EPA-650/4-74-025
OCTOBER 1973
Environmental Monitoring Series
-------
EPA-650/4-74-025
COLLABORATIVE STUDY
OF METHOD FOR THE DETERMINATION
OF NITROGEN OXIDE EMISSIONS
FROM STATIONARY SOURCES
(FOSSIL FUEL-FIRED STEAM GENERATORS)
by
H. F. Hamil and D . E. Camann
Southwest Research Institute
8500 Culebra Road
San Antonio, Texas 78284
Contract No. 68-02-0623
ROAPNo. 26AAG
Program Element No. 1HA327
EPA Project Officer: M.R.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
October 1974
-------
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.
-------
ABSTRACT
A collaborative study was performed on Method 7 proposed by
the Environmental Protection Agency for determining the nitrogen oxide
emissions from stationary sources. Method 7 specifies the collection
of a grab sample in an evacuated flash containing a dilute sulfuric acid-
hydrogen peroxide absorbing solution, and the colorimetric measurement
of the nitrogen oxides, except nitrous oxide, using the phenoldisulfonic
acid procedure. Collaborative tests were conducted at both a coal-fired
steam generating power plant and an oil-fired pilot plant by four collaborative
teams. Statistical analysis of the collaborative test and associated data
disclosed the following findings regarding the reliability of a Method 7
performance test result:
Precision--The estimated repeatability standard deviation of a test
result is 1.893% of the test result value. The esti-
mated reproducibility standard deviation of a test result
is 7. 110% of its value.
Accuracy--Because of chemically significant distortions inherent
in the gas cylinder accuracy test, the accuracy of Method
7 could not be adequately demonstrated.
Minimum Detectable Limit--The estimated minimum detectable
limit of Method 7 is 5. 14 x 1(T7 Ib. /s. c. f.
Sources of Reproducibility Variation--Nearly all (93%) of the
reproducibility variation in a test result is ascribable
to laboratory bias, with the other 7% due to repeat-
ability variation. Most of the apparent laboratory bias
variation actually is not a true laboratory effect, but
rather a day effect primarily caused by dubious daily
spectropholometer re-calibration procedures. Restric-
tion of the spectrophotometer absorbance calibration
range to its more accurate upper region can halve the
analytical procedure's percentage error contribution to
the reproducibility variation.
Various modifications to Method 7 are recommended which should improve
its demonstrated precision.
m
-------
TABLE OF CONTENTS
I. INTRODUCTION 1
II. COLLABORATIVE TESTING OF METHOD 7 2
A. Collaborative Test Sites 2
B. Collaborators 8
C. Philosophy of Collaborative Testing 12
III. STATISTICAL DESIGN AND ANALYSIS 14
A. The Experimental Design 14
B. The Collaborative Test Data 18
C. The Accuracy of Method 7 21
D. The Precision of Method 7 29
E. Accuracy and Precision of the Analytical
Procedure 34
F. The Sources of Variability in Method 7 37
IV. CONCLUSIONS AND RECOMMENDATIONS 45
References 51
APPENDICES
A. Method 7 - Determination of Nitrogen Oxide
Emissions from Stationary Sources A-l
B. Statistical Methods B-l
B.I Outlier and Associated Preliminary B-l
Analysis of the Original Collaborative
Test Data
B.2 Significance of the Port Effect B-6
B.3 Empirical Relationship of the B-7
Standard Deviation to the Mean in
the Collaborative Test Data
B.4 Transformation of the Collaborative B-12
Test Data
B.5 The Underlying Relationship of the B-16
Standard Deviation Components to
the Mean
IV
-------
Table of Contents (cont'd.)
Appendices (continued)
B.6 Estimating the Standard B-18
Deviation Components and the
Reproducibility Standard
Deviation
B.7 The Nitrate Solution Data B-22
B.8 The Variance Components of the B-26
Analytical Procedure
B.9 The Lower Limit of Detectability B-32
References B-34
C. Walden Theoretical NOX Concentration
Calculation _
-------
LIST OF TABLES AND FIGURES
Figure Page
1. Pilot Plant Operational Configuration 3
2. Top View of Test Section 5
3. Dayton Power and Light Company's Tait 6
Station
4. Test Facilities 7
5. Stack Gas Delivery System and Sampling
Manifold 9
6. Cambridge NOV Collaborative Test 10
3C
7. Dayton NOX Collaborative Test 11
8. Collaborative Test of Method 7 - Instructions
for Analysis of Unknown Nitrate Solutions 19
9. The Accuracy of Method 7 28
10. Analytical Standard Deviation Components 38
A A
O and G~~~
Bl. Calibration Curve Discrepancies B-5
B2. Inter-Laboratory Run Plot B-10
B3. Intra-Laboratory Collaborator Block Plot B-13
Table
1. Randomized Block Design of the Cambridge 16
Collaborative Test of Method 7
2. The Original NOX Collaborative Test Data 20
3. The Corrected Cambridge Collaborative Test 22
Data
-------
LIST OF TABLES AND FIGURES (Cont'd)
Table Page
4. The Corrected Dayton Collaborative Test Data 23
5. Gas Cylinder Test Data Summary 25
6. Method 7 Accuracy Data 27
7 . Accuracy of the Method 7 Analytical
Procedure 35
8. Sources of Reproducibility Variation in a
Performance Test Result 40
9. The Analytical Procedure as a Source of
Component Variation 41
10. Outlier Collaborative Data Points Derived
Outside the Acceptable Calibration Range 43
Bl. Inter-Laboratory Run Summary B-8
B2. Intra-Laboratory Collaborator Block
Summary B-ll
B3. Data Transformations to Achieve Run
Equality of Variance B-12
B4. Reported Nitrate Solution Concentrations,
\ig NO2 per 10 ml B-23
B5. Day Averaged Nitrate Solution Concentrations,
Hg NO2 per 10 ml B-24
B6. Average Laboratory Nitrate Solution
Concentration, jig NO, per 10 ml B-25
B7. Nitrate Solution Data Anlayses of Variance B-27
B8. Significance of Nitrate Solution Factors B-28
vn
-------
LIST OF TABLES AND FIGURES (Cont'd)
Table Page
B9. Nitrate Solution Variance and Standard
Deviation Components B-31
Cl. Oxygen Consumption for Oil Combustion C-2
C2. Component of Flow Due to Stoichiometric
Combustion C-3
C3. Walden Pilot Plant Firing Conditions C-3
C4. Theoretical Calculated NOX Concentration
Results C-4
-------
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 7
for nitrogen oxide emissions as given in "Standards of Performance for
New Stationary Sources."^)
This report describes the collaborative testing of Method 7 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.
-------
II. COLLABORATIVE TESTING OF METHOD 7
A. Collaborative Test Sites
Two collaborative tests of Method 7 were conducted. One test
was performed at Walden Research Corporation, Cambridge,
Massachusetts from December 11 to December 15, 1972, while the
second was performed at the Dayton Power and Light Company's Tait
Station, Dayton, Ohio from January 8 to January 12, 1973.
The initial test was conducted on the Walden pilot plant since
precise control of furnace firing conditions plus accurate addition
of nitrogen oxides to the furnace exhaust gas would allow evaluation
of the method under carefully controlled nitrogen oxide emission
levels. A schematic of the Walden combustion pilot plant is shown
in Figure 1. The unit consists of a 400,000 Btu/hour (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 three feet in length and eight
inches in diameter. The flue gas is cooled down to about 300°F by an
air-cooled heat' exchanger 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.
The gas doping system consisted of a 1A gas cylinder containing
pure nitric oxide, glass rotameter (Fischer & Porter 448-209), and simple
-------
cm
c
O
T)
n
H
p
rf-
M-
8
p
i—•
o
o
OQ
C
0
(GAS) OOP ING
V.X SYSTEM
HEAT
EXCHANGER
FURNACE
AUXILIARY .
FAN
DYNASCIENCES
NO
so
X 2
MONITOR
n
SAMPLING
SECTION
ID
FAN
v y
EXTERNAL
READING
METER
HEATER
->EXHAUST
-------
toggle valve. The dopant gas stream is introduced into the high tempera-
ture section immediately after the fire box to come to equilibrium temper-
ature and concentration across the duct before reaching the sample test
section.
The sample test section is shown in Figure 2. 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.
The second collaborative test was conducted at the Tait Station
of Dayton Power and Light Company, Dayton, Ohio. Monsanto Research
Corporation and Dayton Power & Light Company have an agreement
permitting MRC to use DP&L's Tait Station (Figure 3) for investigation
of various instruments and analytical methods for monitoring stationary
combustion sources. A 10-ft x 14-ft utility shed was installed on the
roof of DP&cJL's Tait Station between units 4 and 5 (Figure 4). Units
4 and 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 4 is used to transfer the stack gas from a position
-------
c
4
0
2
O
1.0. FAN
TO
EXHAUST
©
B
3
El
HEAT
EXCHANGER
Figure 2. Top View of Test Section.
-------
Figure 3. Dayton Power and Light Company's Tait Station
-------
Figure 4. Test Facilities.
-------
after the electrostatic precipitator and before the I. D. fan to the MRC
shed.
Inside the shed is a manifold for distribution of the flue gas.
The manifold is 10 feet long, with an upper 2-inch square duct fitted
with 12 outlets and a lower 8-inch square return duct (Figure 5. ).
The sample delivery line was connected directly to the manifold for
use on this test. The 2-inch 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 (Figure 5).
The installation of the Rotron Simplex blower allowed the
addition of ambient air to dilute the stack gas to give different levels of
nitrogen oxides during the collaborative test. Nitrogen oxide concentration
m the stack gas and diluted stack gas was monitored with a calibrated
Dynasciences instrument.
B. Collaborators
The collaborators for both the Cambridge and Dayton tests were
Mr. Charles Cody 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
-------
Manifold
Blower
lUSt
Sp
I
J
I
s^NJXp oo o
~! .. , >...«',. "'**kJ,v,,^jli.sir,-*.:"*.**'>, w'':f, -~»*.s-W^
.-„.-. ..-..• i ;• i ,> 'jf". -• • ••, '.IM-ii-- ••.••"-••••-.<• >^.-
O^Sample o o Ports -^0 o
K^e-T>^S
0 0
.Ji1*;- ^ >>. 1. .^ ••_.••-• :^.- .:V.:..:.: :_..l*..j j£L^^!'__. l^.^.-^Y •*"- | ' [L _IJT * • '-y . :-'A ''- -'" --'-•- -:- ' - ~-~^ ---' ' -^'-'1
~> Valves VL
Manifold
Figure 5. Stack Gas Delivery System and Sampling Manifold.
-------
10
Figure 6. Cambridge NO Collaborative Test
-------
11
Figure 7. Dayton NO Collaborative Test
-------
12
of Monsanto Research Corporation, Dayton, Ohio. The latter two col-
laborators were under subcontract 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.1
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 Southwest 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 7
as written in the Federal Register, December 23, 1971.
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.
-------
13
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 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 col-
laborator and corrected by the test supervisor.
While m.ost of the instructions in the Federal Register are quite
explicit, some areas are subject 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 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 reproducibility of the
method that would be expected in performance testing in the field.
-------
14
III. STATISTICAL DESIGN AND ANALYSIS
A . The Experimental Design
The logistics and other circumstances inherent in emission
sampling from the stack of a stationary emissions source impose limitations
upon the design of a collaborative test to validate the emission measurement
method. In the first place, due to the random nature of stack emissions
concentration, dependent as it is upon plant operating level, fuel
characteristics, stack flow pattern, etc., the true (i.e. .actual) emission
level from the stack is unknown and varies randomly with time despite
efforts to maintain the plant in a steady state of operation. As a
consequence, there are no true values against which to compare the
emissions measurements obtained by the collaborative laboratories
performing the method being evaluated. Nor can one assume that the
emissions level within the stack remains constant, either in time or in
spatial geometry. Because it is physically impossible to locate all four
sets of sampling apparatus so as to sample from precisely the same location
at the same time, the four sampling teams must sample through different
ports in the stack at the same time. While these ports are located so as to
be as geometrically symmetrical as possible, the potential for a port effect
is nonetheless introduced.
Under these circumstances, the Method 7-Nitrogen Oxide Emissions
collaborative test was conducted using a randomized block design at
each of the two test sites: Walden Research Corporation's combustion pilot
plant in Cambridge, Massachusetts, and Dayton Power & Light Company's
-------
15
F.M. Tait Station, Dayton, Ohio. A schematic diagram of the randomized
block design employed at Cambridge is shown in Table 1. As this table
shows, the Cambridge NOX test was conducted at four different blocks of
-7 -7 -7
concentration levels, at approximately 1450 x 10 , 1000 x 10 , 675 x 10 ,
-7 *
and 385 x 10 Ib./s.c.f. NO concentrations. Within each block an
attempt was made to hold constant the NO emission concentration in the
stack for the four runs comprising the block. Each run consisted of the
simultaneous collection of an NO sample from the stack by a 11 four
x
collaborative teams through their assigned port (A,B,C, or D). On the
four runs in each block, the collaborative teams rotated from port-to-port
in a systematic manner to minimize the logistical problems concomitant
with moving the sampling apparatus. Thus in the course of every four run
block, each collaborator had sampled once through each port. The four
runs in a block were conducted at 15 to 20 minute intervals, just as rapidly
as the sampling apparatus could be disconnected, transferred from port to
port, and reassembled. This minimized the random ambient variation in the
true NO emission level in the stack during the collection of a block of data.
Ji
While the four samples collected by a laboratory team in a block are not
replicates in a technical sense (the potential presence of a port effect and
the random fluctuation in the true NO concentration during the taking of
x
* 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
conversion factors for the particular non-metric units used in the
document. For this report, the factor is:
10"7 Ib/s.c.f. = 1.6017 x 10"3 ug/ml.
-------
16
TABLE 1. RANDOMIZED BLOCK DESIGN OF THE
CAMBRIDGE COLLABORATIVE TEST OF METHOD 7
Laboratory Team
Block
(concentration level)
Ib/s.c.f.
-1450 x 10"7
~1000 x 10*
~ 675 x 10
_7
^385 x 10
Run
(sample)
8
9
10
11
12
13
14
15
20
21
22
23
30
31
32
33
Lab 101
D
A
B
C
A
B
C
D
B
C
D
A
C
D
A
B
Lab 102
B
C
D
A
C
D
A
B
D
A
B
C
A
B
C
D
Lab 103
A
B
C
D
B
C
D
A
C
D
A
B
D
A
B
C
Lab 104
C
D
A
B
D
A
B
C
A
B
C
D
B
C
D
A
The letters A, B, C, and D depict the sampling ports to which each collaborative
laboratory team was assigned on each run. The listed samples were collected
for analysis to comprise the sixteen runs of the collaborative test at Cambridge.
Samples 1 to 4 were rejected because the glass wool plugs at the sampling
ports restricted sample collection. The remaining samples (5-7, 16-19,
24-29) were taken from the standard gas cylinders to constitute the accuracy
test.
-------
17
these samples conflict with the replication concept), nevertheless,
within each block the collaborative test has been designed to be closely
analogous to the performance test situation, for determining compliance
via Method 7. Thus, particularly when the port effect can be shown
insignificant, these four samples collected by a collaborative team in a
block can be considered replicates for the purpose of determining the
repeatability of the method. The randomized block design utilized for the
Dayton collaborative test was similar to that shown in Table 1., the only
important difference being that the four blocks of concentration levels were
7 7 -7 -7
approximately 465 x 10 ,355x10 ,225x10 , and 120 x 10 Ib./s.c.f.
Two ancillary tests were also conducted to study various aspects of
the Method 7 collaborative test. One test utilized gas cylinders obtained
from Scott Research Laboratories, Inc. containing mixtures of nitric oxide
and nitrogen whose nitric oxide concentrations had been accurately
determined. The purpose of this gas cylinder test was to provide an inde-
pendent assessment of the accuracy of Method 7 on sources whose NOX
concentrations, while unknown to the collaborative teams, were reported to
the Southwest Research Institute project staff. Three gas cylinders, labeled
X, Y, and Z, were used as the NOX source at both test sites. Along with
the four stack samples collected in every block of the collaborative test,
each laboratory team also collected samples from each of the three gas
cylinders. These samples were later analyzed together with their associated
block samples in the laboratory.
-------
18
A second test involved the replicate analysis of unknown nitrate
solutions to determine the reproducibility, repeatability, and minimum
detectable limit of the laboratory analytical portion of Method 7. Each of the
four laboratories performed triplicate analyses on four different unknown
potassium nitrate solutions during three of the days on which the test
samples were analyzed. An example of the unknown nitrate solution
instruction and reporting sheet is shown in Figure 8.
B. The Collaborative Test Data
The original NO collaborative test data reported to the SwRI project
j£
staff for the Cambridge test and also for the Dayton test are presented in
Table 2. The port from which the sample was collected is shown in
parentheses. An outlier analysis was conducted on this data (cf. Appendix B. 1)
and in the process .numerous detectable calculation errors were uncovered.
The data points that are in error are indicated by an asterisk superscript
in Table 2. Since calculation errors appear to be so prevalent in
obtaining the NOX concentration using Method 7, and since there is a
need to standardize the generation of the absorbance calibration curve
(cf. Appendix Bl), some thought might be given to the development and
use of a standard Method 7 computer program to alleviate these problems.
If the Quality Assurance and Environmental Monitoring Laboratory were to
design and implement a program to compute the Method 7 NO concentration
Jt
from a laboratory's raw data (a program to include the standardization of
measurement units, the generation of a regression calibration line, and
-------
19
Figure 8.
Collaborative Test of Method 7
Instructions for Analysis of Unknown Nitrate Solutions
A series of nitrate solutions are provided to each collaborator.
These solutions are labeled A, B, C, and D, and the concentrations are
unknown to the 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 5. 2 (and 4. 3) of Method 7 and report results as micrograms of
per ml of unknown solution.
Submit the results on this sheet along with your other collaborative
test data.
Analyst
Lab 104
| Oay
i
Day 1
! Date 1-16-73
i
!
Day 2
Date i.ia-?-?
. Day 3
i Date 1-22-73
!
(
Replicate
1
2
3
1
2
3
1
2
3
Concentration, |ag NOg per ml
Solution A
24.8
26.7
26.6
26.0
24.4
25.8
25.1
24.4
25.8
Solution B
13.7
12.7
14.1
12.7
12.9
13.0
13.0
13.3
12.8
Solution C
39.9
37.0
40.0
38.6
37.0
38.3
34.0
34.7
36.2
Solution D
1.0
0.6
0.5
0.4
0.4
0.4
0.6
0.6
0.8
-------
20
TABLE 2.
THE ORIGINAL NOV COLLABORATIVE TEST DATA
.A.
Site Block Sample
Cambridge
1 8
9
10
11
2 12
13
14
15
3 20
21
22
23
4 30
31
32
33
Dayton
1 5
2
3
4
2 9
10
11
12
3 16
17
18
19
4 23
24
25
26
Lab 101
7
10 'lb/scf
1510*{D)
1520*(A)
1570* (B)
Missing (C)
1050* (A)
82 6* (B)
1010*(C)
701*(D)
45 6* (B)
554*(C)
69 6* (D)
734*(A)
364*(C)
395* (D)
376* (A)
377*(B)
467*(A)
488* (B)
487*(C)
458* (D)
335* (B)
339*(C)
365*(D)
359* (A)
234*(C)
227*(D)
227*(AJ
220*(B)
127*(D)
123*(A)
120*(B)
122*(C)
Lab 102
10"7lb/scf
1443*(B)
1588*(C)
1560*(D)
1653*(A)
1486*(C)
1107*(D)
1208*(A)
1166*(B)
1240*{D)
715* (A)
727*(B)
798*(C)
442 *(A)
421*(B)
40 6* (C)
423*(D)
413 (B)
480 (C)
485 (D)
399 (A)
321 (C)
296 (D)
356 (A)
348 (B)
231 (D)
251 (A)
227 (B)
223 (C)
141 (A)
129 (B)
136 (C)
130 (D)
Lab 103
10"7lb/scf 10
1450 (A)
1810 (B)
1500 (C)
1370 (D)
1040 (B)
1000 (C)
941 (D)
996 (A)
763 (C)
750 (D)
806 (A)
697 (B)
412 (D)
447 (A)
385 (B)
423 (C)
497 (C)
529 (D)
496 (A)
491 (B)
362 (D)
373 (A)
421 (B)
408 (C)
212 (A)
227 (B)
215 (C)
189 (D)
114 (B)
103 (C)
115 (D)
100 (A)
Lab 104
"7 lb/scf
1350 (C)
1350 (D)
1410 (A)
1420 (B)
1080 (D)
1030 (A)
1040 (B)
960 (C)
670 (A)
660 (B)
670 (C)
700 (D)
360 (B)
360 (C)
380 (D)
380 (A)
460 (D)
500 (A)
470 (B)
430 (C)
350 (A)
360 (B)
390 (C)
380 (D)
250 (B)
240 (C)
230 (D)
230 (A)
130 (C)
130 (D)
130 (A)
130 (B)
( ) Port from which sample was collected is shown in parentheses.
* Calculation error in this original reported value.
-------
21
the calculation of both the sample volume under standard conditions
and the mass of NC^), then the calculation error problem could be
eliminated. If the program were run by EPA, then the additional problem
of bias in performance test reporting (i. e. , reporting of only the best
twelve of many field test samples in determining compliance) could also
be reduced.
The corrected collaborative test data obtained as a result of
recalculating suspicious points and correcting the discovered systematic
errors are presented in Table 3. (Cambridge data) and Table 4. (Dayton data)
along with some initial summary statistics. These statistics are the mean,
variance, and standard deviation for each run, collaborative team, and
port at each site. The missing Lab 101 point from port C for run 11,
block 1 at the Cambridge site has been replaced with the value 1446 in
Table 3 obtained as the minimum variance unbiased estimate for Lab 101
on run 11 in block 1 under the variance stabilizing logarithmic transformation
(cf. Appendix B.4).
C. The Accuracy of Method 7
A question of vital importance regarding Method 7 is whether this
method is accurate in its measurement of the NO concentration in the
jC
exhaust emitted from the stack of a fossil fuel-fired steam generating power
plant, or whether, on the other hand, the method is biased to give
consistently low or high measurements. The experiment was designed so
-------
TABLE 3. THE CORRECTED CAMBRIDGE COLLABORATIVE TEST DATA
METHOD: EPA METHOD 7 — NITROGEN OXIDE EMISSIONS FROM STATIONARY SOURCES
TEST VARIABLE: X : CONCENTRATION OF NOX AS NO? (DRY BASIS), (4.B./S.C.F. )XlO**?
TRANSFORMATION: x LINEAR
TEST SITE! CAMBRIDGE
COLLABORATORS: LAB 1U1 , LAB 102 i LAB 103 , LAB 104 ,
INTER-LABORATORY RUN SUMMARY
RUN
SAMPLE
LAB 101
DATA PORT
LAB 102
DATA PORT
LAB 109
DATA PORT
LAB 10*
DATA PORT
RUN SUMMARY
MEAN STD DEV
BETA
1
2
3
*
5
b
7
B
9
10
11
12
13
1*
IS
Ib
a
o
10
11
12
13
1*
IS
20
21
22
23
30
31
32
33
1»*0.0
1*50.0
1500.0
l»»b.O
1000.0
789. 0
<)b3.0
fabl.O
*3b.O
530.0
bb*.0
700.0
3*7.0
377.0
359.0
3bO.O
(0)
(•)
(B)
(C)
(A)
(B)
(C)
(0)
(B)
(C)
(D)
(*)
(C)
(D)
(A)
(8)
1337.0
1*72.0
1»*7.0
1531.0
1382.0
1027. 0
1120.0
1081.0
73b.O
bbS.O
b7S.O
7*0.0
»11.0
391.0
37*. 0
3«2.0
(B)
(C)
(0)
(»)
(C)
(D)
(A)
(B)
(0)
(A)
(B)
(C)
(A)
(B)
(C)
(0)
1*50.0
1810.0
1500.0
1370.0
10*0.0
1000.0
1*1. n
99b.o
7b3.0
750.0
sob.b
bS7.0
*12.0
»»7.0
385.0
«23.0
(A)
(B)
(C)
(0)
(B)
(C)
(D)
(A)
(C)
(0)
(A)
(8)
(0)
(A)
(B)
(C)
1350.0
1350.0
1*10.0
1*20.0
1080.0
1030.0
10*0.0
ObO.D
>70.0
bbO.O
b70.0
700.0
SbO.D
3bO.O
380.0
380.0
(C)
(0)
(A)
(B)
(0)
(A)
(B)
(C)
(A)
(B)
(C)
(0)
(B)
(C)
(0)
(A)
131*. 2
1520. S
l*b*.2
1**1.7
1110.5
Ibl.S
lOlb.O
92b.5
bSl.2
bS0.7
703:?
382.5
303. B
37*. 5
388.7
59. 0
200.2
*».*
b7.3
115. 8
81.3
17S.O
1*8.7
90.7
bB.3
20.5
33. *
37.7
11.3
2b.«
.0*23
.131b
.0300
.0*b7
.1303
.120*
.0800
.1132
.228*
.1313
.0471
.0200
.088b
.0057
.0301
.Ob7B
COLLABORATOR SUMMARY
COLLABORATOR
MEAN
STD. DEVIATION
LAB 101
81*.*
*3*.l
LAB 102
910.0
122.*
LAB 103
02*.*
*29.7
LAB 10*
8b3.7
302.8
PORT SUMMARY
PORT
MEAN
STD. DEVIATION
901.*
*09.]
673.8
*fal.S
BBS.7
*25.b
858.*
389.5
ISJ
-------
TABLE 4. THE CORRECTED DAYTON COLLABORATIVE TEST DATA
METHOD: tPA METHOD ' NITROGEN OXIDE EMISSIONS FROM STATIONARY SOURCES
TEST VARIABLE: X = CONCENTRATION OF NOX 13 KOI (DRY BASIS), (LB./S.C.F.)X10*«7
TRANSFORMATION: x LINEAR
TEST SME: UAYTOH
COLLABORATORS: LAB 1U1 . LAB 102 , LAB 103 , LAB 10* ,
INTER-LABORATORY RUN SUMMARY
RUN
SAMPLE
RUN SUMMARY
MEAN STO DEV
BETA
q
10
11
12
19
1*
IS
Ib
10
12
Ib
17
18
14
23
2*
25
2b
ttS.O
•»b5.0
HbS.O
»S7.0
320.0
323.0
318.0
3*2.0
223.0
217.0
217.0
210.0
121.0
117.0
11*. 0
llb.O
(A)
(B)
(C)
(D)
(B)
(C)
(0)
(A)
(C)
(0)
(A)
(B)
(D)
(A)
(B)
(C)
113.0
*BO.O
»B5.0
31*. 0
321.0
2<*b.O
35b.O
3*8.0
231.0
2S1.0
227.0
223.0
1*1.0
124.0
13b.O
130.0
tfl)
CC)
CO)
(*)
(C)
(D)
CA)
CB)
ro)
(A)
CB)
CO
(A)
CB)
CC)
CO)
»<)7.0
524.0
*<«b.O
»11.0
3b2.0
373.0
*21.0
tOB.O
212.0
227.0
215.0
IBS.O
11*. 0
103.0
115. 0
lon.o
CO
CO)
CA)
CB}
(D)
(A)
CB)
CO
CA)
ce)
CO
CD)
ce)
CC)
CO)
C»)
*bO.O
500.0
V70.0
<*30.0
350.0
3bO.O
310.0
380.0
2SO.O
2*0.0
230.0
230.0
130.0
130.0
130.0
130.0
CO)
(A)
(B)
CO
(A)
(B)
(0
CD)
CB)
CC)
CO)
CA)
co
(0]
CA]
(B}
»S3.7
»S3.S
»7S.O
»3S.2
338.2
338.0
378.7
3b1.S
224.0
233.7
222.2
213.0
12b.S
lit. 7
183.7
111.0
3*. 4
27.7
1».2
38. a
W.I
35.1
33.9
30. b
lb.0
ia.D
12. b
11.0
1*.3
,07bB
.OSbl
.021b
.0871
,0b23
.1034
.OBBb
.0888
.0700
.Db3b
.0331
.OB*b
.0183
.1055
.OBBb
.1200
COLLABORATOR SUMMARY
COLLABORATOR
MEAN
STO. DEVIATION
LAB 101
280.0
130.3
LAB 102
2BS.H
121.2
LAB 103
303.Z
1SR.S
LAB 10*
300.b
L32.S
PORT SUMMARY
PORT
MEAN
STD. DEVIATION
211.2
134.2
135.2
213.8
138.2
2S1.2
1»0.3
M
OJ
-------
24
that the gas cylinder test data would resolve the accuracy question with
supporting evidence to be provided by alternative NO determination
techniques available at the test sites.
Unfortunately, the gas cylinder test proved deficient. A summary
of the gas cylinder test data is shown in Table 5. The Method 7 mean is
the average of a combined 15 to 20 measurements made by the four
collaborative teams on samples taken from each gas cylinder. It is
noteworthy that the Method 7 mean is always substantially less than Scott
Research's reported true value for the gas cylinder. The remarkable fact
is that the percentage difference for the high, medium, and low nitric
oxide concentration cylinders is so consistent between the Cambridge and
Dayton sites. At both sites, the high NO cylinder was measured 10% low
by Method 7, the medium NO cylinder was about 13% low, and the low
cylinder was 28% low- As Mr. Paul Sherman of Monsanto Research first
suggested, the lack of oxygen in the gas cylinder samples perhaps interfered
with the Method 7 determinations. If this were the case, since there is
considerable oxygen in real world samples, it would invalidate all the gas
cylinder data and consequently negate the gas cylinder approach to
determining the accuracy of Method 7.
The lack of molecular oxygen in the cylinder samples does lead to
a difference in the total chemistry of the method,' ' as compared to the
chemical reactions occuring in oxygen containing samples. In the cylinder
samples, the only oxidant present in the flask is the peroxide in the
-------
25
TABLE 5. GAS CYLINDER TEST DATA SUMMARY
NO,, Emission Concentration, 10" Ib./s.c.f.
Test Site Cylinder
Cambridge
Dayton
High (X)
Medium (Z)
Low (Y)
High (Y)
Medium (X)
Low (Z)
True Value
Scott Research, +1%
834
493
100
836
482
96
Method 7
Mean
751
433
72
749
415
69
Percentage
Difference
-10.0%
-12.2%
-28.0%
-10.4%
-13.9%
-28.1%
Number of
Measurements
16
20
15
16
16
16
absorbing solution. Under these conditions the NO must be absorbed into
the liquid phase and subsequently oxidized in stepwise fashion to nitric acid.
The overall process is controlled by the rate of diffusion of NO across the
gas-liquid interface and the rates of the various oxidation reactions required
to convert NO to nitric acid.
In stack samples with oxygen present, some reaction between NO
and O, will occur, leading to some oxidation in the gas phase in addition to
that occurring in the absorbing solution. Because of this, the overall
chemistry involved is different for the cylinder samples as compared to
the stack samples, and the results obtained for the determination of oxides
-------
26
of nitrogen in the presence and absence of oxygen, respectively, are not
comparable.
With the gas cylinder test probably invalid, attention must focus
on the alternative NO determination techniques available and employed
JC
at the Cambridge and Dayton sites. Since the Cambridge site was a pilot
plant, Walden Research was able to calculate a theoretical concentration
of NO in the duct at the sample test section based upon the NO doping
Ji
level, the NOX due to fuel combustion, and the volumetric flow calculated
stoichiometrically. The Walden calculation of theoretical concentration is
given in Appendix C. At both the Cambridge and Dayton sites, Dyna-
sciences monitors were available to measure the stack NOX concentrations.
However, the Cambridge Dynasciences monitor was malfunctioning through-
out the course of the Cambridge test due to a deficient fuel cell. Thus the
Cambridge Dynasciences NOX readings were not usable. The Cambridge
theoretical NOX concentrations obtained by Walden Research and the
Dayton Dynasciences monitor readings obtained by Monsanto are
summarized in Table 6 as "true" values for comparison with the corresponding
average Method 7 NOX concentration of the four collaborators in each
block. The Table 6 data are plotted in Figure 9. Figure 9 also contains
the 95% confidence limits for the Method 7 means of each block and
Walden's error range of -f- 11% for the Cambridge theoretical "true block
value" obtained by standard propagation of error analysis.^) The 95%
confidence limits for the Method 7 block means were computed using the
repeatability variance component cr2 and the between laboratory variance
-------
27
TABLE 6. METHOD 7 ACCURACY DATA
Test Site Block
Cambridge
Dayton
\
2
3
4
1
2
3
4
NO Emission Concentration, 10
-7
Ib./s.c.f.
"True
Theoretical
1440
1216
822
417
Value"
Dyna sciences
460
344
219
118
Method 7
Mean
1455
1004
679
385
466
356
224
122
Percentage
Differences
+ 1.0%
-17.4%
-17.4%
- 7.7%
+ 1.3%
+ 3.5%
H- 2.3%
+ 3.4%
-------
28
Figure 9. The Accuracy of Method 7
1600
Concentration
10"7 Ib./s.c.f
4400
1200
1000
800
600
400
200
Method 7 block mean with
95% confidence limits
Cambridge theoretical
"true block value" with
propagation error limits.
0 Dayton Dynasciences
"true block value"
200
400
600
800 1000
Method 7 Mean
1200
1400
Concentration
10-7 Ib./s.c.f.
-------
Z9
component
-------
30
specified for Method 7 in the Federal Register' ' as the average of three
repetitions, each of which consist of four replicate measurements.
Before a detailed statistical analysis of the Method 7 collaborative
test data presented in Tables 3 and 4 can be conducted to determine the
precision of Method 7, several preliminary matters require settlement.
These matters include whether there is a significant port effect to complicate
the analysis, whether the between-laboratory run variance and the within-
laboratory block variance is mean concentration level dependent, and, if so,
what data transformation is required to achieve equality of the run variances.
The Experimental Design section alluded to the potential existence
of a significant port effect in the Method 7 tests (i.e., that because of
possible non-uniform flow in the stack, the true NO emission level at
certain ports would be consistently higher or lower than the average of the
four ports during the course of the test). The significance of this port effect
is tested in Appendix B.2. It is found that no port effect is detectable and
consequently, one is justified in ignoring any port effect in the subsequent
analysis.
The next problem to be considered is whether the variation in the
Method 7 NOX concentration values is dependent upon the NO concentration
itself and, if so, what the underlying relationship actually is. It is clearly
demonstrated in Appendix B.3 through Figures B.2 and B.3 and through the
regression analyses of the data that there is indeed a strong linear relationship
-------
31
of the standard deviation to the mean spanning both the Cambridge and
the Dayton Test data. To be more precise, it appears that the between-
laboratory run standard deviation is proportional to the between-laboratory
run mean and that the within-laboratory block standard deviation is
proportional to the within-laboratory block mean. Appendix B.4 strengthens
the argument for this proportional relationship. In Appendix B.4 it is
shown that Bartlett's test gives the best equality of between-laboratory run
variance by using the logarithmic transformation. And it is further
demonstrated that justifying use of the logarithmic transformation on this
basis is equivalent to justifying that the between-laboratory run standard
deviation is proportional to the between-laboratory run mean. Thus
Appendix B.3, with corroborating evidence from Appendix B.4, provides
ample justification for concluding that the proportional relationships of
standard deviation to mean in both the between laboratory and within
laboratory data classifications are underlying characteristics of
Method 7 measurements. The consequences of these relationships on the
nature of the variance components, (T and <7~ , is worked out in
L
Appendix B.5. (T~ is the variance of the population of laboratory means Uj .
-------
32
with coefficients of variation (3 and (3, respectively. Therefore, by
obtaining estimates of p and pL from the Cambridge and Dayton
collaborative test data, we will have derived estimates of the standard
deviation components ff~ and ff~ through which Mandel defines repeatability
L
and reproducibility.
In Appendix B.6 the methodology for obtaining estimates of
P and p is derived and applied. The 32 collaborator block point estimates
L
of p given in the last column of Table B2 are averaged and multiplied by
the bias correction factor of 1. 0854 to yield the within laboratory
coefficient of variation estimate p = .06558. So the within lab standard
deviation estimate is
-------
33
three repetitions are analyzed in the laboratory on the same day, as cur-
rently anticipated, then m = 12 is appropriate. However, if each repetition's
four samples are analyzed on different days, then because of the very signifi-
cant day effect in Method 7 laboratory analysis (cf. Appendix B.8), the
proper replication factor is m = 4. For the sake of clarity, the repli-
cation factor will hereinafter be assigned the value m = 12. Then the
estimated repeatability standard deviation for Method 7 is CT/N/ m = . 01893^.
With <{> = 96 degrees of firmness, the standard deviation of the uncertainty
in this repeatability standard deviation estimate is 7. 2% of its value.
Therefore, the 95% confidence interval for the true repeatability standard
deviation o-/ = 3. 284 degrees of firmness, the standard deviation of the uncer-
tainty in this reproducibility standard deviation is 39. 0%. The 95% confidence
interval is . 0168H < \larj_, + (r2/ 12 < . I254|i. Therefore, based upon the
Cambridge and Dayton collaborative tests, the probability is 95% that the
-------
34
Method 7 reproducibility standard deviation lies between 1.68% and 12.54%
of the test result average, with a best estimate of 7. 1 1% of the test result
average.
Using Mandel's definitions, the estimates of the repeatability
and reproducibility of Method 7 test results obtained from the Cambridge
and Dayton collaborative tests are as follows:
Repeatability = 2.77 $ I *J~m = 2.77 (.01893^) = .05244^
Reproducibility = 2.77 >v + ^/m = 2.77 (.07110^.) = . 19694ji
LJ
The repeatability of a Method 7 test result is 5.24% of its value, while
the reproducibility of a Method 7 test result is 19.69% of its value.
E. Accuracy and Precision of the Analytical Procedure
Four nitrate solutions, whose effective NO source concentrations
were known to the project staff but unknown by the collaborative
laboratories, were each analyzed in triplicate on each of three days in
conjunction with the collaborative test samples by each of the collaborative
laboratories. The purpose of this nitrate solution study was. to make
possible a determination of the accuracy and precision of the laboratory
analytical procedure portion of Method 7. All the reported nitrate solution
data are presented and summarized in Tables B4, B5, and B6 of
Appendix B. 7.
-------
35
TABLE 7. ACCURACY OF THE METHOD 7 ANALYTICAL PROCEDURE
NO, Concentration, jig per 10 ml. of absorbance sample
Prepared Collaborator 95% Confidence
"True" Value Mean Interval for Mean
0
12
25
37
.00
.50
.00
.50
0
13
25
38
.83
.01
.46
.03
(0.
(11
(23
(36
05, 1
.86,
.94,
.13,
.61
14.
26.
39.
)
16)
98)
93)
Percentage
Difference Difference
0
0
0
0
.83
.51
.46
.53
+ 4 . 08%
+ 1.84%
+ 1.41%
The accuracy of the Method 7 analytical procedure is assessed by
comparing the average reported NO concentrations of the four solutions
Cm
for the four collaborative laboratories against the "true" concentration
values in terms of the working standard solution of potassium nitrate to
which these solutions were prepared. This comparison is presented in
Table 7. The 95% confidence interval for the collaborator solution mean
22 ~2
is based on a variance of
-------
36
Therefore, the laboratory analytical part of Method 7 appears to be
unbiased in the normal working range of the calibration curve. However,
the collaborator mean was always somewhat larger than the prepared true
value. The difference was actually significant for the blank Solution D.
This suggests that the accuracy of the Method 7 analytical procedure
deteriorates considerably at very low nitrate concentrations.
A separate analysis of variance was performed on the data for each
of the four nitrate solutions to determine the significant factors and to
estimate the repeatability variance component. These analyses are
reported in Appendix B.8. They show that, for the analytical portion of
Method 7, the laboratory-to-laboratory variation is overwhelmingly due,
not as might be expected to significant biases from laboratory to laboratory,
but rather to large day-to-day variations in measurements that occur within
every laboratory. This means that, if the samples collected by the four
collaborative teams during the collaborative test had been sent to a single
laboratory for analysis on four separate days (instead of to the four
respective laboratories for analysis), then the resulting run variation in
measurements would be, on the average, nearly as large as that actually
obtained. The analytical laboratory variance and standard deviation
components estimated for the nitrate solution data are shown in Table B9
of Appendix B.8 for each solution. It is noteworthy that, in contrast to
A *
Method 7 itself, the standard deviation components O~ and
-------
37
Figure 10. It is evident that £ , and particularly 9, are linear functions
of the mean with a positive intercept at \i = 0. The regression equations are:
-------
Figure 10. Analytical Standard Deviation Comonents
'I Q
2."
O7 pier 10 ml.
_£__J L_^^— -r .
t ! I - •• • ••,'"! ' .
triln--; fti
:••••! • :'.-•• -: L! •:
•:\ :-
.
2.1
ih :-f'
l.i
-:!~^:ri
1.2'
i.o.
-f-r4-
0.8
. °^~3*
0.6T
.|:-:"::.-'
-...!• :: I:
0.2
^iL
* Lab-to^lab
o.oi
10 15 20 25 30 35 40
IJL, (jig NOg per 10 ml
-------
39
these variance components have been derived, for both Method 7 itself
and, from four concentration levels on the spectrophometer calibration
curve, for the laboratory analytical portion of Method 7. Since variances
of independent factors are additive, it is thus possible to determine to a
surprisingly great extent, the Method 7 sources of variability.
2 ?
The relative importance of o and er in the variability of a
LJ
performance test result is shown in Table 8. Almost 93% of the variation
in a test result is due to measurement variation from laboratory to lab-
oratory. The repeatability variance component is only 7. 1% of the
reproducibility variance. The inference is that sufficient replication
has been specified in the definition of a Method 7 performance test result.
The percentage of the laboratory-to-laboratory variation, the
repeatability variation, and the reproducibility variation attributable to the
laboratory analytical and the field portions of Method 7 may be calculated at
any point along the absorbance calibration curve. The nitrate solution
points of 1.25, 2.50, and 3.75 figNO2 per ml. of absorbance sample
were used to cover the range of the calibration curve. The results are
shown in Table 9. It should be noted that, since the estimates of
-------
40
TABLES. SOURCES OF REPRODUCIBILITY VARIATION IN
A PERFORMANCE TEST RESULT
Variance Component Estimated Variance Variation
Source Component Percentage
Laboratory-to-laboratory
-------
41
TABLE 9. THE ANALYTICAL PROCEDURE AS A SOURCE
OF COMPONENT VARIATION
Lab-to-lab:
* *
Method 7 : (.06853^)
Analytical: (.03ji
% Analytical
% Field
.07705)'
Absorbance Curve Concentration, jAgNOjj/ml,
li = 1.25 |q = Z.50 n=3.75
,00734
,0131Z
100%
0%
.02935
.02312
79%
21%
.06604
.03593
54%
46%
Repeatability; 0" /12
Method 7 : (.06558ji)2/12
Analytical: (. 03142ji + . 02321)'
% Analytical
% Fie Id
712
00056
00033
58%
42%
00224
00086
39%
61%
00504
00166
33%
67%
Reproducibility:
Method 7
Analytical
% Analytical
% Field
•* (T
'/12
00790
01345
100%
0%
03159
02398
76%
24%
.07108
.03759
53%
47%
-------
4Z
while the field percentages, not being estimated directly, are very
unreliable. The main purpose of Table 9 is to indicate that the analytical
reproducibility variability can be reduced dramatically by using only the
upper portion of the absorbance calibration curve range, from absorbance
sample concentrations of, say, 3. 0 jig NO /ml. to 4. 0 jig NO /ml.
£• ft
This confirms the assertion developed in Appendix B.I regarding sample
dilution that the low end of the calibration range yields unreliable NO
mass data. In fact, many of the outlier collaborative data points that were
included in the statistical analysis might, in retrospect, well have been
excluded. They might have been excluded on the grounds that they were
read from the calibration curve either at the extreme low end of the
calibration range where questionable calibration procedures introduced
considerable errors, or far above the calibration range where there is no
proofthat Beers' Law remains valid. These possibly excludable data
points are listed in Table 10. If the present Method 7 were revised to
require that only the go od portion of the calibration curve be used, then
the data points listed in Table 10 could be rejected, and the method's
repeatability and reproducibility coefficients of variation would be
reduced considerably.
The nitrate solution analysis of variance disclosed that nearly all
of the analytical laboratory-to-laboratory variance component O~^ is
attributable to the day-to-day variation in laboratory measurements. It
is likely that the importance of this day-to-day variation derives from
-------
43
TABLE 10. OUTLIER COLLABORATIVE DATA POINTS DERIVED
OUTSIDE THE ACCEPTABLE CALIBRATION RANGE
Concentration Calibration Curve
Site
Cambridge
Cambridge
Cambridge
Cambridge
Cambridge
Dayton
Dayton
Collaborator
Lab 101
Lab 101
Lab 102
Lab 102
Lab 103
Lab 102
Lab 103
Sample
13
15
12
15
9
17
19
Ib./s.c.f.
789
669
1322
1081
1810
251
189
i-'o:
(jig NO
0.876 -
0.766 -
6.64 -
5.61 -
5.32 -
6.65 -
1.14 -
int
2/ml.
low c*iid of range
low end of range
above range
above range
above range
above range
low end of range
-------
44
the daily drift of the spectrophotometer's absorbance readings and the
consequent need for daily recalibration. It was noted that the collaborative
laboratory's calibration curves were not always revised each day, and
that the parameters of the regression line calibration curves were
sometimes so imprecise that errors of from 5% to 8% were bound to be
introduced into the analytical procedure. It is suggested that these
currently allowable but damaging practices be prohibited through a more
careful exposition of these matters in the Method 7 procedure.
-------
45
IV. CONCLUSIONS AND RECOMMENDATIONS
The following conclusions regarding Method 7 (Determination of
Nitrogen Oxide Emissions from Stationary Sources) have emerged from
the preceding statistical analysis of the Method 7 collaborative test data
and associated ancillary data obtained from the Cambridge and Dayton
test sites.
1. Accuracy - Because of unanticipated problems due to the
chemistry of sampling from a nitric oxide and nitrogen mixture lacking
oxygen, the gas cylinder test for determining the accuracy of Method 7
is probably invalid. The supporting accuracy tests based on alternative
NOX determination techniques gave conflicting results; on balance, they
appear to support the hypothesis that Method 7 is accurate. However,
the accuracy of Method 7 has not been adequately demonstrated.
2. Precision - The precision measures of a Method 7
performance test result, i.e., reproducibility and repeatability, are
proportional to the test result itself. The repeatability standard deviation
estimate obtained is cr/
-------
46
repeatability and from 1.68% to 12. 54% of the average for reproducibility.
The width of the reproducibility confidence interval is an unavoidable
penalty caused by the necessary restriction of these collaborative tests
to only four simultaneously sampling collaborative teams. According to
Mandel's definitions, ' the repeatability of Method 7 is-5. 24% of its test
result average and the reproducibility of Method 7 is 19.69% of its test
result average.
3. Minimum Detectable Limit - The estimated minimum detectable
limit of Method 7 is 5. 14 x 10 Ib. Is. c. f. If a.performance test-result
is less than 5. 14 x 10" Ib. /s.c.f. , the actual nitrogen oxide emission
concentration in the stack is indistinguishable from zero.
4. Sources of Reproducibility Variation - The Method 7
performance test result reproducibility variation can be partitioned into
its components and thereby ascribed to its constituent sources. 92.9% of
the test result reproducibility variation is accounted for by laboratory bias
2
component
-------
47
analytical portion of the laboratory bias component is not actually a true
laboratory effect at all, but rather a day effect mainly attributable to
poor or neglected daily spectrophotometer re-calibration procedures.
Assessments of Method 7 have been made by the collaborative
test supervisor and by the collaborators themselves as a result of
their observations and experience in conducting the field and analytical
phases of Method 7. These assessments have included the following
pertinent comments.
1. Method 7 is fairly tedious and time-consuming. As a
result there are ample opportunities for errors to be introduced,
particularly in sample collection and aliquoting.
2. Walden Research Corporation reports that Method 7 for NO ,
as written, is a good test procedure with relatively few weak points.
However, one of these is that the line to the manometer should be left
open during sampling so that any problems with the glass wool plugging or
probe malfunction can be readily observed. The system at this point has
already been leak-tested so there is no danger of sample contamination
from the manometer side. Secondly, it should be emphasized in the procedure
that only a steam bath be used for evaporation of the samples as hot spots
generated with a hot plate could introduce error in the determination.
Thirdly, it has been their experience that certain types of litmus paper, when
dipped into the solutions during the procedure to check alkalinity, introduce
an error. The solution should be checked by dipping a glass rod in the
-------
48
solution and touching it to the litmus paper, wiping the glass rod and
repeating the step until the desired results are achieved. This error is
greater at lower NOX levels. Lastly, due to the many handling steps and
chance for mishap, it is strongly recommended that an aliquoting section
be inserted in the procedure. Aliquoting of samples is a basic procedure
in analytical chemistry and would help in the determination of precision
in the results . It would also guard against loss of sample and data if a
mishap occurs in analysis.
3. Monsanto Research Corporation had two worthwhile suggestions.
In the concentration calculations, the constant 6.2 x 10 should be expanded
to include the second digit after the decimal : 6.24 x 10"5 lb/scf . There
ug/ml
is no justification for rounding this number to 6.2 since the number does come
out 6. 243 when 1. 0 is divided by 1. 6017. An important point is that when the
spectra of the standards and samples generated using this method is scanned
on a calibrated dual beam instrument, the maximum absorbance does not
come at 420 nm as listed in method. The maximum is at 405 nm . It is,
therefore, proposed that the method be changed to read 410 nm or 405 nm.
The instruments on which these measurements were made had been calibrated
with respect to wavelength using holmium oxide glass and the absorbance was
calibrated using a standard absorbance filter provided by the instrument
manufacturer. In addition, the 13th Edition of Standard Methods of
Analysis of Water and Wastewater-Nitrate Analysis, 1971 and ASTM
Standards, Part 23, ASTM designation D-1608-60 recommend 410 nm and
400 nm, respectively. It is always best to do an analysis at the peak maximum
instead of on the side of the peak.
-------
49
The conclusions and pertinent comments presented above, provide
a firm basis for the following recommendations concerning Method 7:
1. Additional collaborative evidence is needed to verify the
accuracy of Method 7. Consequently, valid accuracy tests should be
developed for inclusion in future collaborative tests of Method 7 to provide
the necessary evidence.
2. It is recommended that the current version of Method 7 be
revised to incorporate these concepts:
a. Conduct a thorough critical review of Method 7 as
currently written to locate ambiguous statements and to
modify them so as to be more explicit.
b. Calculation errors were prevalent in the Method 7
collaborative test data. To prevent the occurrence of calculation
errors in the Method 7 performance test results for compliance,
it is recommended that a general Method 7 computer program
be written to calculate the NO concentration test result from
the raw field and laboratory data . All data processing by this
Method 7 program should be controlled by the Environmental
Protection Agency. In addition to insuring proper program usage,
data processing by EPA would also discourage the illegal practice
of taking numerous field samples during the performance test
and reporting only the twelve best measurements, because the
testing laboratory need never calculate the concentration of its
samples..
-------
50
c. Provide more detail regarding the proper spectro-
photometer calibration procedure. These details ought to include
a requirement for daily re-calibration and generation of the
appropriate calibration line. This calibration line should be
forced to pass through the origin, either graphically or by
linear regression. If a regression line is computed, at least
three significant digits should be maintained in the calculated
slope.
d. Restrict use of the calibration line to only the more
accurate portion of the calibration range. If 2.c above is enacted,
the range from 1.0 to 4.0 jj.g NO per ml. of absorbance sample
is considered accurate; otherwise only the range from 2.5 to
4.0 jig NO2 per ml. should be used. If calibration data are
collected between 4.0 and 5.0 |ig NO per ml. and the relationship
£
remains linear, then the effective ranges above could be extended
from 4.0 to 5. 0 jig NO per ml. as the upper limit. This argument
C*
is based on the use of absorbance cells with a 1 cm. path length.
Enactment of these four recommendations could greatly enhance
both the repeatability, and especially the reproducibility, that are herein
reported for the current version of Method 7.
-------
51
References
1. Environmental Protection Agency, "Standards of Performance for
New Stationary Sources," Federal Register, Vol. 36, No. 247,
Dec. 23, 1971, pp. 24876-24893.
2. Margolis, Geoffrey, and Driscoll, John N. , "Critical Evaluation of
Rate-Controlling Processes in Manual Determination of Nitrogen
Oxides in Flue Gasas, " Environmental Science and Technology,
Vol. 6, No. 8, Aug. 1972, pp. 727-731.
3. Strobel, H.A. , Chemical Instrumentation, Addison-Wesley,
Cambridge, I960, pp. 27-29.
4. Mandel, John, "Repeatability and Reproducibility, " Materials
Research and Standards, American Society for Testing and
Materials, Vol. II, No. 8, August, 1971, pp. 11, 12.
5. Environmental Protection Agency, op. cit. pp. 24878, 24879.
6. Mandel, John, op. cit. , p. 9.
7. Mandel, John, op. cit. , p. 12.
-------
A-l
APPENDIX A
Method 7. Determination of Nitrogen Oxide Emissions
from Stationary Sources
Federal Register, Vol. 36, No. 247
December 23, 1971
METHOD »—DBRRMINATION Or NtTROOIN OXtDI
EMISSIONS FHOM STATIONARY SOCTCU
1. Principle and applicability.
1.1 Principle. A grab eompls Is collected
in an evacuated flaak containing a dilute
aulfurlo aeld-hydrogen peroxide absorbing
aolutlon, and the nitrogen oxides, except
-------
21802
RULES AND REGULATIONS
nitrous oxide, are measure eolorlmetrlcally
using tbe phenoldlsulfonlc acid (PDS)
procedure.
1.2 Applicability. This method 1s applica-
ble for the measurement of nitrogen oxides
from stationary sources only when specified
by tbe test procedures for determining com-
pliance with New Source Performance
Standards.
3. Apparatus.
2.1 Sampling. See Figure 7-1.
2.1.1 Probe—Pyrex' glass, heated, with
filter to remove paniculate matter. Beating
Is unnecessary U tbe probe remains dry dur-
ing the purging period.
21.2 Collection flask—Two-liter. Pyrex.'
round bottom with short neck and 24/40
standard taper opening, protected against
Implosion or breakage.
' Trade name.
2.1.3 Flask valve—T-bore stopcock con-
nected to a 24/40 standard taper Joint.
2.1.4 Temperature gauge— Dial-type ther-
mometer, or equivalent, capable of measur-
ing 2- F. Intervals from 25* to 125* P.
216 Vacuum line—Tubing capable of
withstanding a vacuum of 3 Inches Hg abso-
lute pressure, with "T" connection and T-bore
stopcock, or equivalent.
2.1.0 Pressure gauge—TJ-tube manometer.
38 Inches, with 0.1-lneh division*, or
equivalent.
2.1.7 Pump—Capable of producing a vac-
uum of 3 Inches Hg absolute pressure.
2.1.8 Squeeze bulb—One way.
2.2 Sample recovery.
221 Pipette or dropper.
2.2 2 Glass storage containers—Cushioned
for shipping.
IVACUATC
SOuflKSUU
HAS- VAlVtt £T) JAMFU
FM.ru
t»OU NO-GLASS SOCUfT
f NO. IM
JIAS«
KASK SHiaa..-,
GDOUNDGLAK
STANOAJD TACIK.
| REIVE NO. 24/40
GKOUND-CIASS
SOCKET. J HO. 1M
rrau
FOAM INCASE MINT
601UNG FLASH •
?lltf» BOUND BOTTOM SHOT NfCX.
WITH } SUIVE NO. 24/40
Fig-'C 7-1.
'.-.in, ll.uk valtt. and li.-ik.
2.2.3 Glass wash bottle.
2.3 Analysis.
2.3.1 Steam bath.
232 Beakers or casseroles—250 ml., one
for each sample and standard (blank).
2.33 Volumetric pipettes—1, 2. and 10 ml.
2.3.4 Transfer pipette—10 ml. with o.i ml.
divisions.
2.3.5 Volumetric flask—100 ml., one for
each sample, and 1,000 ml. for the standard
(blank).
2.3.6 Spectrcpbotometer—To measure ab-
sorbivnce at 420 urn
2.3.7 Graduated cylinder—100 ml. with
1.0 nil. divisions.
23.8 Analytical balance—To measure to
0.1 me
3. Reagents.
3.1 S.impling.
3 1.1 Absorbing solution—Add 2.8 ml. of
concentrated H,SO. to l liter of distilled
water. Mix well and add 0 ml. of S percent
hydrogen peroxide. Prepare a fresh solution
weekly and do not expose to extreme heat or
direct sunlicht.
3.2 Sample recovery.
3.5.1 Sodium hydroxide (1AM— Dissolve
40 p. K.iOII In distilled water and dilute to 1
liter.
3.2.2 Red litmus paper.
3.2.3 Water—Deionlzed. distilled.
3.3 Analysis.
3.3.1 Fuming sulfurlc acid—15 to 187,, by
weight free sulfur trloxlde.
3.3.2 Phenol—White solid reagent grade.
3.3.3 Sulfurlc acid—Concentrated reagent
grade.
3.3.4 Standard solution—Dissolve 0.5495 g.
potassium nitrate (KNO,) In distilled water
and dilute to 1 liter. For the working stand-
ard solution, dilute 10 ml. of the resulting
solution to 100 ml. with distilled water. One
ml. of the working standard solution Is
equivalent to 25 «g. nitrogen dioxide.
3.3.5 Water—Deionlzed. distilled.
3.3.6 Phenoldlsulfonic acid solution—
Dissolve 25 g. of pure white phenol In 150 ml.
concentrated sulfurlc acid on a steam bath.
Cool, add 75 ml. fuming sulfurlc acid, and
he»t nt 100* C. for 2 hours. Store In a dark.
stoppered bottle.
4. Procedure.
4.1 Sampling.
4.1.1 Pipette 25 ml. of absorbing solution
Into a sample flask. Insert the flask valve
stopper into the flask with the valve In the
"purge" position. Assemble the sampling
train as shown In Figure 7-1 and place the
'probe at the sampling point. Turn the flask
valve and the pump valve to their "evacuate"
positions. Evacuate the flask to at least 3
Inches Hg absolute pressure. Turn the pump
valve to Its "vent" position and turn oft the
pump. Check the manometer for any fluctu-
ation In the mercury level. If there Is a visi-
ble change over the span of one minute.
check for leaks. Record the Initial volume.
temperature, and barometric pressure. Turn
the fla.sk valve to Its "purge" position, and
then do the same with the pump valve.
Purge the probe and the vacuum tube using
the squeeze bulb. If condensation occurs In
the probe and flask valve area, heat the probe
and purge until the condensation disappears.
Then turn the pump valve to Its "vent" posi-
tion. Turn the flask valve to Its "sample"
position and allow sample to enter the flask
for about 15 seconds. After collecting the
sample, turn the flask valve to Its "purge"
position and disconnect the flask from the
sampling train. Shake the flask for 5
minutes.
4.2 Sample recovery.
4.2.1 Let the flask set for a minimum of
16 hours and then shake tbe contents for 2
minutes, connect the flask to a mercury
filled U-tube manometer, open the valve
from the flask to the manometer, and record
the flask pressure and temperature along
with tbe barometric pressure. Transfer the
flask contents to a container for shipment
or to a 250 ml. beaker for analysis. Rinse the
flask with two portions of distilled water
(approximately 10 ml.) and add rinse water
to the sample. For a blank use 25 ml. of ab-
sorbing solution and the same volume of dis-
tilled water as used In rinsing the flask. Prior
to shipping or analysis, add sodium hydrox-
ide (IN) dropwlse into both the sample and
tbe blank until alkaline to litmus paper
(about 25 to 35 drops In each).
4.3 Analysis.
4.3.1 If the sample has been shipped In
a container, transfer the contents to a 250
ml. beaker using a small amount of distilled
water. Evaporate the solution to dryness on a
steam bath and then cool. Add 2 ml. phenol-
dlsulfonlc acid solution to the dried residue
and triturate thoroughly with a glass rod.
Make sure the solution contacts all the resi-
due. Add 1 ml. distilled water and four drops
of concentrated sulfurlc acid. Heat the solu-
tion on a steam bath for 3 minutes with oc-
casional stirring. Cool, add 20 ml. distilled
water, mix well by stirring, and add concen-
trated ammonium hydroxide dropwlse with
constant stirring until alkaline to litmus
paper. Transfer the solution to a 100 ml.
volumetric flask and wash the beaker three
times with 4 to 5 ml. portions of distilled
water. Dilute to the mark and mix thor-
oughly. If the sample contains solids, trans-
fer a portion of the solution to a clean, dry
centrifuge tube, and centrifuge, or filter a
portion of the solution. Measure the absorb-
ance of each sample at 420 nm. using the
blank solution as a zero. Dilute the sample
and the blank with a suitable amount of
distilled water If absorbance falls outside the
range of calibration.
5. Calibration.
5.1 Flask volume. Assemble the flask and
flask valve and fill with water to the stop-
cock. Measure the volume of water to ± 10
ml. Number and record the volume on the
flask.
5.2 Spectrophotometer. Add 0.0 to 16.0 ml.
of standard solution to a series of beakers To
each beaker add 25 ml. of absorbing solution
and add sodium hydroxide (l.V) dropwlse
until alkaline to litmus paper (about 25 to
35 drops). Follow the analysis procedure of
section 4.3 to collect enough data to dra.v a
calibration curve of concentration In A£. NO
per sample versus absorbance.
6. Calculation*.
61 Sample volume.
FEDERAL REGISTER, VOL 3». NO. 247—THURSDAY, DECEMBER JJ. 1971
-------
A-3
RULES AND REGULATIONS
where:
V..—Sample volume at standard condl-
tlona (dry basis), ml.
T.,j — Absolute temperature at standard
condition*. 63O* R.
P. u—Pressure at standard conditions.
29 93 Inches Hg
V, — Volume of flask and valve, ml.
V.— Volume of absorbing solution, 25 mL
P,-Final absolute pressure of flask.
Inches Hg.
P, —Initial absolute pressure of flask.
Inches Hg.
T,—Final absolute temperature of flask.
•R.
T, — Initial absolute temperature of flask,
•R.
6.2 Sample concentration. Read AK NO,
for each sample from the plot of *g. NO,
versus absorbance.
C =
("b- \
cu. ft. \
'«*'»•£/
6.2 X10-*
equation 7-2
where:
C= Concentration ot NO, as NO, (dry
basis). Ib /s c f
m = Masa of NO, In gas sample, #g
V..=Sample volume at standard condi-
tions (dry basis). mL
7. References.
Standard Methods of Chemical Analysis.
Oth ed. New York. D. Van Nostrand Co., Inc,
1962, vol. 1. p 329-330
Standard Method of Test for Oxides of
Nitrogen In Gaseous Combustion Products
(Phenoldlsulfonlc Add Procedure). In: 1968
Book of ASTM Standards. Part 23. Philadel-
phia. Pa. 1968. ASTM Designation D-l 608-60,
p. 725-729.
Jacob. M B . The Chemical Analysis of Air
Pollutants. New York. N Y . Intel-science Pub-
lishers. Inc. 1960. vol 10. p. 351-356
-------
B-l
Appendix B. Statistical Methods
This appendix consists of various sections which contain
detailed statistical procedures carried out in the analysis of the NO
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 Outlier and Associated Preliminary Analysis of the Original
Collaborative Test Data
After a scan of the reported collaborative test data, it was
decided to base the outlier analysis on the rule: "For each collaborative
test run, look at the high and low collaborator's NOX concentration
values. If such a value differs from the nearest reported value in the
run by more than 10% of this nearest value, subject this suspicious
outlier value to further scrutiny by recalculating its NOX concentration
from the raw reported data. " For instance, on sample 14 in block 2
of the Cambridge data (cf. Table 2), the high value (1208, Lab 102)
and the low value (941, Lab 103) were selected. Since 1208 differs
from the nearest value (1040, Lab 104) by more than 10% f TnZo =
16.2%), it was set aside for recalculation as being a suspicious outlier
point. But 941 was within 10% of its nearest value (1010, Lab 101)
and was thus not subjected to calculation.
-------
B-2
The recalculation of certain data points on the grounds that
they appear to be outliers -when compared against the other collaborative
laboratory teams' values for the run poses a question regarding the
philosophy of collaborative testing. Namely, does not such recalculation
of outlier points determined by comparison with the other laboratories
values for the same run tend to favorably bias an other-wise objective
assessment of the precision of Method 7? The point is that, if the
other collaborators' data were unavailable, one would have no inkling
that these erroneous outlier points were actually calculated incorrectly.
Indeed, use of the uncorrected originally reported data does actually
better represent the real world situation under which performance
testing for compliance using Method 7 will actually be conducted. It
was decided, nevertheless, to recalculate outlier points on the
rationale that with only four collaborators in the test, substantial
calculation error in any outlier point could greatly, and in an ideal
sense, unfairly detract from the precision of Method 7. The argument
for recalculation of outlier points could be considerably enhanced
through EPA's adoption of a standard Method 7 computer program by
which it would process all compliance performance testing raw data,
as suggested in Section III.B.
In numerous cases (those indicated by an asterisk in Table 2),
calculation errors were encountered. A calculation error was defined
-------
B-3
as existing when the recalculated value differed from the original
reported value by more than t 0. 5% allowable for round-off differences.
All of Lab 101's data was 4.84% too high because the value 6. 5 x 10"
had inadvertently been substituted for 6.2 x 10" 7—^-1- in the
|i g/ml
Lab 101 computer program calculation of NOX concentration. All
of Lab 102's Cambridge data was 7.8% too high because these calculations
had been performed entirely in the metric system utilizing an incorrect
standard condition conversion constant to compute V . There were
s c
also additional computational errors in the Lab 102 Cambridge NO
Ji
concentration values for samples 12 and 20. The sample 12 error
occurred somewhere in the calculation of Vgc while the sample 20 error
was made in determining the mass of NO? in gas sample from the
absorbance reading.
In the process of recalculating the potential outlier reported data,
it was noted that a variety of procedures were utilized by the collaborative
laboratories to calibrate the spectrophotometer's absorbance reading
versus H-g NO? in the sample at 420 nm. One laboratory (Lab 104)
plotted the calibration data on a graph and then visually drew a curve-
fitting straight line that passed through the origin. Another laboratory
(Lab 103) effectively did the same by visually obtaining the slope of a
straight line through the origin, differing only in that it used this slope
in a computer program rather than using the calibration graph directly.
-------
B-4
The other laboratories (Lab 101 and Lab 102) regressed their calibration
data via least squares to obtain the best fitting straight line expressing
absorbance as a linear function of jig/ml NO in the sample. These
£i
regression lines did not pass through the origin. Figure Bl illustrates
the differences in these two approaches on one of Lab 101's sets of
calibration data. The approach followed by Labs 101 and 102 can introduce
error into Method 7. Near the origin there can be considerable difference
between the two regression lines and a large percentage error is introduced
in using the standard least squares regression line. Also, the practice
of diluting the sample to bring the absorbance within the range of
calibration can magnify errors when an improper dilution is made that
yields an absorbance either at the extreme low end or above the calibration
range. It might be advisable to dictate the use of a regression line
through the origin as the calibration curve and to urge that only the
middle to upper portion of the calibration range be utilized whenever
practicable. However, since no such statements currently exist in
Method 7 as written in the Federal Register (cf. Appendix A), each
laboratory's calibration curve procedures were accepted as correct
in recalculating potential outlier reported data.
The corrected Cambridge data obtained as a result of the outlier
analysis appear in Table 3, while the corrected Dayton data are shown
in Table 4.
-------
FIGURE Bl. CALIBRATION CURVE DISCREPANCIES
B-5
0. 8
Absorbancp
calibration data ppin:
- -sta.Baa-rd.-reg res s io
line
regression through
origin -I
0.0
0 3.0 4.0 5.0
dard Co n c e n t r a t i o n, jig/m 1 , NO 2
-------
B-6
B. 2 Significance of the Port Effect
Because of the limited number of ports available on a stack,
each collaborative team is constrained to a sample from only one port
on each run. Since there is likely to be non-uniform flow through the
stack, a potential port effect is introduced. This section determines
whether there was a significant port effect in either the Cambridge
test or the Dayton test.
The statistical test utilized to assess the significance of the
port main effect was the unsophisticated rank test thatYouden presented
in his address, "The Collaborative Test." The null hypothesis is
that there is no difference between the n = 4 ports. Each of the M = 16 runs
at a test site are considered different materials in the Youden
terminology. Ranks from 1 to 4 are assigned to the ports' data for
each of the 16 runs. These sixteen ranks for a port are summed to yield
its score. The approximate . 05 level lower and upper limits for the two
sided test are scores of 28 and 52, respectively. On the Cambridge test
data, the low score was 35. 5 for port A; ports B and D had the highest
scores of 42. 5. On the Dayton test data, port D had the lowest score (36. 5)
while port B had the highest score (41. 5). Clearly, this test detects no
significant port effect in either the Cambridge or the Dayton test data.
It should be noted the existence of a sizable collaborator main effect
would, by the very nature of the randomized block design employed, tend
to obscure any small port effect that might be present. Thus, while a
-------
B-7
port effect may in fact exist, its influence on the data is undetectable
and hence, in effect, negligible. Therefore, one can proceed with the
precision statistical analysis on the tenable assumption that there is
no port effect.
B. 3 Empirical Relationship of the Standard Deviation to the Mean
in the Collaborative Test Data
A question that is fundamental to the proper statistical analysis
of the collaborative test data is whether, and to what extent, the
variation in the Method 7 NOX concentration values, both within a single
laboratory and between the collaborative laboratories, is related to the
true concentration level of the measurement. To phrase the question
in statistical terminology, is there a functional relationship of the
inter-laboratory (i.e. , between laboratory) run standard deviation to
the run mean and of the intra-laboratory (i. e. , within laboratory)
collaborator block standard deviation to the collaborator block mean?
Let x-• denote the Method 7 NO concentration level reported
J X
by laboratory i (i = 1,2,3,4) on run j (j = 1, 2, .... 16) with runs 1
through 4 comprising block 1, runs 5 through 8 in block 2, etc. Then
the inter(between)-laboratory run j standard deviation estimate may
y' 4 ~—
•j Z ( xij - *. .) where the inter-laboratory
i = l 4
run j mean estimate x.j = — ^ x... The inter-laboratory block
i = 1
4k
k mean estimate is defined as x" , = _ ^ x .. Table Bl contains
K 4 * ' J
j = 4k - 3
-------
B-8
TABLE Bl. INTER-LA BORA TORY RUN SUMMARY
Test Site Block
k
Cambridge
Block Mean
x\ .
-7
10 lb/scf
1455
1004
679
385
Run
j
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Mean
—
x .
' J
1C"7
1394
1520
1464
1442
1110
962
1016
926
651
651
704
709
383
394
374
389
Std. Dev.
s.
J
Ib/s. c.f.
59.0
200.2
44.0
67.3
144.7
115.8
81. 3
179.0
148. 7
90.7
68.3
20. 5
33.9
37.7
11.3
26.4
Coefficient of
Variation
_ C /^w
J " j X.j
.0423
. 1317
.0301
.0467
. 1303
. 1204
.0800
. 1932
. 2283
. 1394
.0973
.0289
.0886
.0957
.0302
.0679
Dayton
466
356
224
122
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
454
494
479
439
338
338
379
369
229
234
222
213
127
120
124
119
34.9
27.7
14.2
38.2
21. 1
35. 1
33. 5
30. 6
16.0
14.9
7.4
18.0
11.7
12. 6
11.0
14.3
.0769
.0561
.0296
.0870
.0624
. 1038
.0885
.0828
.0699
.0638
.0333
.0845
.0925
. 1053
.0889
. 1202
-------
B-9
the inter-laboratory block mean and run mean and standard deviation
estimates for both the Cambridge and Dayton collaborative test data.
The inter-laboratory run standard deviation is plotted as a function of
the inter-laboratory run mean in Figure B2. The extent of scatter in
this data reflects the limitation of having only four laboratories
sampling simultaneously. From this figure it is quite evident that the
run standard deviation increases as the run mean increases. Thus a
stepwise multiple linear regression program was utilized to determine
the best least squares regression line passing through the origin to fit
the Figure B2 data. Regressor variables provided to fit the standard
_-l _*/4 _l/2 _3/4
deviation S. as a function of the mean x included x , x , x , x » x,
5/4 3/2 2
x TJ , 3c , and log x. It was found that the linear function S. = bx .
provided a better fit than any other simple or multiple regression.
Even though there is much scatter in the data, the linear regression
S- = bxt . strongly suggests that the inter-laboratory run standard deviation
is directly proportional to the average inter-laboratory run NOX
concentration.
A similar analysis can be performed on the intra(within)-laboratory
block statistics to see what relationship holds at the intra-laboratory level.
Table B2 presents the intra-laboratory collaborator block means
4k L l 4k
^ =~yy ^
x. = -7 >_ x.. and standard deviations S^ =~yy ^> (x:; - x. )
for each collaborator i in each block k at both the Cambridge and Dayton
-------
FIGURE B2. INTER-LABORATORY RUN PLOT
i
.i
B-10
220
200
180
160
140
120
100
20
Run Mean 10"ll?/8.c.f.
-------
B-ll
TABLE B2.
INTRA-LABORATORY COLLABORATOR
BLOCK SUMMARY
Test Site
Intra- Laboratory Collaborator Block
Block Collaborator
k i
Cambridge
1 Lab 101
Lab 102
Lab 103
Lab 104
2. Lab 101
Lab 102
Lab 103
Lab 104
3 Lab 101
Lab 102
Lab 103
Lab 104
4 Lab 101
Lab 102
Lab 103
Lab 104
Dayton
1 Lab 101
Lab 102
Lab 103
Lab 104
2 Lab 101
Lab 102
Lab 103
Lab 104
3 Lab 101
Lab 102
Lab 103
Lab 104
4 Lab 101
Lab 102
Lab 103
Lab 104
Mean
*i k
io-7
1459
1447
1532
1383
855
1 138
994
1027
583
703
754
675
361
392
417
370
453
444
503
465
333
330
391
370
217
233
211
237
117
134
108
130
Std. Dev.
slk
Ib/s c f.
27. 6
81. 2
192. 6
37. 8
154. 5
128.8
40. 7
49.9
122.0
40.2
44. 9
17. 3
12. 3
15. 1
25. 7
11.6
14.2
44. 6
17.4
28. 9
13.8
27. 3
28.0
18.3
5. 3
12.4
15.9
9.6
2.9
5.6
7. 6
0. 0
Coef. of Variation
b ik = slk/Vk
.0190
. 0561
. 1257
.0273
. 1807
. 1132
.0409
.0486
.2095
.0571
.0596
.0257
.0342
.0386
.0617
. 0312
.0314
. 1004
.0345
.0621
.0415
.0827
. 0716
.0493
.0245
.0534
.0754
.0403
.0252
.0418
.0705
.0000
-------
B-12
test sites. The intra-laboratory collaborator block standard
deviation is plotted as a function of the intra-laboratory collaborator
block mean in Figure B3. Again a definite linear relationship is
evident. Stepwise regression through the origin with the same regressor
variables as above showed that the linear relationship S-, = b5f. ,
r ik i- k
gave a better fit to the data than did any other simple or multiple
regression. The selection of the linear regression S., = bx..,
LK 1 * K
indicates that the intra-laboratory collaborator block standard
deviation is also proportional to the collaborator block mean.
B. 4 Transformation of the Collaborative Test Data
To answer the question of what is the appropriate data trans-
formation to achieve run equality of variance over both the Cambridge
and the Dayton collaborative test data, several likely such transformations
were selected and evaluated using Bartlett's test. These transformations
were the linear (no transformation of x), the logarithmic (loginx), and
the square root (x ). Table B3 contains the results of this transformation
run equality of variance analysis. Since Bartlett's test has the
TABLE B3. DATA TRANSFORMATIONS TO ACHIEVE
RUN EQUALITY OF VARIANCE
Transformation Bartlett's Test Statistic Significance
Linear y = x B = 128. 7 P {y.2(31)^ 128. ?} « . 0001
Logarithmic y = log]0(x) B= 47.7 P{X2(31)^ 47.?}= .029
Square root y = x^ B= 74.9 p{%2(31)» 74.9} < .0001
-------
FIGURE B3. INTRA-LABORATORY COLLABORATOR BLOCK PLOT
B-13
220 - -
200
180 :—• j-
160
Collaborator Eip.ck
Standard Deviatiai>,l<
.bftdga Pfcta
. i Dayton EJatsT
200 400
600
x. .
i-k
800 1000 1200 1400 1600
Collaborator Block Mean, 10"7, Ib/s . c . f.
-------
B-14
null hypothesis of variance equality, it is only for a small value of
the test statistic B that this hypothesis should not be rejected. Clearly
the linear and square root transformations are inferior to the logarithmic
transformation. However, even under the logarithmic transformation,
there is only a 2.9% chance that true equality of run variance would have
produced data with as much scatter in the run variances as that actually
obtained in the collaborative test data. Still, the logarithmic transformation
is '-.he best transformation available and it is far superior to no data
transformation at all.
It was on the above rationale that the logarithmic transformation
was used in substituting a value for the missing Lab 101 measurement
through port C in run 4 (sample 11) in the first block of the Cambridge
collaborative test data. All the data in this block were transformed using
the Logj~ transformation. Then the minimum variance unbiased estimate
of the missing Lab 101 measurement was obtained by adding Lab 101's
net difference from the other three runs' means to the run 4 mean.
This gave a value of 3. 1603 for this missing point in the logarithmic scale
which translates to 1446 x 10~ Ib/s.c.f. in the original linear scale.
It can be shown that acceptance of the data transformation
log x based upon (run) variance equality considerations is equivalent to
acceptance of the direct proportionality of the (run) standard deviation
to the (run) mean. The proof is as follows. Suppose X follows a lognormal
-------
B-15
distribution with mean nx and variance c"x • Then log X has a normal
^logx
^
and variance 0*, . Now the mean and
logx
distribution with mean
variance of X can be expressed in terms of the logarithmic transformed
mean i
and variance ^ logx:
= e
Substituting,
logx
= 1 +
Thus,
logx
= log
r
-------
B-16
This demonstrates that when there is equality of variance under the
logarithmic transformation, then the standard deviation is proportional
to the mean. Therefore, the selection of the logarithmic transformation
above based upon equality of the inter-laboratory run variances under
the logarithmic transformation is equivalent to a demonstration of the
proportionality of the inter-laboratory run standard deviation to the
run mean.
B- 5 The Underlying Relationship of the Standard Deviation Components
to the Mean
From Appendix B. 3 it was shown that the Cambridge and Dayton
collaborative test data exhibit a linear relationship of the intra-laboratory
collaborator block sample standard deviation to the sample mean:
Sik = b*- L.
IK i- k
where b is the sample coefficient of variation. Now, the four sample
measurements made by a collaborator within each block are the closest
possible approximation to replicates, given the randomly varying nature
°f NOx emissions in tne stack of a stationary emissions source. In fact,
these four collaborator block measurements duplicate the circumstances
encountered in making the three field measurements that constitute the
performance test for compliance. Hence, the expected value of the
collaborator block sample standard deviation is or, the within laboratory
standard deviation of replicate measurements. The sample standard
deviation is a biased estimate of the population standard deviation in an
-------
B-17
(4)
underlying normal distribution. For a sample size of n = 4
replicates, the correction factor is i
Define the within lab coefficient of variation as 0 = 1. 0854b. Then
the within lab standard deviation is given by
The inter-laboratory run sample standard deviation was shown
in both Appendix B. 3 and Appendix B. 4 to be proportional to the sample
mean, with a sample coefficient of variation, say C:
Now the variance in the four collaborators' measurements for a run has
both a within laboratory variance component
-------
B-18
Substituting from the intra-laboratory relationship above,
= (1.0854cp.)2 - (1.0854bp.)2
-------
B-19
Let us first consider the within lab standard deviation k
where the index ik is taken over the 32 collaborator block groups of
data at "Cambridge and Dayton. The actual individual values ^/_
/xi-k
are presented as the last column in Table B2. Their average multiplied
by 1.0854 yields
A
p = 1. 0854(. 06042) = .06558
A
Deriving the expected value of P:
K
A
E(p) = E
1.0854 ">~~ Sik
K
K
E(P) = •£
ik = l \ xi-k
- ^ E(S)
Now E I x ~~ fc • Within each block the measurements are
(*)
approximately normally destributed. Under the normal distribution, the
mean and variance are independent. Hence, the sample mean and sample
standard deviation should be nearly independent. Thus the expected value
of their ratio is approximated by the ratio of their expected values.
<:„ vtM 1 «£- E(l. 0854 Sik)
^3O f * I PI 55? ^^ ^2
Tf AHB^HV
ik= 1
K ^—. E(x)
K
— ^> from Appendix B. 5.
K ^•^"^•™ LL
ik=l K
E(p)
-------
B-20
since p = .06558, ff =p^ = . 06558ji. Thus for Method 7, the within
laboratory standard deviation is 6.558% of the mean value.
According to Mandel, the degrees of firmness in this within laboratory
estimate over g = 8 blocks is
= pg(n - 1) = 4-8(4 - 1) = 96
The percentage coefficient of variation of the within lab standard
deviation estimate is thus
%CV*_ = 100-/J = 7.2%
Next consider the standard deviation component 0~, due to
true laboratory-to-laboratory variation. In this case, the estimated
value of the between-laboratory coefficient of variation PL is
32
1.0854
where the run index j extends over the 32 collaborative test runs at
Q
Cambridge and Dayton. The actual i/ values are tabulated in the
/«.j
last column of Table Bl. The estimated value of pb is
Pb = 1.0854(. 08739) = .09485
The expected value of p. is derived below.
i V x .
J = 1 \ .j
E(1.0854Sj)
— under the rationale presented above.
-------
B-21
K /, 2
from Appendix B. 5.
Thus
? A
L = Pi
A 2 *2 A
^ " ^ substituting p> for
= JJL-(. 09485)2 - (.06558)2
= .06853|i
For Method 7, the true laboratory-to-laboratory standard deviation
component is 6. 853% of the mean value.
Mandel defines reproducibility in terms of the results of a
performance test for compliance. The reproducibility standard deviation
A
estimate Ls defined as yd" j_, + Q~ /m where m is the number of
replicate measurements comprising the test result. For the Method 7 test
result, m is usually 12. Thus the reproducibility standard deviation
for Method 7 is given by
+ (.0655811)^2 = .07111
Therefore the Method 7 test result reproducibility standard devi-
ation is 7.11% of the result. Mandel1 s reproducibility degrees of
A A 2 (.06853|i)2
firmness is given below, where \ = O~ L = ^cCQ t£ = 1-092 :
•j^r (•
-------
B-22
= r =r = 3. 284 for the randomized block
(ng - m)* | (1 +ngTr
pg(n - l)m2 P - l
design with p = 4 laboratories making n = 4 replicate measurements in
g = 8 blocks. The percentage coefficient of variation of the reproducibility
standard deviation estimate is
%CV = 100-/-L~ = 39.0%
B.7 The Nitrate Solution Data
The nitrate solution data of all four collaborative laboratories
analyzed in conjunction with both the Cambridge and the Dayton test
samples is presented in Table B.4. As instructed, the data are
reported in units of ng NC>2 per 10 ml of absorbance sample. The
instructions for analyzing these nitrate solutions and the data reporting
form are shown in Figure 8. The Table B4 data averaged over replicates
and daysare shown in Table B5. The Table B6 data are further averaged
over site samples. It is interesting to note in Table B5 that for
Solutions A, B, and C, the average values for samples analyzed along
with Cambridge test samples are consistently higher than the corresponding
average values obtained in the Dayton sample analysis. Another noteworthy
characteristic is the difference in laboratory means shown in Table B6
for the collaborative laboratories. For each of the three actual nitrate
-------
B-23
TABLE B4. REPORTED NITRATE SOLUTION CONCENTRATIONS, jig
per 10 ml
Collaborative
Laboratory
Lab 101
Lab 10Z
Lab 103
Lab 104
Day
With Cambridge Samples
Sol. A Sol.B Sol.C Sol.D
With Dayton Samples
Sol.A Sol.B Sol.C Sol.D
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
1
2
3
22
21
22
25
25
25
24
25
25
26
22
26
29
28
29
27
27
26
27
27
27
27
26
27
27
26
26
26
27
27
26
26
25
25
25
24
.31
.18
.21
.18
.50
.18
.84
.36
.36
.64
.03
.64
.40
.55
.40
.46
.46
.61
.9
.1
.1
.2
.8
.1
.1
.1
.8
.6
.0
.0
.0
.2
.9
.4
.7
.8
11.13
11.13
11.79
11.79
13.10
13.55
12.99
12.99
12.99
12.97
13.20
10.62
16.15
15.73
15.98
11.78
11.78
12.20
13.3
13.8
14.2
13.6
12.3
13.9
13.5
14.2
12.7
13.4
13.4
13.5
14.6
13.4
13.6
13.4
12.7
12.6
35.58
36.50
36.50
38.39
37.89
37.89
37.03
37.66
38.28
34.06
39.53
34.06
37.09
37.52
37.09
39.32
40.17
41.86
40.0
39.2
39.2
40.0
39.2
40.0
41.3
41.3
39.2
41.0
40.2
40.7
39.9
39.9
39.9
38.3
38.8
36.2
1.71
1.08
2.11
2.11
2.11
2.11
2.15
1.61
2.15
0.
0.
0.
2.48
2.74
3.33
0.
0.
0.
1.0
0.4
0.4
0.
0.
0.
0.
0.
0.
0.9
0.8
0.7
0.6
0.8
0.8
0.5
0.6
0.6
23.
22.
23.
23.
23.
23.
24.
24.
24.
23.
25.
24.
24.
26.
23.
20.
22.
21.
26.
28.
25.
23.
27.
27.
27.
26.
27.
24.
26.
26.
26.
24.
25.
25.
24.
25.
21
85
28
16
16
45
20
13
05
44
66
87
23
30
66
80
59
73
6
2
0
3
5
5
5
6
5
8
7
6
0
4
8
1
4
8
11.80
11.44
11.08
11.29
11.01
11.01
11.78
12.06
12.13
12.66
14.23
13.66
13.59
13.66
12.73
12.37
13.30
13.66
13.3
14.2
13.3
14.2
12.5
13.3
12.5
13.3
14.2
13.7
12.7
14.1
12.7
12.9
13.0
13.0
13.3
12.8
36
36
35
34
34
34
36
36
36
37
34
34
34
37
39
40
38
34
40
40
38
38
41
38
40
41
39
39
37
40
38
37
38
34
34
36
.19
.05
.98
.60
.95
.60
.40
.54
.33
.66
.30
.09
.16
.23
.66
.66
.30
.80
.9
.9
.4
.4
.6
.4
.0
.6
.2
.9
.0
.0
.6
.0
.3
.0
.7
.2
0.68
0.39
0.68
0.48
0.36
0.43
-0.21
-0.14
0.43
0.657
1.086
1.014
1.657
1.871
1.657
2.510
1.657
1.942
0.83
0.83
0.83
0.
0.
0.
0.83
0.
0.
1.0
0.6
0.5
0.4
0.4
0.4
0.6
0.6
0.8
-------
B-24
TABLE B5. DAY AVERAGED NITRATE SOLUTION CONCENTRATIONS,
Hg NO2 per 10 ml
Collaborative With Cambridge Samples With Dayton Samples
Laboratory Sol. A Sol.B Sol.C Sol.D Sol. A Sol.B Sol.C Sol.D
Lab 101 24.12 12.38 37.30 1.90 23.50 11.51 35.74 0.34
Lab 102 27.13 13.37 37.86 0.95 23.70 13.31 36.76 1.56
Lab 103 27.02 13.50 39.93 0.20 26.63 13.42 39.93 0.37
Lab 104 26.07 13.40 39.43 0.70 25.51 13.13 37.30 0.59
-------
B-25
TABLE B6. AVERAGE LABORATORY NITRATE SOLUTION
CONCENTRATION, ng NO2 per 10 ml
Collaborative
Laboratory Solution A Solution B Solution C Solution D
Lab 101
Lab 102
Lab 103
Lab 104
23.81
25.42
26.83
25.79
11.95
13.35
13.46
13.27
36.52
37.31
39.93
38.37
1.12
1.25
0.28
0.64
-------
B-26
solutions (A, B, and C), the Lab 103 average was highest, while the
Lab 101 average was lowest.
B. 8 The Variance Components of the Analytical Procedure
A separate analysis of variance was performed on the data
for each of the four nitrate solutions presented in Table B4. The
crossed factors were collaborator C and site S from which the
concurrently analyzed test samples came. The day factor D(CS)
was nested within C x S, and the replicate factor R(CSD) was nested
within days. The resulting analyses and components of variance
for a random effects model are presented in Table B7. The
F-ratios and significance tests for the factors are given in Table B8.
With all four solutions, Table B8 shows that the day factor D(CS)
is very significant (P £. 002),while the collaborator factor C, the
test sample source site S, and the collaborator-site interaction factor
CS are never significant (P^.05). Therefore, the only important
2
variance components are those for the day factor O" D an<^ t'le
replication (within lab) factor
-------
TABLE B7. NITRATE SOLUTION DATA
ANALYSES OF VARIANCE
B-Z7
Sum of
Factor Squares
Solution D Mean = 0 . 827
C 10.798
S .893
CS 11.923
D(CS) 21.137
R(CSD) 2.855
Solution B Mean = 13.006
C 27.218
S 1 . 840
CS 1.956
D(CS) 38.890
R(CSD) 18.153
Solution A Mean = 25.459
C 84.894
S 28.050
CS 28.798
D(CS) 73.498
R(CSD) 48.124
Solution C Mean 38.032
C 117.650
S 25.824
CS 11.049
D(CS) 96.325
R(CSD) 97.346
D.F.
3
1
3
16
48
3
1
3
16
48
3
1
3
16
48
3
1
3
16
48
Mean
Square
3.599
.893
3.974
1.321
.060
9.073
1.840
.652
2.431
.378
28.298
28.050
9.599
4.594
1.003
39.217
25.824
3.683
6.020
2.028
Expected Mean Square
i i * j
18r^+ 90~+ 3^+ o-^
360-N- 9
-------
B-28
TABLE B8. SIGNIFICANCE OF NITRATE
SOLUTION FACTORS
Solution Factor F- ratio Significance
c
s
cs
D(CS)
C
S
CS
D(CS)
C
S
CS
D(CS)
0.906
0.225
3.008
22.202
3.732
0.757
0.268
6.431
2.948
2.922
2.089
4.580
P>.50
P> .50
P= .07
P< .001
P«.15
P >.50
P>.50
P< .001
P«. 18
P«».19
P».15
P< .001
C 6.514 P= .08
S 4.290 P«s.l3
CS 0.612 P >.50
D(CS) 2.968 Pjs.002
-------
B-29
solution data. Now, in both the Method 7 performance test for com-
pliance and in the Method 7 collaborative test situations, the term
repeatability refers to the replicate measurement variation in samples
collected at specific 20 to 30 minute time intervals on a single day and
subsequently analyzed together in the laboratory on a later single day.
The single day for sample laboratory analysis becomes an important
consideration as a result of the preceding analyses of variance showing
that the fluctuation from day-to-day in each laboratories' analyses
was very significantly larger than the single day replicate analysis
fluctuation. Consequently, the appropriate comparable definition of
2
the within lab variance component
-------
B-30
rather than naively assume that collaborator variance component
2
C
from the preceding analyses of variance is synonymous with
L , one must instead take into account the major effect of the day
variance Q~ D and the occasional lesser effects of tf g and ^* cs in
estimating (J" L- Tne Dest approach is to duplicate the design situation
and the calculation method by which Q~ . was estimated from the
.
collaborative test data for estimating (J"* L for tne nitrate solution
data. Consequently, the between-laboratory mean squares were
computed as
MSL =
1
TB
18
S,d,r = l
1
~r
4
c = i XG£
_ 2
,dr " X. Sdr_
for each of the four solutions, at each of the 18 site, day, replicate
combinations. Since the expected value of MSL is E(MSr) = CT L + O" •
A
one can estimate 0" L for each solution, using the estimate of
^r^ _ * 2
<-f - \J R from its analysis of variance given in Table B7. The
A 2
values of MSL and cT j_, so obtained are presented in Table B9 along
with a summary of all the pertinent variance and standard deviation
components for the four nitrate solutions. Note that the nitrate solution
data indicate that the analytical laboratory standard deviation components
A A
and & are not proportional to the mean JJL, as the collaborative
~~~~
/\
test data have shown Method 7 to be. Still the analytical C7~T , and
Li
A
particularly Q~ , do appear to be linear functions of (j.. Linear
-------
TABLE B9. NITRATE SOLUTION VARIANCE AND
STANDARD DEVIATION COMPONENTS
B-31
|igNO2/10ml
MS
Sol.D
0.00
.7689
Sol.B
Sol. A
Sol.C
12.50 25.00 37.50
1.3022 3.8035 5.4684
Repeatability Variation
"
"
jig NO. /10ml
.0595
.2439
.3782 1.0026 2.0280
.6150 1.0013 1.4241
Lab-to-lab Variation
A , A ,
= MS - «-*
L L
, M-gNOL/10ml
.7094
.8423
.9240 2.8009 3.4404
.9612 1.6736
1.8548
-------
B-32
regression yields the following mean level dependent standard deviation
component equations for the analytical laboratory phase:
2/10 ml. Since an absorbance sample of 100 ml is specified in
Method 7, the standard deviation estimates at zero NO concentration
Ji
expressed in mass units are:
= (. 2439|ig N02/10 ml)(100 ml) = 2.439ng NO2
= (. 8423jig N02/10 ml)(100 ml) = 8. 423^g NO2
Xj
-------
B-33
The reproducibility standard deviation at zero NO 2 concentration is
V" A 2 A 2
CT L + CT /12= 8.452ng NO2- Assuming a sample
volume of 2000 ml is collected at standard conditions, the upper 95%
confidence limit for a true concentration u._ = 0 is
\j
c . uo x io-
sc
c f
C = 5. 14 x 10'7 Ib/s.c.f.
Therefore, the minimum detectable limit of Method 7 is 5. 14 x 10"7 Ib/s.c.f.
If a laboratory obtains at a performance test result of 5. 14 x 10~ lb/s. c. f.
using Method 7, there is only a 5% chance that the true nitrogen oxide
emission was zero.
-------
B-34
References
1. Youden, W. J., "The CoUaborative Test", Journal of the AOAC,
Vol. 46, No. 1, 1963, pp. 55-62.
2. Brownlee, K.A., Statistical Theory and Methodology in Science
and Engineering, 2nd. Ed., Wiley, New York, 1965, pp 290-295.
3. Lindgren, B. W., Statistical Theory, MacMillan, New York, 1962,
p. 89.
4. Lindgren, B.W., op. cit. p. 316.
5. Zeigler, R.K., "Estimators of Coefficient of Variation Using
k Samples", Technometrics. Vol 15, No. 2, May, 1973, pp 409-414
6. Mandel, John, "Repeatability and Peproducibility", Materials
Research and Standards, ASTM Vol. 11, No. 8, August 1971, p. 12.
-------
C-l
APPENDIX C. WALDEN THEORETICAL NOX
CONCENTRATION CALCULATION
The theoretical concentration of NOX in the duct at the sample test
section for the Cambridge test is given by
where
[C] = concentration of NOX in the duct in Ib/scf
q = NO flow from the gas doping system (acfm)
QT = theoretical volumetric flow in the duct (acfm)
K = 60 X lO"? Ib/scf NOX due to combustion processes
The calculation of the flow due to the stoichiometric combustion of
the No. 2 fuel oil is shown below.
/O. 871 moles of fuel\ „ [52. 23 moles of combustion products generatedV
QS =\ min / \ 1 mole of fuel /'
( — —j— JX( I = 36. 0 acfm from combustion only
Calculation of the 52. 23 moles of combustion products generated per mole
of fuel is given in Tables Cl and C2.
Qs is then corrected for the excess air present in the duct as follows:
__ QsUOO - %O2 -
QT " (100 - %02 - %C02) - (3.76)(%0z)
where
QT = theoretical flow (acfm)
Qs = flow from stoichiometric combustion (acfm)
%O2 = Fyrite reading
%CO2 = Fyrite reading
-------
C-2
The values for %C>2 an<* %CO2 over the course of the Cambridge test are
shown in Table C3. The averaged Qj result over a block of runs was used
in computing the theoretical concentration.
The theoretical flows and calculated NOX concentrations for each block
of runs is shown in Table C4. A value of K = 60 X 10~7 Ib/scf was used
throughout as the background NOX present due to the furnace combustion. A
propagation of error analysis gave an error range of ±11% in the theoretical
NOX concentrations calculated by this procedure.
TABLE Cl
OXYGEN CONSUMPTION FOR OIL COMBUSTION
Element Wt. %t Moles* Moles* QZ Needed
C 87.7 87.7/12 7.31
H 12.0 12.0/1 12.0/4 = 3.00
S 0.33 0.33/32 0.01
TOTAL 10.32
* pound s moles/ 100 Ib fuel.
ttypical residual oil analysis.
-------
C-3
TABLE C2
COMPONENT OF FLOW DUE TO STOICHIOMETRIC COMBUSTION
Species Moles*
C02
H20
S02
O2 (No excess air)
N2f
7.31
2.00 X3.00 = 6.00
0.01
0
10.32 X3.77| = 38.91
TOTAL 52.23
*pound moles/100 Ib fuel.
t(nitrogen + argon)/oxygen ratio for dry air.
TABLE C3
WALDEN PILOT PLANT FIRING CONDITIONS
Duct
Date
12/11/72
12/12/72
Time % O2 %CO2
Temp. (CF)
High Low
12/13/72
12/14/72
12:20
12:30
1:40
11:30
11:45
11:50
12:20
1:00
12:30
12:55
1:00
1:05
1:20
1:30
1:45
8.5
8.5
8.5
11:30
11:55
12:15
1:50
2:10
2:30
3:15
9.5
9.5
9.0
9.5
9.5
9.5
9.0
9.0
8.5
9.0
9.0
9.0
9.0
9.0
9.0
8.5
9.5
9.0
8.5
9.0
8.5
8.5
9.5
9.0
9.5
9.0
9.0
9.0
9.0
8.5
9.0
9.0
9.0
9.0
8.5
9.0
9.0
9.0
9.0
8.0
480
480
475
480
480
480
480
480
480
475
475
475
475
475
475
480
480
480
470
470
470
470
275
275
290
275
285
285
285
285
285
290
275
280
285
285
285
230
240
250
260
265
275
NO Doping Flow
(I /min)
2.25 *pm
2.25
2.25
2.1
2.1
2. 1
2. 1
1.75
1.75
1.75
1.11
1.11
1.11
1. 11
1.11
0.52
0.52
0.52
0.52
0.52
0.52
0.52
-------
C-4
TABLE C4
THEORETICAL CALCULATED NOX CONCENTRATION RESULTS
Calculated*
Theoretical NO Doping Level of NOX
Date Flow (acfm) Flow (acfm) 1Q-7 Ib/scf
12/11/72
12/12/72 a.m.
12/12/72 p.m.
12/13/72
12/14/72
58.70
63.53
63.16
60.74
60.90
0.0795
0.0742
0.0618
0.0392
0.0184
1660
1440
1216
822
417
*This value includes 60 X 10"? Ib/scf due to furnace combustion.
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
i REPORT NO
EPA-650/4-74-025
3 RECIPIENT'S ACCESSIOf*NO
4 TITLE AND SUBTITLE
5 REPORT DATE
"Collaborative Study of Method for the Determination of
Nitrogen Oxide Emissions from Stationary Sources
(Fossil Fuel-Fired Steam Generators)."
October 5. 1973
. PERFORMING ORGANIZATION CODE
7 AUTHOR(S)
8 PERFORMING ORGANIZATION REPORT NO
Henry F. Hamil and D. E. Camann
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
13 TYPE OF REPORT AND PERIOD COVERED
Environmental Protection Agency, QAEML
Methods Standardization & Performance Evaluation Branch
Research Triangle Park, N. C. 27711
14 SPONSORING AGENCY CODE
15 SUPPLEMENTARY NOTES
16 ABSTRACT
A collaborative study was performed on Method 7 proposed by the EPA for determin-
ing the nitrogen oxide emissions from stationary sources. Method 7 specifies the
collection of a grab sample in an evacuated flash containing a dilute sulfuric acid-
hydrogen peroxide absorbing solution, and the colorimetric measurement of the nitrogen
oxides, except nitrous oxide, using the phenoldisulfonic acid procedure. Collabora-
tive tests were conducted at both a coal-fired steam generating power plant and an
oil-fired pilot plant by four collaborative teams. Statistical analysis of the
collaborative test and associated data disclosed the following findings regarding the
reliability of a Method 7 performance test result: Precision -- The estimated repeata-
bility standard deviation of a test result is 1.893% of the test result value. The
estimated reproducibility standard deviation of a test result is 7.110% of its value.
Accuracy — Because of chemically significant distortions inherent in the gas cylinder
accuracy test, the accuracy of Method 7 could not be adequately demonstrated. Minimum
Detectable Limit — The estimated minimum detectable limit of Method 7 is 5.14 x 10
Ib./s.c.f.Sources of Reproducibility Variation -- Nearly all (93%) of the reproduci-
bility variation in a test result is ascribable to laboratory bias, with the other 7%
due to repeatability variation. Most of the apparent laboratory bias variation actu-
ally is not a true laboratory effect but rather a day effect primarily caused by
dubious daily soectrophotometer re-calibration orocedures. Restriction of the
spectrophotometer absorbance calibration range to its more accurate upper region can
halve the analytical procedure's percentage error contribution to the reproducibility
variation.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b IDENTIFIERS/OPEN ENDED TERMS
c COSATI Ficld/Grou
19 SECURITY CLASS (ThisReport)
Unclassified
21 NO. OF PAGES
101
Un1i mi ted
20 SECURITY CLASS (Thispage)
Unclassified
22 PRICE
EPA Form 2220-1 (9-73)
C-5
------- |