11.9 14 20 . 2 1 0.6 15 19.7 9 .2

Y-3 3 

## VES00 974114 

# • E 12 

# • w 

# • Dl 1 0 

# • E 

# • .: 8 

# • • 0

# ~ 

# • 6 

# • c: 

## B 

# • • c: 4 

# • 0 (,) 

# • • :I! 2 

# • 

# ... 0 

### o.o 5 . 0 10 . 0 15. 0 20 . 0 25 . 0 PM CEMS 

### Response, mA 

### Fi 2 u r e Y - 5. P l ot of co rrelation test data for Facility D . The results of the correlation analysis a re sumnm rized in Table Y -18. None of the models satisfy a ll ofthe correlati on cri teria specified in PS- 1 1 . Although all of th e models meet tlte criter i a for confiden ce 

### and to lerance int erval ha l f range percentages, on l y the polynomial model h as an accep t able c orrelation coefficient. However, the po l ynomial correlation curve h as a m i nimum x value of 7.05 that is greater than the minimum PM CEMS response (6. 7 mA for Run I) value used to develop the correlation curve. As stated in Section 12.4(3Xiii) of PS-1 I , a polynomial correlation curve cannot 

### be used if it ha s o minimum value that exceeds the minimum PMCEM S response v alue used 

### to detennine the correla ti on curve. Consequently , the polynomial co rrelation also is unacceptable . T able Y-18. R es ult s of l nl tlal Correla tio n for F acility D 

# I Correla tion C onfide nce 

# l Tolcro n cc Interval half intervnl half Model type Cor r elation equation ' coefficient ( r) range 

## l ran ge Acceptance Cri teria for PS-1 1**~** 0.85 ,; 10%**~** 25 % 

### Linear 

### I j• - 1.20 + 0.598.• 0.841 5.80"/o 1 8 . 3 % 

### Polynomi al ' 

### j• 6 . 19 . 0.615 

### + 0 . 043 !U' 0.855 7.68% 1 8.2 % 

### Logarithmi c 

### j•

- 11.8 

### + 7 

### . 37Ln( .r) 0.801 6.41% 2 0 .2% 

### Exponential 

### j=**1.6 9e** **~"'"'** 0.806 6.41% 2 1 . 3% 

### Power j= 0.308x' ·" 0.782 6.76 % 22 .6 % 

### Y-34 

## VES009742

### Several options are available for meeting the requirements of PS-I I , including the following: • Re,peat dte correlat i on test: 

### If you suspect p roblems w ith t he manual sampling or the operation of the PM CEMS, you may want to discard all of the test data and c ondu ct a new correlation test. ln 

### such a case , there must be a valid reason for rejecting the entire data set. For example, yo u determine that several ofthe 

### PM samples were contaminated. You sti ll must report all of the rejected data. • Conduct additiona l test runs. You may want to conduct 

### a limited n u mber of add it ional test ru ns (e.g. , five additi onal rwts) if it appears that some of the data are outliers, problems are suspected for s ome of the runs , or the range of PM concentrations measured was not adequate to 

### fully characterize the correlation. In this case , you can develop the correl ation based on all of the data (i.e. , the initial IS 

### runs plus the additional runs), or you can re ject some of the te st rwts, provided you meet t he requirements of Section 8 . 6(3) 

### ofPS

- 1 1, which allows you to reject up to five test ru ns without explanation and additi onal runs if the basis for rejecting them i s specified in the tes t met hod , in PS-1 1 , or in your quality assurance plan. • Relocate the PM CEMS and conduct a new correlation tes t : If the sampling location i s not ideal (e.g., PM concentrations are stratified across the stack at the sampling point), you may want to consider relocating the PM CEMS to another location that is more suitable. In this case, you m ust cond u ct a full correlation test (i.e. , at least 15 valid tes t ru ns) . • Replace the PM CEMS: Certain types of 

### PM CEMS may not be suitab l e for specific s tack gas conditions (e.g ., an in si ru light scattering instrument in a wet stack). If that is the case, you may decide to install a PM CEMS that uses a different measurement princ i ple . If so, you m ust conduct 

### a full correlation tes t with the new instrument. • Cons i der alternat ive solutions: Section 12 . 4(

4) 

### allows you to petition t he regu l atory aut hority for approval of alternatives to the con-elation req u irements of PS-11. For th i s example , we will assume that you decide to conduct five a d ditional test runs. These rwtS are ide n t ifie d as Runs 

## 16 to 20 . Table Y-19 shows the results of the additiona l runs. Figure Y -6 

### shows t he results ofall20 test runs. Table 

### Y- 19. R es ult s of 

### Addition a l Test Run s i PM CEM S 

### respo nse , PM c on ce ntration, Run no. 

## ' m A mglac m 

### 16 

### 5.2 2.4

..... ,... 

### .. 

# - - 1 7 8.6 4 . 8 18 14.1 

### 6.2



### ·- - . ......... 

### ·- 19 14.5 

### 7.0 

### 20 17.3 8.6 

### Y-35 

## VES009743

### 14 

### E 

### :;: 12 

### a, E 10 

# s· s ; 

# "'**~** 

# i 6**~** 

### 4 0 (.) 

### ::E 

### 2 Q. 

### 0 

### • • 

## • Ru n2 

### •



## --**~.** • 

### • 

# -- -· 

## - •



# . • •



### • • 

## • 

# . .. 

# -· ··· - 

### 0 

### 5 10 1 5 

### 20 25 PM CE M S Response , mA 

### Figure Y -6. Plot of original 15 run s plu s 5 a d ditional r un s for Facility D. T able Y -20 show s t he resu l ts of the correlation ana l ysis on aU 20 test rutl S . 

### T be ana ly sis sh ows that the linear 

### a n d polynomial models meet the con-elation crit eria ofPS

- 11 , and no furt h er ana ly ses or testing i s required . With the additional da ta included, th e minimum value for the polynomial correlation curve now occurs at 

### 4 . 2 mA , whic h is less than 

### t.he minimum 

### PM CEMS val ue used«> 

### develop the curve (5.2 mA) . However . a 

### review of Figure Y-6 indicates that Run 2 (7 .4 

### mA , 7.4 

### m gf

ocm) may be 

### on outlier . You 

### may decide to repeat the correlation analysis with Ru n 2 excluded . Table Y-21 shows the re s ults of the onalysis without the dat<l 

### from Run 2 . In 

### the revised a nalysis, all five mode l s meet the criteria ofPS

- 11. The correlation coefficients for the linear a nd po l yt1omial models al so are 

### considerably greater for the r evi sed anal ysis. You have the option of us in g the resu lt s of either ana l yses. In ei ther case, the polynomial model provi des th e bes t fit; ho wever, any ofthe m ode l s tha t satisfy aU 

### of the corre l ation cr i teria in PS · II can be used. Table Y-20. R es ults ofRevt sed Co rrel .a tion A nalys i s with All20 Run s Confi d ence 

### Tolerance Co rrelation Interv al balf interval half Model type Correlation equation coe ffi c ient (r) 

### range range A c cep tan ce Cr it e rio for PS

- 11 > 0.85 s 10% s 25% 

### Linear 

## f • .().905 + 0. 573x 0.861 4 . 25% 14 .7% Polynomial I 

## J• 3 . 94-0 . 263x + 0.031 4X' 

### O. S 15 5 .4 7% 14.4% Logarithmic 

## J •

- 9 .7 9 + 6 . S7Lo(x) 0 . 816 4 . 82 % 16 .7% 

### Exponential 

### js 1. 70c ..

" 1 "' 

### i 0.840**.52'~** 16 .3 % 

### Power ja OJ 6 7.rl.ll 

## I 0.82.4 4 .73% 17.0% 

### Y-36 

## VES009744

### T a ble Y- 21. Resul ts of R evis ed Corr e l ation A naly sis w ith R un 2 E xclud ed 

# I 

# I C o r r el ation Confiden c e To l eranc e I i n terval half Interval h alf 

### '**~~ de** **l** type 

# i C o rrel ati on**eq ua** **tlo~** 

### .. 

## I coefficien t (r ) r a n ge rang e 

## 1 

# - Acceplance Criter ia for 

### PS

- 11 2 

### 0 .85 s I0"/o !25% 

### Linear f= 

### - 1.88 + 

### 0.629.< 0.912 3.63% 

### ' 12.4% Polynomia l f= 

### 2.19

- 0.067x 

### + 0 . 0 2 6x' 0.92 1 4 .5 4 % 12.1% Logarithm i c f= 

### - 11.7 

### + 7 .2 4Ln(x) 0 . 867 4 .40% 15.0"/o Exponen tia l j = 

### 1.4 1ea 11 "' 

### 0 . 909 3.63% 12 .6% P

owe r f= 

### 0.25 J x ' · " 0 . 894 3.90% 

### 13 . 6% The complete ou tput ofthe spre a dsheet for lhe ini tial correlation, the correlation with all five additional test runs, and the correlation with Run 2 e xclu ded are provided 

### in Appendices A .4 through A.6 .



### Y-37 

## VES0097 45

# Appendix A.l Complete Results of Ex ample No. 1

- Initial Correlation Test

VES009746

### CORRELATION TEST PM CEMS AND REFERENCE METHOD TEST DATA PMCEMS PM concentration resoonse ,;,alaan Run X y

1 4 . 9 2 . 1 2 7 . 6 2 .9 3 7 . 8 5 . 1 4 9 . 2 4 . 8 5 10 . 1 2 .9 6 11 . 1 6 . 3 10 12 . 0 8.4 11 18 . 2 8.4 1 2 15 . 7 4 . 9 1 3 13 .9 6 . 3 14 19 .7 13 . 0 1 5 21.0 9.1 1 6 22 . 3 13 . 9 17 24.1 8.7 1 9 24 .7 1 2 .6 2 0 26.4 15.9 2 1 29. 1 1 6 .2 22 29 . 3 13 .5 23 30.5 15 .9 24- 33. 1 16.5

PS-1 1 Example 1-R 1 D-27-04 Jds Fac ii Hy: Location : Emission Unit: Test Dat os : Em i ssion l im i t :

20 

# "I 1 6 c .2 1 4 

# e 1 2 1: 

# ! 

# " l 0 8 

### v 

# l 6 4 2 0 Faci!HyA Anytown USA Boi l er No . 3 Ma rch 6 to 15 , 2004



# • Value 20



# •• 

# • • • • U n Hs mglacm



# • • • • 

# • •

0.0 5.0 1 0.0 1 5.0 20.0 PM CEMS Response

Test Data 

# • • •

25.0 

# • • • 

# •

30.0 35.0

Pago 1 o1 1 10/2912004 

### VES009747CALCULATIONS FOR LI N EAR CORRELATION Emission Unit: Boiler No . 3 Facility : Fa cl!!ty A Loca tion: Anytown USA Test Dates : March 6 to 15 , 2004 PM CEMS 

# I PM """"""'"" ,...Ar ,.... 11 .ATED STA l y 

## I (.,xl 2 

# I CYrYl 2 

# I ( x

;x-)(y,ylj Y" (y'\-

- 1-

- 4 . 9 2 . 1 185 . 86 54.32 100.48 2 . 047 0 .003 2 7 . 6 2 . 9 119 . 53 43 .16 71.83 3 . 517 0.381 3 7 . 8 5 . 1 1 15. 20 19.10 46.90 3 . 626 2.172 4 9 . 2 4 . 8 87.10 21 . 81 43.59 4.388 0 . 169 5 

### I 10.11 2 . 91 71 . 121 43.16) 55.401 4 . 8781 3 . 914 1 6 

### I 11 .06 6 . 3 55 . 85 10.05 23 .69 5 .401 0 . 808 10 

## ..l 12 8.4 42 . 68 1.14 6 .99 5 .9 1 3 6 . 18" 18.2 8.4 0 . 11 1.14 0.36 9.289 0.79u 15.7 4 . 9 8.03 20 . 88 12.95 7.928**9. 6~**  6 . 31 21.461 1 0 . 05 1 14 . 691 6.9471 0.41' 131 1. 36 1 12.461 4 .1 21 10. 1 051 8 . 37! 21 .02 9.1 0 .1 4 -0 . 92 10 . 824 1 2.97 : 16 

### I 22.3 1 3.9 1 9.62 16.69 11 . 52 1 1 17 24.1 8.7 30 . 99 0.59 -4 . 29 12 .50 11 1 "·""" 

### I 1 9 24.7 1 2.6 38 . 03 9.80 1 9.30 1 2.8281 0.052 I 20 26. 4 15.9 6 1 . 89 4 1.34 50 . 58 13 .753 • ono I 2 1 29.08 16 . 2 111 . 24 4 5.29 70. 9 1 22 29 . 3 13 .5 115 .93 16 .24 43.3! 23 30 . 5 15 .9 41 .34 76.9' 24 33 . 1 1 8 .5 81.54 131.54

PS-11 Example 1-R 1G-27-04 . JCis Unearcalcs 15 . 9861 17.401 ( 1.207

Page 1 of 1 1012912004 

### VES009748**~SULTS** OF LI NEAR COR RELAT ION Facility: Facility A Location : Anytown US A Variable Eq ua t io n n Number of data poi nts 

# = X x- - 1 /n"( S um o f (X,)) • 

## s .. Su 

# = Sum((X 1 ·x-)'2) 

# = y y- 

### = 1 /n " (Sum of (y 1 )) 

# = S tt 

## s,. 

# = Sum((y ,y-)•2 ) 

# = s,.. S")' 

# = Sum((xrx-Xy r y-)) 

# = bo bo 

# = y--b,x- - b , t>, 

# = s..;s .. = 

### s._ s._ 

# = SORT ( 1 /( n-2XSum(y;'-y.J"2)) - 

### Y'- y' at mean x value • 

# " t, from table • C l C l 

# = 1( 5,. " SQRT(1/n) 

# = EL Emission Limn 

### = C l % Ct% •CIIEL'100% 

### =

n' n'• n 

## = v, v 1 from table 

# = u •. Un• from tab le 

# = k

r k l = Un' • vf 

# = Tt Tl 

### = 

### k tS.. = TI% TI% • TIIEL " IOO % • 

### Sy 

### S,. 

# = SQRT(S,.,i(n-1)) - 

# ,.. r - 1-(s.

_ •21Sy•2J 

### = r r 

# = SORT((1-$L•21Sy'2)) 

# = 

# . ln dk:8ies c:onelation coefficient i s u ndefined .

P5-11 E xample 1 - R 1 0 - 27.Q4.x l s Value 20 1 8.53 1 , 442 9 . 47 49 3 785 . 2 .Q .621 0 . 544 1 . 910 9 . 4 70 2 . 10 1 0 . 897

20.0 4 .49% 20 1 . 384 1 . 177 1 . 629 3 . 111 15 . 6% 5 .095 0 . 859 0 . 927 Em i ss i on Unit: Boiler No .3 Test Dates : M arch 6 to 15 , 200 4 (Corre l atlOil equation: - 

# r=- - .0.621 + 0 . 544 X 

## I 

## s ....-vo onoou • fA• 

# - · ........ 

# - ........ .. ....... C rit eria for PS ·· - 

# .. Cri te ri on Actual Allowable Acceptable? Correlatio n co efficie nt 0.927 ?. 0 . 85 yes Co nfidence i n terva l 4 .4 9% .:;. 10% ye s To l e ran ce interval 1 5.6% .:;_25% yes ___

- ----·- • Indicates corre l ation coefficien t Is undefi ned . Plot of Unear Regreuton Una

y = 0 . 5445x • 0 . 6207 

# j :, - - ---:------- - - ! 10**~** u 5**~** 

# •**0~-- ~--~** **--~ ----------~--~**  0.0 5 .0 10.0 16 .0 20 .0 25 .0 30.0 35 .0 P M CEM S Rupon10**PS-t1~Test ~Spf**  

# l vWIIon 2-6 10125/04

Linear S u mmary Li n ear S u mmary 

## VES0097 4 9F a clllty: Facility A Loeatioo : Anytown USA 

# I PM CEMS 

# IPt.looo

### · - .. I!Sf)C!!!S! !!lJjocm X y Run 

### 7

2.ii CALCULATIONS FOR PO!.YNOMIAl CORRELATION E.mlufon Unft : Boiler No. 3 Test Dates: March 6 to 15, 2004 .:AlCUI.ATBl: .£ x• "" --;?; IY"·vl' 

### lvt. .- l'Tc.

118 576 10 ! 17 439 3.336 22 1681 ..).1171 UOOf U , , 475 3,702 40 310 I 3 . 809 I 1567 0 , 11 779 7 . 164 .. • • ... - •• • - .. 1 . 030 10,406 1 1 353 1 4.963 70 771 5.358 U . OOI U..Ul I 1u I 1 2 1**~** 1 44 1 728 20 736 101 1. 21 0 5 . 819 6 . 660 0 . 01 I 11 I 18.2 1 8 . 4 1 331 6029 109 . 720 153 2.782 9 . 024 0 . 390 0 . 12( •• ... • • 2<16 3870 60757 77 1,208 7 . 693 7 . 828 0 . 1084

26.4 .&.1 29.00 22 29 . 3

..... 30 .6 

### 33.'

PS-11 E""mple 1-R**10.21~** 

### m 1 93 2.686 37,330 88 1,217 6.771 0 . 222 0.0960 388 7,645 150 . 6 14 256 5045 9 . 842 9.9n 0 . 1204 _

... ---- ·-- 223 191 4 ,021 10 .576 2 . 178 "'1"8;

-- ..

j [iii ' 

### ..... ,.,

## ..... 865,365 1 ,200 ,36 1**~<:ales** 1 . vvo v , ..,..,d I n . g\JI , ,,.,. I 1.&49 0 . 0960 41 .3 4 1 1.271

> , .;J.;J.;J**V,~52** 0 .1 4",. AI' ""' t. r:r ·.469 3 . 879 0 . 1492 16.2 4 1 1.5 ! 1 .79 1...1. 16.221 0 . 1 03 0 . 2046 41 . "' • ' 1 7.884 0 . 379 0 . 431 21 81 .!

Pogo1oll 1012912004 

### VES009750BQU! D Of PQLXN O M LAI COB8 ELADO N F a cility: Fae l!l lty A Loc.a:Uon ; Anytown USA Eminion Unit: Sol., Ho . S Tut Oatu:: MMch tto 1 1- , lOOt 

### I V- £4tAi1'on**___y~** ( c:_o.ntdon equation: y • D.A20 • 0.. 401 x • o..tt311 x 1 

### I



## s 

# s 

# •• ---c;- 

# c 

# c c

c t • &.m. CJI) • ! • ,..., (>d2) = I •S... S$•Slm**SO -~** **~** 

### n• del A•**~S18382·~s:l .,**  (S5S2S4•S · tS3S7•S2SOS3-$7S2S2.S3S3S5- A • 1>1. 

# ... 0• , 

### s,• !I: A•

### •t·~ CO•( )1 0 C 1**•IS352.S1 ~li0**  =- C2

C3' !S1 S2 .n S3WO =-**~** ..**(nS2· 0=**  371 1.3 1 2 208.377)

# ~ 295 

# .., O . QOI 0.

4 0E o.003 6a

t.9 51 2 1 20E•09 1 .3 7S 

### .o.1s1e

• e "rtom !able • 

### 4 ·. • v EL Em l a lon Lhl h • ,... . CI• I ,' S,**'SC¥1( don** **a~ ln** **}•** v , 

## " • 

# " -.;-

s., 

# , , __ ? 

# ..,

# _ _ _ I 1.251<,.. 

# "' S r • IQfi(S u m , 

### i' · 

# , . v1 tom 

# .. 

# -

kl • un' '\11' • T l • k l ' \t ' ·II'Ei 1 100 'SwndiY'}) ' u ' "'

-- ••



# .. 1 . 40( 1.19e 1 . 5 . 0! 085J 0.0 24 "**"'a fT ·!55.c!! 4 1 . 38

PSo-11**~** 1-R 

### to.v-oc..., 

# ..._,.&........,. Stnmaly of**~ce** CtfteM tot PS..11

- 

### cno.mo 

# ....... 

# - . 1 ; Zl? Cor:rell5on ooefticin 092t**~=** 

# ... Coae<lercc**~** 812%

### ~'"""' 

# ...**T~~** 16.$%**~** 

# ..... 

# ... lrd:::all::es cortii!Miion**~is~** Check tct COft'efadon Curve Wnfmtft/Ma:dllltn ComaCion cunot rinrnum pdnt**~** 

# .. t.lnimt.Jnol s lfow:abte x .,..

### ·~ 1!'1 cc rrels tion ane miniMum < mlrlhft!n'l • "Va lu e? _}'Of CorrWlti on curo,e maxifl'Ull l'l*t t NA ExtraDOia1ion litrit for x (1 2 5% of**~m** ll value NA ts correlatiOn curve max im u m > extrapola ion !liM? NA Ptot ot PotynomJal Regresalon Cur.te 2 0 y •**O.OCX37~** • 0 .4 057X • 0 " 20 4 

# .. !**~~** • 

## • 

# • • 1 2 • 1 0 

# ! : • 

# • • 

# • l 

# •· • • 2 

# • 0 0.0 6 . 0 10.0 15<> 200 25 . 0 :10.0 35 . 0 PM CEMS Rtii)Onte

" H COrNIIIIIm l C'lll I**c..v-.~~r~** Sp!Nidll i- HI I**v~u** «11Zto94i

111\12004 

### VES009 7 51CAL CULAT I O N S FOR L OG ARITHM IC CO RRELAT IO N Facility : Facility A Emission Unit: Boiler N o . 3 Location : Anytown US A Test Oates: M areh 6 t o 15 , 2004 PMCEMS 

### PM Ru n 

# •

-- 4 . 9 7 . 6

11

1 2 . 754 4 . 9 0 . 001 20.8851 0 . 174 1 9.1521 18 .0831 I 13 I 13.9 2 .632 6 . 3 0 .026 10 .049 1 0 . 507 8.139f 3.3821 14 

### j 19.7 2 .981 13 0.036 1 2 .46 1

- --- . . - .. - --- 21.02 3 .045 9.1 0.064 0.137 .

22.3 3 . 105 13.9 0.098 19 . 625 I " I 24. 1 3 . 182 8.7 0.152 0.5931 ..(] 

### I 19 

### I 24.7 3.207 12.6 0 . 112 9.7971 1.299 1 M M. O 273 1 5 .9 0 . 232 41.3451 °**~--** 14 

### 2 30 .5 33 . 1 370 1 6 . 2 0 . 334 378 13.5 0 . 34: 4 18 15.9 0 . 39 500 18.5**~** 

### ;:;a; 

## 16.241 41.345 81 . 541 6.391 ;.867 1.67 ).714 14 . 679 1 1 .490 

## i.858

PS.11 Example 1·R 10·27-04.xls Logarithmic Cales Page 1 of 1 1012912004 

### V E S 009 752R ES ULTS O F L OGARITHMIC CORRELA TlON Fa cili ty : Facility A L o ca tion : An yto w n U SA

Variable Eauation n Number of data points • x' 

# .: - = 1/n ' (Sum of ( x 'J) • 

## s,.. S,.. a Sum(()( r x'- )'2) = y y- 

### = 1 /n ' (Sum of (y J) 

# = s ,.. 

### S,.. c Sum((y r y -)"2) 

# = s ,., s .., 

### = Sum((x' r X '-)(y ry - }) 

# = b o 

### bo = y--b , x '- 

### = b , b, • 

## s,.;s, • s.. 

### S.. = SQRT( 11(n-2)(Sum(y fl -y 1)"2}) 

# = Y"' meen 

### Y"' a t mea n x va l ue •**~ from**  tab l e=

C l C l 

# =rs , " SQRT( 1 / n ) 

### = E L E m i ssio n Lim it 

### = C l % Cl% =C I IE L' 1 00 % •

n ' n ' = n 

# = v , v 1 f rom tab l e 

# = u •. u. from tab l e 

# = k r 

### kc e.**·v •**  T l T l 

# = k,'SL 

# = T l% Tl % 

# = T I IEL'100% 

# = Sy 

### S., 

# = SQRT(S,/(n- 1 }) 

# = r 

# r . 1 -(s..•vs., 

## •21 = r r • SQRT((1-S,•21Sy'2})= 'i nd ica tes correlation coefficie nt i s undefi n ed .

PS-11 "- 1-R 11).21.o4 . lllt Value 20 2 .7 9 5 .74

9 . 5 493 47 .8 ·13 . 766

8 . 323 2.305 9.470 2. 1 01 1 .083 20 . 0 5 .4 1% 20 1 . 384 

### 1.1 n 1 . 629 3 . 75 1 8.8% 5.095 0 . 795 0 .892 E mission U n it : Bo iler No . 3 Te s t Oate s : Ma rch 6 to 1 5 , 200 4 ! Correlation eq uation : y 

### = ·13 . 766 

### + 8 . 3 2 3 Ln(x ) 

### I



# _

... 

## ,. . .. .

... ... . 

# - ·,_ _"'_ 

# -- · ·- -· ····-- ·-· . 

# - . . Criterion Actual Allowable Acceptable? Correlation ooertident 0 . 892**~0 85**  yes Confidence inte rval 5 .41 % ! 10% yes Tolerance interval 18 .8% !25% yes • I ndicates correlation coefficient is undefined . Pl.ot of L o g arithmiC Rtgl' t •tlon Curve 

# &**:r------ y~=~** **~~:22=9~ .=,.** **7} ~.:** **.: 76** **----------------**

# 1 " 

# . 

# . t! • • - 

## i ' o _!. 

### o ' 

# • •**~** 5 

## l 

# ol**~/** 

## I

· 5

### OjO 5. 0 1 0 . 0 1 5.

0 20 . 0 25 . 0 30 .0 s:j . O PM CEM S R ea pon ae

PS - 1 1 Co r nt lalicn Tt)st Ca lelil'ltlotl Sc;lr&ldt hMII 

# v.,_ 2-e 10125104

Lt>garilhmlc Slnmlary 1 or.!!II2004 

### VES009753CALCULATIONS FOR EXPONENTIAL CORRELA TIO N Facility : fa cility A Emi ssion Unit : Boiler N o. 3 Locat ion : Anytown USA T est Oates : Ma rch 6 to 15 , 2004 PM PMC EMS Run X y' 

# = L n (y) 4.9 0 . 7 42 1 . 1 64**~** 7.6 2 . 9 1.065 11 . 065 • 7 .8 5.1 1 . 629 4 . 804 0.178 0.078 0.074 4 

## 5 9.2 4,8 1 . 569 87 . 1 0 0 . 258 4 . 743 1 . 452**v.v ~**  10 . 1 2 . 9 1 . 065 7 1 . 12 1. 024 8 . 535 1 . 512**~ ~** **~6** 8.4 2 . 128 42 . 68 0 .003 ·0 . 336 1 . 639 0.239 I II 

### I 10 •.< 8 . 4 2 . 128 0 . 11 0 .003 · 0 . 017 2 . 055 0 . 005 

### I 12 

### I 15 . 71 4 .9 1.589 8.03 0.238 1 . 381 1.887 0.089 13 

## .l 13 . !!J... 6 . 3 1 . 841 21 . 46 0 . 056 1 . 095 1.767 0.005 14 13 2.565 0 . 570 15 9 . 1 2.208 0 . 327 16 

## I 22 .3 1 13 . 9 1

-- 2.632 1 14 . 191 o .308 1 2.0911 2.3291 o.o 92 17 

## l -· 24 .1 1 8 . 7 1 2.163 1 30.991 0 .0071 0.482 1 2.4501 0.082 19 24 .7 12 . 6 ' . -· 2 . 5 34**~63** 0.209 2.818 2.490 0.0021 20 26 .4 15.9 2.766 61.89 0.475 5.424 2.604 0.02f • I 21 29.08 16 . 2 2.78 5 1 1 1 .24 0 . 502 7.469 2.783 0 . 00!**~·** 29.3 13.5 2.603 1 1 5.93 0.277 5 . 66Z 2.791l U. UJ 23 30 .5 15.9 2 . 766 143 . 21 0.475 8 . 251 2.878 0.01 24 33.1 18.5 2 .918 2 1 2 . 20 0 . 707 12 . 250 3 . 052 0.018

P8-11 Example 1 ·R 10·27.<J4 .xl s Exponen tial Cales Page 1 of 1 1012912004 

## VES009754RESULTS OF EXPONENTJAL CORRELA TtoN**ac:illty ~**  FacWily A L.oc-1tJon : Anytown USA



# v- EaUIIIcln n 

## -of data 

## • X 

### .- •**t~ nsum**  of CXJl • 

### s,. S,. • Sl.m(("<x-)'2) • y '(· • 1/n'(Sum ol**('(~)** 

## = s,., S,., • Sum(('( 

### .-1- )'2) = 

### s.,. Sw • Sl.m(("< x •X'f.-1•)) • 

# .... .,. . • f'-b_x- • 

# ""**~· "'ttu··**  b,**b,•Sq~S..•** 

## s.. S , • SORT(11(,...2)(5um(y' , "'\",)' 2)) 

## =**-r-~ r.**  "{"" 8 t rnoiln .r:. value = \ \-from t.able • c r Ct ' • t.•SL•SQRT( 1 1n) • L

C L' L CL

' =v- · . c r UC L' U Ct. ' • +Ct'

Cl a • c"UCL' •**e~~oLCl '**  E

l Enis-si on U m ll 

### = C l % Cl% •CI /EL '1 00% • n' n· • n • v, v, fro m tDb l e = u, IJ.\· from tab l e = k , k, 

### =**~· ·v** **,;;** Tr Tr• k,"SL c LTl ' L TL '• v- '-T r UTl' 

### u · •t. · 

## .-v .. •... n · T l l1 = o'UTL' • e'l Tl'V2 TI% TI% • T I IE L" 1 1Xl% .. 

### s,. S,. • SORl(S,.,I(<>- 1)) =**i'•HSL~ 2)** **•** r r • SORT((1·SL •2JS,I'2)) • 

# ··-1 ' ............... !Aft .. .-..lfl .. l ....... .. ..........**...-~ '** **[:q_ ~**  '.-R t o-274'. 

## v20 18.53 1 ,442 . 2 

## z.on

7.86 96

. 58 0 . 836 2..'!06 0 . 087 0.278 2 .

077 2 . 101 0 . 1 307

1 . 946 2 . 207 1 . ()45 20.0 5.23% 20 1 , 384 1.177 1 .629 0 .453 1.624 2 . 630 3 . 740 1 8.7% 0 . 643 0 . 813 0 . 902 Em is 5ion Unit Boiler No .3 Test. Datu : Mar ch &to 1 5,2004 

# I correlation equation : y 

### = 2.306 e .. ,.,. ' 

# I

.. .

...... . ,_ 

# ... "'"""""" '""""" 

# ................... 

# --· . Qll!rion Adual 

# AI-**~?** 

### eon-. cooflidoot 0 . 902**~35** yeo Cmfodena!- 5 . 23 %**.,._** yeo T

cjera,nc:e "erval 18 . 7%**~25-%** yeo • ln<fic:a1es**"""""'~** coefficlenllo unclellnod . Plot of Exponenti a . l Regression C ui'Ve**>•r----------- --------------------~**  20 c

## ~ 1S 

## 3 § 1 0 

### l s y: 2.3064e OC6 l't



# •**·~--~ --** **------------ --** **---- --** **~** 

# •

• • • 1 0 .

0

### ~- 15 . 0 20.0 2 &. 0 30 .0 PM CEM S RtltPOtiM

PS- I 1 Corr.lllllon r•tt c.lt ul.wi oo Si1' $1 dlt!DIIt v.,bf, :toe**~~** 3&.0



# ·- VES009755CALCULATIONS FOR POWER CORR ELAT ION Facility : Facility A Em i ss i on Un i t: B oiler N o. 3 Location; Anytown USA Test Dates : M arch 6 to 15 , 2004 PM concemraue> PM OEMS

# -r;,;~;j~ 

# I**Measure<i'lr..;~ormed** 

# I CALCULATED ftlii:::JU OTERS Run x 

### t: 

### = Ln(x) y y' - Ln(y) (x'r fl' ('f' r Y'f (t: r ><'l<Y'r Y ) ' 

# ,. I , I 4 . 9 t . 5S9 2 . 1 0.742 1 . 446 1.762 1 .605 0 . 773 0 .001 <**~** 7 . 6 2. 026 2 . 9 1.065 0. 5S3 1 . 024 0 . 773 1 . 249 0 .034 1 7 . 6 2 . 054 5 . 1 1.629 0 . 544 0 . 200 0 .330 1.277 0 . 123 ' 

### I " I 9 . 2 2 . 219 4.6 1 . 569 0 . 326 0 . 256 0 .291 1 . 456 0 . 012ti 

### I

- 10 1 2 . 313 2 . 9 1 . 065 0 . 230 1 . 024 0.465 • - - -**~ ~·~-·**  1 1 . 06l

- 2.403 1 s .31 1 . 641 1 0 . 151 1 o . o5s l 0.0921 1 2 . 485 1 8.41 2 . 1281 0 . 094 ] 0 . 003 1 .().0161 1 2.901 6.4 2 . 128 0 . 0 1 2 0 . 003 0 . 006 2 . 196**0~** 

### I I < I oa . 71 2 . 754 4.9 1 . 569 0 .00 1 0 . 236 0 . 019 2 . 035 0.199 1 

### I

· - ·-**~** 2 .632 6.3 1 . 641 0 .026 0 . 056 0 . 036 1 . 903 0 . 0040 )-- 2 2.961 13 2.565 0.036 0.236 0 . 092 2 .261 0 . 0604 3 .045 9.1 2.206 0.064 0.017 0 . 033 2 .352 0 . 0206 1.105 13.9 2.632 0.096 0.306 0 . 1 74 2 . 4 1 6 0 . 04671 

### I " .... , 3.182 8.7 2. 1 63 0.1 52 0.007 0 . 034 2 . 500 0 . 1133 

### I 19 2 4 . 7 3.207 12.6 2.534 0 . 172 0.209 0 . 1 90 2 . 527 0 .0001 I 20 26.4 3.273 15.9 2.766 0.232 0.475 0 .332 2 . 599 0 .0261 2 1 29.08 3.370 16.2 2.785 0.334 0.502 0 . 4 1 0 2 . 704 0 . 0066 22 29.3 3 . 378 13. 5 2 . 603 0.343 0.277 0 . 306 2.712 0 .01 1 9 23 30.5 3.418 15.9 2.766 0.392 0 . 475 0 . 432 2.755 0 .0001 

### I 2 4 33.1 3.500 1 6.5 2.918 0 . 501 0 . 707 0 . 595 2 . 844 0 . 0055-1

P5-11 Example 1·R 10.27.Q4 . >ds Power Cales Page1ol 1 10/2912004 

## YES009756BeS U L TS OF PQWEB C ORRE L ATI ON Foc: il ty : fK i lity A Loca ti on : A nytown U SA Vanabla EaUIIion 

# v-. n N..-oldetl 

# ... 20 >! 'If-< IM'(S....ol(l(J)& 2. 792 

### s.., 

### s,., • Sum((IC' r 'lf-r2l. 5 .7 4 y' Y'-; t/n ' (S.... ol (Y'J). 2.077 

### Sw Sw· s..m<<Y'd-r2l 

## = 7.B8 

### s,., S,v • Sum((IC' , 'If-XY'r'l- ll • 6.22



# .... t>a'• yo-o,x- = -o.949



# ...**~.** o"'b ," .. 0.387 b, b, • S,.,,S..,= 1.064 

### s, S.. 

## =**SQRT n-2XS..m((** **"-Y' r2))**  • 024 9 >/"- ("' 81 mean x value = 2.077**~** t 1 from table • 2 . 10 1 

### cr C I • I'S l 'SQRT(IIn )• 0 . 1 17 LCl ' LCL' = '· C I ' 1. 960 U

Cl

' UCL ' • V"" ' • C l ' 2. 1 94 Cl Cl• lo' U Cl ' • o'LCI / V2 0936 El Em laakln l l rrit • 20.0 C l % I % • CIIEL . 100% = 4 . 68%

n ' n • • n = 2 0 

## v, v 1 from ta b le • 1 . 384 

# "- u"' from t ab le a 1 . 1 77 k , k t • 

### u.-- ·v , ,.. 1 .629 T l

' Tr • k,S l ll 0.406 LTL ' l 

# .. , • Tl ' 1 .671 UT L' UTL' • ...• + 'f' l' 2.41!3 T

l**•(e~ urL** **·- e~LTL** **V** 3.327 

### n%**'f ~**  • T l1El•1o0% • 1 6 . 6% 

### s. S. • SQRT{S:Jiflol)) • 0 . 643 f i' • 1-(SL '2/S,/'2) • 0 . 850 r r • SQRT(( I.Sl"2/S;I'2)) = 0. 922 • I_ ..... ,_ - ... - .. .........Mt' ..i- .. t loo u rul.all.-.t

i'$1 1**~** 1-R 1.1)-ll oO'.JJs EmiS-Sion Un it: Boiler No . 3 Tnt Oates : Ma rch 6 t o 1 5, 200<l ! correlati on eg uat i o n : y • 0. 38 7 0 x , .,. 

# I

......

_ 

# .... .. .. . .,._ , ,.. "' ' """"' "" "' ""- 

# .... ..... '' Cri1erion Actual 

# --**~:ca"leblo?** Cotre.ta!!ion ooeftlc:iet ( 0.922**~0 85**  )M Confidence- 4 . 68 % <11110 yeo ToleranCe interval 16 .6%**~25%** yeo • lndi::stes cxwrelaUon ooeffic:ienl is**.**

P l ot of Powe r F unct ion Reg r es s ion Cutve**20 ~--------------------** **-------------,** 18 16 

# i 14 

# i y = 0 . 387x '·""' 

# • " 12 

### § 10**~** 

## • g 8 I 

### • u 

### l 8 4 2 0 0 .

0 5 . 0 1 0 .0 150 20 . 0 P M CEMS R"ponee**~$'~** 

## • 

# •

2U 300 3&.o

P$-\1 CclnlllfiiiOn '"' Ceb.llllton SPf91d1Mic VMion :H 

# "'""'"' 

# 1-

VES009757SELECTIO N Of BEST M ODEL Facility : Locat io n ; Model li1ear PolYnomial 

### Logarithmic Exponential Powor Fa cility A Anytown USA

Correlation ooefflclent (a) 0 . 927 0 . 924 0 . 892 0 . 902 0 . 922 ?. 0 . 85 7 Confidence lntOMII haff range**pe~t&ge** 

### Yea 4.49% 

### Yea 6 . 12% 

### Yes 5.A1% 

### Yes 5 . 23% 

### Yes 4 .68% Emission Uni t Boi ler No . 3 Test Datos : M arch 6to 15 , 2004 !: 10%? Tolerance inlefval hal !:25 %? Minimax willlln range percentage allowable range? 

### Yes 15 . 6% 

### Yes 

### lbl Yes 1 6 . 3'/o 

### Yes Yes Ye s 18.8% 

### Yes b 

### Yes 18 .7% 

### Y es Yes 16 . 6% 

### Yes (a) • indicales correlation ooel(rcientls 

### I.Widelned ; mode l does 

### not satisfy critelion . (b) Not app Hcable ; cri1erion appios only t o polynom ial model .**PS~** 11 Corretaticn Test Cab.Miion SP'l!adsheet Version2-6 10/251001 PS-11 EJ<ample 1-R**1~ -o4** **.x ls**  Ba st model :

Best Mode l 

### Ooca model meet al cnlarta?



### Yes Yes Yes Yes Yea LlnNr

10/2912004 

## VES009758

# Appendix A.2 Complete Results of Example No.2- Initial Correlation Test

VES009759

### COR R ELATI O N TE ST PM C EM S A N D REFERE N C E M E T H O D T EST DATA PMCEMS PM concentration lliSDOnSG 

### m l acm R un X 

## v !A 6 .4 1 . 3 16 6.4 12 2A 7 . 5 2 . 3 26 7 . 5 2 . 5 3A 1 1 . 2 2 . 5 3B 1 1.2 2 .8 4A 16 . 4 7 .7 46 16 . 4 7 .9 5A 29 . 9 1 2 . 9 58 29 . 9 1 2 . 5 6A 22 .2 7 .8 68 22 . 2 7 . 3 7A 19 .5 5 . 8 78 19.5 5 . 9 8A 27.4 11 . 7 68 27. 4 12 9A 32.8 20 . 4 9 8 32 .8 20 .9 10A 26 .5 20 .9 108 26 . 5 21.3 1 1A 33 . 5 22 . 3 1 1 8 33 . 5 22.6 12A 28 . 1 18.4 128 28 . 1 17 .8 13A 9 . 6 3.7 136 

### 9 . 6 3 . 9 14A 5 ." 4 .2 148 5 .3 4 .3 !SA 1 8. 1 6.8 1 58 1 8 . 1 , _l.!

PS-1 1 Example 2 · R 1 0 · 27-04.x l s FaeUity : Location : Emission Unit : Test Dates: Em i ss i on limit:

25 I 

# .2 20 

# 1**~** 15 

# 3 I c: 

# 8 10 :;;; 

# s J ll. 0 Facility B Anytown USA Incinerator April 3 to 6 , 2003



# • • Va lu e 24.3



# • • 

# • Un i t t mglaem



# •• • 

# • 

# •

0 .0 5.0 1 0.0 15 . 0 20 .0 25 . 0 P M CEMS Response

Test Data 

# • • 

# • 

# • •

30 .0 35.0 40 .0

Page 1 o1 1 1012912004 

### VES009760CALCULATIONS FOR LINEAR CORRELATION Fa cility: Fa cili ty B Emission Un it. Incinerator locatio n: Anytown USA Test Dates: April 3 to 8 , 2003

Run

A 8 28 PM CEMS 

# I PM con<>onu-d<Klll X 

### 6 . 4 6 . 4 

### 7 . 7 

### y**C'.A.l~ULATEn C::** **T.&TI~T•r a..** **•** DAD J (x,- x 

## 1 • 

## I ( Y;Y

## Y 

## I (x,-x l<Y;Y 

## l 

## I y" 

## I (Y" r Y • 1.31 174.941 74.941 114 . 501 1 . 0651__ 0 .055 _ 1 .;! [ 

# 174.94r

-

n 76.681 115 . 821 1 . 0651 0 .018 2 . 3 58.62 92 , 85 0 .245 2.5 55.60 90.42**~83** > . 60 "" I o o . .ll**~.II** 11.U1**~1 22**  60.31 4.292 2 .226 4A 

### I 16. 4( 7.7 1 10. 4 11 5 . 09 7 . 28 7.788 0 .008 1 48 1 6.4 7 . 9 10. 41 4 . 23 6.64 7.788 0 .013 I 29 .9 12 . 9 8 . 66 30.24 15 . 703 29 . 9 12 . 5 6 . 47 26 . 13 19 . 034 6.62 1 4 .651

- 5.551 11.6871 15 . 105 8 

### I 22 . 21 7 . 3 1 6 . 62 ] 7 .06] -6 . 84] 11.687) 19 . 242 5 . 8 1 0.02 1 1 7.281 0 .5 3 L _ nn 9.872l 16 . 577 78 

### I 19.5 1 5 . 9 i 0.02i 1 6 .461 0.5 11 9.872i 15 . n3 I SA 27.4 11. 7 60.42 3.04 1 3.55 15. 182 12 . 126 I 88 27 . 4 1 2 60.42 4 .18 15.88 15.182 10 . 126 9A 32.8 20 .4 1 73 . 54 __ 109.06 _137_ . 57 ___ 18.812 2 . 521 98 32 .8 20 .9 1 73 . 54 11 9.76 144 . 1 6 18.812 4 . 359 l O

A 26 .5 20.9 47 . 24 11 9.76 75 .22 14 . 577 39 . 978 1 08 26 . 5 21 . 3 47 .24 128.61 ____ 7L97 __ 14.577 45 .li1 A I 33 .5 1 22.3 1 1 92.47) 1 52 . 36) 1 71 . 24) 1 9.283 ) 9 . 1 1 8 33 . 5 22.6 192 . 47 1 5 9. 85 175 . 41 1 9.283 1 1 1 12A 28 . 1 1 8 .4 7 1.80 71. 29 7 1. 54 1 5 . 6531 7 128 28 . 1 17 . 8 

## !:.U!Q 61.52 68.46 13 A

- 9 . 6 3 . 7 1 00 . 53f**;,~.1!>** b<.IJ J . <l 138 9 . 6 3 . 9 1 00.53 1 36.68 60. 7 3**1~1** -·,-· 1 14A 5 . 3 4. 2**205.2~** 33.1 4 82.47**0.3~ ~**  1!' n<n 148 5 .3 4. 3 32.00 81 . 0 4 15A 1 8 . 1 6.8 9 .96 4 . 82 158 

### I 1 8 . 11 7 .11 2.33 1 8 . 16 ) 4 . 36 ) 8.930 ) 3 . 350 P S- 1 1 Example 2

-R 10-27-04 . xls linear 

### caJcs Pago 1 of 1 10/2912004 

### VES00 97 6 1R ESULT S O f LI N EAR CORR E LATION Fac il ity : Facility B L ocation: A n ytown US A

Variable Eauation n Number of data oolnls a 

# - X x -**~** 1/n'(Sum of (xJ)**~** 

## s., S..**~** Sum((x,- x -)"2) 

### = 

### y y- • 1/n'(Sum of (yJ) 

## = 

# s.r S,. = Sum((y r y-)"2)**~** 

### s.,. 

## s.,**~** Sum((XrX -XYrY-)) 

### = 

### bu b,• y-b,x- = b, b 1**~** S.,.IS.. " 

# s.. S, 

### = SQRI(1/(n - 2)(S um(y 1 "-y 1 )'2)) 

### = Y"....., y• al mean x value =



### t,**~** from table 

## = Cl Cl**~** t,"S,'SQBT( 1/ n) = EL Emission Limit 

### = Clo/o C l % =CIIEL '100 %**~**

n ' n · 

# = n = v, v1 from table 

### = 

### u

.,. u , . fr om table 

### = k

T k 1 1! u !\ ''Vr c T l T l • k 1 

### 'Sc 

# = I I % T l % 

# = TI/EL ' 100% 

### = 

### Sy S, = S ORT(Sy/(n -1)) 

### = 

## r r' 

### = 1 - (S, •215, •21 

### = r r 

## = SORT(( 1 -S , 

### •2/Sy•2)) 

# = • Ind ica tes**com~lation** coefficient Is undefined .

PS-11 El<ample 2-R 10-27-04 . xls Value 30 19 .63 2.738

9.96 1,531 1.840 . 8 -3.237 0 . 672 1 3 . 238 9 . 957 2 .048 1 . 2 11 24.3 4 .9 8% 30 1.286 1 .1 68 1 . 503 4 .866 20.0% 7.266 0.801 0.895 E m ission Uni t : In cine ra tor Test Dates : Ap ril 3 to 6 , 2 003 )Correl ation equ a tion : y 

# = -3. 2 37 

### + 0 . 67 2 x) S • 

# -

-

. . ......._ , otA• Criteria f or PS-11 

# - ·**~**.... 

# - 

# _ . .

...

# _**~** -**-- -~**  Criterion Actual Allowable Acoaptable? Correlation coefficie nt 0 . 895**~0 85**  yes Confidence inte<val 4 .98%**~** 10% yes Tolerance int erva l 20.0%**25%** yes • Indicates oorrelaUo n coe lf lcien1 1s undefi ned . PSot o l Linear**Rogn:~sston** Llno 

# 25.,---------- -------, e 

## j 20 l 1 s 

# g 10 

# " !: 5 00 . 0 y = 0.6722x - 32371 

# •• • 10 . 0 20.0 30.0 

### •o.o PM C EM S Respons e

PS-11 CorreiOiion T... Cl t Q.t lation Spteadsheet Vcnlon U 1MSI04

Unear Summary Unear Summary 

## VES009762Facility : Faeil i ty 8 Lo<:atlon : Anytown USA

RlJn 

## I PM CEMS 

## I**PM ~~**  molocm 

### • I 

# v CALCUI.AT!ONS FOR POl.YNOMIAL CORRELATION Emission Unit: lncine , rator Tes t Oates : Apri l 3 to s . 2003

I"' AI l"' ltl 

### 7 

## x'i • • ixYix'viY"itV'-vl'i-·itoA. 262 1 . 678 8 53 2.649 1.8 19 0.1326 f4 . !04T ' · '" 

### l I 262 1 . 678 8 49 2 . 649 2.0911 0 . 13211**78 ~1_**  2. 15 422 3 164 17 129 2. 795 0 245 0 1009 58

- - . -- 422 3 , 164 19 1 4 1 2 . 795 0.087 0 . 1009 •• 125 1.405 15 , 735 28 314**~ ~**  I 4A I 1 11) , ,. 1.1 269 4 ,411 72.339 1 26 2.071 5 .942 L 48 1 6 . 4 7 .9 269 441 1 72,339 130 2 . 125 5 . 942 3.833 

### o .o8< •• "Q . U 12 . 9 894 26 . 731 799 254 386 11.533 17 . 379 20 . 081 0 .07 1.9 12.5 894 28 . 73 1 799.254 374 11.175 17 . 379 23 . 804 0 . 07 ! . 2 7.8 493 10 941 242.891 173 3 844 9 . 872 4.292 0 . 0823**6~** I. QD .2 . 2 7 3 493 10 . 941 242 . 89 1 162 3 , 593 9.872 6 . 614 0 . 0823 7 .06 1 , .. 7A 19.5 5.8 380 7.-4 15 144 .590 11 3 2. 20s 7 . 858 4 236 

### o 0906 17 . 28 

### t . n 78 19 . 5 

### s .u 380 1A 15 144,590 115 2.243 7.858 3.834 o .0906 18. 4 6 1 . n 8A 27 .4 11 . 7 751 20 ,57 1 563,64 1 321 8 .7 84 14 . 655 8 . 732 0 . 0593 3 .04 1. 44 88 27 .4 12 761 20 . 67 1 563,64 1 329 9.009 14 . 655 7 .049 0 . 0 693 . .. ' •• 9A 32.8 20 . 4 1 . 078 35 , 288 1 ,1 57,432 669 2 1 ,947 "" "" " •• • , 1 076 35288 1 1 57432 686 22.485 20 . 884 0 . 000 0 . 1573 ... 

### .,iiT . ..... -, ' 7M 1 8 810 493 1 55 554 1 4 6 77 1 3 . 742 5 1 . 239 0 .0604 1 ' ' •• . . • 1 8.610 493 1 55 564 14 958 1 3 .742 57 . 125 0 .0604 • 37 . 595 1 ,259,445 74 7 25.026 2 1 . 785 0 . 265 0 . 1920 

### 1- I li D I •• . , ... 1 , 1 22**37 ~95**  1 ,259 ,445 757 2 5.36 3 2 1 . 785 0664 0 . 1920 • •• . •**~** • . 

### odl I 1 2A I 28 . 11 1 8.4 700 22. 1 88 623.484 5 17 14 ,529 15 . 300 9 .060 0 .0805 71 . " · ..

· · - -· . ·- . -- " 2. 1 88 623,484 500 14,055 15 . 300 5 . 808 0 .0605 81 . 885 8 493 36 34 1 3.223 0 . 227 0 .07()() 39 . I 0 885 8 493 37 359 3 . 223 0 .4 58 0 .0700 36 , 68 . 2U 1 4 9 789**2** 11 8 .... • ... • .... •• o I o . o • ,**.a~** 

### I '""I t ool 23 121 2 . 556 3.043 0 . 1785 1 32 .001" 

## z.4ii 15A 1 8 . 1 6 . 8 328 5 930 107.328 1 23 2 228 6 . 940 0 .020 0. 0 90 1 I 9 . 11e 1 . Til t SB I 18 . 1 7 . 1 328 5,930 107 .3 28 129 2 , 326 6 . 940 o .ozs 0.0001.1**t~** 

### Q

PS.11 Elc811"9e 2-R 10 · 27-0C ldo**~Coles** Page 1 of 1 1012912004 

## VES0097638C$ULU OF PO!._XHQMlAL CO RftAADOH Fac:ltlty: Fac:lky 8 l oeetion : A nytown USA V-arbb ' e**~lion** 

# • tU!tet ol data = s, S1 = SUm(•) = s, S2 • S4.tn (dZ). s, S>•9un('l3)• 

### s. S< = Sun (>dC) = 

## s. S5=S<n(y!) = 

### s. S6 ::0 S'u'n (dy!) = s, S1 = Sum (l<i2yi) = O..A**-~·n** • I**•SlS1S~S1S'** =



# • • b'O = ($6$2$ot+$1$3S7•S2S883-57S2S2 5353$5 S 458$ 1)fdllll A= 

# ., bl 

## = (..s6$4.SSSlS2•S2StS7-szses2.S753r>SIStSSYdoiA = 

# •• b2,.**(nS2$7+$ SI82•SSS183-S29~7StS1Vttet**  A= 

### s. 

## s..**5Qlt(( ~n.!)Soold(Y"Y)2)**  = 0 0 • n1S2S..Sl'WitiS3S2.SIS4!+S2 S I S3-S2 • 

## c. 00 • (S:!S'•$3')1) • c , Ct • (S3S2.S 1 S4)i'O• c, C2 • (SIS3 · SZ )10 • 

### c, C3 • ii&• S Z )1) = C, C 4 • ( $ 1 $2-nSS};'O • 

### c. C5 • (f\S2.S 1 )10 • \ ., frOm .a b le = EL Emlssloo UI Tl

r l • Cl C l • 't"S 11 ·sqn {oet lil • m ln ) • I I 

### • 1r' :i. "' 1 00 • v , v 1 fl"om table '"' 

# "" l4f' from \a ble = n• n ' 

### = 1kkltt.3 = k ,**un ~=**  Tl T l=k t 

## = n% T • 1\IEL " tOO%= • 1 M• Sun at I • 

### s Sy •**.~qn(Sumo f**  ( yl-)'-)"2/(n·!) = r' • t -(s,• · 2J S)""2 ) 

### = 

### ' • • ""(( I· S,.•>Jl!y" 2) ) •**r..I 8X~.h?**  b, > 01 "'-- y"**·b, 12~** **·** 1.25><- • ll'dtaK 

### co"·•r.aoon**~~•** Wldelhcd 

# -. JO 5811 

# ••.m 585 . 603 tG.9 96.e38 29$ 7 . 703 21 6,1 58**98E+ ~O** 

2.654**~· 73**  0 . 02203

2.873 11 98E+10 0 .

698**0199** 1.895 1:-03 1 04SE.02 ·2630E-04 6.855 E .()6 2 .052**2~ 3** **~36** 5. 91% 1 . 293 1 .1 81 16. 86 1 . 527 4 . 385 1 6.0%

9 . 96 1.21 0 .844 0 .919 minirrun 3.i3 41 , 88 E miuSon Unit : lnc:Stler.lllor

T ut o.tet : April 3 to &. 2003 l eonetatlon**~K~ uation:**  y• 2.. 154 • .0 . 1n x .. 1 . 02203 _**__)** Summary of**Aue~** Critari:a tor PS..1t 

### a.- 

# _,., 

# - ..., CJtliiH ? Correlebon**c::oe~** 0.1'19 !. U , _., 

# ,.. CCJr6jence i rWval 5..tt .. ,Si'"" 

# ,.. Tolerance**irr'~** 18.0%**~-** 

# ...**lndll:::8ts~~ti5 ~**  W'!IK:III>**l~ "**  '-'UI'Y• ai !Jl ""UI'Tll"- .num ComIrion eunoe mi':imurn CIOir'4 3 . 11 M

ii'WftJm 4ikmablt • '4\18 63 Is**~lftion** CUI'Ye trihl iiTU'I'I < l'lti'rlum "viNe? 

# ,..**~lion** curve ITQ( l rrun I)Oh1 NA Ex!la IJrrj; fo r )( tlMt: of maxlrrun X YAIU 8 NA Is c::onelalion CliVe m; ..

_ invm > .U.Opej8\0'1 ll'na? N A Plot of Potyoomlal Reg 

# I'" l ion Curve 25 

## g 20 ) ..**•0 022~**  · 0 1731ll •• t86J9 

# • f 15 

# • 

# 1.. • 

# • <.> 

# • 

# • l 5 

# • •

....... 0 1-- · · ' 0.0 5 . 0 1 0 .0 1 5.0 20.0 25.0 30 . 0 35 . 0 PM CEM S RuponH

P .IICtneltt!orl'f ... CIICUollloll lj.wUII,._I 4 0.0**~latiN 0/2~**  I I 

## ' 

# i

P$.1 1**~2 -R**  10.27-0t. • Ptf);o• i8l**su~** 111 11201M 

## VES009764CAlCU LATION S FOR LOGARIT HMI C CORRELA n ON F a cility : Facility B Emiss io n Unit; I ncinerator Locotlon : Anytown US A Test Oa te s : Apti l3to 6 , 2 003 P

M PM 

## ",;;;;J.;;:,;;,---- 

## I CALCULATEO .

3 355 1 

### 1---.," I """ ' ,...,...., _ ..,. .() .604 1 2,'!01**~** [742 ]**~** 10! 1 0 1 

### 1



### . . . 1 3 .33tll I <i 3 . 336 1 .262 

### i.2s2 1. 668 

# I I I 1 . 6681**~** 1 0 , I 2 . 896 1 56 18. 1 2 . 896 _l_

PS

- 1 1 Example 2 · R 10-27-04 .xls 6 -0.743 1 2 . 7 ' ft .:-... A 4" "

I . 328 33 . 139 6 . 635 . ' , . .,)lltg ,)U , , 1. 328 3 1 . 998 6 5 1 9 - 1 . 346 •••

.006 9 965 -0 . 239 1 0 . 699

.006 8 . 161 -0 . 2 16 1 0.699 I I I !1QQJ f,951] 

### I

Logarilhmic calcs Page 1 o11 11/1/2004 

## VES009765R ESU LTS OF LOGARITHMIC CORRELATION Fa c ility : Fa cili ty B Locat ion: A n ytown US A Variable Equa!lon n Nu mber or data POints 

# = '/( '1( - 

# = 1/n " (Sum of**'~)** 

# =**s~** ... S,.. 

# = Sum((X'rx'-r2) • y y- 

# = 1 / n"(Sum of**(y~)** 

# = S w 

## Sw • Sum((y ; y-)•2) 

### = 

# s.-, s .., 

# = S u m((X 'r

x '-Xy ; .y-J) 

# = bo 

### bo • y-t>, x '- a 

### b , b, 

# = S...,JS,., 

# = s, s, 

# = S QRT (1/(n-2)(Su m (yf-y 1 )"2)) 

### = y"

..

.,.. y• a t mean x value 

# =**~ ~f** **om** tabl e 

# = C l C l 

# =**·s,·sOR /n** **)** 

# = EL E m issio n L im i t 

# = C l % Cl% = CIIEL"100% 

# =

n' n · 

### = n = v , v , fro m tab l e 

# = u • . un' from tab l e c 

### k, k, s:**tv, ~**  T l Tl 

# = k, " SL 

# = Tl% Tl % 

# = T I /E L" 1 00 % 

# = Sy Sy 

### = SQRT(S,,t( n -1 )) 

# =



# ... r" 

# = 1 · (S,'2/S,'2) 

# = r r**~** SQRT(( 1 .S, ' 2/Sy '2)) 

### = 

# . I n d i cates correlation coefficien t i s un defined .

PS-11**~** 2-R 10.27·04.J<Is E m i ss i on Un i t : I nc i nerator Tes t Dat es : A pril 3 t o 6 , 2 003 ! Correlatio n equati on : y • ·17 . 700 + 9.807 Ln(x ) 

### I Value 30 

# -- · · ····- ·

- -.--. 

# - - J · -· ·-- · 

# ·- · - · . 

# - .. 2 . 82 Cri1erion Actual Al lowable Acceptable? 10.93 Correlation coe llident 0.822 !:,0 . 85 

### no

10 . 0 Confidence in terva l 6 . 37%**~10%** yes 1,531 Toleranoe interva l 2 5 . 6%**25%** 

### no 107 . 2 • Indicates con-e l a tio n ooelllcient Is u ndefined .

- 17.700

9.807 P t ot o f L ogarithmic R• g rnslon Curv. 4.14 1 9 . 957 25 2 . 048 1 . 549 24 . 3 6.37% 30 1 .2 66 1.1 68 !j 20 

# • 

# •• 

# .. y • 9 . 80671.n(x) • 17.7 

# • ]; 1 5 

# •**~** 1 0 

# • 

# • 0 5 

## " 

# • l 0 ·5 0 0 5. 0 1 0 . 0 1 5 . 0 20 . 

### • . o 1 . 503 PM CEM S R u p o n &a 6 . 22 25 . 6% 7 . 266 PS -1 1 Co 1r e 1 a1Jon T est 0 . 675 Calcul ullon Sprvodsheet 0 . 822 Vof'liOn 2·6 1()(.1 5104

l.og011thmoc SOn-mary 1012912004 

### VES009766CALCULATIONS FOR EXPONENTIAL CORRELATJON FaciMty : Facl tlty 8 Emission Unit : ln clner1tor Loc1tlon : Anytown USA Test OatH : Ap rl13 to 8 0 2003 PM concootra!Scn PMCEMS macrn Mea!ILnld Translormed CALCULATED STAllSTICAI. PARAMETERS Run X y ll' = Ln(y) 

# ,,.,. . -y Wd1' , ,.,. .. . )(l(d1 '(" CY"rll'iY 1A 6 . 4 1.3 0.262 17 4.94 2.957 22.744 0 , 888 0.3< 18 8A 1.2 0 .1 82 174.94 3 . 239 23. 803 0888 Oil! 2A 7 . 5 2.3 0.833 1 47.06 1 . 320 13 . 934 0.978 

### o. a 28 7.5 2.5 0.916 147.06 1.136 12.923 0 . 978 0 . 0 3A 11 . 2 2.5 0.916 71 .01 1.136 8.900 1.28< 0 . 1: 38 11. 2 2.8 1 . 030 71 . 01 0.907 8 . 025**1~** 0 . 0 4A 16,4 7.7 2.041 10.41 0 . 004 -4 . 191 1 . 715 0 .1i 48 uu 7.9 2 . 067 10.41 0.007 .0 . 274 1 715 0 . 1: 5I\ 29 . 9 12.9 2.557 105.54 0 . 331 5 . 910 2833 0 . 0 58 29 . 9 12.5 2.526 105.54 0.296 5 . 587 2 . 833 0.0 ! 8A 22.2 7 . 8 2.054 6.62 0 . 005 0.166 2 . 1 05 0.0 : 811 22 . 2 7.3 1 .988 6.62 0 . 000 O.Q15 2 . 195 0 . 0 7A 19.5 5.8 1.758 0.0 2 0.050 0 . 028 1.971 0.0 78 19.5 5.9 1 .775 0 . 02 0 . 043 0.026 1 . 971 0.0 SA 27.4 1 1. 7 2.460 60.42 0.226 3.713 2 . 626 0.0 : 88 27. 4 1 2 2.485 60. 4 2 0.253 3 . 910 2 . 626 0.0 9A 32.8 20.4 3.016 1 73.54 1 . 068 1 3 . 6 1 6 3 . 073 0,0 1 98 32 . 8 20 . 9 3.04 0 1 73 .5 4 1 . 119 1 3.935 3 . 073 0,0 1 lOA 26.S 20.9 3.040 47 .2 4 1 . 1 1 9 7.271 2 . 551 0.2 lOB 26.5 2 1 .3 3. 059 47.24 1 . 159 7 .401 2 .5!>1 0.2 I IA 33.5 22.3 3.105 192.47 1 . 260 1 5.575 3 . 1 31 0 , 0 1 118**33.~** 22.6 3 . 118 1 92 . 4 7 1 .291 1 5 . 760 3 . 131 O , QI 12A 28. 1 18 . 4 2 . 9 1 2 71.8 0 O .Be6 7 .884 2 . 504 Q.Q 128 28. 1 17 . 8 2 . 879 7 1 . 80 0 . 805 7 . 603 2 . 684 0.0 I JA 9.8 3.7 1 . 308 1 00.53 0 .454 6.754 1 . 15 1 0.0 138 9.6 3 . 9 1. 361 1 00. 53 0 . 386 6226 1.151 0 . 0 14A 5.3 4.2 1 . 435 205.25 0.299 7 .835 0 . 795 0,4 1 148 5.3 4 .3 1 . 459 205 .25 0 . 2 7 4 7.497 0 .795 0.4 15A 18. 1 6.8 1.9 17 2.33 0 . 004 0.099 1 . 855 0 . 0 158 18 . 1 7 . 1 1 . 960 2 . 33 0.000 0 . 033 1.855 0 . 0

PS-11 E>amp!e 2 · R 10.27-44Jds Exponootial Cales Pogo 1 of 1 10/2912004 

### VES009767R£SUL'Ci Of EXI'OHENTIAL CORRELATION F ad llty : Fac il ity 8 Location : Anytown USA



### van 

# .- s.. y**~ ~** 

b, ' b, b, 

# -s:- '(A-**-- ~** 

C l ' 

# s S. • 

### - x- • 

## s._. • :**~ Sw~** **_** S.,. • Voluo I = 30 1'1 

### ot (xt) ).. 19 . 63**.** 2.738. · n ol**(y' ~)**  = 1 . 98l ! ) :. 22.04 II • 226 . 81 b,' • y'-l>,x- • 0.35E t., • - · 

### • I 1 . 4281 b, • $.,1&.. • O . Oa:l 1"2)1 = 0.340 '/" 01 moan x vM!o = 1.9 ...... Ct• ·**~from** lablo 

### •1**~** 0 . 1 270 

### 1- 1**-~** 

# -**~~-** 24 . 3 3.80% 30 1 . 2 86**~** v , Uw 

### k;" 

## n · L

# ~

- r

· r

ndie$ttt**P$1 ~2~** **to.n ~** **~-** v , from tobte 

### = u,. f rom tabte • k , • u,"v 1 u Tl ' •k, ' Sl • 1.1 61l 1. 5 03 ),SIC 

## ¥C·**~-·** + TI' 

# 2492 Tl • {e"UT L' • e" LR ' V: 3.866

n% • T I IEL. 1 00% • 1 5 ,_ 9%**~**• SORT(S,..J(n·1)) • 0.8 71 (' • I.(Sl "215./'2) = 0.848 ' • SORT({I · Sl•2JS{'2)) 

## =I 0.92 1 

# "" Emission u · nlt : k1 el ....r•tor Test Dotes : A pri l 3 to 8 , 2 003 [ Comtlatlon equation: 

### y • 1.428 o .... ,. • 

# I S • 

# "' __ , ,.,,_ 

# - · 

# -· Criteria f or PS..

- " Crilerion 

# ...,..... 

# - 

# - 1

Correlation c:oe: l&cient 0 . 921**~0 8.5**  

# .,... Conlldonce i - 3 . 80%**~10%** 

# .,... Tole<ala! intenr.>l 15.9')(,**~25'Jf.** )'08 l ndicat .. oorrela5on ooeffident Is 101delln<>d P lot of Expone nti al Regr'f!sslon CLHVe**~.----- --------------** **---------,** 20 &**~** tS 

# !**~** 1 0 

### l 5 0 . • Y = 1.4281eo0121ll

o .o 5 . 0 1 0.0 15 . 0 20 . 0 MO 3 0 . 0 35.0 P M CEM . S R6 1 J)Onl 6



# --- PS - 11 Comii!MionleM C*-' l aion**S~** v.nbnU**1~** 4 00



# "'""""' VES 0097 68CALCULATIONS FOR POWER CORRELAT IO N FKIII!y : Faelllty B Emi.uion Unit lncinetator LoQUon: Anytown USA THt Dates : April 3 to 6 , 2003

PS-11 e-npte 2 · R 10.27-()oi.Jds Flower Coles Pago1d1**1~00<** 

## VES009769Facility : FaCJUity 8 Locallo n: Anytown USA

P$11**~24t** I O.V.()o& . RESULTS OF POWER CORREiA TtO N Emission Unit : l neinetatOr Test D1tes: Apri 3 to 6, 2003 l cornlation equation: y- 0 . 2007 x 

# um--1

Plot of Power Function Regreas iotl Curve**25 ~--------------------** **------------ -,**  

### j 2 0 

# • 

# •**~** I S 

### § Y= 0 . 2007x '· 21 22**~** 10 

### s

.. 5 0 • 0. 0 

### s . o



# -- 10, 0 16

- 0 

### zo . o 25 . 0 3 0 0 3!5 ,0 400 P M CI!: MS Ro•po,.ll

PS- I 1 CQf'fi! l-*'n T ... lion SpotNIH!oec ··.-nU 11)12511)0



# ·- VES009770Facility : Location : Model 

### Unear Polynomia l Logarilhmie Exponential P OWGr FacW i ty B Anytown USA

Correlation coefficient (a) 0.895 0.919 0 . 822 0 . 921 0.892**~0.85?** Yes Yes No Yes Yes SELECTION OF BEST MODEL Emission Unit : Incinerator Test Dates: Apr113to 6 , 2003 Confidence inte<val**~** 10%? Tolerance i nterval half**~25 %?**  Minimax wilhin hall range peteen!age range percentage ellowallle range? 4.98% Yes 20 . 0% Yes b) 5.9 1% Yes 18.0% Yes Yes 6.37% Yes 25 .6% No bl 3 . 80% Yes 15 .9% Yes b)**1%** Yes 18 . 7% Yes b) (a) • i ndicates comllation cooffiQontls undcmod ; mode l does not satisfy critenon. (b) N ot applicable ; c::ntenon applies o nly to polynomia l model.

PS- 1 1 Co'tt 1 3llotl Test CalCulation Sprtad$hMt Vorticn**2~** 11l"25.'04 PS-11 Example 2·R 10.27-04.xls Bcalmodol :

Best Modal Oocs model moot all cri!ena?

Yes Yes N o Yes Yes Exponenllol

1012912004 

### VES009 77 1

# Appendix A.3 Complete Results of Example No. 3

- Initial Correlation Test

VES009772

### CORRELATIO N TES T PM CEMS AND REFERENCE METHOD TEST . DATA P MCE M S PM concen t ra U on response mg/ocm Run X 

### v

1 58 3 . 5 2 7 . 6 9 3 7 . 8 7 . 8 4 16 . 4 25 . 2 5 1 0 . 1 16 . 6 6 11.1 14 . 3 7 12 . 0 19 . 6 8 1 3 . 2 20 . 1 9 15 .7 23.4 10 17 .6 26.7 11 21 . 7 26 . 8 12 21 .0 28 . 9 13 22 . 3 25 . 7 14 2. 4 . 1 26 . 2 15 24 .7 26 . 2

PS.. 11 Example 3-R 10·27 .Q4.xls Facility: Location : Emission Un i t: Test Datos: Emission limit :

35 30 

## g 25

### ~ t' 20 

# .. u 

# s 15 u 

# l 1: 

# l

0 0.0

Test Data Facility C AnytownUSA HWI November 1 to 4 , 2002 Va lue 17 . 45



## \ 

# • • Units mglacm



# •• 

# • •

5.0 10.0 15.0 

# • 

# • •

20.0 PM CEMS Response 

# •• ••

25. 0 30.0

Page 1 of 1 1012912004 

## VES009773CALCULATIONS FOR LI NEAR CORRELATION Emis sion Unit: HWI Fa cility: Facility C Location : Anyto wn USA Te st Dates : Nov em be r 1 to 4 , 2 002

- PM - CEMS 

## j PM_, __ , __ ,,_, I 

### "A'"'" ATED STA ' 

### Run 

### x y 

### (x, -xl' (y ,- yl'**(x, x-** **~)(y yl**  

### I 1 5 .8 3 .5 92.29 272.25 158 . 51 2 7 . 6 9 60 . 94 121 .00 85 . 87 3 7 . 8 7.8 57.86 148.84 92.8(] 4 16 . 4 25.2 0.99 27.04 5.1



### iO 11 

## i2 13 14 15

PS

- 11 E . xample 3-R 10-27-04 . x ls 10 . 1( 16.61 28.161 1 1 .561 18 . 04 11.11 14.31 18.551 32.491**24 5~** 

2 22 . 24. 2 4 . 19.6 1 1 1 . 611 0.16 1 1.3€ 20.1 1 4.87 1 O.D11 · 0 .22 23 .41 0.09 1 11.561 1.0C 26.7 4.81 44 .89 14 . 7C 26 . 8 1 39 . 6 1 1 46.241 

## 42. 3 1 .29 79 .21 49 . 25.7 1 47 . 521 32.491 39 . 

# I 75.57 1 38 44l 53 . 9 26 . 2 86.37 38 .44 57 . 6

Linear Cales**~-~**

### ~ 8 . 942**11 01~**  11.245 13.892 15 . 043 16 . 079

7 . 460 20 . 338**~** 

# < rrd

29 . 621



## 4

. o-- 1T.ii

16 . 4 7 .3 0 . 1 2 

### 6. 

### 9. 17 . 1 7 )I j3 14 .487 20.222

Page 1 ol1 10/29/2004 

### VES009774RES U LTS OF L INEAR CORRELATION Fa cil i ty : Fa . c ility C Location : A nytow n US A Variable Eauation n Number of data points 

### = X x- 

### = 1 /n " (Sum of (x.)) 

### = 

# s... S,. 

### = Sum((x,-x-)"2 ) - y y- • 1 / n " (Sum o f (yJ) 

# = s,. S,. = Sum((y , y-)"2 ) 

### = 

# s... s., 

# = Sum((>.rx-)(Yrrll 

### = 

### bo bo 

# = y--b,x- 

# = b, b 1 

# = S..,tS ,.,. 

### = 

## s , Sc 

# = SQRI(1/(n·2)(S u m(yh ) }"2)) = y • ,.., 

### Y" at mean x value 

### =**~ fr** **om** tab l e •

C l C l =**·s :s** **/n)** = EL E m i ssio n Li m it 

### = C l % C l % = C I IE L ' 1 00% 

### = n ' n ' = n= 

### v, v 1f r o m tab le 

### = 

# "" u • . fr o m tab le 

### = k

T kl = 

### u .. ··v, = Tl T l 

### = 

## J<. ' S.. = I I % T t % 

### = T I/EL ' 100% 

### =**~** 

## s, = SQRT(Sy,/(n - 1 )) 

### = (' 

### r< =**(5 "21~"2)** **=** r r 

### = SQRT(( 1· S,**"21~"2)) •**  • Ind i ca tes correlatio n coe ffi ci en ll s u n de fi n ed .

P5-11 Example 3-R 1 0 · 27 44 . x ls Value 1 5 15.41

561 : 20 . 00



### 905 645 . 2 2 . 267 1 .1 51 3 . 53 0 20 .000

2 .160 1.969

17 . 5 11 . 2 9 % 1 5 1 .485 1. 184 1.75 9 6.2 1 0 35. 6 % 8 .038 0.807 ____Q,_ 89 8 .. Emission Unit HW I T est Oates: N ovember 1 f . o 4 , 2002 !Correl a tion equat i on : y • 2 . 267 + 1 . 151 xI



## --· ··· · -- . 

# --- · - ·· -- -- · ·-· ·- ·-· . 

# - .. Criterion Act u a l Allowable Acceplable? Conelation coefficient 0.898**~0 85**  yes Con fide n ce in terval 1 1.29%**10%** no Tole 

### ranee intarva l 35.6%**~25%** no

I nd icates co rrelation coefficient Is undefined . Plot of Linea r Regress i on Un e 35

# "----=-**~----:-** 

# I .§ 30 

### 1! 2 5 'f ::ll 1 . 1 6 1x + 2.2665

- 2(1

# ~ 1 5 

### 8 1 0 

## l**~** 

## • 0 . 0 5 . 0 1 0 .0 15 .0 20 .0 2M 30 .0 PM CE MS R espon se

P S. 11 ConuiNlh'l Tat Catw la tion Sp.-udlhlel Vcnion 2-6 1()'2.5104

LJnea r Summary Li near Summary 

## VES 00977 5Facility : Facility C Location : Anytown USA

Run I PN CEMS 

## I ""' ""·-···· malaan X 

### I v 3.! CALCULATIONS FOR pQ LYp!OM!Al CQRRELA!JQN Emiss ion Unit : H W I T est Datal: Hovomber 1 to 4, 2002

r.AI r..111 ATEO:**>~** 

### 1**>~** 

### 1 -tt .. :h .. tyA.v"f-**oo~~a** (yJ • ..-f- 1 Cl ) M...l. 195...1. I 132 2.0 11 8 3.138 0 . 131 0 . 4679 772-25 I 91 3.336 68 52.0 8.429 0 . 328 0 2223 121 00 1: I**~** I , . 8 1 , .8 1 

## --e1"i" 475j 3.702 61 475 8.976 1.384 0 . 2.060 1(8 84 1 : L 4 16.4 25.2 269 4 .4111 

### n.339 4 1 3 6.778 24 .851 0 . 121 ().1650 2704 IJ • · - . • • • 102...1. 1.030...1. 10,406 168 1 693 1 4 . 689 3 . 653 0 . 121 4 123 1368 15181 159 1 .7 62 16.838 6A44 0.1224 32491 0.981 I , I •2 1 111M 144 1 728 2.0 736 235 2.822 18 . 600 1 000 0.132.0 0. 18 1 . 01 8 13.2 20 . 1 1 174 2300 30360 265 3502 20 , 69<1 0 . 352 0 . 1488 AA• • AB • ••• •• • ... 3.870 so757 367 5768 24.119 o . 517 o . 1&n ; 452 95 951 470 8.271 25.876 0 . 679 0. 1541 ., 1,21 8 l ;t t' l**~o tt**  

### «1

.. .. ..... .. ... .. ... 497

. • 581

... 610

PS.II E>camjlle 3-R 10·77.0.1.>1!o Polynomoal cates Page loll IM9/2004 

### VES009776&ESUL IS Of POLYNQUI AL CQRR£LAJ!ON h cii1y. FacUlty C l oedon : Anytown U S A fmiuto n U nit HWI T es t**Da te~**  November 1 to 4 , 200 2 Vll'lfl<1tl .. 

### e... .,.**~** ! co mil:l.5on esu -atiOn : x • · 11 .37t .. 4.211 • • -4.10 1 2l ..:' I



### s



# .. "' I = S-ii'YI ()i) = ! •&l'n C 

### a• s-.mc**~** SS•l**S6·~** S7 • S...**()12y~** = elM A •**ns2SJiOS2S2S2•S1SSS2:S!iS~·SZs1SSOS4Sis1** • 

# ""' 4 ,1 21

# ~ 

# -

.**~** 

### tot.ossl bO 

### = (56S254•S1S3S7 • S.z:s&S3.$7$.2$2-$3$3$5 · $4$6S1)141M A.. 

### I

· 18 , )71 1 1)1 •ln:>G::i4• ·:i5S3S2•S2S 1S 1 · S2S6S2 · S7S3n-S4-S1S5)'det A= 4 . 296 b2 • { n&2S1• S 1S&S2• S.SS1SS·S"S2S5·SSSin-S7S 1S 1 )to.t A • .0 . 10123 I ...,. I S: •SQI1(t11(n.,)Sumd(y""'Y)2)• 1.279 0 0• n S2$6..S3 •S 1 S3S2..S1S4 S St 

### = 1.16BE•06 • UJ =**(~YVD** = 3.48 1 

### :, 

## c.

v, 

# ""

s,**~** r 

## 1--1 1



# ....1.2$ltPS-1 1**~** 3-R 10.27-0t .. Sy•t

J lft:ltlhld : 1 • (S3S2.S1 S4 }.10. ..0.4833 C2• 1 ""C37(1'S4 · S2'VD' C4 ;o**(S1S2~).10** 

## · I "'C601 Eml tib Cl•**·s,.** 

### -:;;;We

i'• 

## ' 

# ..**~~'** tom la bte = I kl -= oo"''Yf 

### = I Tl -= k t'$ p 

### = 'r i l E

# ~**·· MJ~** **I** b,, 

### 01 1 't -= .OJ2bt' 7 . 1 24C.o:2 l 2. 1 O J 1.5 1 5 1 .200 1 1.831**~ ~**  8 04 ) .975 

### ""0:981 1.22**~88 1** 

_ ... Su .......SUIIIMM'J' of Acceptt.nee Cthtt. for P $.1 1 Oi:erion 

# - 

# - • ' 

# . .. ,**Contllltion~** OJI87 ! .... 

# ,.. Cor-Mence l

- 5 . 56,. 

### s 13 

# .... 

# T-- 13o4Y.**~** 

# ,... lncfQ.tes c:otfNfon**~** i5 ....-red ctMICk f or COITelation Curw Minimu:ml 'lrla: d -m Cc:lt'N.lAon CUI"4 miirrun POi'1t 

### w. l.i.rimum allowable x wbe NA II**~atim** OUNe mini'Tun < mln lrrun • v1lu o? 

### w. Ccrrel&':':lon curve madnun point 21 2 atlo n lirnll ror,.. 125 % ot man-rum x vttut 300 ts**corre!a~** caiiVe Mral(lmiJtn,. tlhi)OIJiiOn Uml? no**P~** o f**Po~omla l**  Regr e u l on C!.K'Ve 

# .. e 30 

# l2$ "**~** 20 . 

## g 15 u 10 

### il! • 0 0 . 0 

# . .

7 • 

# .....

5 . 0 1 0 . 0 1 5 . 0 20 0 25. 0 PM CEMS R etponN



## ,..., ecw,..,.,. '"'**~·~**

# ...**~. ,**  30.0 

### I

Mbol 2>e IGI2W

11/1 /201)1 

### VES009777CALCULATIONS FOR lOGARITH M IC CORRELATION Facility : Faci lity 

## c Emission Unit : HWl location : Anytown USA Test Dates : November 1 to 4 , 2002 PM CEMS response 

### I PM • Transformed 111Q/acrn CALCULATED STA l tltK:S 

### Run x x'; I n ( x ) y { x, - x'")" {y r yl" { x' r x' l<YrY y" ('f"rY I J" 5 .8 1.758 3 . 5 0.785 272 .250 1 4 . 620 i. 106 2 .578 7 .6 2 . 028 9 0.379 121 . 000 6 . 774 1 .849 0 .421 I ., 7 .8 2 . 054 7 . 8 0.348 148 .840 7 . 196 1. 088 5 .225 • 1 8.4 2 . 797 - · - - A- • A. A • A A •-•**578** 8 .877 10 . 11 2 . 313 1 1 6 . 61 0 . 110) 1 1 .560 1 1 . 1 2.407 14 . 3 0 . 056 r 12 2 . 485 1 9 . 6 0 . 025 0 . 160 u . u<>« " . ... A · - A A rAA

- - • 0,004 0 , 0 1 0

- -AA • A AO 3.1 1 . 045

. 1 05 

### 18f • . 207 1 . 9 

## --::; 1 1 . 560 l.2' )1**~** 8 . 6 1 6



# ..947 1 . l-565 : ,,..,.,.. 

# . 0 . 235 

# • M I 4 . 6931

. ... 4 .175 

### 8.1 1 10.63 '

PS-11 Ex ample J.R 1 0.27-<l4 . xls Logarithmic Cales Page 1 of 1 1012912004 

## VES009778RESULTS OF LOGARITH M IC CORRELATION Facility : Fac ili ty C Loca tion : Anytown USA Variable E auation n N umber ol data polnlS - 

## .: )(- = 1/n " ( Sum ol ( )( J)- 

## s ,... s ..... 

### = Sum( ( )( r x ' - )" 2) " 

### y y- 

# = 1/n " (Su m of (YI)) 

### = 

### s,., S,., a Sum((yrY-)"2) 

### = 

## s.., s .., 

# = Sum (( )( r x '-)( Y rY-)) 

### = b o 

### bo = y--b,)(- " b , b, 

# = s,.,;s('( -**~** 

### S.. 

### = SQRT( 1/(n · 2)(Sum(y ,'· y1)"2)) 

### = Y"'mu n 

### Y" at me an x va l ue 

### =**~ ~**  t rom tab l e 

### =

C l C l 

### =**~·s ,'S** **QRT(1/n)** 

### = EL Em is sio n L i m it 

### = C l % C l % • C II E L'100%-

n ' n ' = n = v , v 1 fro m t ab l e 

### =**u~** 

### u, , from tab l e 

### = k

r k1 = u" ·•v l 

### = Tl T l 

# = k 1 " S L 

# = T l % T l % 

# = T IIEL " 100%" 

## s, S, 

### = SQ R T(Sy,/(n· 1 ))- 

### r 

### r • 1 -(Sc'2/S, •2) " r ra SQRT((1.Sc•21Sy•2))•

-- • lndlcales cotr&lallon coefficient is undefined .

PS-11 EJoJinjl!O 3-R 1 0.27-()l. . ldS V alue15 2 . 64 2 . 96 20 . 0 905 4 9.8

· 24 . 443 16.809 2.290 20 . 000

2 .1 60 1 .277

17.5 7 . 32% 1 5 1.485 1. 1 84 1 .759 4 . 03 23 . 1 % 8 . 038 0. 9 1 9 0.9 59 Emission Unit : HWI Test Dates: November 1 to 4 , 2002 ! Correlation equation : y • ·24 . 443 + 16 . 809

- [n( x ) 

## I

-- • n•• • -• 

## -· ··- 

## ·· - -**~-·** 

## · · - · -· . 

# - . . cntenon A ctual Al l owa ble Aoceptable? Correlatio n coeffide nt 0 . 959**~0 85**  ye s Confidence interval 1-32%**~1 0%**  

### yes Tole 

### ranee In t e rval 23.1% .::, 25 % yes • I n dicates oorrelallon coeffi cie nt is undefined . Plot of Logarithm i C: R eg r easlon Curvo 

### & : ) y • 1 M09l n tx ) • l4 . «3 

# I 

# •--.- 

# .. g2S C2Q 

# j**~ ~**  5

### 0~**-- ~------** **-- --** **--~--~--~** 0 .0

Lcgarilllmic &.n-ma<y & .0 1 0 .0 15 . 0 20 .0 25. 0 30 . 0

PMCEMSRaaponsa

P S. t1 Cotrtku lon T &at CaJQJIIIlon S pte8dlhtet Voralon 2-6 10/25104

10/2912004 

## VES009779CA LCULATIO NS FOR EXPONENTIAL CORRELATION Facility : Facility C Emission Unit : HWI L oeallon : Anytown USA Test Dates : November 1 t o 4 , 2002 PM• PMCEMS ..,AI 

# "''".A TEC 

### Run

1 

### x y y' 

### = Ln{y) (J<r £ )" (y'

### rYl" ( x,-x )(y' 

## , y) Y" 5 . 8 3 . 5 1.253 92 . 29 2.614 15 . 533 2 . 1 15 0 . 744 L 7 . 6 9 2 . 197 60.94 0.452 5 .249 2 . 256 0 . 004 I 1 3 1 7 . 8 7 . 8 2 . 054 57.86 0.665 6 . 203 2 . 272 0 . 048 I •**~** • "" " 3.227 0.99 0.128 0 . 355 2 . 948 2 . 809 28 . 1 6 0 . 004 0 . 320 2 . 4 53 ! . 660 1 18 . 55 1 0 . 044 1 0.9021 2 . 531 

# I 13 

# I 22.31 25.71

- - 3 . 2461 4 7 . "LI v.**·~** 1 4 l4.1 26.21 3 . 2661 75 . 5"1 A •• 15**--** 24.71

- - 26.21 3 .2661 86 .371 0.1571 3 . 681 

### I I

P$-1 1 Example 3-R 10-27-04 . xls Exponential Cales Page 1 of 1 10/2912004 

## VES009780RESULTS OF EXPQNEHDAl CORRELADON fla

. c l lfty : f .c: I IHy C**Loca~on :**  An yt..., U S A

V a riatlle: n**~** 

## • 

# s:- ..**~** 

## s., bo' 

# .. b, 

# s. I s..•l 

# "A

- · L ; r

·

v, 

# ""' k, T

l ' n% s,. 

# ,.--

'**P$ 1~)-ft**  t0.21.()4 • •**~** ...**t~t~** Nurnbet 

### ot dlsa po!ro ; I

x-• 11n ' (S..mof(ll.))• l**~-:** '/-•1 Sw • 

### s....<<Y,., SC)'•l



## " . = : 

### b

, • O"'tJ,g'• : b, ..**s~~ ~**  '/'" at rnoWl x velve = I**~** 1rom u. bfo 

### • I crsl C l • (e" U CL ' .. i : mi ssion L lmi**~00%= :**  v, f

rom t.abte 

### = ; u,. from table= : k r • o ,., " v , * : 

### n • ttc ' S L• , tTL '·**Tl ~** **~t,. "1** **oo%--s:·** Sy•**~** " • 1-(Sl "2/Sy' 2 ) • l i

S\ v ....**~**

# ~ Te70I 

# j 03

659 256 0 .079 1 

## D.35il 2. 87 0 !**I** 0. 1 96<

3. •

1 . 4 85 1 1 .1 84 1 1 . 759 1**~59 1**  0 . 8 12 Emission U nit : H WI T est Dat a: Novemb er 1 t . o 4 , 200 2 

# I correlation !<!Uation : y : 5.256 e ... ,.. • 

# I s..nm.ryof A Crit.na for P S..11 CrMrion AcWof 

# - Correlo1ion ooellldoi . 0 . 8 1 2**~065** Confidence- 19.93%**!~** T

01e1anc:e irterval 66 . 5% !25% 

# . Ind icates COTelati on c:oefficienC is undefined.



# .. 35 

### g "" 11 2S 

### i 

# J: l, .**~** 0 0 . 0



# ........ ............ P lot o f EXponent i• l**~r.atiOn** Cu r'V e



## • 5. 0 Y• 5 .2565e 00785ol

1 0 . 0 15 .D 

### ... o 

# ,..**EM H~•** 

PS- 1 1 Cclrntl*" T.sa C. u !W i on**S~Q~cllltl•** V. r

.tbn 2 · 8**1~ Accc~able?**  no no no

:tO O



# '""""""' V ES009 7 8 1CALC ULAI! O NS F OR POWE R CO RRELA TIO N FacUlty: Facility 

## c Emission Uni t : H WI Location : Anyto w n USA Tes t Dates: N ovember 1to 4 , 2 002

Run

1 PMCEMS X PM• 

### ''"'"""""" 1 

## m""""'"" 1 Transfonned 

### 1 CALCULATED STA1 'I( 

### = Ln ( x) 

## u " _ ' "'u' Y"\2 I •n 

## y• 1 I - ' \ I I 1 . 758 3.5 1253 0 . 785 2.614 1 . 810**310~**

)28 n "ll ,. ,.,., n**"ll~** n ..**~..,** n .._ ., .._ .,. • .,.,. n ......,.._., 2 . 054 0 . 6E

.. ' .. . . 3 . 227 0 . 024 0 . 1< ) .055 

## i1i20 50 r- ..... .. ... ........ ...... .... ... ......... ... .. .. ... 0 . 0( 2.485 1 19 .61 2 . 976 1 0 . 0 25 1 0 . 011 [ -0.0171 2 . 6791 0.081 1 3 . 21 2580L 20 . 11 3 . 001 [ 0 . 004 1 0 . 0 1 1 1 -0.0081 2 . 7931 0 . 0430 1 5 . 7 2 . 754 23.4 3 . 1 53 0 . 0 1 2 0 . 080 0.031 3 . 001 0.023 1 7 . 6 2 . 668 26.7 3 . 265 0 . 050 0 . 17 2 0.093 3.13 7 0.021. 2 1 . 7 3 . 077 26 . 8 3 . 288 0 . 188 0 . 175 0.181 3 . 388 0.0099

21 3 . 045 28.9 3 . 364 0 . 160 0 . 2 44 0.198 3 . 349 0.0002 ! . 3[ 3 . 105 1 25.71 3 .246[ 0 .2121 0 . 1 42 1 0.1741 3.421 1 0.0303 I 1 4 I 24 . 1 

### 1 3 . 182 

### 1 26.2 

### 1 3 . 266 

### 1 o . 290I o . 157l o. 213 l 3 . 5 1 3 

### 1 o.0613I 1 5 24 . 7 3 .207 26.2 3 . 266 0 . 317 0 . 157 0.2 . 23 3 . 543 0.0767

P$-11 Example J.R 1 D-27-04 . XIs Power Cales Page 1 of 1 1012912004 

### VES009 782RESULTS Of PQW£8 COBBELADON Facil ity: F 1clllty C L.oulion: Atlytown USA

Variable 

### e.... ..., value I n**Nun'mOrof da** **ta~ ·**  15 ' f 'K- • 11n"(&m cl ( X' ,**I)~** 2.644 ; 

## s..., S.., • Sum((JI' r ll'

-)'2} • 2.96 '(-. 1/n ' (St.m of (y'J}. 2.870 s..,. Sum(('(r'(-}"2}. 5 . 06 

## s,. s,... Sum((JI' , IC" -)(y'r'(•}}. 3.54 

# ., .. DQ' •**V'-·b~·-** : -0.292 

# .,. bo• tf'Oo'• 0.7 47 b, bt • S.ryJS .. ... : 1 . 196 

### s,_ s,_ • SOR T(11(,...2XS ""'(y' ('-'(.)'2}} = 0.253 '/"'- yM a t mea n x value : 2 . 870**~ from**  t.ab l e • 2 . 1 60



### c r C l •**'Sl' SCIRT(1hl}**  •**1** LC l' LC L '• · C I ' 2 . 7 29 UCl' UC L ' • yo. ' • Cr 3.0 1 1 C 1 Cl • (r UCl " • o" l C l ' V2 2 .4 92 El Em i ssion Li rri l = 17.5 C l % C l '% • CtiEL "100 1 = 14.28'14

n • n'= n • 15 v , v 1 f r om tabl e • 1.4 85 

## "" un' rrM'I t able • 1. 1 84 k , k , 

### a u..- · v, • 1. 759 Tl ' Tl ' • k ,S, • 044 4 L TL' Ln ' • . . n- 2 . 425 

### un · UTL' • Y .... ... 

## n · 3 . 3 14 n Tl • e"'T L' • e "l T

l 'l/2 8 . 093 TO% Tl % • TI /EL'100% = 46.4 % S. ·**~** • SORT(S ., I(r>-1}) = 0601 

# , r' • 1-(S l •21S,1'2} • 0 . 824 

# , r • SORT(( 1 -5L •21SyA2)} 

### = 0 . 906 • ln dieal4!s**eotre ~**  ooefflc l«< t I t un deftnecl**P$ol1~)oR lW7~...at**  Emission U nit; H't'Yl T e st Dates: N o'lerN:loer 1 to 4. 2002 ! correlation equation: y- 0 . 7466 x**..,,.,~**



## ........... ... .._..... 

# -·-- ..

# ..- ·-·- . ......- 

# .. Criterion 

# - ..,_ -·?I Conelatbn ooefticior It 0.908**~0 65**  yes ' Confidence intaval 14 .28% :!1"" no 

### I Tc:Rtance interVal <46.4%**~25%** no _j l ncfgle$ CO<TEiolion ooellic:iool is

- - Plot of Power Function Regreuion Curve 40 3 5 

### :5 30 

# ! 25 c 8 20 c 

# s 15 

## l 1 0 

### s 0 0.0



# -- y 

### = 0 . 7466x1 1959



## • s .

o tO. O tS . O 2 0 . 0 PM CEMS R o• pon .. 2&0 3 0 . 0

S. t t Coi'NIIIon Te 1 t iciAtiU On**~lhi'G l**  I C o'2MM 

# '"""""" VES009783SELECT ION Of BEST MODEL Emioslon Unlt: HWI Facility : location : Facility C Anytown USA Tnt Dat es : N ovember 1 to 4 , 2.002 Mode! 1 Conelalion 

# I > 0 . 85 7 

# I Confidence Interval 

## I < 1 0%? eoellidenl ( a)

- half range percentage - Une ar 

### I 0 . 898 Yes - 1t.29 % No 1.987 Yes 5 . 56% Yes 1.959 Yea 7 . 32% Y es 1 . 812 

### No 1 9.93% • • - Power I 0 . . 908 Yes 1 4 . 28% (a ) • i ndlcates correlalion coefficien t Is undofiOOd ; model does not**sa ~sf**  (b) Not applicable; criterion app l ies only to polynomia l model.

P S-11 Cmlllal:ion Tnt CaloAabon Spreacbheet Vet&ion 2-6 10125104 

## I Tolerance inle<Val half

range pen:enlag e 35.6 '

PS-11 Exam ple 3-R 10.27-0ol .xls Best Model !;:25 % 7 No 

## YeS Yes 

### No 

### No M 1nlmax**w~hin** allowallle range? 

## ...i!!l

N<

Boot modo! : Docs model mool al l cnlerla 7



### No 

### No Yos 

### No N Logorllhmlc

1009/2004 

### VES 009784

# Appendix A.4 Complete Results of Example No.4 Original Test Data

VES009785

### CORRELATIO N TEST PM CEMS AND REFERENCE METHOD TEST DATA PMCE MS P M ooncentratioo 

### re'

mon se mota em Ru n X v

1 6.7 3.1 2 7 . 6 7 .4 3 7.8 2 . 1 ! 4 9 . 2 3.7 ' 5 10.1 6 . 1 6 11.1 2.8 7 12.0 4 . 9 8 18 2 8.3 9 1 3 . 7 4 . 5 10 14 .6 8.2 11 19 .7 13 .0 12 18 .0 11.1 13 20 .3 1 1.9 14 202 1 0 . 6 15 19 .7 9 .2

PS-11 Example 4A-R 1(). 27-04 .xls Facility : Location : Emission Unit: Teat Dates : Emlulon limit:

14 1 2 

## g 10 . 

## i**~** 8 

# • u 

## g 0 6 :I! 4 . 

# ... 2 0 0 .0

Test Data Facility 0 Anytown USA Boiler November 1 to 4 , 2002 Value

18.5



# •

5 .0 

# • • llnl!l mg/acm



# • 

# • • •

10 . 0 

# • 

# •

1 5 .0 PM CE M S Response 

# • • 

# • • • •

20.0 25 . 0

P age 1 of 1 10/29/2004 

## VES009786Fa cili ty : Fac ility D Locatio n : A nytown U S A PM CEMS 

### reSDOnse Run X

1 6 . 7 2 7.6 3 7.8 4 9 .2 5 1 0.1 6 11 . 1 7 12 8 18 .2 9 1 3 . 7 10 14 .6 1 1 1 9.7 1 2 18 13 20 . 3 14 20 . 2 1 5 19 . 7

P5- 11 Exemple 4A·R 10

- 27-04. xl s CALCULATIONS FOR UN EAR CORRELATION Emiss i on Un i t : Boiler Te st Da tes: N o v e mber 1 to 4 , 2 002 PM concent ration mg/acm CALCULATED S TATISTICAL PARAMETERS y 

### (x,-xl• 

## <YdY (x.-x"J{yrYl 

### Y" <Y" r YY 3. 1 52.22 16.21 29 .10 2 .808 0 . 085 7.4 40.03 0.07 -1. 7 3 3.346 1 6.437 2 .1 37 .54 25.27 30.80 3. 4 65 1 . 864 3 . 7 22.34 t1.7 4 16.20 4 . 302 0 .362 6. 1 14.64 1.05 3.93 

### 4 .840 1 . 588 2.8 7. 99 18. 72 12.23 5 .4 37 6 . 956 

### 4 . 9 3 .71 4 . 96 4.29 5.975 1 . 1 56 8.3 1826 1.38 5.01 

### 9 .680 1 . 906 4.5 0 . 05 6.90 0.60 6.991 6 . 2 06 8.2 0.45 1.15 0.72 7.529 0 . 450 13 33.33 34 . 50 33 . 91 10 .577 5 . 872 1 1 . 1 16.59 1 5.79 16. 1 8 9.561 2 . 369 11.9 40.62 22.78 30 .42 10.935 0 .930 10.6 39.35 12.06 2 1 . 79 10 . 876 O.D76 9.2 33.33 4.30 1 1 .97 10.577 1 . 896

linear Cales Page 1 o f 1 1012912004 

## VES009787Fac ility : Facili t y D Location : A n ytown USA

P$-11 Example4A - R 1o- 27-o4 . x ls RESULTS OF LINEAR CORRELATION Emission Unit: Boiler Test Da . tes: N ov e mber 1 to 4 , 2 002 ! Correlation eq uation: y 

## = -1 . 196 

### + 0 . 5 98 

## xI s of A· 

# _

... , 

# . .. . . _.. 

# -· 

# .-.--**-·~~** Criteria for PS-11

--- - -. Criterion Actual Allowable Acceptable? Correlation coefficie nt 0 . 841**~0 65**  no Confi dence interva l 5 . 80%**~10%** yes Tole ra nee in terval 16.3%**25 %**  yes • I nd icates correlation coeffiCient Is undefined . 

### j

# ~ 

# t**~** 10 

### i 8 u 6 

# 8 4 :1 

# .. 2**~** 0 0 .0 Plot or Unoar R ogrosslon Une



## . 

# • • y = 0.5976x · 1.196 

# • 

# -. 5 . 0 1 0 .0 t 5 .0 20.0 2.:5 . 0 PM C EM S Respons e

PS·1t Correlat ion T est C.. l wi•Uoo Sl>roodsheet Veroloo 2-ll 1012510<

Linear Summary Linea r Summary 

### VES009 788Facility : Facility D l.ocaUon : Anytown USA

R un X**~** v 

### 7 CALCULATIONS FOR POLYNOMIAL CORRELATION Emission Unit : Boiler T est Dates: N ovemb9t 1 to 4 , 2002 CALCUlATED 

## 7 1 •' 

# !xviOir' l! '('yl'ldollal!"-v- 301 2._o1s ____**2~ _**  _ 139 , _ 024 o . 854 o . • 111 i Cl 

### 2.'i 439 I 3.3361 56 I 4 27 4 . 032 1 1.348 0.2412 I U . Uf '""' I 128 4 . 043 3 , 775 0 2158 25.27 1 . 87 1 • 1 .. .., .,. 

### 1 rni 7.1641 34j 313 • . 2 19 0 . 210 0 . 1296 •• • • • • • 5 10 . 1 8 . 1 102 1.030 10A06 62 622 4_.23 2812 0 . 13 • • • • "" ... 1, 3681 15 ,1 811 31 I 345 4.733 • ••• • • • 1l 144 I 1 728 20 736 59 706 5.085 I 029 109 720 1 5 1 2 749 9 ,437 I • I '·"' .. . o - 1 88) - 2.57 1 35.228 62 84-5 5 . 945 10 14 . 8 8 . 2 213 3112 45,4 37 120 1 .748 8.502

... .... • ... 388 "r .. .. _., .,........ ..**"'"'~** I:: n.&tt: .OA nn<>

# ~ I u I 10 1 1.1 324 5 832**1~ 976**  200 I**"' ·~**  l:l . i'q.q I .J.444 I u .

.... 203 1 1 .9 4 12 8365 1 69 .8 1 8 242 .. ........ .. .. ..... .. ........... ... ' 20.2 10 . 6 408 8 2 4 2 166 . 497 214 I 4 , 1 9.7 9 .2 38 8 7 ,64 5 1 50 ,614 1 81 I 3 . 5**~** u.vu 1 u .,;c.;**"0~** .............. . 1.

P& 1 1 Example 4 "-R 11).2 7.()4 ... Polynomial Cates "-1ol1 10129/2004 

## VES 009 789RESlJL!& Of POLY N(M !! C0 68 f ' e !IOH Feclity : F' aeUity 0 Location: A nytown US A EmiUion Unit B Oiltr T est D ates : Nowmber 1 to 4 , 1002 

# v

..- 

# _ .....**Va ue**  IU'nbetddau 

### l com&atton eguauon: y • t. llt • 

### .o . e:ts a • O . Mllt I? 

### I 

# " • I S 

### s, St•Sum<•O = 2($ 

### s, S2 • Slm {d2 ). 3,270 

### s, S3 • Smt (1113) . 55.562 

### s. S4. Sum ():141) • 995. 443 

### s. SS•&m6") • ,07 s, 

### se • s..n !><1!'1 • 1.1' 0< s, $1• Sl.l'n (l'i2yt1 = 29 . 463 

# ...... 

# ....... ' I •S2St I I • 2 107E.o7



# .. btl•**(~• 9\$)S7** **S2SSS3-S7S2S2.S3SJS5.S.4S6St~** A = 6 .1 89 b , bl • (nSSS4 • S5S3S2• S2SIS7-s2SeS:NI7S3n-S<S1S5YOoiA •**5** b, b2 • (nS287•S1S8&2 • S5SUa).S2S.'S5·S3Sen.S7$1$ tYO .. A-= 0.()<361 

### s, S. • -( 1 ((1>3- d**~YIZI** • 1.843 D D • n(82S4-SJ')tSt SlS2-StS4)• · S2(S tSl · S2') • 2 . 1 07E..07 Co 

## 00=(•<>•··· · ,.,. 7.963 

### c, Ct • (SSS2·S 1 S4)1t) • · 1 2473 c, C2 • ( SIS3·92")'1) • 4 J4EE.02 c, C3-. nS4·ST)ID •**01 -01**  

### c , C4 • (S1S2- n S3)'1) • · 7. 1 38E-03 

### c, C5 •**S2·~ ')/D**  • 2.561E-04 \ 1 1fl'om llitbllt • 2.179 E L E mh:Wn Limit • 18 , 5 Cl Cl• lf"S.,**"t(J1{~U.·I1Wl••** 1.4 2 1 C l % =CIIEL "tOO= 7 . 68% 

# ,, v 1 from lai*t = 1 .515 

# "" u ff from ta ble = 1 .208 

# .. rf = 1 / d e lta = 7 . 98 

# •• I« = m'"\tf= 1.831 Tl Tl = kl's = 3 .373 Tl n% = 

### · w

a. " 100% • 1 8 . 2%

- • 1/h' Sl.rn d 

### • 7 . 13 Sy • IQI1 S um of (**yi·y-)"2~n-l)** • 3.M = 1-(S "2/Sr"2} = 0 . 7 l1 r r • SQO(( I.S,'2/SY'2)) • O.S55 -..-..? .. >01 mtrimum



# ,.,_ y • -b,/2 .. . 705 1.25l<._ 25.38 •**l'ldiC::*t~~nt•~** PS-1 t Exetrde ofA.R 10..27-Cot..dl ""'''"' .... Summory Sunwnaty ol**~** Oott.n. fot P$-11 Ctllll'!ion 

# - - kc 3 I ? 

# """""""'_....

# .... 0805**~0 85**  

# - Conidlr<e- 7.1SI .. .! 10'1. 

# - Tcltlwloe inttwll 18.2% .f2!N 

# .... .

## -corraladoo-~- C bed for CorTebtion Cwve wtnimUII'IIMUtm 1 nn Careta»n CUM! rt'lf'l1mum po" 705 M

irWoom allowabae • ¥8iJe 6 .7 I to oorrelation CIJl"ie mhl100m < ,...,um x Ylllue? 

# ,. Correralio" tu'WJ maxim.m**~~** NA imil fof x f125')(. of m;uinum ave!UI NA Is ccne lation o. n ve maxhum > exlr9polatlon lrn l t? NA Plol of Polynom.la t R e gl' enk m C urv e 

# .. e 1 2 

## ! 10 

# 1 8

### ~ 

# • " 

# • " 

# .. 2 · 0 

### o

. o )' .**0.4)436~'.** 06 1 5lb .. 6 1 8\l 

## • • 

# • • 

# • • • • 

# • • • •



# • 5 . 0 1 0 . 0 1 5.0 20.0 PM CE MS RupoMe

,..,, Oori'Wib'l r•**Clf~·~~~Mtl** 

### !

25.0

........bfl2>4 t012 ....

11/11'20(M 

### VES009790CALCVLA TIONS FOR LOGARITHMIC CQRRELATION Facility: Fac il ity 0 location : Anytown USA Emission Unit : Boiler Test Dates : November 1 to 4, 2002 P

M · P M · CALCULATED STATIST I CAL PARAMETERS 

### Ru n x 

## I x ' 

### = I n (x) 

## I y 

## I ( x,. · x'l' I 

## (y , . y-)' l<x' rx' ' )(y , y') l y• I (Y" r Yil 2 1 6 . 71 1 . 9021 3.11 o . 439 l 1 6 . 21 41 2 . 669 1_ .. 2 . 244 1 o. < 

### 2 1:6( 2 .028 1 ···- 

### J A I 0 .288 1 0075( · 0 . 147 ( 3 . 173 1 17 . 7 . 8 2.054 2.1 0.261 25.267 2 . 568 3 .364 1 .5 4 9 . 2 2.219 3 . 7 0.120 1 1 .742 1 . 185 4 .580 0.774 I**~** I 10.1 2.313 6 . 1 0.064 1 .054 0 . 259 5.267 0 . 694**~** 1 1.1 2 . 407 2 . 8 0.025 1 8.720 0 . 684 5 . 962 1 0 . 000 I , I 12 2.485 4 . 9 0 .006 4 . 958 0 . 178 6 .536 2 . 678 1 8 1 18 .2 2 . 901 8 . 3 0.113 1. 377 0 .395 9 . 604 1.700 I ft**•~ ~**  ft**~n** 4 . 5 0 .003 6 .899 .0 . 138 7.512 9 .073 8 . 2 0.013 1. 152 0 . 124 7 . 981 0. 048 1 1 

## I 1 9.71 2 . 9811 1 31 0 . 1131 34 . 496 1- 

### n 2.441I 10 . 1871 7 .9 1 2 1 

### 12 18

- 2 . 890 11 . 1 0.106 15.787 1 . 293 9.523 2 . 4881 13 20 .3 3 . 011 11 . 9 0 . 199 22 .785 2 . 1 27 10.408 2 . 2261 14 20.2 3 . 006 1 0 . 6 0.194 1 2 .064 1 . 530 10.3 7 2 0 .0 521 15 1 9.7 2 .98 1 9 . 2 0.173 4.299 0 . 862 10 .187 0.9 75

PS

- 11 E x ample 4A ·R 10·27 · 04 . X1 s Loga ril hmic Cales Page 1 of 1 1012912004 

## YES00979 1RESULTS OF LOGARITH MIC CORRELATION Facility : Facility D Locafton : Anytown USA

Variable Equation n Numbe r of data po i nts ., x' x ' - : 1/ n '(S u m o f (x ' 1

)) 

### = slt

· x · 

## s,, . = Sum((x ' ,-x' -)"'2) 

### = y y- : 1/ n' (S um of (y,)) 

### = 

## s,. S.,,

- Sum ((y r y-)'2 ) =**s,~ ~:**  Su m((x',x ' -)( y, -y -)) = 

### bo bo- y- · b, x'- " 

### b ,**b,=~:** 

# s.. S.. 

### = SQRT (1/(n ·2 X Sum(yi'-y ,)"' 2 )): 

### Y'- y" at mean x valUe -**~ ~f** **om** tableC l Cl =**~** ·s, · soRT(1 /n) 

### = EL Em issk> n Limit 

### = Clo/o Cl% =CI / EL'100% -

n' n' =n = v , v 1 from tab l e 

### = 

### u, u ., from tab l e 

# = k, 

### k. 

### = U n ' - •v , 

### = T l 

### n = kt'SL = TI% TI%- TI/EL ' 100% = 

## s.,. S.,. = SQRT (S,,( n · 1 )) = 

# ,. r" : 1- ( S.. 

### "215.,. '2) : r r 

### = SQRT ((1..S,"21S,'2)) 

### =

. lndica les corre la U on ooefficie nt is u ndeflMd .**P$ ~1** **1** EK:ampl t**~A R** **10 27~4.xts**  Emission Unit : Boiler Test Dates: November 1 to 4, 2002 [Correlation equation: y • -11.764 •**7~3~Ln(x)** 

### I Value 15 ..,.,.,,,,,,.,, y '" ..,._.,..,....,, ,......, -•••v• o u**•~• ~** **~-** • • 2 . 57 Cri ter ion Acl ua l Al l owable Acceplable? 2 . 18 Correlation ooeff-.cie nt 0 .801 >0.85 no

7 . 1 Confidence I n terval 6 .41 % !:,10% yes 1 77 T oleranee i nterval 20 .2%**~25%** yes 16 .0 • I ndicates co rrelation coeffident i s undefi n ed.

· 11.764

7 . 365 PlOt of**L.c91rfthm~ Re~aton**  Cui'Yt: 2 . 127 7 . 127 2 . 160 1.187

18 . 5 6 . 4 1 % 1 5**~---- ----------** **---------- --** **---- ~~--** **-- --,**  

### g 12 

# i 

# • y = 7 .3641ln(l() • 1 1 . 711' 

# • 

# e 10 1! 8 I 

# • •

# ~ 6 

# • " 2 I**.** 

# • 

# .. 1.485 0 1 .1 84 OJ) 5.0 10 . 0 15 . 0 20.0 2M 1 . 759 PM CE M S Rtti)O(Ite 3 . 74 20 .2% 3.55 5 0 . 842 0 . 801 1012S/0o1

&..ooarilh m ie Su rrf1'\ary 10/2912004 

## V

ES00979 2C A LCULAIJO N S F OR EXPONENTlAL C ORR E LATIO N Facili t y: Facility 0 Emi s sion U nit: Boiler L ocation : Anytown USA Test Dat es : N ovember 1 t o 4 , 2002 PM < PM CEMS CALCULATEO! 

## "' · ' I 

# y I y' 

### = Ln(y) 

# I <x.-x1 

# I (l"ri"•J' 

# I (X,·X ·)(y'rYJ 

# I '/" I IY 

# ml' y 1 6 . 7 3.1 1 . 131 5 .007 0 .000**~ ~** **~** 7.4 2. 00 1 -1 . 121 0 .590**~** I , \,J "- • I 0 . 7 42 6 . 631 0 . 260

... "'., <'ll**~** "' <'lll'lol:l 2.438 0 . 006 <J 1\1 , 1 U , l I,QVQ 14 , 64 0.06 1 0.1f7**~** • • • ., 8 • "'"' n 7 99 2.246 0.28 1 0 . 0551 0 453 1 1.6441 0.003 18 . 26 0 . 085 1 .248 2 .223 0 .0 11 I a , ..,.,**~**• .., 1.504 0.05 0 . 1 02 0 .07 3 1. 803 0.089 1 0 1 4 .6 8 .2 2 . 104 0 . 45 0 . 078 0.188 1.887 0.047 11 19.7 13 2.565 33 . 33 0.549 4 . 276 2.364 0 .04 1 1 2 1 8 1 1 . 1 2.407 16. 5 9 0.340 2.374 2.205 0.04 1 _10 . 3 11 . 9 2.4n 40.62 0.426 4 .157 2.420 o .oo3 2 . 361 39.35 0.288 3.367 2 .4 10 0.002 1 . 7 2 . 2 19 33.33 0. 1 56 2.280 2.364 0 .02 1

P$-11 Example 4A · R 10.27-04. x ls Expo nen tia l Cales Pago 1 

## or 1 1012912004 

## VES009793RESULTS Of EXPONEH!!AL CORRELATlOH F• eil lty : hc llfty 0 loatl on: Anylown USA I Vatiable EQUI..., VW. n**~oi<SIQ** nts: 1 x x- • tm•(sum ot ()rJ) • 13.93 S.. S., • Sum((lt.· x- )'2) c 360.5 

## ...:h.. 5.t 

# ... b, b , 

### s.c 

## I 

## s.. . •**~~ ~-**  C I'



### ..!!...



# ""' T, TI' 

# +

'

P$1 1**~** 4A-R 10.V<OtB 

### y-. 1/n' (Sum**of((~)·** 1.82A • Sum((y'r'/'•)"2)• 4.66 S"' • Sum({JCr x ·)(Yr'/'-ll = 33.68 

### b, ; =**f~,x-** 

### = I o .sZ3 ba • • 

### ...,.. = I 1 . 687 b 1 

## = SJS.. 

## =1 0.093 , ) = 0 . 34 1 'I'" at mean x vt*Jc • 1.824**rom** t able = 2 . 1 60 

### c r •**SI. SORT(IInJ**  •**0.1~ 03**  LCe 

### = Y-' • C l ' 1 . 634 UCL ' • v -' • C l' 2.0 15 

### iiiC'G**~** Jmil = 18.5 C l % • CUEL ' IOO% 

### = 6.4 1 % · = n = 1 5 v 1 l rom tabt e = 1 .485 \Iff fr om tabt e = 1 .1 64 k r• u ,., "v 1 =**~** Tl ' • k. "S L = 0 .600 LTL' • v-' • TI' 1 .22 4 lJ TL' :;; ... • + 'r1' 2 .42 4 UT L' • e "LTI,' Ja**3.~7** 

### n% • T I IEL ' IOO% • 21 . 3% • SORT (S / ( n-1)) = 

### o .sn • I·(SI."2/Sy1'2) = 0.650 r • SORT{{1 · SI.•21S,•2)) = 0.606 E , miss i on Unk: Boiler

Test O a tH : Novombt<t 1 to 4 , 2002 [correl ation equation : 

### y**~** 1.687 e 

# o.•• • • I**-·**

# .. 

# · -**-~** UIH"'w "'"'""'• o uo r,;ro o 1 Crierion 

# ........ 

# - -1>10? CorreJation coeffic:iet It 0.808**~O &S**  

### no Cor1f1denoe In- 6.41%**!~** 

# ,... Toleranceintefval 21 . 3% !25 ... 

# ,...

.**Indicates~** ooet6donlls .- • P&ot of Exp onentia . t Regteulon CutW 

# • •r----------- -------------------------, • 1 2 

# • Y s 1. 6872 aP ·ot34 • i 1 0 

# i : " • l • 

## • 2 

## •**-- ----** **-- --~** **----~---------- ~** 

0 . 0 

# ...**E~$u'ml;arf** 1 0 . 0 

# ,., :20.0 P M C EM S**AN~~C nt** **e**

PS· 1 1 Contl ation r•• C.rculallon Sotcllldii!Ht versbft 2:-e 101'Z61CM**0**



# ,..,.,.. VES 009 7 94Facility: Faelllty D Location : Anytown USA

Run

1 PMCEMS1 X 6 . 7 

### 7 . 

## 7. CALCULATIONS FOR POweR CORRELATION Emission Unit : Bo iler Test Date s: N o ve mber 1 to 4 , 2002 PM• I ranslotmed 

### )( = Ln ( x ) 

### y 

### = Ln(y ) 1 . 902 1 . 131 0 . 0068 2 : 028 7 . 4 2.001 0 . 288 0.031 -0. 0951 1 . 1961 0 . 6486 I 2 .054 2 . 1 0.742 0 . 26 1 1 .1 11 0 . 5531 1 . 2271 0 . 2348 1**9** 3 .7 1.308 0 . 120**~** ..... .,ft . .. "V\. ,.. .., .........

. 3 1 3 1 6 . 11 1.808 1 0.064 1 0 . 000 ! . 407 1 2 .81 1 . o:lol o . o25l o.s3 1l __ o . 126l 1 . 63!1 1

_ _ o . 3h7 ' 12 2.485 1 . 589 0 . 019 ft 18 . 2 2 .90 1 2.116 0 . 098 I "' 13 . 7 2.617 4.5 1 .504 0.003 0. 1 02

- 0 . 017 1 . 885 0 . 1454

• A 14, 6 2 .68 1 8.2 2. 104 0.0 1 3 0,078 0 , 032 1 . 960 0 , 0208 '' 19 . 7 2 .98 1 13 2.565 0.173 0.549 0 . 308 2 .3 10 0 . 0648 1 2 18 2 . 890 11 .1 2.407 0.106 0.3 4 0 0 . 190 2 . 205 0 . 0409 13 20 . 3 3 .0 11 11 .9 2.47 7 0.199 0.426 0 . 291 2 .345 0 . 0172

• • AA A 3 , 006 10.6 2,36 1 0,194 0 , 288 0 , 236 2 ,340 0 , 0004 2 .98 1 9.2 2.219 0.173 0.156 0 . 1 64 2 .3 10 0 . 0083

P5-11 Examp!e4A-R 10- 27-04 .xls Power Cales Page 1 of 1 10/2912004 

### VES009795RESULTS Of POWER CORRELADON F adllty:**Fac l~** **ty** 0**Loc-o~tion :**  Anyt.own USA

Varlalllo



## .r s.v**~ ~**  bo' 

# ... b, 

### s, fA-, 

# -"-

cr

v, 

# "" k , u**~**

r ' I

ndicatel I

P$1 1 £);aqllle fA.R 11).27.Qii . Q Vakle 

## ----:;s

,..

_: lln'(Sum of (IC'J) = 2. 565 s,.=&.m<<"•x<-1"2>= 2. 1s y'-. 1/n ' (Sum of (f , )). 1 . 824 • &.m((y',-y'-)"2). 4 .66 s,.,. &.m((IC' , IC'•)fY,-y'-)) = 2.55

S..• SORl bo' • t-<>,x- = -1 1n 

# ......,,.., 0,**t>,•S~=** 1 

### ml 

# I**0~0 1**  'I" e 1me8n x value 

### = 1 824 C l • l 

# _ltlrcm table 

## =j**~~~~**

:m i salon**%~""' '**  I .. . v, f rom table 

## =I 1.4i u,**~om** table 

### •I 1. 1 84 1 K

, • u ,.,: v, 

### •I t. 759 l T

l ' 

### = k, St 

### = !

·· 00% 

# " I '"'""' I**:S.,./(~1)) ~** **"' ~n**  

### I" • 1 · (S L"2/lV 21 

## •J 0 . 612 ! r • 50RTI(t-Sl.•21S(2ll 

### •I 0 .762 t 

### is 1 (i8ri**Emin~** U ni1: Boiler Tes-t Oates : N cwember 1 to 4t 2002 !correlati o n equat ion: y • 0 . 3084 x '· ' 001 

# I 

# --·· .. 

# ··- 

# -· - · 

# -·-·- ,__, 

# .__.. 

# .. Crilerico1 

# - - A<cot>WH? Com!lation coefficienl 0.782**~o as**  no Confidence interval 6 . 76%**~1~** l/00 To1eranoe irr. ervaJ 22.6%**~25 "**  yeo lncicates 

## ""'"""lion coe111aent Is IMldef*lod.

Plot of Power Function Regress Jon Curve

# 14~**----==-** t2 j 

## • 

# i 

# 10 " 8**~** 

### 5 6 

## • 

# • Y 

### = 0 . 3084x'**,.** 

## " l 4 2 

## • • 

# •**00 :~~-----;~----~~** **------ ~~----~** **--------** 50 10 .0 1 S , O 20 . 0 1tl0 P M CEMS R o1 pon•o



# -- 8- 11**Comt~Mkw\** Ttil l eullliof l $pNCletlftt I C/2&0 1



# ·- VES 009 7 96Facility: LDcation : Model Li1ear Potyr[omlal Logarillvnic tial Power Facility D Anytown USA

Correlat ion coeffioont(a) 0 . 841 0 . 855 0 . 801 0.806 0.782 ?. 0 . 85 7 

### No Yes N

o No 

### No SELECTION OF BEST MODE L Emission Unit Boiler Test Dat os: N ovember 1to 4 , 2002 Confidence i nterval**~** 10%? T olerance i1terval haH !:_ 25%7**Mln/max~ln** Does model meet au haW range percentage range percentage alloWable rang e ? crit.oria? 5 . 80% 

### Yes 18.3% 

### Yes (b) 

### No 7 . 68% 

### Yes 18.2% 

### Yes No 

### No 6 .4 1% 

### Yes 20 . 2% 

### Yes b 

### No 6A1% 

### Yes 2 1.3% 

### Yes No 6 .7 6 % Ye . s 22.6% 

### Yes No ( a ) • indicates corro!allon coomctonl l a undetlned; model does not satisfy criterion . (b) Not app l icable: criterion applteo on l y t o polynomial model.

PS-t 1 COtrell.tion T V$l**Ge"~liOn ~.;h!Q9t**  V

ersion 2.&

## ·~ Best modo I : Nono eccoptablo

P5-1 1 Exam p!e4A-R 1 0.27-04 . >do Best Model 1 0129/2004 

## VES009797

# Appendix A.5 Complete Results of Example No. 4 With Five Additional Test Runs

V ES 009 7 98

### CORRELATION TEST PM CEMS AND REFERENCE METHOD TEST DATA PMCEMS PM co n centration msoonse mg/ac m Ru n X y

1 6 . 7 31 2 7 . 6 7A 3 7 . 8 2 . 1 4 9 . 2 3 . 7 5 10 . 1 6 . 1 6 11 . 1 2 . 8 7 12 .0 4 .9 8 18 .2 8 . 3 9 13 .7 4.5 10 1 4 .6 8.2 11 1 9 .7 13.0 12 18 .0 1 1 . 1 13 20 .3 1 1 . 9 14 20 . 2 10 . 6 15 19 . 7 9.2 16 5 . 2 2 .4 17 8 . 6 4 .8 18 14 . 1 6 . 2 19 14 .5 7 .0

_ 20 _ 1 7 .3

----- 8.6

PS.11 E xample 4B-R 20 Runs**10 -2** **7~.>< 18**  Facility : Locatlon : Em i$S io n Unit Test Dates : Em i$Sion limit:

1 4 1 2 

## .§ 10 j;j

### ~ 8 

# .. u 

## g 6 0 ll 4 

# ... 2 0 0 . 0

T est Dara Facility D AnytownUSA Boiler 1 11 1-1 11 .U02,1n

- 1 1 810 3 Vafue

18 . 5



# • • 5 .0 

# • • • Un its mglacm



# • 

# • • 

# • 1 0 .0 

# • 

# • • •

1 5 .0 PM CE M S Response 

# • 

# • 

# • •

# • • 

# •

20.0 25 . 0

Page 1 ol 1 10/2912004 

## VES 009799