EPA-650/4-74-024
DECEMBER 1973
Environmental Monitoring Series
-------
EPA-650/4-74-024
COLLABORATIVE STUDY
OF METHOD FOR THE DETERMINATION
OF SULFUR DIOXIDE EMISSIONS
FROM STATIONARY SOURCES
(FOSSIL-FUEL
FIRED STEAM GENERATORS)
by
Henry F. Hamil and D. E. Camann
Southwest Research Institute
8500 Culebra Road
San Antonio, Texas 78284
Contract No. 68-02-0623
ROAP No. 26AAG
Program Element No. 1HA327
EPA Project Officer: M . Rodney Midgett
Quality Assurance and Environmental Monitoring Laboratory
National Environmental Research Center
Research Triangle Park, North Carolina 27711
Prepared for
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, D.C. 20460
December 1973
-------
This report has been reviewed by the Environmental Protection Agency
and approved for publication. Approval does not signify that the
contents necessarily reflect the views and policies of the Agency,
nor does mention of trade names or commercial products constitute
endorsement or recommendation for use.
11
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ABSTRACT
A collaborative study has been performed on Method 6 promulgated by the Environmental Pro-
tection Agency for determining the concentration of sulfur dioxide emissions from stationary sources.
Method 6 specifies the extraction of a gas sample from the stack, the separation of the sulfur dioxide
from the acid mist including sulfur trioxide, and the measurement of the sulfur dioxide fraction as
sulfate by the barium-thorin titration method. Collaborative tests were conducted at both a coal-fired
steam generating power plant and an oil-fired pilot plant by the same four collaborative teams. Statis-
tical analysis of the collaborative test and associated data revealed the following findings regarding the
reliability, both of a Method 6 determination, and of a Method 6 test result, which is defined as the
average of six determinations:
Accuracy-Method 6 is accurate in the SO2 concentration range below 300 X lO"7 Ib/scf, but
it acquires a significant 5- to 10-percent negative bias below the true concentration
above 500 X 1Q-7 Ib/scf.
Precision—The estimated within-laboratory and laboratory bias standard deviations of a
Method 6 determination are 4.0 and 4.2 percent, respectively, of its value. The
repeatability standard deviation of a test result is estimated as 1.6 percent of its
value. The estimated reproducibility standard deviation of a test result is 4.5 per-
cent of its value.
Minimum Detectable Limit-A conservative estimate of the minimum detectable limit of a
Method 6 test result is 2.1 X 10'7 Ib/scf.
Sources of Reproducibility Variation-Most (75 percent) of the reproducibility variation in a
test result resides in the field sampling phase of Method 6, with the other 25 percent
occurring in the analytical phase. Only 13 percent of the reproducibility variance
is caused by repeatability sources, while the remaining 87 percent results from
laboratory bias sources.
Various modifications to Method 6 are suggested to improve its suitability for field compliance per-
formance testing.
in
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TABLE OF CONTENTS
Page
LIST OF ILLUSTRATIONS vi
LIST OF TABLES wi
I. INTRODUCTION 1
II. COLLABORATIVE TESTING OF METHOD 6 2
A. Collaborative Test Sites 2
B. Collaborators 7
C. Philosophy of Collaborative Testing 7
III. STATISTICAL DESIGN AND ANALYSIS 9
A. The Experimental Design 9
B. The Collaborative Test Data 10
C. The Accuracy of Method 6 15
D. The Precision of Method 6 15
E. Accuracy and Precision of the Analytical Phase 21
F. The Sources of Variability in Method 6 22
IV. CONCLUSIONS AND RECOMMENDATIONS 24
APPENDIX A—Method 6. Determination of Sulfur Dioxide Emissions From Stationary
Sources 27
APPENDIX B-Statistical Methods 31
B.1 Preliminary Analysis of the Original Collaborative Test Data 33
B.2 Examination of the Port Effect 35
B.3 Data Adjustment for True Drift Within Blocks 35
B.4 Relationship of the Standard Deviation to the Mean 41
B.5 Component Standard Deviation, Repeatability and Reproducibility Estimation . . 49
B.6 Analysis of the Unknown Sulfate Solution Test Data 51
B.7 The Minimum Detectable Limit 55
REFERENCES 57
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LIST OF ILLUSTRATIONS
Figure
I Dayton Power and Light Company's Tait Station 2
2 Test Facilities 3
3 Stack Gas Delivery System and Sampling Manifold 4
4 Sample Trains, Dayton SO2 Collaborative Test 5
5 Gas Standard Sampling, Dayton SOj Collaborative Test 5
6 Pilot Plant Operational Configuration 6
7 Top View of Test Section 8
8 Collaborative Test of Method 6, Instructions for Analysis of Unknown Sulfate
Solutions 11
9 Method 6 Accuracy From Standard Gas Cylinder Data 18
B-l Between-Laboratory Run Plot 46
B-2 Within-Laboratory Collaborator Block Plot of Adjusted Data 47
VI
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LIST OF TABLES
Table
1
i
3
4
5
6
7
8
9
10
B-l
B-1
B-3
B-4
B-5
B-6
B-7
B-8
Randomized Block Design of the Dayton Collaborative Test of Method 6 ....
The Corrected Dayton Collaborative Test Data With Replacement Values ....
The Corrected Cambridge Collaborative Test Data With Replacement Values . .
The Dayton Gas Cylinder Test Data . ...
The Cambridge Gas Cylinder Test Data . .
Method 6 Accuracy From SGs Standard Gas Cylinder Test
Method 6 Precision Variability Estimates ...
Accuracy of the Analytical Phase of Method 6
Sources of Reproducibihty Variation in a Method 6 Test Result
The Analytical Phase as a Cause of Method 6 Precision Variation
The Original SO2 Data From the Method 6 Collaborative Test
Youden Rank Test for Significance of Port Effect
Within-Laboratory Analysis of Corrected Dayton Collaborative Test Data With
Replacements . • •
Within-Laboratory Analysis of Corrected Cambridge Collaborative Test
Data With Replacements . . .
Block Summary of Within-Laboratory Anomalies . ...
Witlnn-Block Drift Comparison Method 6 Versus Monitoring and Calculation
Methods . . .
The Corrected Dayton Collaborative Test Data With Replacements, Adjusted
for True Drift . . . . . ...
The Corrected Cambridge Collaborative Test Data With Replacements.
Aduisted for True Drift . ... . . . .
Page
9
13
14
16
17
19
?.o
21
23
23
34
36
37
38
39
40
42
43
B-9 Within-Laboratory Analysis of Corrected Dayton Collaborative Test Data With
Replacements Adjusted for True Drift.... . . . . 44
B-l 0 Within-Laboratory Analysis of Corrected Cambridge Collaborative Test Data
With Replacements Adjusted for True Drfit .... 45
vn
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LIST OF TABLES (Cont'd)
Table Page
B-l I Adequacy of Transformations to Achieve Equality of Run Variance 48
J3-12 Reported Sulfae Solution Concentrations, KT7 IbSOj/scf 52
B-l 3 Sulfate Solution Concentrations Averaged Over Days, 10~7 lbSO2/scf .... 53
B-14 Average Laboratory Sulfate Solution Concentrations, 10~7 lbSO2/scf .... 53
B-l 5 Analyses of Variance of Sulfate Solution Data by Concentration 54
B-l 6 Significance of Sulfate Solution Factors 54
B-l 7 Analytical Coefficient of Variation 55
B-l8 Method 6 Analytical Phase Precision Variability Estimates 55
viii
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I. INTRODUCTION
This report describes the work performed and results obtained on Southwest Research Institute
Project 01-3487-001, Contract No. 68-02-0623, which includes collaborative testing of Method 6 for
sulfur dioxide emissions as given in "Standards of Performance for New Stationary Sources."*1 **
This report describes the collaborative testing of Method 6 in a coal-fired steam generating
power plant and in an oil-fired pilot plant, the statistical analysis of the data from the collaborative
tests, and the conclusions and recommendations based on the analysis of data.
'Superscript numbers in parentheses refer to the List of References jl the end nt I Ins report.
-------
II. COLLABORATIVE TESTING OF METHOD 6
A. Collaborative Test Sites
Two collaborative tests of Method 6 were conducted. One test was performed at the Dayton
Power and Light Company's Tait Station, Dayton, Ohio from February 5 to February 8, 1973.
The second was performed at Walden Research Corporation, Cambridge, Massachusetts, from
March 5 to March 8, 1973.
The first collaborative test was conducted at the Tait Station of Dayton Power and Light Com-
pany, Dayton, Ohio. Monsanto Research Corporation and Dayton Power & Light Company have an
agreement permitting MRC to use DP&L's Tait Station (Figure 1) for investigation of various instru-
ments and analytical methods for monitoring stationary combustion sources. A 10 X 14 ft utility
shed was installed on the roof of DP&L's Tait Station between Units 4 and 5 (Figure 2). Units 4 and
Figure 1. Dayton Power and Light Company's Tait Station
5 are both tangentially fired, steam boilers burning pulverized coal. The only difference between the
two units is that Unit 5 now has a set of mirror-grid electrostatic precipitators in operation in addition
to the electrostatic precipitators employed on Unit 4. The maximum electrical output of each unit is
140 megawatts. The sample delivery line shown in Figure 2 is used to transfer the stack gas from a
position after the electrostatic precipitator and before the induced draft fan to the MRC shed.
Inside the shed is a manifold for distribution of the flue gas. The manifold is 10 ft long, with an
upper 2-in.-square duct fitted with 12 outlets and a lower 8-in.-square return duct (Figure 3). The
sample delivery line was connected directly to the manifold for use on this test. The 2-in. black iron
connecting pipe was wrapped with heating tape and insulated. The entire system is heated, and the
temperature can be controlled by sections. Additional sample preparation capabilities include a Rotron
Simplex spiral blower for supplying dilution air (Figures 3, 4, and 5).
-------
Figure 2. Test Facilities
-------
Manifold
Exhaust
"Lf \—-Blower
c3
t '••ly'V? >:v>.^; •;^:^;: . • • ••"'•^:f-^:^v;.-,^n;.;-ir'';;'j!^1
'.. •.«:• . •;.—. .. :..;-..•;._ . • .- .' -'.-.• •• -t..•'.-...-.....;_..<.•.-.,.
o oSample o o Ports -*o o
0 0
^
Manifold
Figure 3. Stack Gas Delivery System and Sampling Manifold
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Figure 4. Sample Trains, Dayton SO2 Collaborative Test
The installation of the Rotron Sim-
plex blower allowed the addition of am-
bient air to dilute the stack gas to give
different levels of sulfur dioxide during
the collaborative test. Sulfur dioxide con-
centration in the stack gas and diluted
stack gas was monitored with a calibrated
Dynasciences instrument.
The second test was conducted on the
Walden pilot plant. A schematic of the
Walden combustion pilot plant is shown
in Figure 6. The unit consists of a 400,000
BTU/hr (Jackson and Church) furnace with
a combination gas/oil burner. The waste
heat is discharged and the exhaust gas from
the burner is passed into a series of carbon-
steel test sections 3 ft in length and 8 in.
in diameter. The flue gas is cooled down
to about 300°F by an air-cooled heat ex-
changer and passed into a second series (3)
of carbon-steel test sections (sampling areas).
The gas is pulled out of these test sections
by a Westinghouse induced-draft fan and
exhausted through corrugated pipe at roof
level.
On furnaces of this type, a thermal
safety switch is incorporated in the burner
shroud. It was planned to achieve different
levels of SO2 by firing the furnace on Nos. 2,
4, and 6 fuel oil. Accurate fuel feed rate
measurements, along with fuel analyses and
Orsat analyses, were to be used to calculate
theoretical SO2 levels in the flue gas. Due to
unseasonably warm weather, when attempts
were made to run with Nos. 4 and 6 fuel
oil, the shroud overheated and the furnace
shut down. Attempts to lower the heat output by decreasing the fuel feed rates led to unstable
burner conditions and furnace failure.
Figure 5. Gas Standard Sampling, Dayton SO2 Collaborative Test
Therefore, the decision was made to conduct the entire test using No. 2 fuel oil, with a
known sulfur content, and to achieve the desired levels of SO2 by doping the flue gas with accu-
rately measured amounts of SO2. By so doing, theoretical SO2 levels could still be calculated for com-
parison with test data.
The gas doping system consisted of a 1A gas cylinder containing pure sulfur dioxide, glass rotameter
(Fischer & Porter 448-209), and a simple toggle valve. The dopant gas stream is introduced into the high
temperature section immediately after the fire box to come to equilibrium temperature and concentra-
tion across the duct before reaching the sample test section.
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(GAS) DO PING
SYSTEM
HEAT
EXCHANGER
FURNACE
AUXILIARY
FAN
OYNASCIENCES
+ S02
MONITOR
1
SAMPLING
SECTION
FAN
EXTERNAL
READING
METER
FUEL
HEATER
->EXHAUST
Figure 6. Pilot Plant Operational Configuration
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The sample test section is shown in Figure 7. The sampling ports show both the earlier number
code and the letter code, designated on December 12, 1972. The sampling probe was designed to be
at the centroid of the duct, although the sample gas velocity profile is essentially flat across the duct.
B. Collaborators
The collaborators for both the Dayton and Cambridge tests were Mr. Rudy Marek (Dayton) and
Mr. David Tarazi (Cambridge) of Southwest Research Institute, Houston Laboratory, Houston, Texas.
Mr. John Millar of Southwest Research Institute, San Antonio Laboratory, San Antonio, Texas,
Mr. James Becker of Walden Research Corporation, Cambridge, Massachusetts, and Mr. Paul Sherman
of Monsanto Research Corporation, Dayton, Ohio. The latter two collaborators were under subcon-
tract to Southwest Research Institute, and, in addition to serving as collaborators, had the responsibility
for site preparation and test facility maintenance at their respective test sites. Throughout the remainder
of this report, the collaborative laboratories are referenced by randomly assigned code numbers as
Lab 101, Lab 102, Lab 103, and Lab 104. These code numbers do not correspond to the above ordered
listing of collaborators.
Collaborative tests were conducted under the general supervision of Dr. Henry Hamil of South-
west Research Institute. Dr. Hamil had the overall responsibility for assuring that the collaborators
were competent to perform the test, that the test was conducted in accordance with the collaborative
test plan, and that all collaborators adhered to Method 6 as written in the Federal Register, Decem-
ber 23, 1971.
C. Philosophy of Collaborative Testing
The concept of collaborative testing followed in the tests discussed in this report involves con-
ducting the test in such a manner as to simulate "real world" testing as closely as possible "Real world"
testing implies that the results obtained during the test by each collaborator would be the same results
obtainable if he were sampling alone, without outside supervision, and without any additional informa-
tion from outside sources, i.e. test supervisor or other collaborators.
The function of the test supervisor in such a testing scheme is primarily to see that the method
is adhered to as written, and that no individual innovations are incorporated into the method by any
collaborator. During the test program, the test supervisor observed the collaborators during sampling
and sample recovery. If random experimental errors were observed, such as mismeasuremcnt of
volume of absorbing solution, improper rinsing of flasks, etc , no interference was made by the test
supervisor. Since such random errors will occur in the every day use of this method in the field,
unduly restrictive supervision of the collaborative test would bias the method with respect to the
performance test results which will be obtained when the method is put into general usage. However,
if gross deviations were observed, of such magnitude as to make it clear that the collaborator was not
following the method as written, these would be pointed out to the collaborator and corrected by Mu-
test supervisor.
While most of the instructions in the Federal Register are quite explicit, some areas jre subject
to interpretation. Where this was the case, the individual collaborators were allowed to exercise
their professional judgment as to the interpretation of the instructions.
The overall basis for this so-called "real-world" concept of collaborative testing is to evaluate
the subject method in such a manner as to reflect the reliability, repeatability, and reproilucihilily
of tJie method that would be expected in performance testing in the field
-------
c
4
Q
00
1.0. FAN
TO
EXHAUST
&
B
3
t
HEAT
EXCHANGER
F
Figure 7. Top View of Test Section
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III. STATISTICAL DESIGN AND ANALYSIS
A. The Experimental Design
A randomized block design was employed to collaboratively test Method 6 at both the Dayton
site (Dayton Power & Light Company's Tait Station) and the Cambridge site (Walden Research Cor-
poration's combustion pilot plant). Table 1 provides a schematic representation of the randomized
block design utilized in the Dayton
Table I Random^d Block De«gnof,he Dayton Collaborate
Test of Method 6
As ^ tab,e illustrates the
r>^iA j^j^r
Dayton test was conducted at four
different blocks of emission concen-
tration levels; these blocks had SO2
concentration levels of about 840 X
10-7,580X 1(T7, 175 X lO^and
1090 X 10~7 Ib/scf.* These blocks,
each of which consisted of four runs
sampled at 60-min. intervals, were
obtained on consecutive days. The
intent was to maintain a constant
true SO2 emission concentration lev-
el in the stack on the four runs with-
in each block to permit an accurate
determination of the repeatability
precision of Method 6. Each run in-
volved the simultaneous collection
of an exhaust sample from the stack
over a 20- to 23-min. interval by each
of the four collaborative laboratory
teams through their assigned port (A,
B, C, or D) During the course of con-
ducting each block's four runs, as Ta-
ble 1 shows, the laboratory teams ro-
tated systematically from port to port
so that each team sampled once from each port The systematic rotation facilitated the transfer of sam-
ling apparatus between runs.
In terms of experimental design, the Cambridge test of Method 6 was similar in nearly all aspects
to the Dayton test. Only a few of the details were different. The four Cambridge blocks had SO2 con-
centration levels around 145 X 10-7,550X 10'7,830X 10-7,and 1010 X 10'7 Ib/scf. The time in-
terval between runs within a block was reduced from 60 min on the Dayton test to 45 mm on the Cam-
bridge test as the collaborators became more proficient in sampling set-up. The intent was to mimmiyc
drift in the true emission concentration during each block's runs by conducting these runs in flic shortest
feasible time frame.
1 LI'A policy is to express all measurements in Agency documents in metric units When implementing tins practice will result in undue
LOSI or difficulty in clarity, NERC/RTP is providing conversion factors for the particular nonmetric units used in the document I or
llus report, the factor is
Block
(concentration level),
Ib/scf
-840 X 10-1
(2/5/73)
-580 X 10-'
(2/6/73)
-175 X 10-'
(2/7/73)
-1090 X lO"7
(2/8/73)
Run
(sample)
1
2
3
4
11
12
13
14
15
16
17
18
25
26
27
28
Laboratory Team
Lab 101
B
C
D
A
C
D
A
B
D
A
B
C
A
B
C
D
Lab 102
C
D
A
B
D
A
B
C
A
B
C
D
B
C
D
A
Lab 103
A
B
C
D
B
C
D
A
C
D
A
B
D
A
B
C
Lab 104
D
A
B
C
A
B
C
D
B
C
o
A
C
D
A
B
Notes The letters A, B, C, and D denote the sampling ports to which each
collaborative laboratory team was assigned on each run The twelve
sample numbers not listed here (5-10, 19-24) were obtained from
standard gas cylinders in the gas cylinder lest to assess the accuracy of
Method 6
IO'7 Ib/scf = 1 6017 X 10'3 jig/mS
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Various potential complications result from the real-world conduct of a mathematically idealized
experimental design because the ideal assumptions on which a straight forward statistical analysis of
the experimental design is based may prove to be wholly or partially invalid in the actual practical ap-
plication. In the randomized block designs for the Method 6 tests conducted at Dayton and Cambridge,
there are two readily apparent possible complications. The first is that the true SO2 emission concen-
tration in the stack, instead of remaining constant throughout the four runs comprising a block as the
randomized block design implies, does in fact vary significantly during the block's runs. Should such
"true drift" actually occur within a four-run block, it would invalidate the usual repeatability deter-
mination technique. It should be noted that because the time intervals between the runs within a
block were necessarily larger on the Method 6 tests (45 to 60 min) than on the Method 7 tests (15 to
25 min), the existence of the true drift situation is more likely in the Method 6 collaborative test data.
The second potential complication is the existence of a port effect. Although the four ports through
which the collaborative teams simultaneously sample were designed so as to be geometrically equiva-
lent, they do not, of course, provide all four teams with access to the same sampling location at the
same time. Thus, there is a possibility that there are consistent differences between the true SO2 con-
centrations at the sampling ports, some having consistently higher SO2 concentrations than others. If
this phenomenon exists, it is termed a port effect. If either of these potential complications exist to
the extent that they are detectable in the collaborative test data, then suitable statistical techniques
must be applied to counteract such effects by appropriately adjusting the reported test data prior to
statistical analysis.
In addition to the Method 6 collaborative test itself, two auxiliary tests were also conducted at
both the Dayton and Cambridge sites to complement the information regarding Method 6 available
from the collaborative tests. A gas cylinder accuracy test was conducted to provide a good indepen-
dent assessment of the accuracy of Method 6. This test involved three different standard gas cylind-
ers furnished by Scott Research Laboratories at each test site that contained mixtures of sulfur diox-
ide and nitrogen. Scott Research determined the sulfur dioxide concentration of each cylinder with
an accuracy of ± 1 percent. The three gas cylinders were labeled X, Y, and Z. On each of the four col-
laborative test days, each collaborative team obtained one sample from each cylinder according to the
Method 6 procedure. These samples were later analyzed in the laboratory along with the day's collab-
orative test samples. Thus, the Method 6 values can be compared against the Scott Research measure-
ments which were unknown to the collaborative teams to determine the accuracy and any possible
bias in Method 6.
The second test involved the repeated analytical determination of the SO2 concentration implicit
in foui unknown sulfate solutions to isolate the accuracy and precision of the sample analysis phase of
Method 6. Four accurately determined sulfuric acid solutions were prepared by Southwest Research
Institute and furnished to each collaborative team for sample analysis, together with the collaborative
test and gas cylinder samples. A complete factorial design was specified for this unknown sulfate solu-
tion test in which each laboratory was to analyze a 10-mB aliquot of each solution in triplicate on each
ot throe days during which each site's test samples were being analyzed. An example of the unknown
sulfate solution instruction and reporting form is presented as Figure 8.
B. The Collaborative Test Data
In Section B. 1 of Appendix B, the original reported Method 6 collaborative test data are present-
ed and a preliminary analysis of this data is conducted. The apparent outlier points were recalculated.
Through this process, considerable calculation errors were uncovered in Lab 102's SO2 concentration
values. The presence of these calculation errors suggests the need for a standard EPA computer pro-
gram for Method 6 to calculate the SO2 concentration from the raw input to be provided in the
10
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Collaborative Test of Method 6
Instructions for Analysis of Unknown Sulfatc: Solutions
A scries of sulfaLc solutions are provided to each collaborator.
Those solutions are labeled A. B, C, and D, and the concentrations arc
unknown to (he collaborators.
Each unknown solution is to be analyzed in triplicate on each of
three separate days. Use a. 10 ml aliquot, and follow the procedure in
Section 4. 3 of Method 6 and report results as lb/ft3 assuming a sample
volume of 1 cubic foot at standard conditions.
Submit the results on this sheet along with your other collaborative
test data.
Analyst
Lab 104
Day
Day 1
Date 3-13-73
Day 2
Date 3-14-73
Day 3
Date 3-15-73
Replicate
1
2
3
1
2
3
1
2
3
Concentration, lb/fty
Solution. A
3.61 x 10"
3.63
3.59
3.56 "
3^54
3.56
3.59
3.61
3.58 "
Solution B
0
0
0
0
0
0
0
0
0
Solution C
5.35 x 10~5
5.35
5.35
5.14 "
5.36 "
5.36 "
5.44
5.41
5.32 "
Solution D
_ C
1 .81 v -10
1.80
1.78 "
•i an 'i
1.81
1.80
1.83 "
1.81
1.83
Figure 8 Collaborative Test of Method 6. Instructions for Analysis of Unknown Sulfate Solutions
11
-------
•specified units. The preliminary analysis also uncovered a potentially serious weakness of Method ti-
the repeated collection of extraordinarily low SO2 samples without any field indication that the sam-
pling had been deficient Six of these very low samples were collected (three by Lab 102 at Dayton
and three by Lab 101 at Cambridge). Both Labs 101 and 102 felt that malfunctioning of the sam-
pling train, probably a leak that went undetected despite performance of the method's leak testing
procedure, was the cause of their low samples. Lab 102 had substantial evidence to support its claim
of leakage and its location of this leakage in the socket joint of the midget bubbler that connected to
the bail joint off the probe. After Lab 102 accidently broke and replaced the bubbler in one of its two
sampling trains, its low SO2 sampling problem disappeared. Efforts must be made to determine if this
sporadic under-sampling problem which apparently afflicts Method 6 is due to leakage or to some other
malfunction in the sampling apparatus. Then a means of detecting the problem condition in the field be-
fore or during Method 6 sample collection must be devised and suitable acceptance criteria established.
The six extraordinarily low sample values were considered erroneous because of probable sampling
tram malfunction, and thus rejected.
The corrected Method 6 collaborative test data from the Dayton site and from the Cambridge
site are presented in Tables 2 and 3, respectively. All observed calculation errors have been corrected
in these tables. Also, the one missing observation of Lab 102 and the six erroneous observations of
Labs 101 and 102 were given replacement values according to the minimum variance unbiased estimat-
ing procedure described in Section B.4 of Appendix B under the variance stabilizing logarithmic trans-
formation. Tables 2 and 3 also provide run, collaborator, and port summaries consisting of the mean,
the standard deviation, and, for each run, the coefficient of variation.
Two possible complications to the statistical analysis, because of the idealized assumptions usual-
ly made in this analysis, are examined in Appendix B. These complications were described in the prev-
ious section The possibility that a significant port effect was present in the corrected collaborative
test data gathered at either the Dayton or the Cambridge site is explored in Section B.2 of Appendix B.
No significant port effect is detectable in either site's data. The other complication, that the true SO2
concentration may have drifted substantially from run to run within some blocks of the collaborative
test data, is investigated in Section B.3 of Appendix B. By comparing the within-laboratory and the
between-laboratory coefficient of variation estimates for each block, it is discovered that the within-
laboratory estimates are larger than the expected maximum in five of the eight blocks. Drift in the
true SO2 concentration is a plausible explanation for this. Furthermore, in three of these five blacks,
there is a significant positive correlation over the block's four runs between the average of the collab-
orators Method 6 values and the site's best SO2 monitoring method. A significant positive correlation
indicates that both the Method 6 averages and the monitoring method readings rise and fall simultan-
eously The only reasonable explanation for such synchronous Method 6 and monitoring SO2 mea-
surements in these three blocks is that corresponding variations in the true SO2 concentration have
caused them. It is therefore concluded that these three blocks, the third and fourth blocks of Dayton
data and the second block of Cambridge data, were subject to substantial drift in the true SO? concen-
tration from run to run. However, in the other two blocks with excessive within-laboratory variation,
there is insufficient evidence to warrant this conclusion as the explanation. The corrected collaborative
test data in the three drifted blocks were adjusted for the drift so that reasonable within-laboratory
standard deviation and repeatability estimates could be made. The adjustment used gave the same
Method 6 mean to each run in an adjusted block. The adjusted Method 6 collaborative test data are
shown in Tables B-7 and B-8 (Appendix B) with the adjusted points denoted with a "t " symbol. As
a result of adjustment, the within-laboratory coefficient of variation estimates assume reasonable values.
12
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Table 2 The Corrected Dayton Collaborative Test Data With Replacement Values
METHOD: METHOD b — DETERMINATION OF SULFUR DIOXTOF EMISSIONS FROM STATIONARY SOURCES
TEST VARIABLE: X = CORRECTED 902 CONC. AT STD. CPNn. WITH REPLACFMENTS (DRY BASIS), JO**(-7) LB/SCF
TRANSFORMATION: x LINEAR
TEST STTE: DAYTON
COLLABORATORS! LAfl 101 , LAB in8 . LAB 103 , LAB in*
INTER-LABORATORY RUN SUMMARY
RUN SAMPLE
i i
2 8
3 3
* *
5 11
b 18
7 13
8 1*
* 15
10 lb
11 17
18 18
13 25
1* 2b
IS 27
lb 28
COLLABORATOR SUMMARY
COLLABORATOR
MEAN
STD. DEVIATION
PORT SUMMARY
PORT
MEAN
STD. DEVIATION
LAB 101
DATA PORT
729. fB)
"12. fC)
7S1. (D)
8bS. (A)
515. (C)
fal2. fD)
S8b. (A)
588. (B)
175. fD)
182. (A)
170. (B)
157. (C)
10*0. fO
lObO. (B)
1170. (C)
imo. fO)
LAB mi
b70.0
351.1
A
b7n.7
3»7.0
L*B in?
DATA PORT
1*8. ft)
12*.* fO)
81*. (A)
110.* (B)
b02.* (0)
SB*. (A)
583.* fB)
bP7. fC)
803. fA)
180. fB)
182. fC)
17*. (D)
1070. fB)
1802. (C)
1801. fD)
108*. fA)
LAB in?
70*. 7
371. t
B
3SP.*
LAB 103
DATA PORT
103. (A)
11*. (B)
828. fC)
BbQ. (D)
boo. fB)
578. (C)
582. fD)
183. (C)
IBS. (D)
180. fA)
IbP. (B)
1037. (D)
11*2. (1)
117b. fB)
11*7. fC)
LAB 103
b1?.2
3b5.1
C
hflO.h
3b*.7
LAB 10*
DATA PORT
71*. fD)
73b. (A)
*b3. (B)
78b. (C)
558. fA)
S2b. ffl)
528. fC)
S3*. (»)
18*1 (C)
ibi. (n)
Ibb. (A)
BB1. fCl
18b. (D)
1081. (A)
ioni. fB)
LAB 10*
b!3.1
313.7
D
bbS.l
3*1.?
RlfN SUMMARY
MEAN STD DEV COEF OF VAR
883.5
871.5
71D.S
855.8
588.7
573.5
Sbl.7
587.0
183.8
182.7
175.2
Ibb.8
1001.0
1017.5
llbl.O
1082.5
111.*
10.5
28. b
51.*
20.7
35.fi
27.1
32.1
8.2
b.7
'.0
81.*
si|o
Sb.b
.!*»«
.1038
.0351
.ObOO
.0352
.Ob85
.0*81
.OSbb
.07b2
.0121
.0382
.0*2*
.08bO
!o583
•Replacement value.
-------
METHOD:
TEST vtRUbLE:
TEST SITE:
COLLABORATORS:
Table 3. The Canceled Canilsiiilge CoUat>o>nt\\ c Test Data With Replacement Values
METMHO »> OETEPHINiTEnN OF SULFUR 01 OX IMF E«!SSinwS F»OM ST»TfON»RV SOURCES
x = cimuFCTfn so? CCHC. »T STO. CONO. «IITH REPLACEMENTS (D«Y RASIS). io«*(-7> LB/SCF
CAMBRIDGE
LA« lul , LAB 108 > L>B 103 , LAB in*
INTER-LABORATORY RUN .SUMMARY
RUN
1
8
3
S
b
7
B
q
10
11
18
13
IS
Ib
SAMPLE
*
b
7
B
10
11
18
14
80
81
84
8b
87
88
LAB
DATA
134.
M8.»
158.
547*.
5b5.
543.
8*7.
83?!
4»0.
1080**
101
PORT
(0)
CO
CB>
CO
(B)
C»)
(C)
(0)
CO
CO
(D)
(O
CB)
LAB
DATA
151.
Mb.
513.
SbB.
B?b.
B3B.
88».
850.
1183.
BB8.
108b.
899.
108
PORT
CB)
CO
CO)
CB)
CO)
CA)
CC)
(A)
CB)
CC)
CO)
LAB
DATA
151*
ISO.
Sib*.
SSb.
818*.
787.
838.
inbi.
IDfal.
1053.
1070.
103
PORT
CO)
CO)
CA)
(0
CB)
fC)
CO)
CB)
CO
(0)
LAB
DATA
ISO.
588*.
SbO.
bO*.
sns.
804.
B3».
885.
1007.
10* RUN SUMMARY
PORT
(A)
CB)
fC)
fD)
CB)
CC)
CO
CD)
CB)
CA)
CB)
MEAN
M4.8
l*s".7
S50*.7
57?. S
S43.8
83D.5
Blb.S
880.5
813. B
1038.7
473.5
1034. n
484. 5
STO oev COEP OF '
7.1 .0078
8.* .OlbS
1.8 .0887
3.* .083*
»S.7 .0455
38. b .0701
?».(. .0*30
33.* .OSb3
14. » .0833
1».S .0177
83. n .0880
15.4 .0188
77.4 .075*
7».l .07bl
38.4 .037*
70.1 .0704
COLLABORATOR SUMMARY
COLLABORATOR
MEAN
STO.
DEVIATION
LAB
b87
33H
mi
.8
.B
LAB
337
108
.1
LAB
b34
351
103
.7
.8
LAB
b25
384
10*
.7
.4
PORT SUMMARY
PORT
MEAN
STD.
DEVIATION
A
353
!B
B
387
is
C
334
!l
0
b87.7
338.8
•Replacement value.
-------
C. The Accuracy of Method 6
One of the major tasks of this collaborative study is to determine if Method 6 gives accurate (i.e.,
unbiased) measurements of the true SO2 concentration emitted by the stationary source being sam-
pled. As discussed in Tlie Experimental Design section, the gas cylinder test was designed as the prim-
ary means to ascertain the accuracy of Method 6. At each test site, three different standard gas cyl-
inders, obtained from Scott Research Laboratories and containing known mixtures of sulfur dioxide
and nitrogen, served as the SO2 source for Method 6 sampling. Samples were collected by each col-
laborator from each cylinder on each of the four test days. The corrected Method 6 SO2 concentra-
tions obtained are presented and summarized in Tables 4 and 5, respectively, for the Dayton and Cam-
bridge cylinder data. Three erroneous measurements were obtained by Lab 102 from Cylinder Z at
the Dayton site, apparently due to that sporadic leakage problem discussed previously. These errone-
ous Lab 102 measurements are denoted in Table 4 by an E following their value; they were not in-
cluded in the calculation of any of the summary statistics shown in this table.
A summary of the pertinent accuracy data on Method 6 from the gas cylinder test is presented
in Table 6. For each cylinder at the two test sites, Table 6 displays the "true value" determined by
Scott Research for the cylinder, the mean of the collaborators' Method 6 measurements from the cyl-
inder, uncertainty intervals for both these values, and the percentage difference in their values. The
95-percent confidence interval for the collaborators' Method 6 mean is based on a variance of aj/4 +
-------
Table -t 'the Day/on (,a\ Cvlmder Tat Data
METHOD: METHOD b DETERMINATION OF SULFUR DIOXIDE EMISSIONS FRn* STATTONior «OliPfES
TEST VARIABLE: X = CORRECTED MJZ CCMC. AT STP. C0*t». FR
2 8
3 ZO
1 8*
5 b
b 1
7 21
B 82
q s
10 10
11 H
11 as
COLLABORATOR SUMMARY
COLLABORATOR
HE AN
STD. DEVIATION
PORT SUMMARY
POUT
ME*N
STD. QEVIATION
LAB
DATA
121.
lio]
bji!
bll.
1110.
I8b0.
1270.
iabo.
t»B
bSb
X
ei
101
PORT
(Y)
m
(Y)
(It
(Z)
(Z)
(Z)
(X)
(X)
(X)
fX)
ini
.7
,S
;*
LAP in?
DATA PORT
1»0. (Y)
1»3. (Y)
13b. (Y)
13b. (V)
•n. E (Z)
bi. E CZ)
8fcS. E fZ)
bSB. fZ)
13**. (X)
1277. (X)
neol (x)
LAB 10!
sesl?
Y
nn.q
7.3
LAB 103
DATA PORT
137. fY)
ise. (Y)
I?". CYJ
1SB. fYl
b30. (Z)
b.S
LAR
DATA
13".
132.
n1*!
S7».
ses.
S7Z.
Sb7.
1123.
Ilb3.
1138.
1071.
LAB
bO*
in»
PORT
(Y)
(V)
fY)
fY)
fZ)
(Z)
fZ)
(Z)
(X)
(X)
(X)
(X)
10*
.e
-RUN SUMMARY
MEAN STD DEV
lib. 2 S.fl
13*. ? S.«
127. P 7.1
lib. I 7.5
f>0«.7 31.0
bl«.P Z^.s
5<
-------
Table 5 The Cambridge Gas Cylinder Test Data
METHOD: METHOD h --- DETERMINA TIOM Hf SULFUP OIOXfOF FMISSIONS FRfl*
TEST VARIABLE: X s CORRECTED S02 CONC. AT STO. CY
MEAN STO >)FV COFF PF
107. n S.O ,"3'B
1*8.2 fa. 7 .""5?
b3l.5 ]C>.7 .ng(,<;
••»*•. P I»1.Q ,?I*7
h"H.S 7.5 .1117
1?S?.P hb.5 ."Sin
12bn.c P7.7 .0220
1213. 5 «0.7 ,0»»7
-------
1600
1400
1200
1000
-
;
-.-
:
-
_
--
-
-
--
i
~*
Anal
10-7
-
. .
it
:
-
1 —
r
— M--
--
--
4-
T
-I-
:
-
_
-
•
1
1
-
r
:
M
-
:
• -
s
-
.. -
_ .. .
i •
::
E
_4~
]
—
--•
— j- •)-
~ ' t
' i
i
H
i
ft'
s
rowra
yzed Value,
Ib/ecf
1 1 1 1 LJJ
-
-
!
i
- 1
. .4.
• !
• "I
" '
i\
/
1
r-
•
.?
-
^
/
..,..
~
4
frt
ft?
t
-,
i
_ _j '
f
t
-t-
i
/
/
-
i
!
'
4X-
.u ..
1
1
•[-pi --
rr
'! i ± : .:
T ;
: i '
"T T~t
~rr " ;
t
^T
I
^
~?
f\
?
^
~?
2
j
AT
"hh
41 — - . .
;
- H
J
1 1 t
,,ipx--.
•
^ If
d? 4 U
y •
7
^ I
I ^
£
7
2
'
2
^
j/^
~g
- - -
. _ .1.
-If iff-
lit ..
; i
. jJJLj-r-l Pit
14
r ' T f - 1
x Cx - 4
I
- - -j- M- -
_x[4- - | 4^-H
1 '1 1 1 J 1
-Ti^ + T1 # +
2
^
^
7
^
2
7
2
:: IIIIE.
x
_L
T
" Scotl
t modi
J ' WVLJLfVl
««*w
IL _|_ Metlh
p m^ai
confl
^
•
i
fi
0<
e
o<
i
d
[i
-
-
;
L^
/n
n
r
1
r
-
I
1
1"I~
lea
ed
i w
16
witl
enc
• r
>
-
V
it
c
1
e
t -
--
t
re
h
0
9
i
j]
[
y
/\
\
-\
^
-
j
-
i
i
(
- 1
i
-
— i •
-f
B
-i
rue
at-
un
llab
5-p
ate
Tf"
i —
i
/
i
i
n
•1
• -
I
i
I
I
T
r
T
If
1
1
j-i-
value
Gaekc
:ertai
orato
ercer
rval
FFI i
i
T
-H:
•; -
I
s by
I
nty
r
t
200 400 600 800 1000 1200
True Gaa Cylinder SO2 Concentration (Scott Research) 10"7 Ib/acf
800
600
400
200
Figure 9. Method 6 Accuracy From Standard Gas Cylinder Data
18
-------
Table 6. Method 6 Accuracy From SO2 Standard Gas Cylinder Test
Test Site
Day tun
Cambridge
Cylinder
YLow
Z Medium
XHigh
XLow
Z Medium
YHigh
Sulfur Dioxide Concentration, I0~' tb/scf
True Value-Scott Research*
Value
137.0
676
1300
142.8
706
1370
±l-Peicent
Uncertainty Range
(135.6,1384)
(669,683)
(1287,1313)
(141 4, 144.2) '
(699,713)
(1356, 1384)
Method 6
Collab.
Mean
1309
6204
12292
145.4
636.6
12488
95-Percent Confidence
Interval for Mean
(1247, 137.1)
(5897,651 2)
(1170.5, 12879)
(138.5, 152.3)
(606 2, 667 0)
(11892, 1308.4)
Mean
Percentage
Difference, %
-45
-82
-54
+ 18
-98
-88
*Scott Research measured the SO, concentration or each cylinder by a modification of the West-Gaekc method
in which the cylinder sample was diluted in glass to about 3 ppm prior to the West-Gaeke determination.
it is a composite of a and OL : a£ = a2 + aj . Other useful precision measures, the repeatability and
reproducibility standard deviations, are derived from the component standard deviation measures to
provide similar information regarding a Method 6 test result. Throughout this report, the value t oj
a Method 6 test result T is defined as the average of three Method 6 repetitions, where each repeti-
tion is the average of two Method 6 SO2 concentration determinations cr, sampled at 1-hr intervals
This test result definition is admittedly somewhat deficient and artificial. Each repetition of a Meth-
od 6 performance test for compliance at fossil fuel-fired steam generator plants is stipulated in the
I'ederal Register (2) as the determined SO2 emissions rate Qs c"r. Here Qs is the volumetric flow rate
determined experimentally by Method 2 in conjunction with Methods 1, 3, and 4. The obvious de-
ficiency of T is that the emissions rate Qs Fr , rather than the average SO2 concentration
~, =—^ <>,. defines a repetition. T is artificial because it is not actually the criterion to be used
~ i=\
in compliance performance testing. But the actual SO2 criterion, the emissions rate averaged over three
repetitions, requires concurrent precision analyses of Methods 1,2,3, and 4 in addition to Method ft
Hence it is beyond the scope and intent of this report, which pertains exclusively to Method 6. HONV-
ever, T is extremely useful for determining the precision characteristics of Method 6 in the compliance
performance testing framework. Except for the volumetric flow rate factor, T does reflect the com-
pliance performance test situation in which Method 6 will be used-three repetitions ejch consisting
of two SO2 samples taken according to Method 6.(3) Thus. T accurately represents the Method (•> con-
tribution to the average SO2 emissions rate criterion used in compliance performance testing Conse-
quently, the repeatability and reproducibility standard deviations. o/^/Tn and \/aj + a -/in. respect IN el\.
for Method 6 are appropriately specified with respect to the test result T. so that in = 6
The precision estimates for Method 6 were obtained by a coefficient of variation jiul\sis The
fundamental assumption of this analysis, that the Method 6 variance component stjiulaid deviations
are actually proportional to the true SO2 concentration sampled, is examined in Section B 4 of
19
-------
Appendix B on the collaborative test data. Analysis of this data reveals that both the within-labora-
tory standard deviation a and the between-laboratory standard deviation ab of Method 6 can be con-
sidered proportional to the true SO2 concentration n. These conclusions from Section B.4 of Appen-
dix B are based on plots and regressions of the appropriate data, and on the implications of the finding
that the logarithmic data transformation best achieves equality of run variance. It was demonstrated in
the prior Method 7 collaborative test report(4* that the proportionality of both a and ah to p implies that
the laboratory bias component standard deviation OL is also proportional to p. Hence the proportion-
ality prerequisite to using the coefficient of variation analysis in estimating the precision measures of
Method 6 is satisfied.
All the standard precision measures of Method 6 are calculated in Section B.5 of Appendix B,
both from the Dayton and Cambridge Collaborative test data itself and from the gas cylinder test data
from these sites. The coefficient of variation analysis is the basis for these calculations. The preci-
sion estimates obtained are summarized in Table 7. Here c is the value of a Method 6 determination,
whereas / is the value of a Method 6 test result. Note that the Method 6 precision estimates from the
Table 7. Method 6 Precision Variability Estimates
Source
of Test
Data
Collaborative
Test
Gas Cylinder
Test
Precision
Variability
Measure
Within Lab
Between Labs
Lab Bias
Repeatability
(m = 6)
Reproducibility
(m = 6)
Within Lab
Between Labs
Lab Bias
Repeatability
(m=6)
Reproducibility
Test
Data
Version
ADJ
CWR
Comp
ADJ
Comp
CD
CD
CD
CD
CD
Component Estimates
Coef of Var
P
0 = 0 040
06 = 0 058
0 L = 0 042
JJ = 0 044
3ft = 0 063
fL = 0 044
Std Dev ,
a
o = 0 040 c
&i = 0 058 c
o/, = 0 042 c
& = 0 044 c
05= 0.063 c
oj, = 0 044 c
Test Result Estimates
Std Dev
0016;
0045 ;
0018;
0048;
Mandel Del
0045;
0125 1
0050;
0132;
*Test Data Version Codes
CD - Corrected data
CWR - Corrected data with replacement values
ADJ - Corrected data with replacements adjusted for true drift
Comp - Composite of CWR and ADJ data set estimates
collaborative test data are derived from different versions of the data. The between-laboratory standard
deviation estimate o& is made from the corrected collaborative test data with replacement values shown
in Tables 2 and 3. This is the valid version of the test data because the between-laboratory variability
on each run is not affected by the drift in the true SO2 concentration that was discovered in Section
B 3 of Appendix B. However, this drift does interfere with the within-laboratory variability estimation
which involves comparing a laboratory's Method 6 SO2 determinations over the four runs in a block.
Hence, the a and repeatability estimates for Method 6 are derived from the corrected collaborative test
data with replacements adjusted for true drift, which is displayed in Tables B-7 and B-8 Since aj =
a\ - o2, the laboratory bias standard deviation estimate is a composite derived from both of these col-
Ijboralive test data sets. Similarly, the reproducibility estimate is also a composite. By contrast, all the
20
-------
Method 6 precision estimates from the gas cylinder test are obtained from the same data set, i.e., the
corrected gas cylinder data presented in Tables 4 and 5. The agreement between the collaborative
test data and the gas cylinder test data in the derived Method 6 precision estimates is excellent. Not
only are the comparable estimates of similar magnitude, but the proportions of the between-labora-
tory variance attributable to the within-laboratory and the laboratory bias components remain re-
markably constant. The uncertainty in the Method 6 test result reproducibility and repeatability es-
timates due to the design limitations of the collaborative test are also Investigated in Section B.S of
Appendix B. With a 7.2 percent percentage uncertainty, the 95-percent confidence interval about
the Method 6 repeatability standard deviation estimate, 1.6 percent of the test result value t, is from
1.4 to 1.9 percent of t. The estimated reproducibility standard deviation of a Method 6 test result,
4 5 percent of t, has a much larger percentage uncertainty of 36.5 percent because the collaborative
test had to be restricted to only four collaborators. Consequently, the 95-percent confidence interval
for the true reproducibility standard deviation of a Method 6 test result is much broader, ranging
from 1.3 to 7.7 percent of /. Mandefl5) defines repeatability and reproducibility as the quantities
that would be exceeded only 5 percent of the time by the difference between two randomly selected
test results for repeatability both test results are obtained by the same laboratory, for reproducibility,
the test results come from different laboratories Using Mandel's definition, the repeatability of a
Method 6 test result is 4.5 percent of its value and its reproducibility is 12.5 percent of its value.
E. Accuracy and Precision of the Analytical Phase
An unknown sulfate solution test was conducted along with the Method 6 collaborative study to
assess the accuracy and precision of the analytical phase of Method 6 separately. Four different sulfate
solutions, with the actual concentrations concealed, were provided each collaborative laboratory for
Method 6 sample analysis, along with the collaborative test and gas cylinder samples. Sample aliquots
of 10 mC each from each solution were to be analyzed by every collaborative team in triplicate on each
of three sample analysis days along with the samples from both test sites. The reported sulfate solution
data are presented and summarized in Tables B-12, B-13, and B-14 of Appendix B.
The accuracy of the analytical phase of Method 6 can be determined by comparing the average of
all the reported Method 6 SO2 concentrations for each solution against the "true" effective SO2 con-
centration represented by that sulfunc acid solution. This comparison is provided in Table 8. The
Table 8 Accuracy of the Analytical Phase of Method 6
Solution
B
D
A
C
Sulfur Dioxide Concentration. 10~T Ib/scf
Prepared
"True" Value
000
17625
352.50
52875
CoUab
Mean
0.10
17440
34897
52203
95-Percent Confidence
Interval Tor Mean
(-039.059)
(17060,17820)
(341 37, 356 57)
(51063,53343)
Difference
+010
-1 85
-353
-672
Difference, %
-1 05
-100
-1 27
95-percent confidence interval for the means over all four collaborators of Solutions D, A, and C is
based on a standard deviation of^tf/4 + a2112 = v/(0.022y)2/4 + (0.01 \uYP2 = 0.01 lju. For
tlu blank Solution B, its actual standard deviation components from Table B-17 are used to com-
pu e its interval standard deviation of 0.250. The prepared "true" SOj concentration level of each sol-
ut'on lies well within the 95-percent confidence interval about the collaborators' mean Method 6 deter-
mination. Thus, the analytical phase of Method 6 is unbiased within the precision oj the method The
low value bias of Method 6 is not due to its analytical phase.
A separate analysis of variance has been performed on the data for each unknown sulfate solution.
These Analyses point up a considerable collaborative laboratory site interaction effect and a lesser day
21
-------
effect as the principal components of the laboratory bias in the Method 6 analytical phase. The labor-
atory site interaction effect is shown in Section B.6 of Appendix B to be caused partially by variations
in the ways different chemists perform the analytical phase of Method 6 and partially by variations
that the same chemist introduces into his Method 6 analytical procedure at different times. The infer-
ence is that considerable gains in the precision of Method 6 could be made if the analytical procedures
were specified in greater detail.
Separate precision estimates for just the analytical phase of Method 6 can be derived from the
unknown sulfate solution data. These estimates are obtained in Section B.6 of Appendix B and shown
in Table B-18 of the same appendix.
The minimum detectable limit for a Method 6 test result is estimated in Section B.7 of Appendix B
as 2.1 X 10~7 Ib/scf. This value is a conservative estimate: it may well be too large. It represents the
smallest Method 6 test result value / that is significantly larger than a zero sulfur dioxide emission con-
centration when the reproducibility precision of Method 6 is taken into account. Thus, if a laboratory
obtains a Method 6 test result that is less than 2.1 X 10~7 Ib/scf in performance testing for compliance,
such a test result cannot be distinguished from a zero sulfur dioxide emission concentration m the stack
F. The Sources of Variability in Method 6
The preceding statistical analysis sections provide the basis for analyzing the souices of precision
variability in a Method 6 test result. The variability in a test result is measured by its reproducibility var-
iance oj? + o2/6. This formula permits a simple yet informative partitioning of the reproducibility var-
uiiee into the repeatability variance component <72/6 and the laboratory bias component oj . Table 9
iiidiciilcs that this partition apportions 13.2 percent of the Method 6 reproducibility variation to repeat-
ability and the remaining 86.8 percent to laboratory bias. The repeatability component reflects the
reduction in the within-laboratory variation in a single Method 6 determination caused by taking dupli-
cate Method 6 determinations on each of three repetitions during performance testing The relatively
\mall size of (he repeatability component suggests that taking m = 6 replicate Method f> determinations
in'r performance test is sufficient The laboratory bias component reflects all the differences between
the laboratories performing the Method 6 collaborative test. These differences include different anal-
ysts, different field operators, variation in Method 6 procedural details not specified m the method,
measuring instrument variation, etc. Clearly, the laboratory bias factors are the primary contributor to
Method 6 reproducibility variation Obviously some laboratory bias factors are unavoidable sources of
variation Others, however, are amenable to improvement.
The reproducibihly variance of a Method 6 test result can also be partitioned according to the phys-
ical activity and associated location, field sampling or laboratory analysis, that introduces the variability
The unknown sulfate solution test provides an independent assessment of the variability in the labora-
tory analytical phase of Method 6. The balance of the Method 6 reproducibility variability must be due
to field sampling. Table 10 is constrvicted on this rationale, with the analytical phase variability esti-
mates obtained from Table B-18. Table 10 discloses that only 24.6 percent of the Method 6 reproduc-
ibility varution is due to the analytical procedure. The preponderant 75.4 percent is attrthmubie to
Jield xaini.lntg variation sources. With respect to repeatability variation, the field sampling phase is jn
even moie pronounced source of variation because 92.4 percent of repeatability variation is ascribed to
it. In relative terms, the variability caused by the analytical phase of Method 6 is concentrated in I he
laboratory bias sources where it makes up 27 2 percent of the tola! Table 10 makes n clear lh.it the
field sampling phase of Method 6 causes much more variation than docs the analytical pha^e Conse-
quently, if Method 6 is to be improved, it is in the field sampling phase that the major improvements
bhould be sought
22
-------
Table 9 Sources of Reproducibihty Variation in a Method 6 Test Result
One major field sampling problem
has already been identified in the prelim-
inary analysis of the collaborative test
data. This problem, which causes spora-
dic grossly deficient sample collection, is
due to leakage or some similar malfunc-
tion in the sampling train. Means must
be developed, either to prevent the occur-
rence of this malfunction, or at least to
provide positive evidence that it is occurr-
ing so that the sample can be discarded.
In fact, the statistical analysis of the Method 6 collaborative test data is based on the assumption that
such a means will be developed, because the six outlier points afflicted with this problem were replaced
prior to the analysis.
Table 10. The Analytical Phase as a Cause of Method 6 Precision Variation
Source of
Variance
Repeatability
Laboratory Bias
Reproducibihty
Estimated Variance Component
y 16 = (0 040 f)'/6 = 0 00027 t '
o/ =(00421)' =000176/J
61 + V 16 = 0.00202 f*
Variation
Percentage, %
132
868
1000
Source of Variance
Repeatability 6'/6
Laboratory Bias o£
Reproducibihty o£ + o* 16
Precision Variance in Method 6
Method 6
0 00027 /*
0001 76 r1
0 00202 t1
Analytical Phase
0 00002 /'
0 00048 /'
0 00050 r*
Percent
Analytical, %
76
272
246
Percent
Field, %
924
728
754
Several specific sources of the Method 6 analytical phase variability have also been identified in
the statistical analysis. The unknown sulfate solution test has shown that use of different chemists by
the same laboratory to analyze Method 6 samples causes considerable variability. And modifying the
details of the analytical procedure that are not specified in the method, either uniformly or haphazardly,
is known to cause much of the analytical phase variability. This latter source of variability can be reduc-
ed by revising the method as written, either to specify how analytical details should be performed, or to
caution against error-inducing situations. For instance, evaporation of some of the isopropanol that is
contained in the barium perchlorate tit rant will increase the effective normality of the titrant and pro-
duce a low bias in the Method 6 determinations obtained. Thus, a note oj caution should be appended
(o Method 6 warning that all isopropanol-containmg solutions be kept in capped containers
23
-------
IV. CONCLUSIONS AND RECOMMENDATIONS
The preceding statistical analysis of the Method 6 collaborative study conducted at the Dayton
and Cambridge test sites provides a firm foundation for evaluating Method 6-Determination of
Sulfur Dioxide Emissions from Stationary Sources. The following conclusions regarding Method 6
have emerged:
(I) Accuracy-Method 6 is accurate at low SO2 concentrations, but it acquires a low value
bias at higher concentrations. The unbiased region is below 300 or 400 X 10"7 Ib/scf.
Above 500 X 10'7 Ib/scf, Method 6 SO2 concentration determinations tend to lie from
5 to 10 percent below the true concentration, which is a significant difference. The bias
lies in the field sampling phase of the method, since analysis of the standard sulfate
solutions indicate that the analytical phase of the method is unbiased.
(2) Precision-All precision standard deviation measures of a Method 6 SO2 concentration
determination are proportional to the determination itself. The estimated standard devi-
ation of the within-laboratory precision variation in Method 6 determinations, a, is 4.0 per-
cent of the determination. The estimated standard deviation of the biased laboratory-to-
laboratory precision variation, aL, is 4.2 percent of the determination. In the compliance
performance testing framework, a Method 6 test result / is pragmatically defined as the
average of six Method 6 determinations made by a single laboratory. The estimated repeat-
ability standard deviation of a test result is o/N/5'= 7 6 percent of t The reproducibility
standard deviation of a test result is estimated as^/al + iff 6 = 45 percent oft The 95 per-
cent confidence limits for the true standard deviations range from 1.4 to 1.9 percent of t
for repeatability, and from 1.3 to 7.7 percent of/ for reproducibility. By Mandel's defini-
tions^, the repeatability of a Method 6 test result is 4.5 percent of / while the reproduci-
bility of a Method 6 test result is 12.5 percent oft
(3) Minimum Detectable Limit-The estimated minimum detectable limit of Method 6 is
2.1 X 10'7 Ib/scf. If a Method 6 test result is less than 2.1 X IO'7 Ib/scf, the actual
sulfur dioxide emission concentration in the stack is indistinguishable from zero. Since
this estimate is based on a conservative assumption, the true minimum detectable limit
of Method 6 is probably even lower than this.
(4) Sources of Reproducibility Variation-The reproducibility variation in a Method 6 test
result can be partitioned into its components in two independent ways. The activity
phase partition reveals that 75 4 percent of the reproducibility variation occurs in the
field sampling phase, with only 24 6 percent arising from the laboratory sampling analy-
sis phase. The source partition divides the reproducibility variance into the /3 2 percent
accounted for by repeatability variation and the remaining 86 8 percent attributable to
laboratory bias variation. Repeatability variation measures the amount of variation in
Method 6 test results obtained by a single laboratory on identical groups of replicate
samples using the same field operators, the same laboratory analyst, and the same instru-
mentation. The low repeatability variation suggests that the specified conduct of two
Method 6 determinations on each of three repetitions provides sufficient Method 6 repli-
cation. The laboratory bias variation reflects the differences that exist, both within the
same laboratory and between different laboratories, in the field operators, the analysts,
the equipment, and the performance of unspecified Method 6 procedural details that
combine to produce Method 6 determinations. Clearly, the major component of the
24
-------
Method 6 test result reproducibility variance is laboratory bias variation occurring during
field sampling, if Method 6 is to be improved substantially, the major effort will have
to be directed toward the variability sources causing this component.
Through their experience in performing Method 6, the collaborative laboratories have developed
considerable insight into the method's strengths and weaknesses. Two of these laboratories have
offered constructive comments on Method 6 and recommendations for improving it.
Walden Research Corporation reports that Method 6 for SO2 has some weak areas in the
sampling section with a proven analytical section. A major defect in Method 6 involves the pump
for the sample train as shown in Appendix A, Figure 6-1. The needle valve should be on the vacuum
side of the pump with a pressure relief crossover system on the pump. Without this system, the
lifetime of a pump is drastically shortened. A vacuum gauge should be put in the line to show plug-
ging of the probe or other malfunction. Regarding sample collection, there is no visible indication
even when the impmgers are bubbling that a sample of SO2 is actually being collected in the im-
pingers, even after leak testing the system. The absorbing solution is neutral hydrogen peroxide
initially; after sampling to collect a suitable concentration of SO2, the hydrogen peroxide should
become strongly acidic (approximately pH 1-2). Consequently, a simple test with pH indicating paper
at the termination of the sampling period will indicate if SO2 has been collected. This could be per-
formed in the field while the possibility still exists for securing more samples. A short section on the
chemical interferences of the barium ion titration with a note for good lighting to see the endpomt
would be useful in the analysis section. Lastly, there is no mention in the analysis section ofhmits on
the spread of the results from analysis of identical aliquots. Walden Research ran duplicate, and some-
times even triplicate, titration analyses of the sample solution, the results occasionally differed by 5
percent or more. It is felt that if the titration of identical aliquots differs by 10 percent or more, then
more aliquots should be run and those that differ by 10 percent be discarded. If the 10 percent limits
are unreasonable, other limits should be set to prevent averaging of widely varying results.
Monsanto Research Corporation has several recommendations. For ease of field work, the
glass wash bottles should be replaced with polyethylene bottles To aid in sample filling and rinsing,
5- and 15-ml graduations ought to be affixed to the bottoms of the midget bubbler and impmgers.
Finally, to ensure better rinsing of the impmgers and connecting tubes, the contents of the storage
container should be diluted to 100 ml, instead of 50 ml, in a volumetric flask. Then, all the quan-
tities used during analysis could be doubled to improve the precision of the analytical phase.
The collaborators' recommendations presented above remedy some of the Method 6 weaknesses
pointed out in this report. In particular, if the pH indicating paper suggestion for detecting insuffi-
cient sample collection proves to be practical, then it could signal in the field that the recurrent
Method 6 gross under sampling problem has occurred, and an additional replacement sample could
c-asily be taken. Some such field indicator procedure must certainly be developed for insertion m
N' ^thod 6 to alleviate this undetected under-sampling problem.
Several additional recommendations are in order. A standard reporting form and an accom-
panying computer program should be developed for Method 6. The raw Method 6 measurements
would be recorded in specified units on the reporting form, keypunched, and input to the computer
program which would calculate the corresponding sulfur dioxide concentration determinations.
While Method 6 is not unusually prone to calculation errors, such a data system would circumvent
25
-------
the ever-present calculation verification problem. During the statistical analysis, it was discovered
that evaporation of isopropanol from the barium perchlorate titrant, when it is left standing in an
open container, does occur and will bias the resulting Method 6 SO2 concentration determination.
So a note of caution should be inserted in Method 6 to warn that all solutions containing isopro-
panol should be kept in capped containers
Basically, Method 6 appears to be a reliable SO2 concentration determination technique. If
the current version of Method 6 (cf. Appendix A) is rewritten to specify more of the procedural
details, and to incorporate as many of the above recommendations as prove themselves feasible,
then it should become a more reliable method for use in field compliance testing at new stationary
sources.
26
-------
APPENDIX A
METHOD 6. DETERMINATION OF SULFUR DIOXIDE
EMISSIONS FROM STATIONARY SOURCES
Federal Register, Vol 36. No. 247
December 23, 1971.
27
-------
RULES AND REGULATIONS
PLANT.
DATE_
RUN NO.
CONTAINER
NUMBER
WEIGHT OF PARTICULATE COLLECTED.
mg
FINAL WEIGHT
TARE WEIGHT
WEIGHT GAIN
FINAL
INITIAL
' 'OUID CCM.ECTED
TOTAL VOLUME COLLECTED
VOLUME OF LIQUID
WATER COLLECTED
IMPINGER
VOLUME.
ml
SILICA GEL
WEIGHT.
9
9* ml
CONVERT WEIGHT OF WATER TO VOLUME BY DIVIDING TOTAL WEIGHT
INCREASE DY DENSITY OF WATER. (1 g ml):
" VOLUME WATER, m.
Figure5-3. Analytical data.
663 Concentration In Ib/cu ft.
>id equation 5-5
M*-TiX il imiojn ol pirn.-ulili! mailer collected,
N , „ ,-\ u'umc ol fis sunp'c Ihioucb dry sis mrlor
ClrilirJ conJIllonjl. til (I
67 iMjkinrilc \nrintlou
M,,.,
A,,
•V.lr.A.
X 100
I- J'wM e>f lv«ii5Ur bf Wblfif. 1 g hiiL
fl-H-al ru conjunt. 21 JJ Liclia Ilr-cu ft /III
-
M [-,/>«• Mbl'xular «ri VM of W..I/T. u Ib /Ib -mole
\'m m \ filu.i>» uf .-as untile IlironKh the dry E*s m
(n *l*r LOII'lltl'lIL*). CU ft
T.-AI/Wjl» avtri.<> dry Koa niter
.
r»..-Ili-'.n'Uis pressure L! sampling ilt«, Incli'a
Ill-
All* A r* rare prr.nr sunk fis temperature (»«
fw 4-2i 'I:
•=T',..I 5jm|,l>n; UTI». mln
\,a-li>k 1^5 tii'xny rulLuiuted by Milhwl 2
r-iaiti'.n 'i-1. It /£ure Inrhnt 17^
of nozzl^, v\ ft
!*.<•
68 Acceptable results The following
range sets the limit on acceptable Isoklnetic
sampling results
II 90^ < I < 1 10%. the results are acceptable
otherwise, reject the results and repeat
the test
7 Reference
Addendum to Specifications (or Incinerator
Testing ttt Federal Facilities. PHS. NCAPC
Dec 6. 1967
Martin. Robert M . Construction Details of
Isoklnetic Source Sampling Equipment. En-
vironmental Protection Agency. APTD-0581
Rom. Jerome J . Maintenance. Calibration.
and Operation of Isoklnetic Source Sam-
pling Equipment, En\lromnental Protection
Agency. APTD-0576
Smltb. W S. R T Sblgehara. and W F
Todd. A Method of Interpreting Stack Sam-
pling Data. Paper presented at the 63d An-
nual Meeting of the Air Pollution Control
Association, St Louis. Mo. June 14-19. 1970
Smith. W. S . et al . Stack Gas Sampling
Improved and Simplified with New Equip-
ment. APCA paper No 67-119. 1967.
Specifications for Incinerator Testing at
Federal Facilities. PHS. NCAPC. 1967
METnOD 6 - DETERUINAT1ON OF SULPUB DIOXIDE
EMISSIONS FROM STATIONARY SOURCES
1 Principle and applicability
1 1 Principle A gas sample Is extracted
from the sampling point In tbe stack The
acid mist, Including sulfur trioxlde. Is sepa-
rated from tho sulfur dioxide The sulfur
dioxide fraction Is measured by the barium-
thorln tltratlon method
1 2 Applicability This method Is appli-
cable for the determination of sulfur dioxide
emissions from stationary sources only nhen
specified by the test procedures for determin-
ing compliance with New Source Performance
Standards.
2. Apparatus.
2 1 Sampling See Figure 6-1
2 1.1 Probe— Pyrex ' gloss, approximately
5 to 6 mm. m. with a healing sjstem to
prevent condensation and a filtering medium
to remo\e paniculate matter Including sul-
t uric acid mist
213 Midget bubbler — One. with glass
wool packed In top to prc\ent sulfuric ncid
mist carryover
2 1 3 Glass wool
214 Midget Impiugers— Three
215 Drying tube — Packed with G to 16
mesh Indlratlug-type silica gel. or eqimnlcni.
to dry the sample
216 Vnlie — Needle \nl\e or eqtil\alent
to adjust flow rate
2 1 7 Pump — Le.-ik-frec. \ncmun tvpe
218 Rite meter — Roiameter or equiva-
lent. to mcisurc a 0-10 set h flow rangr
2 1 9 Dry pns meter — Sufiv- , I nrciiMto
to mcisurc the sample \ol. . ..inn i
2 1 10 Pitot tube— T)pc S. or cqimnlcm
liquation 5-0 'Ttndo nnmes
FEDERAL REGISTER. VOl 36. NO 247—THURSDAY, DECEMBER J3, 1971
29
-------
nectary only :; a sample traverse Is it-
quired, or II uUcK gun \elac:ty varies wrH
ilm-s.
22 Ea.-nplo rf-.ivr.-y.
Z2.1 Glass wash bottles— Two.
? 2.2 Po'ye-.!.- Icne storage bottles— To
t ire Unptnger samples.
2.3 Analysis.
PROBE (END PACKED
WITH QUARTZ OR
PYREX WOOL
TYPE SPITOT TUBE •
STACK WALL
MIDGET BUBBLER MIDGET IMPINGERS
GLASS WOOL /
SILICA GEL DRYING TUBE
THERMOMETER
•PUMP
DRY GAS METER ROTAMETER
Figure 6-1. SOj sampling train.
8J.I Pipettes—Transfer type. 8 ml. and
10 ml. sizes (0.1 ml. divisions) ana 25 ml.
•Ize (0.2 ml. dlTlsloni).
23.2 Volumetric flasks—80 ml., 100 ml.,
and 1,000ml.
2.3.3 Burettes—8 ml. and 50 ml.
2.3.4 Erlenmeyer flask—125 ml.
3. flcagcnti.
3.1 Sampling.
3 1.1 Water—Del on I red, distilled.
3.1.2 Isopropanol. 80%—Mix 80 ml. of Iso-
propanol with 20 ml. of distilled water.
3.1.3 Hydrogen peroxide. 3^—dilute 100
ml. of 30% hydrogen peroxide to 1 liter with
distilled water. Prepare fresh dally.
3.2 Sample recovery.
3.2.1 Water—Dclonlzed. distilled.
3.22 liopropanol. 80',.
33 Analysis.
3.3.1 Water—Detonlzed. distilled.
33.2 Isoprcrnno!.
83.3 Thorlr. Indicator—l-(o-arsonophen-
yla70|-2-naph-.l'jl-3.C-dlsuironlc acid, diso-
dlum salt (or e'j'jlvalcnt). Dissolve 0.20 g. In
100 ml. distilled water.
33.4 Barium perchlorat* (001 N)—Dis-
solve 1.95 c. of barium pcrchlorate
|Ba(ClO,),-31l O! In 200 ml d:sti::rd water
velocity. Take readings at least every five
minute* and when significant changes In
stack conditions necessitate additional ad-
justments in flow rate. To begin sampling,
position the tip of the probe at the first
sampling point and start the pump. Sam-
ple proportionally throughout the run. At
the conclusion of each run, turn on the
pump and record the final readings. Remove
the probe from the stack and disconnect It
from the train. Drain the Ice bath and purge
the remaining pan of the train by drawing
clean ambient air through the system for 15
minutes.
43 Sample recovery. Disconnect the 1m-
plngers after purging. Discard the content*
of the midget bubbler. Pour the contents of
the midget Implngers Into a polyethylene
shipment bottle. Rinse the three midget Im-
plngers and the connecting tubes with dis-
tilled water and add these washings to the
same storage container.
4.3 Sample analysis. Transfer the content!
of the storage container to a 80 ml. volu-
metric flask. Dilute to the mark with de-
lonlzed. distilled water. Pipette a 10 ml.
aliquot of this solution Into a 125 ml. Erlen-
meyer flask. Add 40 ml. of liopropanol and
two to four drop* of thorln Indicator. Titrate
to a pink endpolnt using 0.01 IV barium
perchlorate. Run a blank with each series
of samples. ,
6. Calibration.
6.1 Use standard methods and equipment
and dilute to 1 liter with liopropanol. Stand-
ardize with sulfunc acid. Barium chloride
may be used.
3.3.5 Sulfurlc acid standard (0.01 N) —
Purchase or standardize to ±0.0002 N
against 0.01N NaOH which his previously
been standardized against potassium acid
phthalate (primary standard grade).
4. Procedure.
4.1 Sampling.
4.1.1 Preparation of collection train. Pour
15 ml. of 80% Isopropanol Into the midget
bubbler and 16 ml. of 3% hydrogen peroxide
into each of the first two midget Implngers.
Leave the final midget Implnger dry. Assem-
ble the train as shown In Figure 9-1. Leak
check the sampling train at the sampling
site by plugging the probe Inlet and pulling
a 10 Inches He vacuum. A leakage rate not
In excess of 1 % of the sampling rate Is ac-
ceptable. Carefully release the probe Inlet
plug and turn off the pump. Place crushed
Ice around the loiplngers. Add more Ice dur-
In- the run to keep the temperature of the
cxscs leaving the lost Implnger at 70* P. or
less.
4.1 2 Sample collection. Adjust the sam-
ple now rate proportional to the stack gas
which have been approved by the Adminis-
trator to calibrate the rotameter, pltot tub*.
dry gas meter, and probe heater.
6.2 Standardize the; barium perchlorate
against 25 ml. of standard suit uric acid con-
taining 100 ml. of Isopropanol.
0. Calculations.
8.1 Dry gas volume. Correct the sample
volume measured by trie dry gas meter to
standard conditions (70* P. and 29.93 Inches
Hg) by using equation 9-1.
where:
C»o,— Concentration of sulfur dioxide
at standard conditions, dry
basis, Ib./cu. ft.
7.06 X 10-»- Conversion factor. Including the
number of grams per gram
equivalent of sulfur dioxide
(32 g./g.-eq.), 463.8 g./lb., and
1.000 ml./l.. Ib.-l./g-ml.
V,—Volume of barium perchlorate
tltrant used for the (ample.
ml.
V,,—Volume of barium perchlorate
tltrant used for tile blank, ml.
N~ Normality of barium perchlorate
tltrant. g.-eq./l.
V..,. —Total solution volume of sulfur
dioxide, 60 ml.
V4—Volume of sample aliquot ti-
trated, ml.
V.,,, —Volume of gas sample through
the dry gas meter (standard
conditions), cu. ft., see Equa-
tion 8-1.
"in. llg\ T. ) equation 9-1
where:
V«.,4—Volume of gas sample through the
dry gas meter (standard condi-
tion*), cu. ft.
V,.—Volume of gas sample through the
dry gas meter (meter condi-
tion*), cu. ft.
T,|4-Absolute temperature it standard
conditions. 630* R
T.,-Average dry ga* meter temperature,
R.
PMr—Barometric pressure at the orlflce
meter, inches Hg.
P,,4—Absolute pressure at standard con-
dition*, 29.93 Inches Hg.
8.2 Sulfur dioxide concentration.
^ -.id equation 6-3 3
O
7. Keferencei.
Atmospheric Emission* from Sulfurto Acid
Manufacturing Processes. U.S. DHEW. PKS.
Division of Air Pollution, Public Health Serv-
ice Publication No. 999-AP-1S. Cincinnati.
Ohio. 1965.
Corbett. P. P.. The Determination of BO,
and SO, In riue Oases, Journal of the Insti-
tute of Fuel. 24:237-243. 1961.
Matty, R. E. and E. K. DIehl. Measuring
Flue-Gas SO, and SO,, Power 101:94-87. N%-
vember, 1967.
PMton. W. P. and J. A. Brine. Jr., New.
Equipment and Technique* (or Sampling
Chemical Process Gases, J. Air Pollution Con-
trol Association. 13, 162 (1963).
METHOD 1—omiUINATIOK OT NmOOIN OXDB
EMISSION! nOK RATION4IY SOUICTS
1. Principle and applicability.
1.1 Principle. A grab sample I* collected
In an evacuated flask containing a dilute
•ulfurtc acid-hydrogen peroxide absorbing
solution, and the nitrogen oxides, except
No. 247—I'M! -
I
FEDERAL REGISTER, VOL. 36, NO. 147—THURSDAY, DECEMBER 23, 1971
-------
APPENDIX B
STATISTICAL METHODS
-------
APPENDIX B. STATISTICAL METHODS
This appendix is composed of various independent sections, each of which contains a statistical
analysis pertinent to a particular question or problem encountered in the analysis of the Method 6
collaborative study data. Reference to these sections has been made at various junctures in the
Statistical Design and Analysis part of the body of this report.
B.I Preliminary Analysis of the Original Collaborative Test Data
The original SO2 collaborative test data from the Method 6 tests conducted at Dayton and Cam-
bridge are shown in Table B-l. The port from which the sample was collected is given in parentheses
following the reported SO2 concentration value. A simplistic outlier analysis was used to detect calcu-
lation errors and outlying observations suitable for rejection on physical grounds. A comparison of
the four values reported by the collaborators on each run (i.e., for each sample) was made. If either
of the extreme values differed from its closest value by more than 10 percent of this value, such out-
lier observations were extracted for further scrutiny. Each outlier observation was recalculated using
the collaborator's reported raw data. Physical grounds for rejection of the outlier observation were
sought when it differed greatly from the other three sample values.
Through this process, random and systematic calculation errors and six observations that were
low by one or more orders of magnitude were uncovered. All of Lab 102's reported values were high
by 9.62 percent of the reported value. This is because Lab 102 obtained a sulfuric acid normality of
0.010869N in its original standardization and used this value in its calculations; a later replicated
standardization gave its normality as 0.009915N. Additional Lab 102 calculation errors were also
discovered in Samples 12, 14, 15, 16, 17, 18, 25, 26, 27, and 28 at Dayton and in Sample 26 at
Cambridge. After these calculation errors had been corrected, there remained six Method 6 observa-
tions (Samples 4, 11, and 13 by Lab 102 at Dayton and Samples 5, 7, and 27 by Lab 101 at Cam-
bridge) m which the reported SO2 concentrations were extraordinarily low. On all six observations,
a typical volume of gas had been sampled, but very little barium perchlorate was needed to titrate to
a pink endpoint. Lab 102 was utilizing two bubbler-impinger sampling trams alternatively when its
low samples were collected. After Sample 13 had been run on February 6, the bubbler in one of
these sampling trains was broken in the field. Thereafter, Lab 102's alternate low SO2 collection
problem disappeared. Lab 102 reports that this problem could not be detected in the field despite
vigorous leak testing of the sampling train to a no-flow condition on the flowmeter. In their opinion,
the malfunction was in the impmger section of the defective sampling tram, most likely in the socket
joint of the bubbler that connected to the ball joint off the probe. Subsequently, Lab 102 visually
m pected all ball-and-socket joints to guard against a recurrence of this problem. Now Lub 101 also
felt that one of its two alternated sampling trains did not function properly on its three low-sample runs
at Cambridge. It is therefore reasonable to likewise ascribe the three low Lab 101 values at Cambridge
ro some undetectable leak in one of their sampling trains. On the plausible grounds that a physical
malfunction in the sampling train, such as an undetectable leak, had prevented proper Method 6 sampl-
ing on all six of the extremely low measurements, these six observations were considered erroneous
at'., treated as if they had been missing observations.
The values of the one missing observation (Dayton, Lab 102, Sample 2) and of the six erron-
eous, observations (Dayton, Lab 102, Samples 4, 11, and 13, Cambridge, Lab 101, Samples 5, 7,
and 27) were replaced with suitable correction values. These correction values were the minimum
variance unbiased estimates obtained under the variance stabilizing logarithmic transformation
33
-------
Table B-l. The Original SO2 Data From the Method 6 Collaborative Test
Site
Dayton
Cambridge
Block
1
2
3
4
1
2
3
4
Sample
1
2
3
4
11
12
13
14
15
16
17
18
25
26
27
28
4
5
6
7
8
9
10
11
18
19
20
21
29
26
27
28
SO, Concentration from Method 6, 10'' Ib/scf
Lab 101
729 (B)
912 (O
789 (D)
865 (A)
595 (C)
612 (D)
586 (A)
588 (B)
175 (D)
182 (A)
170 (B)
157 (C)
1040 (A)
1060 (B)
1170 (C)
1090 (D)
139 (D)
23| (A)
152 (B)
3f (Q
412 (A)
597 (B)
565 (C)
593 (D)
847 (B)
807 (C)
837 (D)
862 (AJ
940 (Q
990 (D)
185t (A)
990 (B)
Lab 102*
1040 (C)
Missing (D)
892 (A)
21 t (B)
38f (D)
672 (A)
46f (B)
697 (Q
232 (A)
206 (B)
95 (C)
200 (D)
1234 (B)
1382 (C)
1385 (D)
1246 (A)
168 (B)
160 (C)
160 (D)
157 (A)
562 (C)
623 (D)
668 (A)
690 (B)
905
-------
(cf. Section B.4) for the run and block in which they occurred. Table 2 (see main report) contains
the corrected Dayton data, and Table 3 of the main report shows the corrected Cambridge data
The seven replacement values for the missing and erroneous observations are denoted in these tables
by an asterisk following the replacement value.
B.2 Examination of the Port Effect
Because there were just four ports available for sampling at both the Dayton and Cambridge
sites, each collaborative team could sample from only one port on each run. Since the possibility
of nonuniform flow through the sampling duct always exists, one must determine whether there was
a significant sampling port effect in the corrected Method 6 data at either the Dayton or the Cam-
bridge site.
The statistical test used to determine the significance of the port main effect was the rank test
that Youden presented in his address, "The Collaborative Test."(7) The application of this rank test
to the corrected Method 6 data at both the Dayton and Cambridge sites is shown in Table B-2. Ranks
from 1 to 4 were assigned to the ports' data for each run, with a rank of 1 being assigned to the port
with the lowest Method 6 value, a rank of 2 to the port with the next higher value, etc. For runs in
which one of the collaborators obtained a missing or erroneous data point, a rank of 2.5 was assigned
to the port from which this missing or erroneous sample was taken; the other ports were then
assigned the ranks 1.25, 2.5, and 3.75 according to their data values. The sixteen ranks assigned to
each port on the 16 runs were summed to yield its port rank score. Table B-2 shows that every port
rank score is well within the 0.05 lower and upper limits for its two-sided test. Thus, the rank test
does not detect any significant port effect in either the Dayton or-Cambridge Method 6 test data.
However, because of the nature of the randomized block design employed in these tests, a sizable
collaborator main effect would tend to obliterate any small port effect that might be present. But
since any port effects that might actually have existed have had no detectable influence on the
Method 6 test data, the assumption that there are no port effects at either site is valid.
B.3 Data Adjustment for True Drift Within Blocks
For each run of a Method 6 collaborative test, the expected value of the run variance sf is E(sj)
= °2 + al > where a2 is the within-laboratory variance component and a\ is the laboratory bias vari-
ance component. E(sJ) is often termed the between-laboratory variance and denoted as a\ It is
demonstrated in Section B.4 that the between-laboratory standard deviation is proportional to the
true SO2 concentration ab = 06/u. Thus, E(sf) = a\ = 0^2. Since a\ = a2 + o\ , one suspects that
the within-laboratory standard deviation component a is also proportional to the concentration mean
This suspicion is strengthened when one recalls that this relationship (a = /3ju) was true for the Method 7
collaborative tests(8) conducted at these same sites. Hence, let's assume that a = 0/u for Method 6 too
The equations a\ = a2 +al,ab = |36 n, and a = 0M imply that OL = 0Ln where 0L is defined by
0
Now in most collaborative tests, the within-laboratory variance component estimate a2 and the
ki .oratory bias variance component estimate a\ have the same order of magnitude. Thus, given that
°b = $lc2 and assuming that a2 = 0V . where c is the Method 6 SO2 concentration determination.
it is reasonable to expect that the ratio fl2/^ will lie between 0 I and 0.9 for most of the blocks in a
collaborative test. Thus, the ratio 0/06 will usually lie between 0.3 and 0.95 for most blocks How-
ever, one can expect great variation in the ratio 0/0t from block to block, with some values even in
excess of 1 .0. The 06 estimate for each run is based on the four collaborators' simultaneous
35
-------
Table B-2 Youden Rank Test for Significance of Port Effect
Site
Dayton
Cambridge
Run
Sample
Ranked Data
Ports
Sample
Ranked Data
Ports
B
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
1
2
3
4
II
12
13
14
IS
16
17
18
25
26
27
28
2
375
2
I 25
3.75
2
1 25
2
1
3
2
3
2
2
4
3
3
1 25
4
25
1 25
3
2.5
3
4
4
3
2
1
3
2
4
2S
1
375
25
4
375
1
2
2
I
4
4
1
3
1
4
25
3
25
25
25
4
3
I
4
1
3
4
1
2
4
5
6
7
8
9
10
II
18
19
20
21
29
26
27
28
3
2.5
2
375
4
4
1
2
2
1
2
I
3
2.5
1
2
1.25
I
1.25
2
1
4
1
I
2
3
4
2
4
375
3
1
25
4
2.5
1
3
2
4
4
4
4
2
4
I
I 25
2
4
3.75
3
25
3
2
3
3
3
3
3
2
25
4
Port Rank
Scores
Null
Hypothesis
Alternative
Hypothesis
Approximate
5 Percent
Two-Tailed
Limits
Conclusion
380 435 375 410
All sampling ports are equivalent
The true SO, concentration
sampled differs systematically
from port to port
(28.5,51.5)
Reject alternative hypothesis
There is no significant port
effect
3575 3625 4225 45.75
All sampling ports are equivalent
The true SO, concentration
sampled differs systematically
from port to port
(284,516)
Reject alternative hypothesis.
There is no significant port
effect
me.isutcjiients, it contains only three degrees of freedom. Likewise, the experimental design for
Method 6 allocated only four measurements by each laboratory in each concentration level block.
HeiKc, the estimate 0 also possesses only three degrees of freedom. Thus, each block estimate of
j3/j3ft can vary widely from the true underlying ratio 0/0b, but averaging $b and 0 over many blocks
should gicatly reduce such variation.
Now let's compare the Method 6 collaborative test data against these expectations. In addition
to presenting the corrected Method 6 collaborative test data. Tables 2 and 3 of the main report also
provide a run summary (the run mean, standard deviation, and coefficient of variation) on each run
ut the Dayton and Cambridge sites. The estimate jlb of the between-laboratory coefficient of varia-
tion tor a block is computed as the product of the standard deviation unbiasmg factor 1.0854 times the
iiverage of the four sample coefficients of variation of the block's four runs. Tables B-3 and B-4 present
36
-------
METHOD:
TEST VARIABLE:
Table B-3 Within-Laboratory Analysis of Corrected Dayton Collaborative
Test Data with Replacements
METHOD t, --- DETERMINATION np SIIIFUU DIOXIDE FMTSSIONR FROM STATIONARY SOURCES
x = coRREcTEn soa CONC. »T STO. CONR. WITH PE«»L»CFMENTS CORY B»STS), io**(-7)
TRANSFORMATION; X LINEAR
TEST SITE:
COLLABORATORS:
DAYTON
LAB 101 ,
LAB 102 , LAB 103
LAR in*
INTRA-LABORATORY COLLABORATOR BLOCK SUMMARY
OJ
BLOCK MEAN
1 837.2
2 578. S
3 17b.9
* 1087.5
COLLABORATOR
1
2
3
*
1
2
3
*
1
2
3
*
1
2
3
*
LAB
LAB
LAB
LAB
LAB
LAB
LAB
LAB
LAB
LAB
LAR
LAB
L«B
LAB
LAP
LAB
101
102
103
10*
101
102
103
10*
101
102
103
10*
101
102
103
10*
MEAN
823
899
87b
7*9
59b
,7
.b
>b
.«•
,9
.2
.5
.9
.3
COEF OF i
.0983
.nts*
.0*51
.0*19
.0198
.0207
.0232
.0275
.Obl7
.ObB*
.0*29
.0*57
.052*
.ObS2
.05*1
.Q829
-------
METHOD:
TEST VARIABLE:
TRANSFORMATION!
TEST SITE:
COLLABORATORS:
Table B~t Withm-Laboratory Analysts of Corrected Cambridge Collaborative
Test Data with Replacements
METHOO b DETERMINATION OF SULFUR FtinXTDF FMISSIHNS FROM STATIONARY SOURCE"
X s CORRECTED SO? CONC. AT STf). COWO. WITH REPLACEMENTS (DRY BASIS), |0**(-7) LB/SCF
X LINEAR
CAMBRIDGE
LAP inl , LAB 108 , LAS 103 . LAB 10*
INTRA-LABflRATORY COLLABORATOR BLOCK SUMMARY
U)
00
BLOCK MEAN
1 l»b.S
Z 544.0
3 B87.B
* 1008.7
COLLABORATOR
1
e
3
»
1
8
3
*
1
2
3
*
1
8
3
»
LAB
LAP
LAP
LAB
LAB
LAB
LAB
LAB
LAB
LAB
LAB
LAB
1 AB
LAB
LAB
LAB
101
10B
103
10*
ini
ice
103
10*
101
10Z
103
10*
mi
102
103
10*
MEAN
1»»
1*7
J»9
l»b
5*1
574
SB?
5*7
838
83*
88n
918
485
447
inbj
441
.n
.0
'.1
.7
.7
.5
.0
.8
.5
.J
•»
.1
.5
mg
.0
9TO
5
%
q
*
fl7
51
11
»S
83
If
Zfe
13
33
15*
b
20
DEV
.b
,£
.0
.9
.7
^g
«a
.0
.8
.0
,J
* fa
.8
.7
.•»
.5
COEF OF '
.0384
.08B«
.0333
.014b
.IblB
.088*
.Q£BB
.0888
.0877
,01»*
.031'
.Olbb
.0337
.18SO
. OPbS
.Q80b
-------
(he within-laboratory collaborator block summaries for the corrected collaborative test data at Dayton
and Cambridge, respectively. The within-laboratory coefficient of variation estimate 0 for a block is
calculated as 1.0854 times the average of the four collaborators' sample coefficients of variation for that
block. A summary of the eight Dayton and Cambridge blocks, including the block estimates ft/,, 0, and
&lfih , is shown in Table B-5. This table shows that the ratio 0//3fc exceeds the usual upper limit of
Table B-5. Block Summary of Within-Laboratory Anomalies
Cita
alte
Dayton
Cambridge
nin..|.
Block
1
2
3
4
1
2
3
4
Block Coefficient of
Variation Esdma
Between
Labs, pft
00935
00551
00515
0.0713
00316
0.0719
0.0238
0.0705
Within
Libs, p
00681
0.0247
00617
0.0691
00328
0 1 062
00246
OOS04
tes
Ratio,
0ltb
073
045
1 20
0.97
1.04
1 48
1 03
072
Run Correlation of
Method 6 Means
to Monitor Values,
'B
05951
-04051
09281
09759
-0.9784
09248
0.6858
06198
Significance
of Run
Correlation,
Pr{r > rB}
0.20
>O.SO
0.038
0011
>0.30
0.040
0 16
0 19
0.95 in five of the eight blocks. The ratios 0/0ft = 1.20 in block 3 of the Dayton data and 0/06 = 1.48
in block 2 of the Cambridge data are excessive. These ratios are indicative of a serious problem in the
contemplated statistical analysis that requires a documented explanation and, if necessary, remedial
action. The facile explanation for these predominantly high ratio values is that Method 6 lacks any
substantial laboratory bias. But this explanation runs counter to all collaborative test experience.
A more likely explanation is that the true SO2 concentration drifted from run to run in some of the
blocks. This second explanation can be tested by comparing the mean of the four collaborators'
Method 6 values for each run against the SO2 monitoring technique employed at that test site This
comparison is shown m Table B-6. An Envirometncs SO2 monitor was employed at the Dayton site.
Two techniques were used at Cambndge-Walden's theoretical calculation of the S02 concentration
and a Dynasciences SO2 monitor. Walden reports that the theoretical calculated values are preferable
for comparison purposes, with the Dynasciences monitor readings serving primarily as indicators of
the fluctuation in the SO2 concentration during each run Table B-6 shows fairly strong positive
correlations between the Method 6 mean and the appropriate monitoring technique in several blocks,
especially block 3 at Dayton and block 2 at Cambridge. These correlations indicate the existence
of sufficient drift in the true SO2 concentration during some blocks that it was readily detectable
by several independent measurement techniques. The actual correlation coefficient rB between the
Method 6 run mean and the appropriate monitoring technique over the four samples comprising a
block is shown for all eight blocks in Table B-5. The significance of these block correlation coeffi-
cients was determined with a one-sided test using the standard test statistic rB\/n- 2A/11 - r| which has
the / distribution with n - 2 degrees of freedom(9), where n = 4. As Table B-5 shows, blocks 3 and
4 at Dayton and block 2 at Cambridge all possess significant correlations. The logical inference is
tlidt the true SO2 concentration did indeed drift significantly from run to run in these three blocks.
The existence of substantial drift in the true SO2 concentration invalidates the withm-labora-
tory analysis given in Tables B-3 and B-4 and the within-laboratory coefficient of variation estimates
|3 presented in Table B-5. The problem now is to decide which blocks contain substantial true drift
cind how to adjust the data in such blocks so as to permit a meaningful within-laboratory analysis.
39
-------
Table B-6. Within-Block Drift Comparison Method 6 Versus
Monitoring and Calculation Methods
Site
Dayton
Cambridge
Block
1
2
3
4
1
2
3
4
Sample
,
2
3
4
11
12
13
14
IS
16
17
18
25
26
27
28
4
5
6
7
8
9
10
11
18
19
20
21
29
26
27
28
SO, Concentration, 10'' Ib/scf
Method 6
Run Mean
823.5
871.5
798.5
8552
588.7
5735
5697
5820
1832
180.7
T7S2
166.2
10090
10975
1161 0
10825
1492
1445
1480
1457
4790
5507
5725
593.8
830.5
816.5
820.5
8438
10327
9735
10390
9895
Environme tries
Monitor
745
798
696
696
497
505
522
528
174
166
162
157
903
961
1002
969
Walden
Calculation
168
179
173
177
513
642
670
644
945
895
931
938
1190
1140
1204
1207
Dynasciences
Monitor
157-166
166-190
190
157
472-497
472-513
563
638-696
853-903
894
903
927
1192-1226
1226-1242
1217-1250
1217-1267
The decision rule utilized to determine which blocks of four runs were plagued with a drifting true
SO: concentration requires that both of these criteria be met:
(1) The coefficient of variation ratio 0/06 for the block is greater than the reasonable upper
limit of 0.95;
(2) The correlation coefficient rB between the Method 6 run means and the run monitor
readings for the block is significant at the 0.05 level (i.e., there is less than one chance in
twenty that this high a positive correlation would occur by chance).
A perusal of Table B-5 reveals that both of these criteria are met by blocks 3 and 4 of the Dayton
data and by block 2 of the Cambridge data. Thus the data obtained by each collaborator on
40
-------
each run in these three blocks will have to be adjusted for the true drift that occurred in order
to achieve a valid within-laboratory analysis.
The data adjustment technique that was used in these three blocks was to adjust each collabora-
tor's value in a run by the amount necessary to give the run the same mean as the block. Thus, the
Method 6 mean of each run in these adjusted blocks is the same. Since it is very probable that the
Method 6 run mean is at least a good proportional estimate of the true SO2 concentration, this data
adjustment technique should remove most, if not all, the true drift inherent in the corrected data for
these blocks. The data adjustment formula used was
where Xf, is the corrected_data value and YtJ is the adjusted data value for collaborator i on run y,
X.j is the run / mean and X.. is the block mean. The adjusted data used for the within-laboratory
analysis is shown in Tables B-7 and B-8 for the Dayton and Cambridge data, respectively. The
adjusted data points are denoted by a f following their value. Tables B-9 and B-10 present the within-
laboratory analysis of this adjusted data. The P/Pb ratios of the three adjusted blocks are reduced from
1 .20, 0.97, and 1 .48 for the corrected data to 0.76, 0.41 , and 0.72 for the adjusted data. So the
adjusted data are certainly more reasonable. Furthermore, the data comparisons performed in Sec-
tion B-S imply that the adjusted data obtained are the proper data on which to base the within-labora-
tory precision analysis.
B.4 Relationship of the Standard Deviation to the Mean
In order to analyze the collaborative test data according to the coefficient of variation approach,
it is first necessary to justify the fundamental assumption of that approach; namely, that the precision
standard deviations of Method 6 are actually proportional to the true concentration value. The
basic precision standard deviations for which the proportional relationship must be verified are the
between-laboratory (run) standard deviation and the within-laboratory (collaborator block) standard
deviation. This section will present the necessary verification data for these two standard deviation
relationships.
The direct evidence for proportionality comes from plotting and regressing the pertinent stan-
dard deviation versus mean data. The values of the between-laboratory standard deviations and means
for each run are presented in the run summaries of Tables 2 and 3 (main report) on the corrected col-
l.iborative test dnta with replacements. Figure B-l is a plot of this between-laboratory data. Despite
the considerable scatter inherent in this plot because of the necessary limitation of the collaborative
study to only four collaborators, a proportional relationship, in which the between-laboratory standard
deviation of a run increases as the mean of the run increases, appears likely. To classify the relation-
ship, stepwise multiple linear regression through the origin was performed on this between-laboratory
data. The potential regressor variables_proyided_to fitjhe standard deviation st as a function of the
mean A^were X~l , X1", Xl/2, X3", X, Xs", X™, X2 , and log X. The power function s, =
0 0\099X** has a 0.901 1 correlation with s,, while the linear function s, = 0.05992* ., has a
s!1 iitly lower correlation of 0.8997. The other simple and multiple regressions are all inferior to these
two. Because of the scatter in the data, the exact functional between-laboratory relationship remains
uncertain But the proportional linear relationship appears to be among the best.
Shown in Tables B-9 and B-10 are the within-laboratory standard deviation and mean values
calculated for each collaborative laboratory in each block from the corrected Method 6 collaborative
test data adjusted for true drift. These within-laboratory data are plotted as Figure B-2. Again
41
-------
'It Me R-7 ll.e Canceled Dayton Collaborative Test Data with Replacements,
Adjusted fot 'Ime Drift
METHOD: METHOD k HFTE»H]Ki»11 f)M OF 3ULFUP DIOXTOF EM'SSIONS FROM STATIONARY SOURCES
TEST VARIABLF: X = COURFCTm sne CONC. AT Sfn. CONO. ADJUSTED FOR TRUE DRIFT. in»«f-7) LB/SCF
TRANSFORMATION: x LINEAR
DAYTON
L*B 101 . LAB 102 . L«B 103 , LAB 101
TEST SITE!
COLLABORATORSl
INTER-LABORATORY RUN SUMMARY
RUN SAMPLE
i i
3 3
5 11
b 12
7 13
B 1«
" 15
10 Ib
11 17
12 18
13 25
1* ?b
IS 27
Ib 29
COLLABORATOR SUMMARY
COLLABORATOR
MEAN
STD. DEVIATION
Pom SUMMARY
PORT
MEAN
STD. DEVIATION
LAB
DATA
721.
012.
7B«.
BbS.
SOS.
b!2.
S8b.
589.
IfaB.t
178.T
171. «
Ib7.+
105n*-t
1017. t
LAR
b7D
350
A
b7Q
3*7
101
PORT
fB)
CC)
(0)
CC)
CD)
CB)
CD)
CA)
ra)
CC)
CA)
CB)
CC)
ini
.P
.3
.'
.3
LAB
DATA
02*!*
oiol*
58**.
583.*
Hb.t
iba.t
193.t
inzlt
113b.t
lOSS.t
l>»
70*
B
350
1112
PORT
fC)
CA)
CB)
cn)
CA)
CB)
fA)
CB)
CO
CO)
(B)
CC)
102
• C
'.->
LAB
DATA
103.
«2n!
BbO.
bOO.
582!
I Bill
lai.t
UlS.t
1103.'t
1152.t
LAB
Ib*
C
bBO
Ibl
103
PORT
CA)
CB)
CC)
CO)
CB)
CO
CO)
CO
CO)
CA)
CO)
CA)
CB)
CC)
in 3
'.i
.b
.b
LAB
DATA
71*.
7Bb!
SSB.
S2b.
529.
IbS.t
180. t
170. t
17b.t
•»fc7.t
lOlblt
LAB
b!3
311
0
bbS
3*8
10* RUN SUMMARY
PORT
CD)
CC)
CC)
CO)
CB)
CO
(D)
CA)
CO
(D)
in*
.1
.7
.1
.1
MEAN
823.5
871.5
709.5
855.2
589.7
573.5
5b«.7
582.0
I7b.2
17b.7
174..2
17b.?
IOB7.0
1087.5
1088.0
1087.5
STD OEV
111.*
10.5
28. b
51.*
20.7
35. B
27.o
32.0
b!o
b.7
7.0
o*"»
51.0
Sb.b
COEF OF i
!lD39
.03S<)
.ObOfl
.0352
,0b25
.0702
.0337
.0380
.0*00
*OBb8
,0»b8
.0521
•Replacement value.
t Value adjusted lor true drift.
-------
lable B-S The Corrected Cambridge Collaborative Test Data with Replacements,
Adjusted for True Drift
METHOD: METHOD b — - DFTERHINATION OF SULFUR DIOXIDE EMISSIONS FROM STAT1
TEST VARIABLE: X = CORRECTED 308 CONC. AT RTD. CONO. ADJUSTED FOR TRUE DRIFT, ir
TRANSFORMATION: x LINFAP
TEST SITEl CAMBRIDGE
COLLABORATORS: LAB loi , LAB 1(18 , LAB 103 , LAB in*
INTER-LABORATORY RUN SUMMARY
RUN SAMPLE
1 »
8 5
3 b
* 7
5 B
b 1
7 10
B 11
1 IB
10 H
11 80
18 81
13 81
1* 8b
15 87
Ifa 88
COLLABORATOR SUMMARY
COLLABORATOR
MEAN
STD. DEVIATION
PORT SUMMARY
PORT
MEAN
STD. DEVIATION
LAB 101
DATA PORT
131. C»)
1*8.* C»)
158. CB)
1*3.* CC)
*88.t CA)
S1S.T CB)
5*8. t CC)
5*8. f CO)
8*7. CB)
807. CC)
837. CD)
Bb8. C*)
1*0. CC)
110. CO)
1080.* (A)
110. CB)
LAR 101
b87.8
333.8
A
b»2.*
351.1
LAB ins
DATA PORT
153. CB)
l»h. CC)
l»b. (0)
1*3. CA)
563. t CC)
Sbb.t CD)
SBb.t C*)
5B*.t CB)
88b. CO)
B38. CA)
82*. CB)
850. CC)
1123. CA)
B82. CB)
108b. (C)
811. (0)
LAB 108
b31.7
33b.3
B
h38.7
387.1
LAB 103
DATA PORT
1SS. CO
1*3. CD)
151. (A)
150. CB)
SSI.f CD)
Sl*.t CA)
533.1 CB)
S0*.t CC)
B**. CA)
812. CB)
7R7. CO
838. CD)
lObl. CB)
lObl. CO
1053. (0)
1070. C»)
LAB 103
b31.7
351.7
C
1.21.*
331.1
LAB 10*
DATA PORT
ISO. CA)
1*7. CB)
1»3. CC)
1*7. CO)
S78.t CB)
S20.T CC)
S37.T CO)
SSl.t CA)
8nS. CC)
801. CD)
83*. CA)
885. CB)
1007. CD)
Ibl. CA)
117. (B)
HI. CC)
LAB 10*
b25.7
381.*
0
b87.7
331. b
MEAN
1*1.8
1*4.5
1*8.0
1*5.7
5*1.0
5*8.7
5*1.5
5*8.7
830.5
81b.S
880.5
8*3.8
1038.7
173.5
1031.0
1B1.S
RUN SUMMARY
3TD DEV COEF OF VAR
7.1
8.*
s!»
*5.7
38.b
8».b
33.*
11.*
1*.S
83.0
15.1
77.1
38.'1
70.1
.0*78
.OlbS
.0897
.083*
.0833
."'03
.0**8
.ObOl
.0833
.0177
.0880
.0188
.075*
.07bl
.037*
.0701
•Replacement value.
t Value adjusted for true drift.
-------
Table B-!s Within Lchoraiory Analysts of Corrected Dayton Collaborative Test Data
wiih Replacements Adjusted for True Drift
METHOD b — DETERMINATION nF SULFUR DIOXIDE EMISSIONS FROM STATIONARY SOURCES
TEST VARIABLE: K a CORHECTFO 302 CPNC. AT STD. CnNCI. AOJII3TED FOR TRUE DRIFT, ]D**(-7) LB/SCF
TEST STTEt DAVTON
COLLABORATORS! LA9 101 . LIB 1DZ , LAB 103 . LAB 10*
INTR*-L*BORATORV COLLABORATOR BLOCK SUMMARY
BLOCK MEAN COLLABORATOR
1 837.2
1
2
3
*
2 578. 5
1
2
3
»
3 17b.*
1
2
3
*
* 1087.5
I
2
3
»
LAB mi
LAB 102
L»B 1P3
LAB 10*
LAB 101
LAB 102
LAB 103
LAB 10*
LAH 101
LAB 102
LAB 103
LAB 10*
L*B 101
LAB 102
LAB 103
LAB 10*
MEAN 3TD DEV COEF OF '
823
844
H7fc
7*4
S45
54*
S8R
«3b
171
182
170
171
io*n
11*1
112S
443
.7 81.0 ,fl<*«3
.0 58.8 .ObS*
• 9 3*. '
f .0*53
.7 11.* ,fl»14
.2 11.8 .0148
.0 12.3 .1807
.2 13. b .0232
.5 1*.7 .0275
.0 5.0 .0240
.7 11.5 .Ob28
.0 2.
.7 b.
.0 98.
.2 *2.
.5 21.
.2 25.
."137
.0382
.02b3
.0371
.0184
.0256
-------
METHOD!
TEST VARIABLE:
TRANSFORMATION!
TEST SITE:
COLLABORATORS:
Table B-IO Within-Laboratory A nalysis of Corrected Cambridge Collaborative Test
Data with Replacements Adjusted for True Drift
METHOD b — DETERMINATION OF SULFUR DIOXTOF EMISSIONS FROM STATIONARY SOURCES
X a CORRECTED 302 CONC. AT STD. CONf). ADJUSTED FOR TRUE DRIFT, )n«*(-7) LB/SCF
X LINEAR
CAMBRIDGE
LAB 101 , LAB 102 / LAB 103 , LAB 10*
INTRA-LABORATORV COLLABORATOR BLOCK SUMMARY
on
BLOCK MEAN
1 l*b.9
2 5*9.0
3 827.8
« 1008.7
COLLABORATOR
1
Z
3
»
1
2
3
*
1
2
3
*
1
2
3
*
LAB
LAB
LAB
LAB
LAB
LAB
LA*
LAB
LAB
LAB
LAB
LAB
LAB
LAB
LAB
LAB
101
102
103
10*
101
102
103
10*
101
102
103
10*
101
102
103
10*
MEAN
1»*
1*7
1*9
l»b
5*1
579
527
5*7
R3B
83*
920
818
985
997
l"bl
991
.0
.0
.7
.'
.7
.7
.5
.0
.2
.5
.2
.2
.0
.5
.2
.0
STO DEV
5
*
5
2
*b
9
2*
23
23
12
2b
13
33
12*
b
20
.b
.2
.0
.9
.3
.3
.2
.1
.2
.P
.2
.b
.2
.7
.9
.5
COEF
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
OF I
0389
0289
0333
Ol9b
OBSb
OlbO
0*59
0*22
0277
01»*
0319
Olbb
0337
1250
OObS
020b
-------
140
120
100
200
400 600 800 1000
X . j . Run Mean 10'7 Ib/scf
Figure B-l. Between-Laboratory Run Plot
1200
46
-------
140
120
100
20
200 400 600 800 1000 1200
Xi>k Collaborator Block Mean, 10~7 Ib/scf
Figure B-2. Within-Laboratory Collaborator Block Plot of Adjusted Data
47
-------
Transformation
Linear y = x
Logarithmic' y = log, 0(x)
Square root y = <>/?
Bartlett's
Test Result
B = 120.1
B = 499
fl = 795
Significance
flr{x*(31) > 120 l} « 0.0001
/V{x'<31»499} = 0017
^•{x'Ol)* 79 5} < 00001
despite the scatter, a proportional linear relationship appears as good as any other. Stepwise
multiple linear regression through the origin of the within-laboratory standard deviation s,k as a
function of the mean X, k was conducted on^the same set of regressor variables listed above. The
proportional linear function s ik = Q.03114X, k with a correlation of 0.7880 proved to be the best.
Indirect evidence regarding the proper relationship of the between-laboratory standard devia-
tion to the mean over the Method 6 runs is obtained from Bartlett's test for equality of variance.*10)
This test was used to evaluate the linear (no transformation of X~), the logarithmic (log! 0X~), and the
square root lyT> transformations as means of achieving equality of the between-laboratory run vari-
ances of the corrected collaborative test data with replacements. The Bartlett's test results are shown
in Table B-l 1. The logarithmic transformation yields far better equality of run variance than either
the linear or the square root transformations. However, even under the logarithmic transformation,
TableB.} 1. Adequacy of Tramforma Mm to Achieve there is Onlv a l -7-percent chance
Equality of Run Variance that an actual underlying equality
of run variance process would have
produced data with as much scatter
in the between-laboratory run vari-
ances as that observed in the
Method 6 collaborative test data.
Yet the logarithmic transformation
is the best transformation available;
it is markedly superior to no data
transformation at all. In the previous Method 7 collaborative test report*'' \ it was demonstrated
tlut when the logarithmic transformation of a set of data yields equality of variance (so that the
djla probably have a lognormal underlying distribution), then the standard deviation is proportional
to the mean. The Bartlett's test results shown in Table B-l 1 indicate that the logarithmic transfor-
mation is the transformation of the Method 6 collaborative test run data which best provides equality
of the between-laboratory variance. Thus, by the above theorem, the Method 6 between-laboratory
standard deviation is proportional to the mean of the run's Method 6 collaborator values.
Tlie preceding evidence provides the basis for drawing conclusions regarding the true nature of
the between-laboratory standard deviation Ob and the within-laboratory standard deviation a of
Method 6. From both the direct graphical-regression evidence and the indirect equality of variance
implications gained from the Method 6 run data, the natural inference is that the underlying between-
laboratory standard deviation for a run is proportional to the run's true SO2 concentration ju. Ob -
PhU- It is also proper to conclude that the underlying within-laboratory standard deviation a over runs
sampled by a laboratory at the same true SO2 concentration jz is proportional to that concentration:
a = fti. This latter conclusion is based primarily on the plot (Figure B-2) and on the regression of the
within-laboratory collaborator block data adjusted for true drift. Supporting evidence for the a = p>
coefficient of variation relationship derives from the pnor conclusion that o& = j3j,/j, because since
cJ5 = 0" + a\, it is probable that the component a2 would behave like its aggregate a\.
Incidentally, Bartlett's test for equality of run variance was originally applied to the corrected
collaborative test data, and its logarithmic and square root transformations, with the seven missing
and erroneous data points removed (cf. Tables 2 and 3). Results very similar to those reported in
Table B-l 1 were obtained. Hence, the logarithmic transformed corrected data were utilized as the
proper basis for deriving the seven replacement values denoted by asterisks in Tables 2 and 3 for the
seven points considered as missing. Minimum variance unbiased estimates for each of these seven
misMiig points were obtained by the following procedure applied to the logarithmic transformed
Jjta. "Call the laboratory missing a value on a run the missing laboratory. Compute the missing
48
-------
laboratory's average difference from the other laboratories' run means over all the complete runs in
the block. Add this average difference to the mean of the other laboratories' values on the missing
point run to give the minimum variance unbiased estimate of the point in the transformed scale. Con-
vert this value back to the original scale and use it to replace the missing point's value." An example,
the erroneous value reported by Lab 102 in Sample 4 of block 1 of the Dayton test data, should
serve to clarify this procedure. The complete runs in block 1 are for Samples 1 and 3. The Lab 102
average of the logarithmic values for Samples 1 and 3 is 2.9437. The average of the other laboratories'
sample means for these runs is 2.9071. The average difference for Lab 102 in block 1 is thus + 0.0366.
The mean of the Lab 101, Lab 103, and Lab 104 values for Sample 4 is 2.9223. Then the transformed
replacement value for Lab 102 in Sample 4 is 2.9223 + 0.0366 = 2.9589. The antilog of 2.9589 is
910. Thus, 910 is the replacement value for Lab 102 on Sample 4 of the Dayton data. All seven
replacement values are shown in Tables 2 and 3 (main report) followed by an asterisk.
B.5 Component Standard Deviation, Repeatability and Reproducibility Estimation
In this section, the standard deviations associated with the relevant variance components of a
Method 6 SO2 concentration determination c are estimated from the Dayton and Cambridge collab-
orative test and gas cylinder test data. Also estimated are the repeatability and reproducibility of a
Method 6 test result T, in which the value is defined as the average of three repetitions, each of which
consists of two Method 6 determinations*
where cri- is the Method 6 SO2 concentration obtained on determination / of repetition r. This test
result is artificial in that three repetitions of the emissions rate Qscr , where Qs is the experimental
volumetric flow rate determined by Method 2, are actually used instead of / to determine sulfur
dioxide performance test compliance/1 2) Yet T is a very useful artificial construct because it per-
mits assessment of the relative importance of the repeatability component versus the laboratory
bias component in Method 6 reproducibility under the regulated field sampling situation in which
Method 6 will be employed. Throughout this section, calculation formulas are presented for com-
puting statistics. These calculation formulas were derived in the prior Method 7 test report(1 3)
under the identical coefficient of variation underlying situation shown in Section B.4 to exist in
the Method 6 collaborative tests.
First, estimates will be derived from the Dayton and Cambridge Method 6 collaborative test
data. The within-laboratory coefficient of variation 0 is estimated from the 32 collaborator block
coefficient of variation point estimates A,* /X, * shown in Tables B-9 and B-10 for the corrected
data with replacements adjusted for true drift.
32
=0.040037
So the within-laboratory standard deviation estimate of a Method 6 determination c is 6 =
j3c = 0 040037c. The between-laboratory coefficient of variation is similarly estimated from the
32 run coefficient of variation point estimates shown in Tables 2 and 3 (main report) for the
49
-------
corrected data with replacements:
32
flfc = ^£ (*//*/> = T [1.708541 ] = 0.057952
y=i
The laboratory bias coefficient of variation estimate is calculated from 0 and
A =V$ -P2 =v/(0.057952)2 -(0.040037)2 =0.041898
Thus the laboratory bias standard deviation estimate is aL =PLc = 0.041898c. The repeatability stan-
dard deviation of a Method 6 test result is estimated as
a/y/m = (0.040037 /)/x/5"= 0.016345 t
The repeatability standard deviation estimate has 0 = pg(n - 1) = 4 • 8 • (4 — 1) = 96 degrees of firm-
ness. Hence, the percentage uncertainty standard deviation of the repeatability standard deviation
estimate is
= 100 J-^-= 100 J-4-= 7.
Thus the 95 percent confidence interval for the repeatability standard deviation of a Method 6
test result is given by
0.016345 / ± 1.96 (0.0722)(0.016345 t) = 0.016345 / ± 0.002312 t = (0.01403 /, 0.01866 t)
The reproducibility standard deviation estimate of a Method 6 test result is
^al +a2lm = ^(0.041898 /)2 + (0.040037 /)2/6 = 0.044974
The degrees of firmness in this reproducibility standard deviation estimate are
= (4-8)2 (1.095+ t/6)2
(ng-m)2 (l+/ig7)2 (4-8-6)2 1+4-8. 1.095)2
pg(n - \)m2 p-\ 4 -S-3-62 3
where 7 = (dL /a)2 = (0.041898 M/0.040037/i)2 = 1 .095. So the percentage uncertainty standard de-
viation of the reproducibility standard deviation estimate is
= 100 = 100 ~ = 36.45%
Therefore, the 95 percent confidence interval for the reproducibility standard deviation of a Method 6
test result is
0.044974 t ± 1.96 (0.3645) (0.044974 t} = 0.044974 / ± 0.032130 t = (0.01284 /, 0.07710 /)
SO
-------
In Mandel's system(14), the terms repeatability and reproducibiJity represent the maximum allow-
able deviation that could occur between two test results if the test results are to be considered con-
sistent with each other at the 95-percent confidence level:
Repeatability = 2.77 • a/^/m = 2.77(0.016345 7) = 0.04528 T
Reproducibility = 2.77 Jb\ +62/m = 2.77(0.044974 7) = 0.12458 1
The values calculated in this paragraph are the precision estimates for Method 6 derived from the
corrected collaborative test data at the Dayton and Cambridge sites.
One can also derive alternative Method 6 precision estimates from the corrected gas cylinder test
data. The gas cylinder precision estimates calculated below for Method 6 serve to confirm the esti-
mates obtained from the collaborative test data:
1.0854
& = [0.940948] =0.044405
a = 0.044405 c
- 1.0854
24
[1.382856] =0.062540
0£ = >/(0.062540)2 - (0.044405)2 = 0.044039
a = 0.044039 c
= 0.044405//v/6~= 0.018128 /
a£ +d2/m= v/(0.044039 O2 + (0.044405 02/6 = 0.047624 t
The gas cylinder data give slightly higher precision estimates for Method 6 than does the collaborative
test data. However, when one considers the uncertainty computed in the repeatability and reproduci-
bility estimates above, it is remarkable that the gas cylinder precision estimates agree so well with the
collaborative test precision estimates. If the four collaborative laboratories participating in the Method
f> collaborative tests at Dayton and Cambridge are indeed representative of the population of labora-
tories that will perform Method 6 with respect to their adherence to and execution of the method, then
the Method 6 precision estimates derived from the collaborative test data are probably quite accurate.
Note also that the ratio a\aL has the value 0.956 from the collaborative test estimates and the value
I 008 from the gas cylinder test estimates. When the sensitivity of the ratio a/aL is taken into account,
the closeness of these values confirms the validity of the adjustment procedure used in Section B 3 to
modify the corrected collaborative test data with replacements prior to estimating a. The Method 6
precision estimates calculated both from the collaborative test data and from the gas cylinder test data
art- summarized in Table 7 (main report).
B.6 Analysis of the Unknown Sulfate Solution Test Data
An unknown sulfate solution test was conducted as part of the Method 6 collaborative study to
isolate the accuracy and the precision of the analytical phase of Method 6. 10-mfi samples of four
51
-------
sulfate solutions, labeled Solution A, Solution B, Solution C, and Solution D, in which the concen-
trations were unknown to the collaborative laboratory teams, were analyzed in triplicate on each of
three days in conjunction with the collaborative test and gas cylinder data by each collaborative team
along with both sites' data. Figure 8 (body of report) which is a copy of the instruction and report-
ing form, suggests the data layout. The unknown solution, the collaborator C, and the site 5 of the
concurrently analyzed samples are crossed factors in the full factorial design. The day factor D(CS)
is nested within C X S, and the replicate factor R(CSD) is nested within days.
All the reported unknown sulfate solution test data is presented in Table B-12. Table B-l 3 is a
summary of the Table B-l 2 data averaged over replicates and days to show the collaborator and site
interaction effects. A site comparison of the Table B-l 3 data by collaborator is interesting. Lab 101
Table B-12 Reported Sulfate Solution Concentrations, Iff
Collaborator
Lab 101
Ub 102
Lab 103
Lab 104
Day
1
2
3
1
2
3
1
2
3
]
2
3
Repl
1
2
3
1
1
3
1
2
3
1
2
3
I
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
With Dayton Samples
Sol A
349
349
349
349
349
349
351
350
350
348
348
352
337
351
344
313
366
340
350
350
352
352
348
352
348
348
350
352
352
347
345
346
347
346
345
346
Sol. B
-030
-0.70
-070
-090
-030
0.00
-1 00
-130
000
099
1 07
0.87
094
088
088
070
031
031
0.0
00
00
00
00
0.0
00
00
0.0
00
00
00
00
00
00
00
00
00
Sol C
528
528
527
530
529
531
530
529
531
525
518
520
500
509
511
509
512
522
524
526
524
524
526
526
524
524
526
522
517
512
518
518
515
523
520
520
Sol D
174
174
173
172
173
174
173
174
175
177
179
174
167
170
169
172
171
175
178
176
176
176
174
176
174
174
176
166
169
169
174
174
173
171
173
169
With Cambridge Samples
Sol A
357
353
353
352
352
351
353
353
351
348
346
344
343
350
343
342
343
345
337
338
340
338
337
337
337
338
338
361
363
359
356
354
356
359
361
358
Sol B
00
1.6
1.6
0.0
17
23
00
00
-1 7
00
00
00
00
00
00
00
0.0
00
00
00
00
00
00
00
0.0
00
00
00
00
00
00
00
00
00
00
0.0
Sol C Sol D
525
527
527
533
534
533
538
528
531
515
517
516
511
520
521
514
509
518
506
504
506
507
506
506
504
506
506
535
535
535
534
536
536
544
541
532
173
167
173
173
177
176
174
172
174
174
173
167
196
192
177
177
173
176
171
169
169
172
169
171
171
169
171
181
180
178
180
181
180
183
181
183
52
-------
Table B-I3. Sulfate Solution Concentrations A veraged
Over Days, IO'7 Ib SO2/scf
Collaborator
Lab 101
Lab 1 02
Lab 103
Lab 104
With Dayton Samples
Sol A
349.4
3510
3500
347.3
Sol B
-0.58
077
000
000
Sol C
5292
514.0
5249
518.3
Sol D
1736
1727
175.6
1709
With Cambridge Samples
Sol A
3528
3449
3378
3586
Sol B
061
000
000
000
Sol C
5307
5170
5057
5364
Sol D
1732
1783
1702
1808
shows little variation, except for Solution B, between the two sites. Lab 102 shows more variation,
but there is no consistent site pattern over the four solutions. However, Lab 103 obtained consis-
tently lower determinations with its Cambridge samples than with its Dayton samples, while Lab
104 obtained consistently higher determinations with its Cambridge site samples. It is noteworthy
that Labs 101 and 104 had the same chemist analyzing both sites' samples, while Labs 102 and 103
used one analyst for the Dayton site samples and a different analyst for the Cambridge site samples.
Table B-14 is a further summarization of the Table B-12 data in which the two sites' data are also
Table B-14 Average Laboratory Suifatc Sohmon averaged to show only the laboratory
Concentrations, I0'7lb so2/scf effects. Lab 103 appears to have a low
laboratory bias in Table B-14, but it can
be seen from Table B-13 that only the
analysis of the Cambridge site samples
is responsible for this apparent bias.
A separate analysis of variance
was performed on the data for each of
the four unknown sulfatc solutions that
are displayed in Table B-12. Based on a
random effects model, the four analyses
of variance and their variance components
are presented in Table B-l 5. The signifi-
cance of the variance components for each unknown solution is shown in Table B-l6. Clearly the
collaborator C (i.e., pure laboratory bias) and the site 5 factors have no significant effect on the
analytical phase of Method 6 at any SO2 concentration level in the working range However, the
collaborator site interaction factor CS has a very significant effect (P < 0.014) at all SO2 concen-
tration levels. This is a result of the interesting collaborator-site data pattern of Table B-l 3 pointed
out in the previous paragraph. The change in the analyst performing the Method 6 analytical phase
by Labs 102 and 103, i.e., the operator factor, certainly, contributes to the size of the collaborator
site interaction effect. Lab 103 showed a uniform marked reduction in Method 6 SO2 determinations
when a different chemist analyzed the Cambridge samples. But the Lab 104 SO2 determinations
ror the Dayton samples it analyzed were consistently low, much lower than its Cambridge samples.
Lab 104 had the same chemist analyze all of its Method 6 SO2 samples, both from Dayton and from
Cambridge. So another factor in addition to the operator factor must also be responsible foi the
magnitude of the collaborator site interaction effect. Lab 104 reported uniformly lower SO2 con
centrations using Method 6 on alt the samples it analyzed (i.e., the collaborative test data, the gas
cylinder data, and the unknown sulfate solution data) from the earlier Dayton test, than from the
later Cambridge test (cf. Tables 2, 3, 4, 5, and B-l 3). A plausible explanation is that the effective
normality of the barium perchlorate titrant was inadvertently increased in analysis of the Dayton
Collaborator
Lab 101
Lab 102
Lab 103
Lab 104
Prepared SO,
Concentration
Solution A
351 1
3479
3439
3529
35250
Solution B
0.02
039
000
000
000
Solution C
5299
5155
5153
5274
528 75
Solution D
1734
1755
1729
1758
17625
53
-------
Table B-15. Analyses of Variance ofSulfate Solution Data by Concentration
Factor
Sum of
Squares
D.F
Mean
Square
Expected Mean Square
Variance
Component
Solution B-Mean = 0 101
C
S
CS
WCS)
R(CSD)
196
020
8.85
7.06
806
3
3
16
48
0.6S
020
295
044
017
isi5*isrs
3o* + oj.
°K
•J.-0
8J = 0
8^ = 0279
6'D = OJ09\
8^ = 0.168
Solution D-Mten =1744
C
S
CS
D(CS)
R(CSD)
1183
1100
6030
6673
3447
3
1
3
16
48
394
1100
2010
41 7
72
18oJ, + 90^ + 305, + oJ,
36oL -f 9o' + 3o' +• o1
9oJ_ + 3o' + o'
„»
o'=0
6' =0
6' =1770
o^=US3
8J-718
Solution A -Mean = 3490
C
S
CS
D(CS)
R(CSD)
8505
161
14409
5084
8300
C
S
CS
rxcs)
R(CSD)
32326
125
31762
562.7
5000
3
1
3
16
48
2835
161
4803
318
173
18o' +9o' +3o' +o'
36oi + 9o'_ + 3d1 + o'
9o' + 3o' + o'
3o' + o'
°R
Solution C-Mtan = 522 0
3
1
3
16
48
1077.5
125
1058.7
352
10.4
i3*S*3*i
9o' + 3o' + o'
3o» + o'
"i
o"=0
o1 =0
6'cs ' 49 84
o' =4.83
a^ = 1729
oj,= 105
0^ = 11372
£> =8.25
ojj = 10.42
Table B-16. Significance of Sulfate
Solution Factors
Solution
B
U
A
C
Factor
C
S
CS
D(CS)
C
S
CS
D(CS)
C
S
CS
D(CS)
C
S
CS
D(CS)
F- Ratio
0221
0066
6688
2627
0196
0547
4820
5808
0.590
0033
15 115
1 838
1018
0.004
5.645
1 125
Significance
^>050
^>050
P = 0 004
f = 0.005
f>QSO
P>OSO
P = 0.014
P<0001
P>OSO
P>QSQ
P<0001
P = OOS
P * 0.50
P>050
P = 0.008
P * 0.40
samples. The Lab 104 analyst says that the same flask of
titrant was used for both the Dayton and the Cambridge sam-
ples. However, he did modify his procedure for filling the
burette during sample analysis of all the Cambridge samples.
In analyzing the Dayton samples, the titrant was transferred
to an intermediate beaker and left standing until needed in
titrating each sample to a pink endpoint. Later the analyst
realized that the isopropanol would probably evaporate from
the standing beaker to yield a higher effective titrant nor-
mality. So in analyzing the Cambridge samples, the barium
perchlorate titrant was kept in the stoppered flask until needed
in the titration step. Since isopropanol will evaporate from
an open standing beaker, the Lab 104 procedure change is
the likely explanation for the low Method 6 SO2 concentra-
tion determinations it made on all Dayton samples. Thus,
uniform analysis procedural variation is another causative
factor behind the sizable collaborator site interaction effect.
54
-------
Table B-16 shows that the day factor D has a significant effect on the analytical phase of Method 6,
but only at low SO2 concentration levels. Based on the large effect of the ostensibly minor Lab 104
procedural change discussed above, it is reasonable to believe that small Method 6 procedural variations
made from day to day caused the day effect. Such procedural variations would logically have greater
impact on the lower Method 6 SO2 concentration determinations.
The precision variability measures of the Method 6 analytical phase can be estimated by coeffi-
cient of variation analysis. Since the variance component estimates given in Table B-l 5 for the blank
Solution B are very small in comparison with the estimates for the other solutions, the necessary pro-
portionality of standard deviation to mean is a plausible assumption. The within-laboratory standard
deviation component a is estimated from the replication variance component 6^ , while the between-
laboratory standard deviation ab is estimated from the between-laboratory mean square
s.d.r= 1
., irf (Xcsdr — X sdr)
at each of the 18 site, day, replicate combinations for each of the four solutions. As Table B-l 7 dis-
closes, estimates of 0 = 0.01103 and 06 = 0.02448 are obtained for the analytical phase of Method 6
from the unknown sulfate solution data by this method. In Table B-l 8 all the precision variability
estimates for the analytical phase of Method 6 are presented as a result of a coefficient of variation
analysis.
Table B-l 7 Analylical Coefficient of Variation
Solution
B
D
A
C
Mean IQ-'Ib/scf
True
M
0.00
17625
3S2SO
52875
Method 6
~x"
010
17440
34897
522.03
Within Laboratory
Std Dev,
S = J%
0410
2680
4.158
3227
Beta,
0
001520
001180
000610
(3 = 0.01103
Between Laboratory
Std Dev,
Sb=jMS^
0639
5.161
7.865
11 551
Beta,
h
0.02928
0 0223 1
0.02184
06 = 0 02448
Table B-l8 Method 6 Analytical Phase Precision Variability Estimates
Source
of Test
Data
Unknown
Sulfate
Solution
Test
Data
Precision
Variability
Measure
Within Lab
Between Labs
Lab Bias
Repeatability
(m = 6)
Reproducibility
(rn = 6)
Test
Data
Version
CD
CD
CD
CD
CD
Component Estimates Test Result Estimates
Coef. of Var ,
*
(3 = 001103
(J6 = 0 02448
0L = 002185
Std Dev ,
a
o = OOH03c
ob = 0 02448 c
SL = 002l85c
Std Dev
0 00450 t
002231 /
Mandel
Def
0 01247 /
006 ISO/
55
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B.7 The Minimum Detectable Limit
The minimum detectable limit of Method 6 is the smallest Method 6 test result value / that is
significantly larger than zero in the reproducibility sense. As Table 10 indicates, the reproducibility
variance can be partitioned into an analytically induced portion and a field-induced portion. The
unknown sulfate solution test, which included repeated analysis of a blank Solution B, provides an
excellent means for estimating the actual analytical reproducibility variance at n = 0. From Table
B-l 7, the analytical reproducibility variance at ji = 0 is estimated as CT£ + o2/6 = (si -s2) +s*J6 =
(0.639-0.410)2 + (0.410)2/6 = 0.2682 X(10-7 Ib/scf)2. Now Table 10 shows that only 24.6
percent of the Method 6 reproducibility variance is caused by the analytical phase in the working
Method 6 range where a = /3p. While Table B-l7 suggests that the analytical phase is responsible for
considerably more than 24.6 percent of the variation at ju = 0, we will nevertheless make the conser-
vative assumption that the 24.6 percent figure remains valid. On this assumption, the Method 6
reproducibihty variance at|/ = 0is given by (100%/24.6%) (0.2682) (10~7 Ib/scf)2 = 1.090 X
(10~7 Ib/scQ2. Then the upper 95 percent confidence limit for a true concentration M = 0 is C 9 s =
1 -96 V1.090XOO-7 Ib/scf)2 = 2.05 X lO'7 Ib/scf. So the minimum detectable limit of a Method
6 test result is 2.05 X 10~7 Ib/scf. When a laboratory obtains a Method 6 test result value / as high
as 2.05 X 10"7 Ib/scf, there is at most a 5-percent chance that the true sulfur dioxide emission con-
centration was zero.
56
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REFERENCES
1. Environmental Protection Agency, "Standards of Performance for New Stationary Sources,"
Federal Register, Vol. 36, No. 247, December 23, 1971, pp. 24876-24891.
2. Environmental Protection Agency, op. cit, p. 24879.
3. Environmental Protection Agency, op. cit., pp. 24878-24880.
4. Hamil, Henry F., and Camann, David E., Collaborative Study of Method for the Determination
of Nitrogen Oxide Emissions from Stationary Sources, Southwest Research Institute Report
for Environmental Protection Agency, October 5, 1973, pp. B-17, B-18.
5. Mandel, John, "Repeatability and Reproducibility," Materials Research and Standards,
American Society for Testing and Materials, Vol. 11, No. 8, August, 1971, pp. 12, 13.
6. Mandel, loc. cit.
7. Youden, W.J., "The Collaborative Test," Journal of the AOAC, Vol. 46, No. I, 1963, pp. 55-62.
8. Hamil, Henry F., and Camann, David E., op. cit., pp. B-16, B-17.
9. Brownlee, K.A., Statistical Theory and Methodology in Science and Engineering, 2nd Ed.,
Wiley, New York, 1965, pp. 413-414.
10. Brownlee, op. cit., pp. 290-295.
11. Hamil and Camann, op. cit., pp. B-14 to B-16.
12. Environmental Protection Agency, op. cit., p. 24879.
13. Hamil and Camann, op. cit, pp. B-18 to B-22.
14. Mandel, John, loc. cit.
57
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TECHNICAL REPORT DATA
(Please rend Instructions on the reverse before completing)
I REPORT NO
EPA-650/4-74-024
3. RECIPIENT'S ACCESSION NO
4 TITLE AND SUBTITLE
Collaborative Study of Method for the Determination of
Sulfur Dioxide Emissions from Stationary Sources
(Fossil Fuel-Fired Steam Generators.
S REPORT DATE
December 10, 1973
6. PERFORMING ORGANIZATION CODE
7 AUTHOR(S)
H. F. Hamil and D. E. Camann
8 PERFORMING ORGANIZATION REPORT NO
SwRI Project No. 01-3487-001
9 PERFORMING ORGANIZATION NAME AND ADDRESS
Southwest Research Institute
8500 Culebra Rd.
San Antonio, Texas 78284
10 PROGRAM ELEMENT NO
1HA327
11 CONTRACT/GRANT NO
68-02-0623
12 SPONSORING AGENCY NAME AND ADDRESS
Environmental Protection Agency
NERC, MSPEB, QAEML
Research Triangle Park, N. C. 27711
13. TYPE OF REPORT AND PERIOD COVERED
14. SPONSORING AGENCY CODE
15 SUPPLEMENTARY NOTES
16 ABSTRACT
A collaborative study has been performed on Method 6 promulgated by EPA for deter-
mining the concentration of sulfur dioxide emissions from stationary sources. Method
6 specified the extraction of a gas sample from the stack, the separation of the
sulfur dioxide from the acid mist including sulfurtrioxide, and the measurement of the
sulfur dioxide fraction as sulfate by the barium-thorin titration method. Collabora-
tive tests were conducted at both a coal-fired steam generating power plant and an oil
-fired pilot plant by the same four collaborative teams. Satistical analysis of the
collaborative test and associated data revealed the following findings regarding the
reliability, both of a Method 6 determination, and of a Method 6 test result, which
is defined as the average of six determinations: Accuracy : Method 6 is accurate in
the SO, concentration range below 300c 10 Ib/scf, but it acquires a significant
5- to 70% negative bias below the true cone, above 500 x 10 Ib/scf. Precision: The
estimated within-lab and lab bias standard deviations of a Method 6 determination are
4.0 and 4.2%, respectively, of its value. The repeatability standard deviation of a
test result is estimated as 1.6% of its value. The estimated reproducibility standard
deviation of a test result is 4.5% of its value. Minimum Detectable Limit: A 7
conservative estimate of the minimum detectable limit of a Method 6 test Is 2.1 x 10
Ib scf. Sources of Reproducibility Variation: .Most (75%) of the reproducibility
variation in a test result resides in the field sampling phase of Method 6, with 25%
occurring in the analytical phase. Only 13% reproducibility variance is caused by
reoeatability sources, while 87% results from lab bias sources.
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63
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