EPA-650/4-74-021
COLLABORATIVE STUDY
OF
METHOD FOR THE DETERMINATION OF
PARTICULATE MATTER EMISSIONS FROM
STATIONARY SOURCES
(FOSSIL FUEL-FIRED STEAM GENERATORS)
by
Henry F. Hamil
Richard E. Thomas
SwRI Project No. 01-3487-01
EPA Contract No. 68-02-0623
Prepared for
Methods Standardization Branch
Quality Assurance and Environmental Monitoring Laboratory
National Environmental Research Center
Environmental Protection Agency
Research Triangle Park, N. C. 27711
Attn: M. Rodney Midgett, Research Chemist
Section Chief, Stationary Source Methods Section
June 30,1974
SOUTHWEST RESEARCH INSTITUTE
SAN ANTONIO CORPUS CHRISTI HOUSTON
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This report has been reviewed by the Office of Research and Development, EPA, and approved for publication.
Approval does not signify that the contents necessarily reflect the views and policies of the Environmental Pro-
tection Agency, nor does mention of trade names or commercial products constitute endorsement or recommendation
for use.
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SOUTHWEST RESEARCH INSTITUTE
Post Office Drawer 28510, 8500 Culebra Road
San Antonio, Texas 78284
COLLABORATIVE STUDY
OF
METHOD FOR THE DETERMINATION OF
PARTICULATE MATTER EMISSIONS FROM
STATIONARY SOURCES
(FOSSIL FUEL-FIRED STEAM GENERATORS)
by
Henry F. Hamil
Richard E. Thomas
SwRI Project No. 01-3487-01
EPA Contract No. 68-02-0623
Prepared for
Methods Standardization Branch
Quality Assurance and Environmental Monitoring Laboratory
National Environmental Research Center
Environmental Protection Agency
Research Triangle Park, N. C. 27711
Attn: M. Rodney Midgett, Research Chemist
Section Chief, Stationary Source Methods Section
June 30, 1974
Approved:
John T. Goodwin
Director
Department of Chemistry
and Chemical Engineering
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SUMMARY AND CONCLUSIONS
This report presents the results obtained from a collaborative test of Method 5, a test procedure for determining
particulate emissions from stationary sources. Method 5 specifies that particulate matter be withdrawn isokinetically
from the source and its weight determined gravimetrically after the removal of uncombined water.
The test was conducted at a fossil fuel-fired steam generating power plant using four collaborating laboratories.
Sixteen sample runs were made over a two-week period by the collaborators for a total of 63 individual determinations.
The reported values of one of the laboratories were not included in the analysis. Conversation with other person-
nel who participated in the test, and inspection of the laboratory's sampling train subsequent to the test, provided info-
mation which indicated that the determinations made were not representative of Method 5 results.
Of the remaining determinations, one was eliminated due to failure to maintain isokinetic conditions. The remain-
ing values were subjected to statistical analysis to estimate the precision that can be expected with field usage of
Method 5. The precision estimates are expressed as standard deviations, which are shown to be proportional to the mean
determination, 5, and are summarized below.
(a) Within-laboratory: The estimated within-laboratory standard deviation is 31.1% of 5, with 34 degrees of
freedom.
(b) The estimated between-laboratory standard deviation is 36.7% of 8, with 2 degrees of freedom.
(c) From the above, we can estimate a laboratory bias standard deviation of 19.5% of 5.
The above precision estimates reflect not only operator variability, but, to an extent, source variability which
cannot be separated from these terms. The results summarized above were obtained from a single test using the
data from three collaborators. Further testing would, of course, be necessary to obtain conclusive results.
Comments on the use of Method 5 from the collaborators are included, and recommendations are made for
the improvement of the method.
in
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TABLE OF CONTENTS
Page
LIST OF ILLUSTRATIONS vi
LIST OF TABLES vi
I. INTRODUCTION 1
II. COLLABORATIVE TESTING OF METHODS 2
A. Collaborative Test Site 2
B. Collaborators 6
C. Philosophy of Collaborative Testing 7
III. STATISTICAL DESIGN AND ANALYSIS
A. Statistical Terminology 8
B. Collaborative Test Design 9
C. Collaborative Test Data 10
D. Precision of Method 5 10
IV. COMMENTS AND RECOMMENDATIONS 14
APPENDIX A—Method 5—Determination of Particulate Emissions From Stationary Sources . . . 17
APPENDIX B-Statistical Methods 21
B.1 Preliminary Analysis of the Original Collaborative Test Data 23
B.2 Significance of the Port Effect 23
B.3 Transformations 23
B.4 Empirical Relationship of the Mean and Standard Deviation in the Collaborative
Test Data 24
B.5 Underlying Relationship Between the Mean and Standard Deviation 26
B.6 Weighted Coefficient of Variation Estimates 28
B.7 Estimating Standard Deviation Components 30
LIST OF REFERENCES 33
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LIST OF ILLUSTRATIONS
Figure Page
1 Allen King Power Plant, Northern States Power and Light Co. 2
2 Allen King Power Plant .Overall Site Configuration 3
3 Allen King Power Plant, Sampling Site Configuration 4
4 Average Velocity Profiles 5
5 Sample Platforms and Ports 6
6 Work Area and Sample Port 6
7 Control Console Operation 7
8 Impinger Train Operation 7
B.I Interlaboratory Run Plot 25
B.2 Intralaboratory Collaborator-Block Plot 26
LIST OF TABLES
Table Page
1 General Information—Allen King Power Plant 2
2 Hourly Average Coal Burned 10
3 Original Particulate Collaborative Test Data 10
4 Particulate Collaborative Test Data Arranged By Block 11
B.I Significance of Port Effect 24
B.2 Data Transformation to Achieve Run Equality of Variance 24
B.3 Interlaboratory Run Summary 25
B.4 Intralaboratory Collaborator-Block Summary 26
B.5 Bias Correction Factors for Sample Standard Deviations 27
B.6 Run Beta Values and Weights 31
B.7 Collaborator-Block Beta Values and Weights 31
n
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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 5 for particulate emissions as given in
"Standards of Performance for New Stationary Sources."^ '
This report describes the collaborative testing of Method 5 in a coal-fired steam generating power plant and gives 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 at the end of this report.
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II. COLLABORATIVE TESTING CF METHOD 5
A. Collaborative Test Site
Arrangements were made for collaborative testing of Method 5 at the Allen King Power Plant of Northern States
Power Company near St. Paul, Minnesota. Through a subcontract with Thermo-Systems, Inc., access to the plant, sam-
pling ports and platforms, and other sampling facilities were provided, and logistical support obtained. Facilities were
installed which provide for simultaneous sampling by four collaborators, each collaborating team working on a separate
platform with a separate sampling port.
The power plant was visited in December, 1972 to inspect the facilities being constructed and to investigate several
potential problems including length of probe required, effect of positive pressure in the duct, and statistical details of
planning and conducting collaborative tests.
Table 1 gives some information on the Allen King Power Plant, and Figure 1 shows a view of the power plant. Fig-
ure 2 shows the overall site configuration, and the sample site configuration is in Figure 3. Velocity profiles across the
sampling area within the duct are shown in Figure 4. The profiles were obtained by averaging the velocities of all four
collaborators at each traverse point from four randomly selected sampling runs. Due to the width of the duct, a wall-to-
wall traverse could not be made with a 10-foot probe. Sampling the entire duct width would have required sampling
from the center line of the duct out to the wall on all four ports for a single sampling run. This procedure would
have required moving all four sampling trains through a 34-inch high crawl way underneath the duct on each run, and
due to the time required would have precluded taking two samples per day. Since this study involved evaluation of
TABLE 1 GENERAL INFORMATION-ALLEN KING
POWER PLANT
Rated Capacity-550 megawatts
(Normally Operated nearly full load at all times)
Age of facility
Stack height
Stack diameter
Coal usage at full load
Coal used
Coal sulfur content
Syr
800 ft
26 ft at bottom, 1 8 ft at top
240 tons/hr
Southern Illinois
3-1/4 percent
A small amount of Montana coal (sulfur content
about 1-1/2 percent) is available for use during
pollution alerts. Combustion chamber consists of
twelve cyclone units exhausting into a common heat
exchanger system. The emission gas splits into two
identical gas streams shortly upstream of twin elec-
trostatic precipitators which normally collect 98 to
99 percent of the fly ash (by weight). The twin
emission gas streams meet again at the base of the
vertical stack. Our sampling ports for the collabora-
tive tests are in the south—left horizontal duct, just
upstream of the vertical stack. Approximately
1 million cfm of emission gas passes through each of
the twin emission gas streams.
Internal horizontal duct dimensions at 27 ft high
sampling ports 12 ft wide
Two sampling ports, one on each side of the duct,
are located 6 ft above the center line of the duct;
and two sampling ports, one on each side of the
duct, are located 6 ft below the center line of the
duct. The opposing ports are offset 6 in. vertically
to prevent interference.
FIGURE 1. ALLEN KING POWER PLANT
NORTHERN STATES POWER AND LIGHT CO.
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\
South
Duct
Inner
Stack
North
Duct
to
O
FIGURE 2. ALLEN KING POWER PLANT
OVERALL SITE CONFIGURATION
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Inner
Stack
X
r
9'
20'
South Duct
j-4 12'—-H
WU
WL
EU
u
_J.
EL
~r
.1.
FIGURE 3. ALLEN KING POWER PLANT
SAMPLING SITE CONFIGURATION
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u
8
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Method 5 rather than characterization of the site, a modified tranversing procedure was adopted in which the samples
were obtained from a seven-foot wide section of the duct, beginning and ending two and one-half feet from the interior
duct walls. This seven-foot section could be traversed from either side of the duct, so that a sampling run consisted of
taking one-half the sample from an upper (or lower) port, followed by a port change, and taking the other half of the
sample from the other port on the same side of the duct. A total of 24 traverse points. 12 on each port, were used on
each run. Figure 5 shows an overall view of the sampling platforms and ports on one side of the duct, while Figure 6
shows a view of an individual work area and sample port.
FIGURE 5. SAMPLF PLATFORMS AND PORTS
B. Collaborators
HGUKl, 6. WORK ARhA AND SAMPLK PORT
The collaborators for the Allen King Power Plant test were Mr. Mike Taylor and Mr. Hubert Thompson of
Southwest Research Institute, Houston Laboratory, Houston, Texas; Mr. Charles Rodriguez and Mr. Ron Hawkins of
Southwest Research Institute, San Antonio Laboratory, San Antonio, Texas; Mr. Gilmore Sem, Mr. Vern Goetsch.
and Mr. Jerry Brazelli of Thermo-Systems. Inc, St. Paul, Minn.; and Mr Roger Johnson and Mr. Harry Patel of Environ-
mental Research Corporation, St. Paul, Minn.* As mentioned earlier in the report, Thermo-Systems, Inc. had the respon-
sibility for site preparation and liaison between test crews and plant personnel.
Collaborative tests were conducted under the general supervision of Mr. Nolhe Swynnerton of Southwest Research
Institute. Mr. Swynnerton had the overall responsibility for assuring that the test was conducted in accordance with the
collaborative test plan and that all collaborators adhered to Method 5 as written in the Federal Register, December 23,
'1971. The collaborating teams foi the test were selected by Dr. Henry Hamil of Southwest Research Institute.
*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.
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FIGURE 7. CONTROL CONSOLL OPERATION
HGURE 8. IMPINGER TRAIN OPERATION
In Figures 7 and 8, members of the collaborative teams are shown in the operation of an impinger tram and a
control console during one of the test inns.
C. Philosophy of Collaborative Testing
The concept of collaborative testing followed in the tests discussed in this report involves conducting 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 information 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 mismeasurement of volume of impinger solution, improper rinsing of probe, etc., no inter-
ference was made by the test supervisor. Since such random errors will occur in the everyday use of this method in the
field, unduly restrictive supervision of the collaborative test would bias the method with respect to the held test lesults
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, the deviations would be
pointed out to the collaborator and corrected by the test supervisor.
While most of the instructions in the Federal Register are quite explicit, some areas are sub|ect to interpretation
Where this was the case, the individual collaborators were allowed to exercise their professional judgement as to the
interpretation of the instructions.
The oveiall 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 and precision of the method that would be expected in peiformance test-
ing in the field.
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III. STATISTICAL DESIGN AND ANALYSIS
A. Statistical Terminology
To facilitate the understanding of this report and the utilization of its findings, this section explains the statis-
tical terms used in this report. The procedures for obtaining estimates of the pertinent values are developed and
justified in the subsequent sections.
We say that an estimator, 6, is unbiased for a parameter 6 if the expected value of 0 is 9, or expressed in nota-
tional form, E(Q) = 0. From a population of method determinations made at the same true concentration level, M.
let Xj... .,xn be a sample of n replicates. Then we define:
1 "
(1) x = — /I x, as the sample mean, an unbiased estimate of the true determination mean, 5, the center of
",= 1
the distribution of the determinations. For an accurate method, 6 is equal to p, the true concentration.
1 "
(2) s1 = yP (x, - x)2 as the sample variance, an unbiased estimate of the true variance, o2 . This
n- 1^
term gives a measure of the dispersion in the distribution of the determinations around 5.
(3) s = \/s as the sample standard deviation, an alternative measure of dispersion, which estimates a, the
true standard deviation.
The sample standard deviation, s, however, is not unbiased foi a/ ' so a correction factor needs to be applied.
The correction factor for a sample of size n is an, and the product of an and s is unbiased for a. That is, E(ans) = a.
As n increases, the value of an decreases, going for example froma3 = 1.1284,a4 = 1.0854 to a10 = 1.0281. The for-
mula for ctn is given in Appendix B.5.
We define
as the true coefficient of variation for a given distribution. To estimate this parameter, we use a sample coefficient
of variation, |3, defined by
where j3 is the ratio of the unbiased estimates of a and 6, respectively. The coefficient of variation measures the
percentage scatter in the observations about the mean, and thus is a readily understandable way to express the
precision of the observations.
The experimental plan for this test called for 16 runs. On each run, the collaborative teams were expected to
collect simultaneous samples from the stack in accordance with Method 5, Since the actual particulate emission
concentration in the stack fluctuates, one can in general expect different true concentrations for each run. To
permit a complete statistical analysis, the individual runs are grouped into blocks, where each block has approxi-
mately the same true emission concentration level.
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We can apply the statistical terms of the preceding paragraphs both to the collaborators' values during a
given run and to each collaborator's values in a given block. In this report, statistical results from the first situa-
tion are referred to as run results. Those from the second situation are referred to as collaborator-block results.
For example, a run mean is the average of each collaborator's concentration level for the run as obtained by Method 5.
A collaborator-block coefficient of variation is the ratio of the unbiased standard deviation to the sample mean for all
the collaborator's runs grouped in the block.
The variability associated with a Method 5 concentration determination is estimated in terms of the within-laboratory
and the between-laboratory precision components. In addition, a laboratory bias component can be estimated. The
following definitions of these terms are given with respect to a true stack concentration, p..
• Within-laboratory -The within-laboratory standard deviation, a, measures the dispersion in replicate single
determinations made using Method 5 by one laboratory team (same field operators, laboratory analyst, and
equipment) sampling the same true concentration, ju. The value of a is estimated from within each col-
laborator-block combination.
• Between-laboratory-The between-laboratory standard deviation, a^, measures the total variability in a
concentration determination due to simultaneous Method 5 determinations by different laboratories
sampling the same true stack concentration, /u. The between laboratory variance, a^, may be expressed as
a=a+ a2
and consists of a within-laboratory variance plus a laboratory bias variance, a£ . The between-laboratory
standard deviation is estimated using the run results.
• Laboratory bias— The laboratory bias standard deviation, a/, = \/a6 ~~ °2 > is that portion of the total
variability that can be ascribed to differences in the field operators, analysts and instrumentation, and
due to different manners of performance of procedural details left unspecified in the method. This term
measures that part of the total variability in a determination which results from the use of the method by
different laboratories, as well as from modifications in usage by a single laboratory over a period of time.
The laboratory bias standard deviation is estimated from the within- and between-laboratory estimates
previously obtained.
B. Collaborative Test Design
The sampling was done through four ports, two on the east side (EU and EL) and two on the west side (WU and
WL). The experiment was designed so that on each day, each collaborator took one sample from the east side ports,
and one from the west. At the middle of each run, the collaborators using the upper ports shifted to the lower ones,
and those on the lower ports began to use the upper ones. In this manner, any potential port effect was intended to
be nullified.
After receiving and making preliminary calculation checks on the data, an attempt was made to group the
samples into blocks. Considerations in setting up blocks included time— whether each week constituted a block,
load— whether megawatt hour load was a basis for a block, and coal burned— whether the particulate concentration
was a function of the amount of coal burned. There is no accurate procedure for the determination of true particu-
late concentrations, and thus it was impossible to establish blocks based on true or theoretical concentration levels.
The plant provided its daily logs of the hourly operating characteristics of the plant, and the pertinent informa-
tion was extracted from these logs. It was assumed that the amount of particulate matter which was emitted should
depend upon how much fuel was burned. Thus, the average amount of coal burned during the course of each run
was determined, and this was selected as the blocking criterion. These amounts are listed in Table 2.
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TABLE 2. HOURLY AVERAGE
COAL BURNED
Natural blocking of the sample runs appeared to be in groups of four,
from the highest fuel burn average to the lowest. The result was four blocks
each of size four, in a randomized block design, as will be shown in Table 4.
C. Collaborative Test Data
The concentrations obtained by the collaborators are presented in
Table 3. The port sequence used to obtain the sample is also shown. Port
sequences are referred to as A (EL to EU), B (EU to EL), C (WU to WL),
and D (WL to WU). Reported concentrations marked with a dagger are
those for which the isokmetic variation was determined to be outside the
acceptable range of 90 to 110 percent.
The concentrations used in the analysis of Method 5 were those reported
by Labs 102, 103 and 104 only. The observations from Lab 101 are generally
lower than those from the other collaborators. Discussions with personnel
at the test site revealed that the glass joints of the filter holder were being
sealed with a stopcock grease unsuitable for the high temperatures (250°F+)
present in the filter oven. Prior to each run, the sample train was leak
checked according to the method. This leak check is performed prior to applying heat to the filter oven. Upon heat-
ing the oven, there is a strong possibility that the melting of the low temperature grease used led to the development
of leaks during the run. Such leakage around the filter holder fitting would introduce ambient air into the sample
train as a diluent, which would lower the concentration level in the sample.
Day
8-14
8-15
8-16
8-17
8-20
8-21
8-22
8-23
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Coal Burned
ton
351.0
247.2
304.1
322.0
231.4
300.9
232.6
228.8
232.1
241.3
246.0
214.4
225.5
244.5
229.2
238.3
Block
1
2
1
1
3
1
3
4
3
2
2
4
4
2
4
3
TABLE 3. ORIGINAL PARTICULATE
COLLABORATIVE TEST DATA
Ib/scfX 10-7*
Sample
(Run)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Lab
101
381 6 (A)t
51.4 (C)
237 0 (D)
85.3 (B)
139.7 (A)
50.8 (D)
114.8 (D)
63.8 (A)
87.9 (A)
72.7 (C)
96 0 (D)t
103.2 (A)
315.2 (B)
54 8 (C)
1127 (D)
56.5 (B)
102
137 3 (B)
191 2 (D)
176.8 (C)
185.3 (A)
194.9 (B)
173 6 (C)
335 7 (C)
1904 (B)
405 3 (B)
217 5 (D)
188.5 (C)
198.5 (B)
2109 (A)
205.2 (D)
138.8 (C)
167.3 (A)
103
58.4(C)
146.2 (B)
225.7 (A)
154.9 (C)
102.2 (D)
146.9 (A)
313 9 (B)
122.0 (D)
1970(0)
1309 (B)
1245 (A)
161 8 (C)
157 4 (D)
107 0 (B)
112.3 (A)
103 8 (C)
104
334.4 (D)f
151 5 (A)
375.1 (B)
103.5 (D)
102.8 (C)
163.8 (B)
132.3 (A)
125 9 (C)
161.8 (C)
151 3 (A)
351.2 (B)
111 5 (D)
119.4 (C)
- (A)
123. 8 (B)
99. 9 (D)
( ) Port sequence of sample collection in parenthesis.
*EPA policy is to express all measurements in Agency documents
in metric units. When implementing this practice will result in
undue cost or difficulty in clarity, NERC/RTP is providing con-
version factors for the particular non-metric units used in the
document. For this report, the factor is
10^7 Ib/scf = 1.6018 X 103 Mg/m3.
•j-Isokmetic variation outside acceptable range.
At the conclusion of the test, inspection of the
filter holder assembly revealed that the stopcock
grease melted and ran inside the filter holder, saturat-
ing half of the fritted glass filter support. The effect
of this was not immediately determinable, but it is
sufficient cause to suspect the validity of data from
Lab 101. On the basis of the above arguments, it was
decided to perform the data analysis without that
lab's values.
Sample 14 from Lab 104 is missing due to a
malfunction in the digital temperature indicator that
caused them to abort aftei beginning the run. In this
case, as was the case for the values with unacceptable
isokmetic variation factors, no attempt was made to
replace the values. The analysis was performed only
on those values which were actually taken during the
sample period. The concentrations upon which the
analysis was performed are presented in Table 4.
D. Precision of Method 5
In a particulate matter determination, no
measurement of the accuracy of the method can be
obtained. There are no on-stream techniques for
analysis and no indicators of true concentration
10
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TABLE 4. PARTICULATE COLLABORATIVE TEST DATA ARRANGED BY BLOCK
Method: EPA Method 5 -Determination of Participate Emissions Fiom Stationary Sources
Test Variable: X = Concentration of Participates, (Ib/scf) X 10'
Transformation: X Linear
Test Site. Allen King Power Plant
Collaborators. Lab 102, Lab 103, Lab 104.
Inter-Laboratory Run Summary
Block
1
2
3
4
Run
1
3
4
6
2
10
11
14
5
7
9
16
8
12
13
15
Lab 102
Data
137.3
176.8
185.3
173.6
191.2
217.5
188.5
205.2
194.9
335.7
405.3
167.3
190.4
198.5
210.9
138.8
Port*
(B)
(C)
(A)
(C)
(D)
(D)
(C)
(D)
(B)
(C)
(B)
(A)
(B)
(B)
(A)
(C)
Lab 103
Data
58.4
225.7
154.9
146.9
146.2
130.9
124.5
107.0
102.2
313.9
197.0
103.8
122.0
161.8
157.4
112.3
Port
(C)
(A)
(C)
(A)
(B)
(B)
(A)
(B)
(D)
(B)
(D)
(C)
(D)
(C)
(D)
(A)
Lab 104
Data
334 .4Et
375.1
103.5
163.8
151.5
151.3
351.2
O.OMt
102.8
132.3
161.8
99.9
125.9
111.5
119.4
123.8
Port
(D)
(B)
(D)
(B)
(A)
(A)
(B)
(A)
(C)
(A)
(C)
(D)
(C)
(D)
(C)
(B)
Run Summary
Mean
97.8
259.2
147.9
161.4
163.0
166.6
221.4
156.1
133.3
260.6
254.7
123.7
146.1
157.3
162.6
125.0
Std Dev
55.8
103.3
41.3
13.5
24.6
45.3
116.9
69.4
53.3
111.7
131.6
37.8
38.4
43.7
46.0
13.3
Coef of Var
0.5702
0.3986
0.2796
0.0837
0.1509
0.2718
0.5279
0.4448
0.4002
0.4285
0.5167
0.3060
0.2629
0.2777
0.2828
01063
*Port designation is the sequence of ports from which the sample was taken.
tE indicates an erroneous value due to isokmetic variation being out of acceptable range.
$M indicates no value was reported for that collaborator in that run.
levels. Also, no type of standard sample for laboratory analysis can be prepared, either, which would give an estimate
of lab bias and of the analysis component of the total variation. Thus, the only technique available for evaluating
Method 5 is that of estimating the precision of the concentration estimates obtained and the degree to which the
results may be duplicated by a separate independent laboratory.
In order to determine our variability estimates, we need to determine what factors have a significant effect on
the variation in the reported values. As previously stated, the possibility of a port influence on the concentration
obtained was considered, and the test was designed to minimize the effect or the possibility of a lab-port interaction.
The hypothesis of no port effect is tested in Appendix B.2 and found to be an acceptable one. As a result, the port
factor may be eliminated from further analysis without apparent consequence.
In analyzing the data, two common variance stabilizing transformations, the logarithmic and square root, are
applied. For the data under each of these transformations, and the data in its original form (linear), Bartlett's test
for homogeneity of variances is used to determine the effect of the transformation. A transformation which
satisfies the equality of variance hypothesis gives an indication of the nature of the distribution of the data and
of any functional dependence between the mean and the variance or standard deviation of the data. The results
of these tests are presented in Appendix B.3.
11
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For the interlaboratory run data, the transformation which achieves the highest degree of equality of variance is
the logarithmic. As was demonstrated in a previous collaborative study by Hamil and Camann/2' this is a strong indi-
cation of an underlying linear relationship between the population mean and standard deviation, 6 and a, respectively.
As a further indication, a regression equation is fitted to both the run component and the lab-to-lab component
in Appendix B.4. Figure B.I represents a no-intercept model regression line for the sample means and sample standard
deviations from the run data. The correlation coefficient for the model is 0.939. Figure B.2 presents a similar analysis
for the collaborator-block means and standard deviations. The correlation coefficient for this model is 0.862. Both
values indicate a significant linear relationship at the 5 percent level of significance.
The consequence of this is to provide a model for the variance components, a2 and 0% . Let a2 be defined as
the variance associated with the replicates (samples) within a single laboratory and ffjj be the variance associated with
the differences of means between laboratories. From the above argument, we have
and
at, = 0,5
where c and c^ are [unknown] constants. This implies that while 6, a, and a^ may vary from run to run or site to
site, the relationships a/5 and a^'6 remain constant. If we let
a
rf
and
Ob
I'*
then we have constant coefficients of variation, )3 and |3j, for the within-lab and between-lab components, respectively,
and a and a/, may be defined as a percentage of the mean. In Appendix B.5, this relationship is established, and |3
and |3fc are defined.
In Appendix B.6, the manner of obtaining estimates using a linear combination of the beta values is obtained.
The values are given weights relative to the number of determinations used to obtain the estimate. In Appendix B.7,
the estimates of the precision components are obtained.
The estimated within-lab coefficient of variation is (3 = (0.31 1), which gives an estimated within-laboratory
standard deviation of
= (0.311)5.
This estimate has 34 degrees of freedom associated with it.
The estimated between-laboratory coefficient of variation, j3^ , is (0.367), which gives an estimated between-
laboratory standard deviation of
ob = (0.367)5.
This estimate has 2 degrees of freedom associated with it.
12
-------
Using these, we can estimate the laboratory bias standard deviation. From the formula in section A.,
= V(0-367)262 -(0.311)282
= (0.195)6.
13
-------
IV. COMMENTS AND RECOMMENDATIONS
Assessments of Method 5 have been made by the collaborative test supervisor and by the collaborators them-
selves as a result of their observations and experience in conducting the field testing. These assessments have included
the following:
(1) In previous field experience as well as in conversations with many other persons using the method, it has
become obvious that this method is more elaborate and time-consuming than most stack sampling methods.
This results from mechanical design of the equipment plus the necessity to move heavy equipment items
to the sampling point, especially if the sampling point is on a high stack. The necessity for mounting the
sampling probe and sample box assembly on a rail for traversing across the stack also complicates the
mechanical arrangement of equipment. These difficulties are inherent in the method as published, however,
and cannot be avoided.
(2) The extensive use of large amounts of glassware and ground glass connecting joints in the sampling train
may result in leaks arising during the course of the run, which will influence the test result.
(3) The movement of equipment required in obtaining a test result often leads to breakage of the glassware
used in the sample equipment. In addition, mechanical shock placed on the equipment by raising it to
platforms high on the stacks, from which sampling often must be done, can affect the calibration of the
equipment as well as cause further glassware damage.
(4) The recovery of particulate matter from the probe is a probable cause of high and low reported concen-
tration levels. During the extraction of the probe, the tip may scrape against the inside of the stack, result-
ing in an additional amount of particulate matter becoming lodged in the probe tip. This matter is then
weighed and analyzed as part of the sample. A loss of particulate matter may occur during the probe wash,
if care is not taken. It was noted that, from run to run and collaborator to collaborator, there was consider-
able variation in the relative amount of particulate collected in the probe wash as compared to the filter
collection.
(5) The collaborators observed that the particulate matter collected was extremely hygroscopic. Even though
such precautions as placing dishes of desiccant(P2 Os) inside the balance were taken, the accuracy of the
particulate weight determinations is doubtful. As a result, the variation in concentration levels between
labs is doubtlessly affected by the manner in which the filter particulate collection was handled as it was
being weighed.
The comments presented above and the conclusions previously drawn provide a firm basis for the following
recommendations.
(1) Further testing at power plants is warranted in order to assess the precision of Method 5. The relatively
high values for the precision estimates may be representative of the true values. However, with usable
data from only three of the collaborators, and with only one site being tested, these results are inconclu-
sive, and additional testing should be arranged.
(2) The collaborators made frequent calculation errors in the collaborative test data and there were differences
among labs in the number of significant digits carried. To prevent these from unfairly influencing the result
of a performance test for compliance, it is recommended that a standard Method 5 computer program be
written to calculate compliance test results from raw field data.
(3) It is recommended that a standard technique for cleaning the filter apparatus be specified in detail in the
method. As it stands now, the cleaning technique used varies somewhat from lab to lab, depends greatly
on the carefulness of the laboratory team, and is undoubtedly a major source of error.
(4) It is recommended that the technique for cleaning the probe be specified in greater detail in the method.
Much of the variation in the method results from the probe cleaning, and details should be included in the
14
-------
method concerning the handling of the probe during sample recovery and the manner of recovering particulate
matter from the probe.
(5) During sampling, many problems arise from the equipment used to obtain the samples. The design and
reliability of much of the equipment now available for use with Method 5 do not seem adequate.
As previously noted, the amount of glassware used in the equipment leads to unreliability, both in the
equipment itself (from the high breakage levels) and in the performance (due to the probability of leaks
arising during the course of the run). It is recommended that improvements be made in the equipment
design and that efforts be made to eliminate the use of glassware and ground glass joints wherever pos-
sible. Improvements in this area should be made at an early date, if at all feasible.
By implementing these recommendations, the variation associated with Method 5 test results, both within- and
between-laboratory, should be able to be better separated from analytical and mechanical components.
15
-------
APPENDIX A
METHOD 5-DETERMINATION OF PARTICULATE EMISSIONS FROM
STATIONARY SOURCES
Federal Register, Vol. 36, No. 247
December 23, 1971
17
-------
RULES AND REGULATIONS
2.1.4 Filter Holder—.Pyrex' glass with
heating system capable at maintaining mini-
mum temperature of 325' V.
2.1.5 ImplngerB / Condenser—Four impln-
gers connected In series with glass ball joint
fltunge. The flrat, third, and fourth impln-
gers are of the Greenburg-Smlth design,
modified by replacing the tip with a % -Inch
3D glass tube extending to one-half Inch
from the bottom of the flask. The second 1m-
pinger is of the Greenburg-Smith design
with the standard tip. A condenser may be
used In place of the impingere provided that
the moisture content of the stack gas can
still be determined.
2 1.6 Metering system—Vacuum gauge,
leak-free pump, thermometers capable of
measuring temperature to within 5° F., dry
gas meter with 2% accuracy, and related
equipment, or equivalent, as required to
maintain an isoklnetlc sampling rate and to
determine sample volume.
2.1.7 Barometer—To measure atmospheric
pressure to ±0.1 Inches Hg.
2.2 Sample recovery.
3.2.1 Probe brush—At least as long as
probe.
2.2 2 Glass wash bottles—Two.
2.2.3 Olaas sample storage containers.
2.2.4 Graduated cylinder—250 ml.
2.3 Analysis.
23.1 Glass weighing dishes.
2.3.2 Desiccator.
2.3.3 Analytical balance—To measure to
±0.1 ing.
2.3.4 Trip balance—300 g. capacity, to
measure to ±0.05 g.
3. Reagents.
3.1 Samp.ling.
3.1.1 Filters—Glass fiber, MSA 1106 BH>.
or equivalent, numbered for Identification
and prewelghed.
3.1.2 Silica gel—Indicating type, 6-18
mesh, dried at 175" C. (350° F.) for 2 hours.
3.1.3 Waiter.
3.1.4 Crushed ice.
3.2 Sample recovery.
3.2.1 Acetone—Reagent grade.
3.3 Analysis.
3.3.1 Water.
IMP4NGER TRAIN OPTIONAL MAY BE REPLACED
BY AH EQUIVALENT CONDENSER
METHOD 5—DETERMINATION or PARTICTJLATI
EMISSIONS FEOM STATIONARY SOURCES
1. Principle and applicability
11 Principle Particulate matter is with-
drawn Ifiokinetically from the source and its
weight is determined gravlmetrically after re-
moval of uncomtoined water.
1.2 Applicability. This method is applica-
ble for the determination of particulate emis-
sions from stationary sources only when
specified by the test procedures for determin-
ing compliance with New Source Perform-
ance Standards
2 Apparatus.
2.1 Sampling train The design specifica-
tions of the particulate sampling train used
by EPA (Figure 5—1) are described in APTD-
0501. Commercial models otf this train are
available
2.1.1 Nozzle—Stainless steel (316) with
sharp, tapered leading edge
2.12 Probe—Pyrex1 glass with a heating
Bystern capable of maintaining a minimum
gas temperature of 250° F. at the exit end
during sampling to prevent condensation
from occurring. When length limitations
(greater than about 8 ft.) are encountered at
temperatures lese than 600° F., Incoloy 825 ',
or equivalent, may be used. Probes for sam-
pling gas streams at temperatures in excess
of 600° F. must have been approved by the
Administrator.
2.1.3 Pltot tube—Type S, or equivalent,
attached to probe to monitor stack gas
velocity.
REVERSE-TYPE
PITOT TUBE
HEATED AREA FILTER HOLDER / THERMOMETER CHECK
^VALVE
,VACOUM
LINE
THERMOMETI
DRY TEST METER
AIR-TIGHT
PUMP
Figure 5-1. particulate-sampling train.
332 Desiccant- -Drierite,1 indicating
4 Procedure.
4.1 Sampling
4 1.1 After selecting the sampling site and
the minimum number of sampling points,
determine the stack pressure, temperature,
moisture, and range of velocity head.
412 Preparation of collection train.
Weigh to the nearest gram approximately 200
g of silica gel. Label a filter of proper diam-
eter, desiccatea for at least 24 hours and
weigh to the nearest 0 5 mg in a room where
the relative humidity Is less than 50%. Place
1OO ml. of water in each of the first two
Impingers, leave the third impinger empty,
and place approximately 2OO g of preweighed
silica gel in the fourth impinger Set up the
train without the probe as in Figure 5-1.
Leak check the sampling train at the sam-
pling site by plugging up the inlet to the fil-
ter holder and pulling a 15 in Hg vacuum A
leakage rate not in excess of 0.02 c f m at a
vacuum of 15 in. Hg Is acceptable Attach
the probe and adjust the heater to provide a
gas temperature of about 250° F at the probe
outlet. Turn on the filter heating system.
Place crushed Ice around the implngers, Add
'Trade name.
1 Trade name.
'Dry using Drierite1 at 70° F.±10° F.
more ice during the run to keep the temper-
ature of the gases leaving the last impinger
as low as possible and preferably at 703 F ,
or less Temperatures above 70° F. may result
in damage to the dry gas meter from either
moisture condensation or excessive heat.
413 Particulate train operation. For each
run, record the data required on the example
sheet shown in Figure 5-2 Take readings at
each sampling point, at least every 5 minutes,
and when significant changes in stack con-
ditions necessitate additional adjustments
in flow rate. To begin sampling, position the
nozzle at the first traverse point with the
tip pointing directly into the gas stream
Immediately start the pump and adjust the
now to isokinetic conditions. Sample for at
least 5 minutes at each traverse point; sam-
pling time must be the same for each point.
Maintain Isoklnetlc sampling throughout the
sampling period. Nomographs are available
which aid In the rapid adjustment of the
sampling rate without other computations
APTD-O576 details the procedure for using
these nomographs. Turn off the pump at the
conclusion of each run and record the final
readings. Remove the probe and nozzle from
the stack and handle In accordance with the
sample recovery process described in section
42
FEDERAL REGISTER, VOl. 36, NO. 247—THURSDAY, DECEMBER 53, 197]
19
-------
RULES AND REGULATIONS
AMBIENT TIWttATU«_
BAHOICTUC mS5O«_
ASSUMED MOtSTME. *__
HEATEBMKSnTMQ
MQtf LENGTH.».
NOZZLE DIAMETER. (•.
SCHEMATIC Cf PACK CTOSS SECTION
IRA VEJtK POUR
NUMKR
TOTAL
SAHKtNO
TW
(M, •**
AVfHAGt
STATIC
PflEUUK
!fsl. (•, Hf.
STACK
TEkVUATU*
(V.*f
vciocm
HEAD
(*M.
FHUSUW
ofHKWTUL
Acwoa
Mtfict
UCTCB
UH.
!*>*>
GASSAUU
VOLUME
I*-).*1
GAS &AMFU TEITEIUTUK
AT OUT GAS UCHR
INUT
IT-fcl.'f
A*9.
OUTLET
(T» ^l. * F
A**.
A.B
SAHAfKnt
T£M>£RAtUK.
°F
rewflwrure
OF CAS
LEAVING
COHDEKER OR
LAiT MPIHGER
°F
Tn—Average dry gas meter temperature,
P,,.,—Barometric pressure at the orifice
meter, laches Hg.
AH—Average pressure drop across the
orifice meter, Inches H,O.
13.6=Specific gravity of mercury.
P.,4 = Absolute pressure at standard con-
ditions, 29.92 Inches Rg.
8.3 Volume of water vapor.
0.0474
4.2 Sample recovery. Exercise care in mov-
ing the collection train from the test site to
the sample recovery area to minimize the
loss of collected sample or the gain of
extraneous participate matter. Set aside a
portion of the acetone used In the sample
recovery as a blank for analysis. Measure the
volume of water from the first three 1m-
plngers, then discard. Place the samples in
containers as follows:
Container No. 1. Remove the alter from
Its holder, place In this container, and seal.
Container No. 2. Place loose participate
matter and acetone washings from all
sample-exposed surfaces prior to the filter
In this container and seal. Use a razor blade,
brush, or rubber policeman to lose adhering
particles.
Container No. 3 Transfer the silica gel
from the fourth Implnger to the original con-
tainer and seal. Use a rubber policeman as
an aid in removing silica gel from the
implnger
4.3 Analysis. Record the data required on
the example sheet shown in Figure 5-3.
Handle each sample container as follows:
Container No. I. Transfer the filter and
any loose particulate matter from the sample
container to a tared glass weighing dish,
desiccate, and dry to a constant weight. Re-
port results to the nearest 0 5 nag.
Container No. 2. Transfer the acetone
washings to a tared beaker and evaporate to
dryness at ambient temperature and pres-
sure. Desiccate and dry to a constant weight.
Report results to the nearest 0 5 mg.
Container No. 3. Weigh the spent silica gel
and report to the nearest gram.
5. Calibration.
Use methods and equipment which have
been approved by th« Administrator to
calibrate the orifice meter, pitot tube, dry
gas meter, and probe heater. Recalibrate
after each test series.
6. Calculations.
6.1 Average dry gas meter temperature
and average orifice pressure drop. See data
sheet (Figure 6-2).
6.3 Dry gas volume. Correct the sample
volume measured by the dry gas meter to
standard conditions (70° *„ 29.92 Inches Hg)
by using Equation 5-1.
v..td
equation 5-*
where:
Vw,ti= Volume of water vapor In the gas
sample (standard conditions) .
cu. ft.
Vi0 = Total volume of liquid collected in
Imptngers and silica gel (see Fig-
ure 6-3), ml.
pa,o= Density of water, 1 gymL
1 Ma,o— Molecular weight of water, 18 lb./
Ib.-mole.
R= Ideal gas constant, 21.83 Inches
Hg — cu, ft./lb.-mole-°R-
T.ta = Absolute temperature at standard
conditions, 630* R-
P.n — Absolute pressure at standard con-
ditions, 29.92 Inches Hg.
6.4 Moisture content.
v -
°~
'17.71
°R
in. Hg>
equation 5-3
where:
Bwo ^Proportion by volumeof water vapor ill tliegas
stream, dlmensionl&ss.
^'•m31 Volume of water in the gas sample (standaid
conditions) , cu. ft.
^"•td =- Volume of gas sample through the dry gas mctr r
(standard conditions), cu. ft.
6.5 Total particulate weight. Determine
the total particulate catch from the sum of
the weights on the analysis data sheet
(Figure 5-3) .
6.6 Concentration.
6 8.1 Concentration In gr./s.c.f .
c'.
ing.
equation 5-1
where:
V».ld
= Volume of gas sample through the
dry gaa meter (standard condi-
tions), cu. ft.
«Volume of gas sample through the
dry gas meter (meter condi-
tions) , cu. ft.
'Absolute temperature at standard
conditions, 530° R.
here:
equation 5-4
c'.= Concentration of particulate matter in stack
gas, gr./s.c.f., dry basis.
M.»Total amount of particulate matter collected,
mg.
"•w^Volume of gas sample through dry gas meter
(standard conditions), cu. ft.
20
-------
APPENDIX B
STATISTICAL METHODS
21
-------
STATISTICAL METHODS
This appendix consists of various sections which contain detailed statistical procedures carried out in the analy-
sis of the particulate matter 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. Each Appendix B section is an independent
ad hoc statistical analysis pertinent to a particular problem addressed in the body of the report.
B.1 Preliminary Analysis of the Original Collaborative Test Data
Preliminary checks were made on the originally reported data in order to eliminate calculation errors and to
ensure that all concentrations were obtained using the specified formulas and correction factors. In this manner,
results presented are representative of actual differences in the concentration levels found, rather than due to improper
or inaccurate use of the equations. Thus, we can discern more clearly the variability that is associated with Method 5
itself.
The concentrations from the three collaborators, Labs 102, 103, and 104, were analyzed with two missing
observations. In Run 1, Lab 104 was only 77 percent of isokinetic, and the result was considered invalid. On Run 14,
Lab 104 was forced to abort as a result of equipment malfunction, and no value was reported. The analysis was per-
formed on the remainder of the observations, with no attempt to replace these values.
In each lab, there are values which appear, at first glance, to be outliers. These are of a magnitude of approxi-
mately twice that of the rest of the samples for that lab. However, these occurred with such regularity (2 to 3/lab)
that it was decided not to make any adjustment for them in the analysis. Indeed, they appear to be representative
of the type of error that occurs when Method 5 is used on a power plant.
B.2 Significance of the Port Effect
The sampling at the Allen S. King Power Plant was done through four sample ports, two on either side of the
duct. The ports were designated East Upper, East Lower, West Upper, and West Lower (EU, EL, WU, WL). On each
run, a sampling team began on one side at either the upper or the lower port, shifting at the halfway point of the run
to the other port on the same side. The result is four port combination patterns: EL to EU, EU to EL, WU to WL,
WL to WU, assigned the designations A, B, C and D respectively.
The test for port effect was made using the four sequences as different ports, rather than merely East vs West.
It is felt that this provides a more complete evaluation of the possible differences. The analysis is done using
Youden's(4) rank test.
Each sequence is assigned a rank within each run. The ranks are then summed for each sequence and the results
compared against confidence limits tabled by Youden. The test is presented in Table B.I.
The null hypothesis to be tested is that there is no port (port sequence) effect. This hypothesis may be
rejected, at the 0.05 level of significance, only if the high port sum or the low port sum falls outside the limits of the
confidence interval. Since the highest sum, 44 (WL to WU), is less than the upper limit of 52, and the smallest sum,
33 (EU to EL) is greater than the lower limit of 28, the hypothesis may not be rejected. Thus, we can assume no
differences due to ports, and further analysis is done under that assumption.
B.3 Transformations
As a means of obtaining information about the nature of the distribution of the concentrations, the values
were examined to determine what kind of transformation best gives an equality of variance for the sample data.
23
-------
TABLE B.I. SIGNIFICANCE
OF PORT EFFECT
Youden's Rank Test
TABLE B.2. DATA TRANSFORMATION TO ACHIEVE
RUN EQUALITY OF VARIANCE
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Port*
Rank
Sums 40
2
1
2
3
4
4
4
3
2
1
4
3
3
2
3
3
33 43 44
H0: No Port Effect
C/0.95<28,52)
Conclusion Accept Ho, No
Port Effect
*Port Sequences:
A(ELto Ell),
B(EU to EL),
C(WU to WL),
D(WL to WU).
Transformation
Linear
Logarithmic
Square Root
Test
Statistic
19.071
10.902
13.753
Degrees
of Freedom
15
15
15
Significance
0.20
0.75
0.55
For each transformation used, Bartlett's test for homogeneity of
variance was used to ascertain the degree of equality obtained.
The data were examined in their original form (linear) and
passed through two transformations, the logarithmic and the square
root. The results are presented in Table B.2 for the run component
data. The significance levels are taken from a table of x2 with
15 degrees of freedom.
The logarithmic transformation clearly attains the best results,
implying that the run data follow the lognormal distribution. In addi-
tion, this is an indication, as presented in Hamil and Camani/2\ that
there is an underlying linear relationship between the mean and the
standard deviation of the distribution of the run data.
B.4 Empirical Relationship of the Mean and Standard
Deviation in the Collaborative Test Data
In order to properly analyze the data from the collaborative
test, it is necessary to investigate the relationship between the mean
and the standard deviation for both the interlaboratory and intra-
laboratory components. We wish to determine to what extent the
variability in the concentrations is related to the actual concentration
level. Therefore, let
be the concentration reported by lab i in block/ of run k.
be the mean for run k in block; across labs,
r-3
sik =A / ~~'- (xijk ~~*./A;)2 > be the run standard deviation, assuming 3 collaborators.
9';=1
Table B.3 gives the values of the sample means and standard deviations obtained from the St. Paul test.
Asterisks denote those values taken over only two responses due to a missing or erroneous data point.
By visual inspection, it appears that there is a linear trend between x.jk and s,-^; that is, as x.jk increases, so
does Sjk. A least squares regression line is calculated for these points and presented in Figure B-l. A no-intercept
model is used since a mean of zero could only logically occur when each reported concentration was identically
equal to zero, thus resulting in a zero standard deviation.
A correlation coefficient between x ^ and s,^ is calculated to be 0,939 for the no-intercept model. This value
is significant at a level greater than 10 percent. The coefficient of determination is 0.881, indicating 88.1 percent of the
variation in the magnitude of the standard deviation is attributed to the variation in the magnitude of the sample mean.
24
-------
TABLE B.3. INTERLABORATORY RUN SUMMARY
Block
1
2
3
4
Run
*1
3
4
6
2
10
11
*14
5
7
9
16
8
12
13
15
Mean
Ib/scfX 10'
97.85
259.20
147.90
161.43
162.97
166.57
221.40
156.10
133.30
260.63
254.70
123.67
146.10
157.27
162.57
124.97
Std Dev
Ib/scfX 107
55.79
103.31
41.35
13.51
24.59
45.27
116.88
69.44
53.35
111.67
131.61
37.84
38.41
43.68
45.97
13.29
*Runs with only 2 determinations.
Thus, we have empirical evidence that the linear
relationship indicated by the transformation data
in Appendix B.3 is present.
We can perform a similar analysis for the
intralaboratory collaborator-block data. Let us
denote
~xij. as the mean for collaborator /', block/
3 =
as the collabora-
tor-block standard deviation, assuming
four runs per block.
The values obtained for Xj/. and s,y are
presented in Table B.4. Asterisks denote those
values based on only three runs due to missing
values. A no-intercept regression line is fitted to
Run Standard Deviation
10~7 Ib/scf
25 50 75 100 125 150 175 200 225 250 275 300
Run Mean, 10~7 Ib/scf
FIGURE B.I. INTERLABORATORY RUN PLOT
X.
Jk
25
-------
TABLE B.4. INTRALABORATORY COLLABORATOR-
BLOCK SUMMARY
Block
1
2
3
4
Collaborator
Lab 102
Lab 103
Lab 104*
Lab 102
Lab 103
Lab 104*
Lab 102
Lab 103
Lab 1 04
Lab 102
Lab 103
Lab 104
Mean,
Ib/scfX 107
168.25
146.47
214.13
200.60
127.15
218.00
275.80
179.22
124.20
184.65
138.37
120.16
Std Dev
Ib/scf X 10 7
21.22
68.57
142.62
13.44
16.23
115.35
113.54
100.13
29.03
31.71
24.89
6.37
*Blocks with only three observations.
Si;
175
150
125
100
75
50
25
Collaborator-Block
Standard Deviation, 10~7 Ib/scf
these points and represented in Figure B.2.
As before, the linear tendency of the Sy's
relative to the Jc,y.'s is apparent.
The value of the correlation coeffi-
cient is 0.862, which again has a significance
level greater than 10 percent. The coeffi-
cient of determination is 0.742.
B.5 Underlying Relationship Between
the Mean and Standard Deviation
In Appendix B.4, the empirical rela-
tionship between the mean and standard
deviation for the between-laboratory com-
ponents is established. This implies that
•V =
25 50 75 100 125 150 175 200 225 250 275
Collaborator-Block Mean, 10~7 Ib/scf
FIGURE B.2. INTRALABORATORY COLLABORATOR-BLOCK PLOT
X,;
26
-------
TABLE B.5. BIAS CORRECTION
FACTORS FOR SAMPLE
STANDARD DEVIATIONS
n
2
3
4
an
1.2533
1.1284
1.0854
" where b is the sample coefficient of variation. The collaborator block standard
deviation, s/f, represents an estimate of the within-lab standard deviation, a. How-
ever, it has been shown(5) that the sample standard deviation is a biased estimate
and that a correction factor must be applied to remove the bias. The correction
factor is given by
r(-
where n is the size of the sample, and F represents the standard gamma function. Values of an are presented in Table B.5.
Thus, E(anSjf) = a and
a = E(anS(/)
If we let J5 = anb , we have
where a and 5 are the true mean and standard deviation for the distribution of the collaborator-block data.
In Appendices B.3 and B.4, the linear relationship between the run mean and standard deviation is established,
that is
where b' represents the sample coefficient of variation for the run data. The expected value of sjk is a2 +
a within-laboratory component plus a laboratory bias component. As before, s,^ is a biased estimator for
\/a2 + QI , and the bias may be corrected in the same manner. Thus we have
and defining fe = aMfe', we have
27
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where a£ represents the true laboratory bias variation. From this relationship, it can be shown^ that
or
OL -
where
Thus, it is established that for both the within-laboratory component and the laboratory bias component,
there is a linear relationship between the standard deviations, a and GI , and the mean 6.
B.6 Weighted Coefficient of Variation Estimates
The technique used for obtaining estimates of the coefficients of variation of interest is to use a linear combi-
nation of the individual beta values obtained. The linear combination used will be of the form
/-!
where ft/ is the/th coefficient of variation estimate, k is the total number of estimates, and Wj is a weight applied to
the/th estimate.
As previously discussed, the individual estimate of j3 is obtained as
for a sample of size n. This estimator is shown in B.5 to be unbiased for the true coefficient of variation. However,
since we are dealing with small samples to obtain our individual estimates, weighting is more desirable in that it pro-
vides for more contribution from those values derived from larger samples. There is more variability in the beta
values obtained from the smaller samples, as can be seen by inspecting the variance of the estimator. We have that
Var(|3) = Var ( °^
fr 1
= a> -(1+202)
l_2« J
for normally distributed samples,(3) and true coefficient of variation, /J. Rewriting this expression, we have
28
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0+202)
and all terms are constant except for a2 and n. Thus, the magnitude of the variance changes with respect to the
factoi oi^/n. Now, since an decreases as n increases, the factor Q$i/n must decrease as n increases, and the variance
is reduced.
The weights, w/, are determined according to the technique used in weighted least squares analysis' ', which
gives a minimum variance estimate of the parameter. The individual weight, w,-, is computed as the inverse of the
variance of the estimate, ft, and then standardized. Weights are said to be standardized when
"/=!
To standardize, the weights are divided by the average of the inverse variances for all the estimates. Thus, we can
write
= Uj
u
where
and
1
M,-=-
Var(ft)
1 K 1
Now, from the above expressions, we can determine u,, u and w,- for the beta estimates. For any estimate, ft,
1
Var(ft)
<
for sample size n,. and
u = —
k —' n2
k /= 1 ««/
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Thus, the ;'th weight, w/, is
w, =
*«,
The estimated coefficient of variation is
*/=!
1=1
k «c
V '
2-i
B.7 Estimating Standard Deviation Components
In Appendix B.3 and B.4, the relationships for the between-laboratory and within-laboratory standard deviations,
Oj, and a, are established as
and
30
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where fa and (3 represent the true coefficients of variation, and 6 is the true mean determination. In Appendix B.5
it is shown that for the laboratory bias standard deviation, QI , the above expressions imply
In Appendix B.6, the technique for obtaining an unbiased estimate of a coefficient of variation as a linear
combination of the individual values is discussed. The estimator is of the form
where J3 is the estimated beta from the iih sample and w,- is a weight applied. For the between-laboratory coefficient
of variation, this becomes
1
16
= 77 £
TABLE B.6 RUN BETA
VALUES AND WEIGHTS
Run
I
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Beta Hat
0.7146
0.1703
0.4497
0.3155
0.4516
0.0944
0.4835
0.2967
0.5831
0.3067
0.5957
0.3134
0.3191
0-5575
0.1200
0.3453
Weight
0.573
1.061
1.061
1.061
1.061
1.061
1.061
1.061
1.061
1.061
1.061
1.061
1.061
0.573
1.061
1.061
TABLE B.7 COLLABORATOR-
BLOCK BETA VALUES
AND WEIGHTS
Block
1
2
3
4
Collaborator
Lab 102
Lab 103
Lab 104
Lab 102
Lab 103
Lab 104
Lab 102
Lab 103
Lab 104
Lab 102
Lab 103
Lab 104
Beta Hat
0.1369
0.5081
0.7516
0.0727
0.1385
0.5971
0.4468
0.6064
0.2537
0.1864
0.1952
0.0576
Weight
1.054
1.054
0.731
1.054
1.054
0.731
1.054
1.054
1.054
1.054
1.054
1.054
The individual beta values and their weights are shown in Table B.6. Substituting these into the formula we have
ft, =(0.367)
and as a result
= (0.367)5
For p = 3 laboratories, there are 3 — 1 = 2 degrees of freedom associated with this estimate.
Similarly, for the within-laboratory coefficient of variation, we have
. 1 I* -
31
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where fy is an estimated beta value from a collaborator-block combination, and wy is the corresponding weight. The
individual values and their weights are shown in Table B.7. Substituting into the above formula, we obtain
0= (0-311)
which implies that
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LIST OF REFERENCES
I. Environmental Protection Agency, "Standards of Performance for New Stationary Sources," Federal
Register, Vol. 36, No. 247, December 23, 1971, pp 24876-24893.
2. 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 Environ-
mental Protection Agency, October 5, 1973.
3. Cramer, H., Mathematical Methods of Statistics. Princeton University Press, New Jersey,
1946.
4. Youden, W. J., "The Collaborative Test," Journal of the AOAC, Vol. 46, No. 1, 1963, pp 55-62.
5. Ziegler, R. K., "Estimators of Coefficients of Variation Using k Samples," Technometrics, Vol 15,
No. 2, May, 1973, pp 409-414.
6. Dixon, W. J. and Massey, F. J., Jr., Introduction To Statistical Analysis, 3rd Edition. McGraw-Hill,
New York, 1969.
33
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TECHNICS* REPORT DATA
[Please read [inunctions tin the r^crse hi:tore complettn/!)
! REPORT NO.
EPA-650/4-74-021
3. RECIPIENT'S ACCESSION-NO.
4. TITLE ANDSUBTITLE
Collaborative Study of Method for the Determination of
Particulate Matter Emissions from Stationary Sources
(Fossil Fuel-Fired Steam Generators)
5. REPORT DATE
June 30, 1974
6. PERFORMING ORGANIZATION CODE
7. AUTHOH(S)
Henry F. Hamil and Richard E. Thomas
8. PERFORMING ORGANIZATION REPORT NO
SwRI 01-3487-01
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Southwest Research Institute
8500 Culebra Road
San Antonio, Texas
10. PROGRAM ELEMENT NO.
1HA327 (ROAP 26AAG)
11. CONTRACT/GRANT NO.
68-02-0623
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Protection Agency, NERC
Quality Assurance & Environmental Monitoring Laboratory
Methods Standardization Branch
Research Triangle Park, N. C. 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final Report
14. SPONSORING AGENCY CODE
15. SUPPLEMENTARY NOTES
16.ABSTRACT ifofs report presents the results obtained from a collaborative test of Method
5, a test procedure for determining particulate emissions from stationary sources.
Method 5 specifies that particulate matter be withdrawn isokinetically from the source
and its weight determined gravimetrically after the removal of uncombined water. The
test was conducted at a fossil fuel-fired steam generating power plant using four colla
borative laboratories. Sixteen sample runs were made over a two-week period by the
collaborators for a total of 63 individual determinations. The reported values of one
of the laboratories were not included in the analysis. Conversation with other person-
nel who participated in the test, and inspection of the laboratory's sampling train
subsequent to the test, provided information which indicated that the determinations
made were not representative of Method 5 results. Of the remaining determinations, one
was eliminated due to failure to maintain isokinetic conditions, the remaining values
were subjected to statistical analysis to estimate the precision that can be expected
with field usage of Method 5. The precision estimates are expressed as standard devia-
tions, which are shown to be proportional to the mean determination, <5, and are sum-
marized as follows: (a) Within-lab: The estimated within-lab standard deviation is 31.1
of
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