VHX-IFA7.3-FR79-1
OAQPS-78-LVI-B-13
NOVEMBER 1979
TECHNICAL EEPORT
Preoared for
Office of Air Quality Planning and Standards
Emission Standards and Engineering Division
Environmental Protection Agency
VECTOR RESEARCH, INCORPORATED
Ann Arbor, Michigan
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VRI-EPA7.3-FR79-1 OAQPS-78-LVI-B-13
ANALYSIS OF FGD
SYSTEM EFFICIENCY BASED ON
EXISTING UTILITY BOILER DATA
R. FARRELL
T. DOYLE
N. ST.CLAIRE
NOVEMBER 1979
TECHNICAL REPORT
Preoared for
Office of Air Quality Planning and Standards
Emission Standards and Engineering Division
Environmental Protection Agency
VECTOR RESEARCH, INCORPORATED
Ann Arbor, Michigan
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CONTENTS
Page
1.0 INTRODUCTION AND SUMMARY 1-1
2.0 PREDICTED BEHAVIOR OF THIRTY-DAY AVERAGES OF EFFICIENCY ... 2-1
2.1 Scope Of Analysis 2-5
2.2 Analysis Results 2-7
2.3 Methodology 2-37
3.0 DESCRIPTIVE STATISTICS ON FGD SYSTEM EFFICIENCY DATA .... 3-1
3.1 Data Set 3-1
3.2 Lognormal Transformation 3-2
3.2.1 The Untransformed Variable 3-2
3.2.2 The Transformed Variable 3-5
3.3 Estimated Parameters and Comparability Among Units . . 3-7
3.3.1 Means and Standard Deviations 3-7
3.3.2 Autocorrelation 3-11
3.3.3 Autoregressive Model 3-13
3.4 Possible Confounding Factors 3-13
4.0 COMPARISON WITH ENTROPY RESULTS 4-1
4.1 Predicted Exceedences 4-1
4.2 Process Structure 4-2
4.3 Differences Among Sites 4-4
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1-1
1.0 INTRODUCTION AND SUMMARY
The Environmental Protection Agency (EPA) promulgated new standards
of performance for electric utility steam generating units, on
June 11, 1979. In addition to restricting the levels of pollutants that
these units emit into the atmosphere, the standards require a 90 percent
reduction in potential S02 emissions if they exceed 0.60 1 fa/mill ion
BTUs of heat input. On August 10, 1979, a petition for reconsideration
of these standards was submitted to EPA by the Utility Air Regulatory
Group (UARG).l Part of this petition requested that EPA reconsider the
90 percent removal requirement. This request was based on analyses per-
formed by Entropy Environmentalists, Incorporated, which were documented
in Appendix B of the UARG Petition entitled "A Statistical Evaluation of
the EPA FGO System Data Base Included in the Subpart DA NSPS Docket".
The analysis included a numerical simulation of l,000_y_ears of flue gas
desulfurization (rGD) efficiency to examine the impact of the 90 percent
efficiency standard promulgated by EPA.
Vector Research, Incorporated, (VRI) is under contract to EPA to
provide statistical and analytical support to the Agency on an as needed
basis. On November 1, 1979, VRI was tasked to simulate or otherwise
analytically describe FGD system efficiency to permit examination of the
questions raised by the Entropy findings. The primary purpose of the
task was to determine the levels of system efficiency and variability in
^Petition for Reconsideration, Docket Number OAQPS-78-1.
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1-2
this efficiency that would be necessary to maintain at most one exceed-
ence oer year for a thirty-day rolling average on a 90 percent efficiency
standard. The VRI simulation was to be based on analysis of data pro-
vided by EPA describing the efficiency of 11 flue gas desulfurization
units and to additionally describe results over a wide range of facility
narameters. The data analysis and simulation results were to be suoolied
to EPA within two weeks of initiation of the task. The authors were
supported in this effort by Dr. Richard Cornell, a YRI associate, and
other VRI staff.
This reoort presents the results of VRI's analysis activities and is
organized into four chapters. This introductory chapter provides a
description of the task and a summary of major results. The second chap-
ter describes the results obtained concerning the behavior of various
thirty-day averages for parametrically described FGD systems. The range
of parameters used in generating these results was based in part on the
statistical analysis of the data. This analysis is discussed in chanter
three. The final chapter then discusses comparisons between VRI's
results and those reported by Entropy Environmentalists, Incoroorated.
The major conclusions of this analysis were as follows:
(1) The use of thirty-day moving averages of efficiency results in
low-variability efficiency measurements at a facility, even
when the daily data shows much larger variability. This
results in averages which cluster much more closely around the
central value of the efficiency measurements than do the daily
efficiencies.
[2) Existing facilities show significant correlations in the
efficiencies of sulfur removal on successive days. These
autocorrelations, as well as the median levels of efficiency
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1-3
and the fundamental variability of the process, influence the
closeness with which thirty-day averages will remain clustered
about their mean.
(3) The minimum long run average efficiency levels (described here
in terms of the geometric mean) at which a facility must be
operated in order that the ratio at which thirty-day rolling
averages occur below 90, 89, 88, 87, 86, or 85 percent be held
to one oer year are shown in exhibit 1-1 for facilities with
autocorrelations of 0.7 and various fundamental variability
levels, some of which clearly represent good engineering and
operating practice and some of which may not. Exhibit 1-2
shows similar data but for a failure rate of one failure per
ten years. As the exhibits show, the rate of occurence of
30-day rolling averages below 90 percent would be above one oer
year for facilities wiht a 92 percent geometric mean efficiency
and daily variaility anywhere from 0.20 to 0.60. These
facilities would, however, have rates below one per year if the
threshold were 89 percent and the daily variability were no
greater than 0.26, or if the threshold were 88 percent and the
daily variability was no greater than 0.32, or if the threshold
were 87 percent and the daily variability was no greater than
0.38, or if the threshold were 86 percent and the daily
variability was no greater than 0.43, or if the threshold were
85 percent and the daily variability was no greater than 0.48.
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EXHIBIT 1-1: MINIMUM GEOMETRIC MEAN EFFICIENCIES REQUIRED
TO MAINTAIN NO MORE THAN ONE FAILURE PER YEAR
Daily
Std. Dev
(in log)
.20
.21
.22
.23 -
.24
.25
.26
.27
.28
.22
.30
. 31
'.32
. 33
.34
.35
.36
.37
.38
.39
.40
.41
.42
.43
.44
45
.46
.47
.48
.49
.50
.51
.52
.53
.54
. 55
. 56
. 3 /
.58
.59
. 50
Std. Oev.
of 30-Day
Average1
(.0068)
(.0071)
(.0075)
(.0079)
(.0082)
(.0086)
(.0090)
(.0093)
(.0097)
(.0101)
(.0105)
(.0109)
(.0112)
(.0116)
(.0120)
(.0124)
(.0128)
(.0133)
(.0137)
(.0141)
(.0145)
(.0150)
(.0154)
(.0153)
(.0153)
(.0157)
(.0172)
(.0177)
(.0182)
(.0186)
(.0191)
(.0196)
(.0201)
(.0206)
(.0212)
(.0217)
(.0222)
(.0228)
(.02331
(.0239)
f. 02451
<90%
92.2
92.3
92.3
92.4
92.5
92.6
92.7
92.3
92.9
93.0
93.1
93.2
93.3
93.4
93.5
93.5
93.7
93.3
93.8
93.9
94.0
94.1
94.2
94.3
94.4
94.4
94.5
94.6
94.7
94.3
94.9
94.9
95.0
95.1
95.2
95.2
95.3
95.4
95.5
95.5
95.5
Minimum Efficiency
For Threshold Shown
j'QQ0/ ^QQ°^ s~ O 70/ ^QCS/
Ow.'c ^OO/o ^G//c ^OD/c
91.4 90.6 89.8 89.0
91.5 90.7 39.9 89.2
91.6 90.8 90.1 39.3
91.7 90.9 90.2 89.4
91.8 91.1 90.3 39.6
91.9 91.2 90.4 39.7
92.0
92.1
92.2
92.3
92.4
92.5
92.6
92.7
92.3
92.9
93.0
93.1
93.2
93.3
93.4
93.5
93.6
93.7
93.3
93.9
94.0
94.1
94.2
94.2
94.3
94.4
94.5
94.6
94.7
94.8
94.9
94.9
95.0
95.1
QK.2
91.3
91.4
91.5
91.6
91.7
91.9
92.0
92.1
92.2
92.3
92.4.
92.5
92.6
92.7
92-8
92.9
93.0
93.1
93.2
93.3
93.4
93.5
93.5
93.7
93.3
93.9
94.0
94.1
94.2
94.3
94. -1
94. 5
94.5
94.7
94.7
90.6
90.7
90.8
90.9
91.1
91.2
91.3
91.4
91.5
91.6
91.8
91. 9
92.0
92.1
92.2
92.3
92.4
92.5
92.7
92.8
92 9
93.0
93.1
93.2
93.3
93.4
93.5
93.6
93.7
93.8
93.9
94.0
94.1
94.2
94.3
89.3
90.0
90.1
90.2
90.4
90.5
90.5
90.8
90.9
91.0
91.1
91.3
91.4
91.5
91.6
91.7
91 9
92.0
92.1
92.2
92.3
92.5
92.6
92.7
92.3
92.9
93.0
93.1
93.2
93.3
93.4
93.5
93.7
93.3
o? g
<85%
88.2
88.4
38.5
88.7
88.3
89.0
39.1
39.3
89.4
39.5
89.7
39.3
90.0
90.1
90.2
90.4
90.5
90.6
90.8
90.9
91.0
91.2
91.3
91.4
91 5
91. 7
91.3
91.9
92.0
92.2
92.3
92.4
92.5
92.5
92.7
92.9
93.0
93.1
93.2
93.3
0*5 d
Facility autocorrelation =
:In computing the 30-day average variability, a geometric mean
emission level cf 92* was assumed.
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1-5
EXHIBIT 1-2:
MINIMUM GEOMETRIC MEAN EFFICIENCIES REQUIRED TO
MAINTAIN NO MORE THAN ONE FAILURE PER TEN YEARS
Minimum Efficiency
For Threshold Shown
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1-5
The rates would be below one occurence per ten years for
combinations of thresholds and daily variabilities as follows:
Threshold Oaily Variability
89" no greater than 0.21
88% no greater than 0.27
87* no greater than 0.32
86% no greater than 0.37
85% no greater than 0.41
Data for auto correlations other than 0.7 can be found in the
body of the report.
(4) There is very little change in these estimates of minimum effi-
ciencies when the assumptions concerning the type of statisti-
cal distribution used to represent the efficiency data are
varied. Both normal and lognormal distributions provide rea-
sonable fits to the existing daily efficiency data, with the
lognormal probably slightly better than the normal. (Because
the lognormal distribution appears to fit the data better than
the normal, it has been used in generating exhibits 1-1 and
1-2, and in general throughout the analyses.) Both distribu-
tional assumptions produce very similar results in terms of the
predicted behavior of thirty-day averages taken on a rolling
basis.
These conclusions, as well as many other observations, are discussed in
more detail in the body of this report.
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2-1
2.0 PREDICTED BEHAVIOR OF THIRTY DAY AVERAGES OF EFFICIENCY
This chapter describes the main results of this analysis. The
princioal question of interest is the behavior of thirty-day moving
averages of efficiency, and specifically the rate at which such averages
would din below selected thresholds. The behavior of the moving or
rolling average was examined for various true (average) efficiencies,
variabilities, and time dependencies.
In a setting where penalties could be imposed when such averages
fell below a regulatory threshold, EPA would expect to set the threshold
level so that facilities designed, constructed, and operated in
accordance with good engineering practice would produce very infrequent
threshold crossings, while facilities not in accord with good engineering
practice would show averages below the threshold on a more frequent
basis. That is, the threshold should correspond to some value
approximately at the minimum expected to be seen regularly from
well-engineered and operated facilities. This analysis is not designed
to analyze what levels of performance correspond to good engineering
practice, but to show the relation between the operating characteristics
of a facility and the rates at which various threshold values of
thirty-day averages would be crossed. This information can then be
combined by EPA with expert knowledge of the achievable levels of
engineering and operating performance in designing regulatory policies.
Although the precise method of computing the thirty-day average
might vary somewhat, this analysis has assumed that a daily average
efficiency is generated each day from more frequent measurements of
emissions, and that these daily averages are then averaged for a period
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2-2
of thirty days. Such thirty-day averages might be computed each day,
each week, each month, or at any other frequency, based on the thirty-day
period ending with the computation day. The behavior of averages at
various computation frequencies will be discussed. We believe that this
general scheme contains most policies of interest. In the case of
oossible chanqes in the precise methods of computing averages from hourly
or more frequent data, the analysis encompasses policies with essentially
the same effects as those which might be adopted. All the analyses have
assumed that data would be available for each day of operations.
In order to predict the behavior of the averages involved, assumo-
tions must be made about several basic properties of the measurements of
scrubbing efficiency at a facility. These assumptions concern the long-
run level of scrubbing efficiency achieved, the type and amount of daily
variability which will be observed, and any temporal patterns or correla-
tions which might be expected in the observed efficiency.
Before presenting any numerical analyses of the issues, it is neces-
sary to define the various types of measurements which were used in
describing and analyzing the process. The level of scrubbing efficiency
achieved will be discussed in terms of several different related quanti-
ties. For some purposes, it is necessary to consider the measured daily
efficiency: this quantity is produced by reducing more frequent measure-
ments of inlet and outlet sulfur concentrations to a daily efficiency
figure. These measurements may also be considreed in terns of the equiv-
alent measurements of emissivity, which is 1-efficiency, so that an
efficiency of 90 percent corresponds to an emissivity of 10 percent.
Daily efficiency or emissivity measurements (which were the basic
data used in the detailed data analyses of actual facilities, as
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2-3
described in chapter 3.0, and which also form a basis in terms of which
all these analyses were conducted) are observed to vary when measured
repeatedly at a single facility. This variation is stochastic or
probabilistic, rather than deterministic, in nature. That is, the exact
measurement which will be obtained at some future time is not completely
determined from our knowledge of the process, but includes elements of
randomness.
Describing the randomness in the daily measurements involves
describing the distribution of the daily measurements (that is, the
frequencies with which the measurement takes on various values) and the
interrelations among the daily measurements for different days. The
distribution of the daily measurements is tyoically described in terms of
a measure of the center of the measurements observed (such as the
mean, the geometric mean, or the median) a measure of the variability of
the measurements about this center (such as the standard deviation or
geometric standard deviation), and the particular shape or type of
distribution which descirbes the variability (such as the normal or
lognormal distribution). The interrelationships between measurements on
various days are typically measured in terms of the correlation between
measurements on successive days.
The mean (sometimes called the arithmetic mean) of the measurements
is simply the long-run average of the measurements. The geometric mean
is the value which would be obtained by taking the antilogarithm of the
mean of the logarithms of the measurements. The geometric mean of
measurements is always less than the arithmetic mean, no matter how the
measurements are distributed. The median of measurements is the value
such that 50 oercent of the measurements are above it and 50 percent
-------
2-4
below. The standard deviation cf measurements is the root-mean-square
average of the deviations of the measurements about their own mean. The
geometric standard deviation is the root-mean-square average of the
deviations of the logarithms cf the measurements about the mean of the
logarithms. The correlation (or autocorrelation), of a sequence of
measurements varies between -1 and +1. a correlation of +1 indicates
perfect correlation that is, in our case, successive measurements at a
single facility would be identical. A correlation of 0 indicates no
dependence between successive measurements. Correlations below 0
indicate that high measurements are followed by low and low by high.
All of these terms may be applied to any sequence of measurements.
In the specific problem at hand, they may be anplied to daily efficiency
measurements, daily emissivity measurements, or thirty-day averages of
either. Generally, daily efficiencies are discussed in this analysis in
terms of the geometric mean emissivity (or the equivalent efficiency) and
the geometric standard deviation of emissivity. This geometric standard
deviation may be thought of as a percentage variability in the measure-
ments so that a geometric standard deviation of 0.20 would indicate a
daily variation of about 20 percent of the daily mean. These scales of
measurement were chosen because they were those which had been used in
past studies of the same general topics. The thirty-day averages are
typically discussed in terms of the frequencies with which particular
levels of emissivity would be exceeded by the thirty-day averages or in
terns of their mean and standard deviation (arithmetic, not geometric).
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2-5
2.1 SCOPE OF ANALYSES
In the specific problem at hand, the evidence supoorts the use of a
model in which observed dependencies in sequences of efficiency measure-
ments are viewed as produced by correlations between immediately succes-
sive days. The evidence on this point is discussed in the next chapter.
In such a model (an autoregressive model of laq one) the only correlation
parameter required to describe the pattern is the basic correlation
between the observations on successive days. All other dependencies are
then computable from this correlation coefficient. In terms of these
oarameters, the region of the narameter space examined in this analysis
was:
(1) Long-run geometric mean emissivities of six percent to nine
percent, with particular attention to the value of eight
percent, corresponding to a 92 percent efficiency.^
(2) Daily geometric standard deviations of 0.20 to 0.50 and
distributions of measurements described by a probability
distribution of emissivities similar to the lognormal or normal
distribution, probably having more similarity to the lognormal
(see chapter 3.0). It must be remembered that these daily
variabilities in emissivity lead to much smaller variabilities
in the thirty-day-efficiency. For example, a typical facility
with daily emissivities of the order of nine percent with a
1 Although the 92 percent figure is not the geometric mean efficiency
but the efficiency corresponding to the geometric mean of emissivity,
we will, when approoriate, refer to such values as geometric means
without intending to mislead.
-------
2-6
50 percent variability would have daily efficiencies of 91
percent, with a daily error of 4.5 percent, and thirty-day
average efficiencies of about 91 Dercent with a variability of
only about one Dercent.
(3) Day-to-day correlations between successive observations of 0.0
to 0.7.
The results of this analysis address three topics:
(1) The average number of times per year that thirty-day-average
efficiencies, computed daily (350 times per "year"), would be
below various thresholds as a function of the facility ooerat-
ing parameters assumed.
(2) The minimum long-run level of efficiency which a facility would
have to maintain to limit its average threshold crossings on
the same rolling average to one per year, one per two years,
one per five years, or one per ten years as a function of the
level of variability and correlation of daily observations at
the facility. These efficiencies are presented in terms of
geometric means, keening the method of description for all
daily data consistent. At these levels, the long-run rate of
excessive emissivity measured in terms of thirty-day rolling
averages, would be held to the one per year or other rate as
qiven. The actual number of excesses in a specific year would,
of course, vary, so that at a rate of one per year, some years
would have two, for examole, and others zero.
(3) The potential effects of changing the frequency of computation
of the averages on the rate at 'which threshold crossing would
occur.
-------
2-7
Following the presentation of these results, a very brief section
discusses the methods of commutation used to generate the estimates.
2.2 ANALYSIS RESULTS
The most basic and fundamental results of this analysis simoly
describe the mean, standard deviation, and distribution of the tnirty-day
averages as functions of the elementary process parameters describing the
level of efficiency, the variability of the daily observations, and the
autocorrelation. Exhibit 2-1 shows the means and standard deviations of
the thirty-day rolling averages for a sampling of parameter values in the
region examined. Several observations can be made from that data. The
most basic is simply that the mean efficiency is different than the
efficiency level described by the geometric mean emissivity. This
difference simply reflects the differences in meaning between the mean
and the geometric mean. The difference would remain even if the data had
beem normally distributed: the geometric mean of a normally-distributed
datum is not identical to its mean, and the relation between the two
values in the parameter region of interest is almost precisely the
relation between the same parameters in the lognormal distribution.
A second observation is that the variabilities of the thirty-day
averages are much lower than the variabilities of the daily data. This
reduction in variability is the basic reason why taking averages of
sequences of observations is useful in obtaining consistent estimates of
actual performance levels. The third observation which can be made from
the exhibit is that both the mean and the standard deviation of the
thirty-day averages are clearly influenced by the variability and
autocorrelation in tne efficiency process, as well as by the level of
efficiency.
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2-8
EXHIBIT 2-1: MEAN AND STANDARD DEVIATION OF 30-DAY AVERAGES
Process Parameters
Geom. Mean Geon. Std. Dev.
Autocor.
Thirty-Day Average
Mean Std. Dev.
.51 CO
.9100
.5100
.3130
CT 1ft
31 'n
, .u^
.31 CO
.31 CO
. 3100
.91 CO
.31 CO
.3130
. 91 CO
.9100
. 91 CO
C' ~n
.9200
.92CO
.5200
. 92 CO
.92CO
.3200
.9200
. 9200
.52CC
.32CO
.32 CO
.9200
.9200
."200
.9200
.92 CO
.92 TO
27n/"i
* w WW
**?^n
^-> u'u
-92CC
.9300
.9200
.92CC
. 92 CO
.3200
.5200
.92CO
~7^H
?Juv
-^ **«
.5200
.9300
. 3400
. 5-00
. 3-00
.5400
.54CC
.2COO
. :coo
"innr
. f-U-_,
.2COQ
.200C
.2C03
.2000
.4000
! 1COO
.5CCO
.3000
.5000
.5COO
.2000
.2CCC
.2300
.2000
. 2000
. 2000
.3000
.4COC
.4CCO
.4000
..5000
:CCO
iicco
.2000
.2000
.2CCO
.2000
.2000
.20CO
.
.1000
.4000
.5CQO
.3000
. 5CCO
.5000
.2000
.20GO
.2COO
.2300
.3COC
3.COCO
.3COO
.5CCO
.7CCC
3. OOCC
.3COO
.5000
.7000
3.0000
.3000
.3CCO
70CO
n i^nn
U. b'VUU
.3000
-5CQG
.7CCO
3.3000
.3000
.3000
.7000
3.0000
.3000
r,nnn
. -vjuJ
.7000
.7030
O.OCOO
.3CCC
.5CGG
.7CCO
0.0000
.2000
.5000
-5CCO
.7000
0 OCOO
.2030
5COC
.7000
0.3000
. 3COO
.7300
.3030
.2300
.5000
7COC
.0000
.2000
. 30S2
5C32
. 3032
.3082
. 9059
.=05?
.3059
.3059
.5025
.3025
. 5025
.3025
. 3980
.3980
.3980
.3930
.5124
. 3134
.913*
.9134
.3152
.5152
.5122
.
.3093
.3093
.3093
.9053
.3235
.3235
.32S6
. 32S6
3253
.3253
.3253
.9253
'9242
3242
3242
.3207
.3237
.9207
.3333
.32£3
.3372
. 3272
.0075
.CC53
^ n * *\
. JU/ W
.:oaa
. 1
.3099
.3162
.3215
.3031
.C05S
.3047
.3063
.3C73
.01C5
.3066
.31-5
. CC25
.3035
on *i
.1
.3C5£
.3033
.3051
.3325
.0047
:-4co
. -4C
.54CO
. 3*00
.4CCC
" ^r
-------
2-9
Additional analyses not easily presented in tabular form addressed
the shape of the distribution of the thirty-day rolling averages.
Questions had been raised about whether these averages would be distrib-
uted normally. The distribution was found to be very nearly, although
not exactly, normal. Although the averages were much more nearly normal
than the approximately lognormal daily measurements, all of the analyses
took account of the remaining non-normality; no results were based on
normal approximations.
The data in exhibit 2-1 was presented in terms of facility operating
parameters which were simply chosen to sample the region of greatest
interest. The actual values of the basic process parameters are avail-
able for some experiments at specific facilities. Exhibit 2-2 shows the
parameters describing the processes at these facilities. The actual
statistical analysis of the data to produce these estimates of the
parameters is described in chapter 3.0. Exhibit 2-3 shows the means and
standard deviations of thirty-day average efficiency observations which
would be expected if a new facility with a 92 percent geometric mean
efficiency had the same operating conditions (process variability and
autocorrelation) as with each of the individual existing facilities.
As can be seen in these exhibits, there is considerable variation
among the results at the individual sites. There cannot be a strictly
statistical decision as the degree to which any particular site repre-
sents good engineering and operating practices, state-of-the-art systems,
well-calibrated and maintained measuring equipment, and otherwise is
appropriate for use in extrapolations to future facilities. Any analyses
of these issues must be made by engineers rather than statisticians.
Accordingly, the remaining analyses of the behavior of the thirty-day
-------
2-10
EXHIBIT 2-2: PROCESS PARAMETERS OF ACTUAL FACILITIES
Unit
Louisville NorthV
Louisville South/
Pittsburgh I
Pittsburgh II
Philadelphia
jThica^go_tO ~ ^
Shawnee TCA \TV-^-
Shawnee Venturi ^
Conesville B
Lawrente
A
'*/
Geometri c
Mean
^ 84.4
<£~~ 83.3
80.8
85.4
97.0
89.2
88.5
^"' 96.0
l%|^ 86.0
IL'CJ^ 92.5
95.4
Geometri c
Standard
Deviation
.295x
.343 ;~7
.234
.212
.359
.118
.182
.368
.447
.474
.835
Auto-
Correlation
.6955
^ .6949
.4683
-.1428
.2524
.6983
.5995
.8897
.7131
.6255
.6386
-------
z-n
EXHIBIT 2-3: THIRTY-DAY AVERAGE MEAN. AND STANDARD
DEVIATION FOR 92%-EFFICIENT FACILITIES WITH
VARIABILITY AND AUTOCORRELATION OF ACTUAL
FACILITIES
Standard
Variability and Mean Deviation
Autocorrelation
from: Louisville North 91.64% 1.03%
Louisville South 91.52% 1.22%
Pittsburgh I 91.78% 0.57%
Pittsburgh II 91.82% 0.32%
Philadelphia 91.47% 0.73%
Chicago 91.94% 0.39%
Shawnee TCA 91.87% 0.52%
Shawnee Venturi 91.44% 2.05%
Conesville A 91.16% 1.66%
Conesville B 91.05% 1.48%
Lawrence 88.70% 3.70%
-------
2-12
average processes will continue to be presented, as was the initial
material in exhibit 2-1, in general parametric terms. The appropriate
cases from these parametric results may then be selected by engineers to
be used in any further analyses.
In using the parametric results, it may be approoriate to examine
the expected behavior of processes with one or more parameters equal to
those of specific existing facilities (as was done in generating exhibit
2-3), or to consider the fact that the measurements from existing
facilities are from finite, and generally fairly limited, data samples,
and to consider the possible errors in estimation which may be present.
When this second technique is used, it may be of interest to know that
the Shawnee TCA and Pittsburgh II (taken together, assuming that their
true long-run levels of variability are identical as the data suggests)
have a 95 percent confidence interval on the long-run geometric standard
deviation running from 0.16 to 0.23, and that lousiville North and South
taken together have a 95 percent confidence interval from 0.29 to 0.36.
(The corresponding 99 oercent intervals are from 0.15 to 0.25 for Shawnee
TCA and Pittsburgh II and 0.28 to 0.38 for the Louisville facilities.)
Exhibit 2-4 shows the rate (in occurrences per 360-day year) at
which 30-day averages of efficiency computed daily would fail to meet a
threshold level of 90 oercent efficiency for a facility with,an actual
efficiency level of 92 percent- and variability parameters as shown.
Each estimated rate is shown with an associated standard error of
estimate in parentheses. These estimates are for a facility with a
lognormal distribution of emissivity. Facilities with high values of
^Corresponding to a geometric mean emissivity of eight percent.
-------
0
M
2-13
EXHIBIT 2-4: FREQUENCY OF OCCURENCE (OCCASIONS PER YEAR)
OF BELOW - 90== AVERAGES IN A 92£ EFFICIENT
FACILITY WITH LOGNORMAL OBSERVATIONS
PROCESS AUTOCORRELATION
0 0.3 0.5 0.7
0.0 0.002 (.002) 0.189 (.031) 2.514 (.095)
C , 0.320 (.0215) 2.570 (.0865) 9.900 (.332) 25.045 (.7705;
>
0
A
I
L
V
V
A
R , 10.233 (.180) 26.3935 (.186) 41.2375 (.3975) 62.4455 (.7365)
I
A
B
I
L
I
T
Y
52.241 (.2655) 72.1555 (.3950) 87.608 (.5515) 102.496 (.9325)
» 3
Lognormal distribution.
Figures in parentheses are standard errors.
-------
2-14
either variability (40 percent or greater) or day-to-day correlation (0.7
or greater) would be exoected to fail to meet the threshold more than one
time per year, with facilities with high values of both variability and
correlation failing to meet the threshold for major fractions of their
operating days.
Exhibit 2-5 shows a comparison of these results with those which
would be expected on similar facilities where the variability of the
emissivity was normal1- rather than lognormal. As can be seen in the
exhibit, the pattern of dependency between the plant operating parameters
and the rate at which the threshold is not met remains essentially the
same. That is, the rate of threshold failures does not depend in any
major way on the shape of the statistical distribution of the
observations (within the general area of reasonability).
Exhibit 2-6 shows the expected rate at which thirty-day averages
below thresholds other than 90 percent would occur for various
variability and correlation parameters. Exhibits 2-7 through 2-9 show
this same information for geometric mean emissivities other than eight
percent (corresponding to more or less efficient facilities). All of
these exhibits were derived using the lognormal distribution of emis-
sivity observations; rates of threshold failure for the normal case
differ by only small amounts, just as in the 92 percent-efficient cases.
Exhibits 2-10 through 2-13 show the efficiency levels (1.00 -
geometric mean emissivities) at which facilities with various variability
and correlation parameters would maintain a rate of threshold failure no
higher than one per year (with rolling averages computed daily). These
-Truncated at 0 efficiency.
-------
2-15
EXHIBIT 2-5:
FREQUENCY OF OCCURENCE (OCCASIONS PER YEAR) OF
BELOW-90% AVERAGES IN A S2% EFFICIENT FACILITY
WITH NORMAL OR LOGNORMAL OBSERVATIONS
PROCESS AUTOCORRELATION
0.2 0.5
Lognormal:
0,0
Normal:
0.0
0.002 (.002)
0.009
0.189 (.031)
0.051
2.514 (.095)
1.206
0
M
.L
R
T
Q
A
I
L
Lognormal:
0.320 (.0215) 2.670 (.0865) 9.900 (.332) 25.045 (.770i)
Normal:
0.090
1.639
6.678
21.403
V
A
^
r
/i
n
3
I
L
Lognormal:
10.233 (.180) 26.3935 (.186) 41.2375 (.3975) 62.4^55 (.7365)
Normal:
7.742 22.777 39.689 64.527
Lognormal:
52.241 (.2555) 72.1565 (.3950) 87.608 (.5515) 102.496 (.9325)
Normal:
52.061 75.449 92.764 112.50
Lognormal distribution cases above
normal cases.
Figures in parentheses are standard
errors.
-------
2-16
EXHIBIT 2-6:
0
M
I
3
J
A
Y
\
3
FREQUENCY OF OCCURENCE (OCCASIONS PER YEAR) OF
BELOW-THRESHOLD AVERAGES IN A 92% EFFICIENT FACILITY
(with standard errors in parentheses)
PROCESS AUTCCCRRELA7ION
20-day u
30-
-------
2-17
EXHIBIT 2-7: FREQUENCY OF OCCURENCE (OCCASIONS PER YEAR) OF
BELOW-THRESHOLD AVERAGES IN A 94% EFFICIENT FACILITY
(with standard errors in parentheses)
PROCESS AUTOCORRELATION
Q
M
I
3
D
A
A
R
I
A
3
30-day y
30-day a
eff<90%
- "
-------
2-18
EXHIBIT 2-8: FREQUENCY OF OCCURENCE (OCCASIONS PER YEAR) OF
BELOW-THRESHOLD AVERAGES IN A 93% EFFICIENT FACILITY
(with standard errors in parentheses)
PROCESS AUTCCCRREL.47I2N
V
A
3
*
5
20-day u
30-day -
eff<905
*? "* '
" <38%
"
-------
2-1S
EXHIBIT 2-9: FREQUENCY OF OCCURENCE (OCCASIONS PER YEAR) OF
BELOW-THRESHOLD AVERAGES IN A 91% EFFICIENT FACILITY
(with standard errors in parentheses)
PROCESS AUTOCORRELATION
0
M
-I,
R
h
I
[_
Y
i.
A
3
i
V
30-day y
30-day s
eff<90%
y "
J535
-iff \
i <-?")
257C
1135
0325
016)
4725
103}
3195
182E
955}
:4i)
9195
911}
537E
394)
2675
2125
Conditions:
Facility with 9 * geometric
mean sTrissv/ity {91* efficiency)
Lognomal distribution cf
observations
-------
2-20
EXHIBIT 2-10:
MINIMUM GEOMETRIC MEAN EFFICIENCIES REQUIRED
TO MAINTAIN NO MORE THAN ONE FAILURE PER YEAR
Daily
Std. Dev.
(in log)
.20
.21
.22
.23
.24
.25
.26
.27
.28
.29
.30
. 31
'.32
.33
.34
.35
.36
.37
.33
.39
.40
.41
.42
.43
.44
. 45
!46
.47
.43
.49
.50
.51
.52
. 53
.54
. 55
. 56
.57
.53
.59
.50
Std. Dev.
of 30-Day
Average'
(.0054)
(.0057)
(.0060)
(.0063)
(.0065)
(.0063)
(.0071)
(.0074)
(.0077)
(.0080)
(.0083)
(.0087)
(.0090)
(.0093)
(.0096)
(.0099)
(.0103)
(.0106)
(.0109)
(.0113)
(.0116)
(.0119)
(.0123)
(.0127)
(.0130)
(.0134)
(.0138)
(.0141)
(.0145)
(.0149)
(.0153)
(.0157)
(.0161)
(.0165)
(.0159)
(.0174)
(.0173)
(.0182)
(.0187)
(.0192)
(.0196)
01 a
-?i w
91.9
92.0
92.1
92.1
92.2
92.3
92.4
92.5
92.6
92.6
92.7
92.8
92.9
93.0
93.1
93.1
93.2
93.3
93.4
93.5
93.5
93.5
93.7
93.8
93.9
94.0
94.0
94.1
94.2
94.3
94.4
94.4
94.5
94.6
94.7
94.7
94.8
94.9
95.5
f\£ rt
S5.0
Minimum Efficiency
For Threshold Shown
<8B% <88% <87% <86%
91
91
91
91
91
91.4
91.5
91.6
91.7
91.3
91.9
92.1
92.2
92.3
92.4
92.5
92.5
92.6
92.7
92.8
92.9
93.0
93.1
93.2
93.3
93.4
93.4
93.5
93.6
93.7
93.8
93.9
94.0
94.0
94.1
94.2
94.3
94.4
94.5
94,5
90.1
90.3
90.4
90.5
90.6
90.7
90.3
90.9
91.0
91.1
91.2
92.0 91.3
91
91.4
91.5
91.6
91.7
91.8
91.9
92.0
92.1
92.2
92.3
92.4
92.5
92.6
92.7
92.8
92.8
92.9
93.0
93.1
93.2
93.3
93.4
93.5
93.5
93.7
93.3
93.9
93.9
94.0
39.3
89.4
89.6
39.7
39.8
39.9
90.0
90.1
90.2
90.3
90.4
90.6
90.7
90.3
90.9
91.0
91.1
91.2
91.3
91.4
91.5
91.5
91.7
91.3
91.9
92.0
92.1
92.2
92.4
92.5
92.5
92.7
92.8
92. 9
93.0
93.1
93.2
93.2
93.3
93.4
93.5
88.5
88.6
38.7
88.9
39.0
89.1
89.2
39.4
39.5
39.6
89.7
89.8
39.9
90.1
90.2
90.3
90.4
90.5
90.5
90.3
90.9
91.0
91.1
91.2
91.3
91.4
91.5
91.7
91.8
91.9
92.0
92
92
92.4
92.5
92.6
92.7
92.8
92. 2
93.0
87.7
87.3
87.9
88.1
38.2
88.3
88.5
38.5
38.7
33.8
39.0
39.1
89.2
39.4
89.5
89.6
89.7
39.3
90.0
90.1
90.2
90.3
90.5
90.6
90.7
90.3
90.9
91.1
91.2
91.3
91.4
92.1 91.5
2 91.6
3 91.3
4 91.9
5 92.0
92.1
92.2
92.3
92.4
92.5
Facility autocorrelation =0.55
In computing the 30-day average variability, a geometric mean emission
level of 92^ was assumed.
-------
2-21
EXHIBIT 2-11:
Daily
Std. Dev.
(in log)
.20
.21
.22
.23
.24
.25
.26
.27
.28
.29
.30
.31
.32
.33
.34
.35
.36
.37
.38
.39
.40
.41
.42
.43
.44
.45
.46
.47
.48
.49
.50
.51
.52
.53
.54
. 55
.56
.57
.58
.59
.60
Std. Dev.
of 30-Day
Average'
(.0053)
(.0061)
(.0064)
(.0067)
(.00701
(.0073)
(.0076)
(.0080)
( . 0083 )
(.0086)
(.0089)
(.0093)
(.0096)
(.0099)
(-0103)
(-0106)
(-0110)
(.0113)
( 0117)
(.0121)
(.0124)
( 0128)
(.0132)
(.0135)
(.0139)
(.0143)
(.0147)
(.0151)
(.0155)
(.0159)
(.0164)
(.0168)
(.0172)
(.0177)
(.0181)
(.0186)
(.0190)
(.0195)
(.0200)
(.0205)
(.0210)
MINIMUM GEOMETRIC MEAN EFFICIENCIES REQUIRED
TO MAINTAIN NO MORE THAN ONE FAILURE PER YEAR
Minimum Efficiency
For Threshold Shown
<90%
-------
2-22
EXHIBIT 2-12:
MINIMUM GEOMETRIC MEAN EFFICIENCIES REQUIRED
TO MAINTAIN NO MORE THAN ONE FAILURE PER YEAR
Daily
Std. Dev.
(in log)
.20
.21
. 22
.23
.24
.25
.25
.27
.28
.29
.30
..31
71
. Jd
.33
.34
.35
.36
.37
.33
.39
.40
.-"!
.*42
.43
.44
.45
.46
.47
.43
.49
.50
. 51
.52
.53
.54
* ^
, 56
. 57
.53
.59
.50
Std. Dev.
of 30-Day
Average '
(.0052)
(.0066)
(.0069)
(.0072)
(.0075)
(.0079)
(.0082)
(.0086)
(.0089)
(.0093)
(.0096)
(.0100)
(.0104)
(.0107)
(.0111)
(.0115)
(.0118)
(.0122)
(.0126)
(.0130)
(.0134)
(.0138)
(.0142)
(.0146)
(.0150)
(.0154)
(.0159)
(.0163)
(.0157)
(.0172)
(.0175)
(.0181)
(.0185)
(.0190)
(.0195)
(.0200)
(.0205;
(.0210)
(.0215)
(.0220)
(.0225)
Minimum Efficiency
For Threshold Shown
<89% <88% <87% <86%
92.0
92.1
92.
92.
92.4
92.5
92.6
92.7
92.8
92.3
92.9
93.0
93.1
93.2
93.3
93.4
93.5
93.5
93.6
93.7
93.3
93.9
94.0
94.1
94.1
94.2
94.3
94.4
94.5
94.5
94.6
94.7
94.3
94.9
94.9
95.0
95.1
95.2
95.2
95.3
95.4
91.2
91.3
91.4
91.5
91.5
91.7
91.8
91 °
92.0
92.1
92.2
92.3
92.4
92.5
92.5
92.7
92.3
92.9
93.0
93.1
93.2
93.3
93.4
93.5
93.5
93.7
93.7
93.8
93.9
94.0
94.1
94.2
94.3
94.4
94.4
94.5
94.5
94.7
94.3
94.9
94.9
90.4
90.5
90.6
90.8
90.9
91.0
91.1
01 2
91.3
91.4
91.5
91.5
91.7
91.8
92.0
92.1
92.2
92.3
92.4
92.5
92.6
92.7
92.8
92.9
93.0
93.1
93.2
93.3
93.4
93.5
93.5
93.7
93.7
93.8
93.9
94.0
94.1
94.2
94.3
94.4
94.5
89.5
39.7
39.9
90.0
90. 1
90.2
90.3
90.5
90.6
90.7
90.8
9Q.9
91.1
91.2
91.3
91.4
91.5
91.6
91.7
91.8
92.0
92.1
92.2
92.3
92.4
92.5
92.5
92.7
92.3
92.9
93.0
93.1
93.2
93.3
93.4
93.5
93.5
93.7
93.3
93.9
94.0
88.8
38.9
39.1
89.2
89.3
89.5
39.6
89.7
39.9
90.0
90.1
90.2
90.4
90.5
90.5
90.7
90.9
91.0
91.1
91.2
91.3
91.5
91.5
91.7
91.3
91.9
92.0
92.1
92.3
92.4
92.5
92.6
92.7
92.3
92.9
93.0
93. 1
93.2
93.3
93.5
93.6
38.0
88. 2
38.3
38.4
83.6
33.7
33.9
39.0
89.1
89.3
39.4
39.5
89.7
39.3
39.9
90.1
90.2
90.3
90.5
90.6
90.7
90.8
91.0
91.1
.2
,3
. 5
91.
91.
91.
91.6
91.7
91.3
91.9
92.1
92.2
92.3
92.4
92.5
92.6
92.3
92.9
93.6
G-3 1
Facility autocorrelation = 0.55
'In computing the 30-day average variability, a geometric mean emission
level of 92^ was assumed.
-------
2-23
EXHIBIT 2-13:
MINIMUM GEOMETRIC MEAN EFFICIENCIES REQUIRED
TO MAINTAIN NO MORE THAN ONE FAILURE PER YEAR
Daily
Std. Dev.
(in log)
.20
.21
.22 .
.23
.24
.25
.25
.27
.28
.29
.30
.31
.32
.33
.34
.35
^ 0
.37
.38
.39
.40
.41
.42
.43
.44
.45
.46
.47
.48
.49
.50
. 51
.52
.53
.54
. 55
. 56
. zl
.58
. E9
'.SO
Std. Dev.
of 30-Day
Average'
(.0068)
( . 0071 )
(.0075)
(.0079)
(.0082)
(.0086)
(.0090)
(.0093)
(.0097)
(.0101)
(.0105)
(.0109)
(.0112)
(.0116)
(.0120)
(.0124)
(.0128)
(.0133)
(.0137)
( - 0141 )
(.0145)
(.0150)
(.0154)
(.0153)
(.0153)
(.0167)
(.0172)
(.0177)
(.0182)
(.0186)
(.0191)
(.0196)
(.0201)
(.0206)
(.0212)
(.0217)
(.0222)
(.0228)
(.0233)
(.0239)
(.0245)
Minimum Efficiency
For Threshold Shown
<90% <89% <88% w w
93.4
93.5
93.7
93.3
93.9
88.2
88.4
88.5
88.7
88.8
89.0
89.1
39.3
89.4
39.5
89.7
89.8
90.0
90.1
90.2
90.4
90.5
90.6
90.8
90.9
91.0
91.2
91.3
91.4
91 5
91.7
91.8
91.9
92^0
92.2
92.3
92.4
92.5
92.6
S2.7
92.9
93.0
93.1
93.2
93.3
93.4
1
Facility autocorrelation =0.70
In computing the 30-day average variability, a geometric mean emission
level of 92S was assumed.
-------
2-24
minimum efficiency critical values are accurate to within at least 0.2
percent (two tenths of one percent). Exhibits 2-14 through 2-25 show
similar data for threshold failure rates of one per two years, one per
five years, and one per ten years. (Given the randomness of the process,
there is no set of operating conditions that can achieve a true zero rate
of failure; some failures will occur randomly under any conditions.)
Policies in which averages are computed less frequently than daily,
but are still thirty-day averages for the last thirty-days at the time of
computation (for example, averages computed weekly or monthly) would, of
course, result in fewer threshold failures per year for all facilities,
whether or not operated in accordance with good practice, simply because
there would be fewer occasions per year on which failures could occur.
The effect on the rate of failures per year is, in fact, exactly
proportional to the frequency of computation of the average.^- Thus, if
weekly averaging were used, in which a thirty-day average was computed
for the thirty-day period ending, for example, on each Friday, the rate
of threshold failures per year for any set of operating parameters would
simply be one-seventh of that shown in the preceding exhibits. If
averages are computed once every thirty days, the rate of failures per
year would be one-thirtieth of that in the exhibits, etc. The exhibited
critical operating levels at which one failure per year would occur, of
course, no longer apply if the frequency of average computation is
changed.
-This fact can be proven conroletely mathematically for all the pro-
cesses considered here, whether involving the normal, lognormal, or
other distribution. Somewhat in violation of intuition, the orooosition
remains true no matter what the correlation structure of the daily
observations.
-------
2-25
EXHIBIT 2-14; MINIMUM GEOMETRIC MEAN EFFICIENCIES REQUIRED TO
MAINTAIN NO MORE THAN ONE FAILURE PER TWO YEARS
Daily Std. Oev. Minimum Efficiency
Std. Dev. of 30-Day For Threshold Shown
(in log) Average1
<90% <89% <88o
-------
EXHIBIT 2-15:
2-26
MIMIMUM GEOMETRIC MEAN EFFICIENCIES REQUIRED TO
MAINTAIN NO MORE THAN ONE FAILURE PER TWO YEARS
Minimum Efficiency
For Threshold Shown
(.0058)
(.0061)
(.0064)
C.0067
\ WWW I J
(.0070)
(.0073)
(.0076)
(.0080)
(.0083)
(.0086)
(.0089)
(.0093)
(.0096)
(.0099)
(.0103)
(.0106)
(.0110)
(.0113)
(.0117)
(.0121)
(.0124)
(.0128)
(.0132)
(.0135)
(.0139)
(.0143)
(.0147)
(.0151)
(.0155)
(.0159)
(.0164)
(.0168)
(.0172)
(.0177)
(.0131)
(.0186)
(.0190)
(.0195)
(.0200)
(.0205)
(.0210)
32.
92.
92.
32
32.
92.
92.
92.
92.
92.
92.
93.
S3.
93.
93.
93.
93.
93.
93.
93.
93.
93.
94.
94.
94.
94.
94.
94.
94.
94.
94.
94.
94.
94.
94.
95.
95.
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95.
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95.
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8
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91.
91.
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at
91 .
91.
91.
91.
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92.
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92-
92.
92.
92.
92.
93.
93.
93.
93.
93.
93.
93.
93.
93.
93.
93.
94.
94.
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90.
90.
90.
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91.
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91.
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91.
91.
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92.
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93.
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3
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0
2
3
4
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5
7
8
0
1
2
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2
3
4
5
6
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3
g
6
88.
38.
89.
89.
39.
89.
39.
89.
89.
90.
90.
90.
90.
30.
SO.
90.
90.
91.
31.
31.
91.
91.
91.
91.
91.
91.
92.
92.
92.
92.
92.
92.
92.
92.
32.
33.
93.
93.
93.
S3.
93.
,3
9
T_
2
2
5
6
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9
0
1
2
4
5
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0
1
2
3
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5
7
3
Q
f*
U'
^
3
£
s
V
7
3
9
0
i
7
3
4
5
88.0
88.2
38.3
38.4
33.5
38.7
88.9
39.0
89.1
89.3
89.4
89.5
39.7
39.3
39.9
90.1
90.2
30.3
3C.5
90.5
90.7
90.3
91.0
91.1
31.2
91.3
SI. 5
91.5
91.7
SI. 3
SI. 9
92.1
92.2
92.3
S2. 4
S2.5
32.5
52. 3
92. S
33.' 5
93.1
Facility autocorrelation =0.60
In computing the 30-day average variability, a geometric mean
emission level of 92* was assumed.
-------
2-27
EXHIBIT 2-15:
MINIMUM GEOMETRIC MEAN EFFICIENCIES REQUIRED TO
MAINTAIN NO MORE THAN ONE FAILURE PER TWO YEARS
Daily
Std. Dev.
(in log)
.20
.21
.22
.23
.24
.25
.25
.27
.23
.29
.30
.31
.32
5-3
ww
.34
.35
.36
.37
.38
.39
.40
.41
.42
.43
.44
.45
.46
.47
.48
.49
.50
.51
.52
.53
.54
. 55
. 55
^7
*> /
.58
. 59
.60
Std. Dev.
of 30-Day
Average^
(.0062)
(.0066)
(.0069)
(.0072)
(.0076)
(.0079)
(.0082)
(.0086)
(.0089)
(.0093)
(.0096)
(.0100)
(.0104)
(.0107)
(.0111)
(.0115)
(.0113)
(.0122)
(.0126)
(.0130)
(.0134)
(.0138)
(.0142)
(.0146)
(.0150)
(.0154)
(.0159)
(.0163)
(.0167)
(.0172)
(.0176)
(.0181)
(.0185)
(.0190)
(.0195)
(.0200)
(.0205)
(.0210)
(.0215)
(.0220)
(.0226)
92.1
92.2
92.3
92.4
92.5
92
92.7
92.8
92.9
93.0
93.1
93.2
93.3
93.4
93.5
93.5
93.6
93.7
93.8
93. 9
94.6
94.1
94.2
94.3
94.4
94.5
94.5
94.7
94.7
94.8
94.9
95.0
95.1
95.1
95.2
95.3
95.4
95.4
95.5
95.6
Minimum Efficiency
For Threshold Shown
<88% <37%
91.3
91.5
91.6
91.7
91.8
92.
92.
92.
92.4
92.5
92.6
92.7
92.8
92.9
93.0
93
93
93
93
93
93
.1
,2
,3
,4
,5
,6
93.7
93.8
93.9
94.0
94.0
94.1
94.2
94.3
94.4
94.5
94.6
94.7
94.7
94.3
94.9
95.0
95.1
95.2
90.6
90.7
90.8
90.9
91.0
5 91.9 91.2
92.0 91.3
91.
91.4
91.5
91.6
91.7
91.8
91.9
92.0
92.2
92.3
92.4
92.5
92.6
92.7
92.8
92.9
93.0
93.1
93.2
93.3
93.4
93.5
93.5
93.7
93.8
93.9
94.0
94.1
94.2
94.3
94.4
94.4
94.5
94.6
94.7
89.8
89.9
90.0
90.2
90.3
90.4
90.5
90.7
90.3
90.9
91.0
,1
,3
,4
,5
91.
91.
91.
91.
91.5
91.7
91.9
92.0
92.1
92.2
92.3
92.4
92.5
92.6
92.7
92.9
93,0
93.1
93.2
93.3
93.4
93.5
93.5
93.7
93.8
93.9
94.0
94.1
94.2
94.3
89.0
89.1
39.3
89.4
89.5
89.7
39.8
89.9
90.1
90.2
90.3
90.5
90.6
90.7
90.9
91.0
91.1
91.2
91.3
91.5
91.6
91.7
91.8
92.0
92
92
92
92
92.5
92.5
92.8
92.9
93.0
93.1
93.2
93.3
93.4
93.5
93.6
93.7
93.3
88.2
88.4
88.5
83.5
88.3
88.9
89.1
89.2
39.4
39.5
89.6
89.8
89.9
90.1
90.2
90.3
90.5
90.6
90.7
90.9
91.0
91.1
91.2
91.4
91.
91,
91,
01
92.0
92.1
92.2
92.4
92.5
92.6
92.7
92.8
92.9
93.1
93.2
93.3
93.4
Facility autocorrelation = 0.65
-In confuting the 30-day average variability, a geometric mean
emission level of 92* was assumed.
-------
2-28
EXHIBIT 2-17: MINIMUM GEOMETRIC MEAN EFFICIENCIES REQUIRED TO
MAINTAIN NO MORE THAN ONE FAILURE PER TWO YEARS
Daily Std. Oev. Minimum Efficiency
Std. Dev. of 30-Day For Threshold Shown
(in log) Average1
<<5Q%
-------
2-29
EXHIBIT 2-18:
MINIMUM GEOMETRIC MEAN EFFICIENCIES REQUIRED TO
MAINTAIN MO MORE THAN ONE FAILURE PER FIVE YEARS
Minimum Efficiency
For Threshold Shown
<89%
-------
2-30
EXHIBIT 2-19:
MINIMUM GEOMETRIC MEAM EFFICIENCIES REQUIRED TO
MAINTAIN MO MORE THAN ONE FAILURE PER FIVE YEARS
Daily
Std. Oev.
(in log)
.20
.21
.22
.22
.24
.25
.26
.27
.23
.29
.30
.31
.32
.33
!34
.35
.36
.37
.38
.39
.40
.41
.42
.43
.44
.45
.46
.47
.48
.49
.50
CT
. 3x
.52
-> w
.54
* *
.56
. Z 1
.53
.59
.*50
Std. Oev.
of 30-Day
Average^-
(.0058)
( . 0061 )
(.0064)
(.0067)
(.0070)
(.0073)
(.0076)
(.0080)
(.0083)
(.0086)
(.0089)
(.0093)
(.0096)
(.0099)
(.0103)
(.0106)
(.0110)
(.0113)
(.0117)
(.0121)
(.0124)
(.0128)
(.0132)
(.0135)
(.0139)
(.0143)
(.0147)
(.0151)
(.0155)
(.0159)
(.0164)
(.0153)
(.0172)
(.0177)
(.0131)
(.0136)
(.0190)
(.0195)
(.0200)
(.0205)
(.0210)
Minimum Efficiency
For Threshold Shown
92.2
92.3
92.4
92.5
92.6
92.6
92.7
92.3
92.9
93.0
93.1
93.2
93.3
93.1
93.5
93.5
93.7
93.8
93.9
93.9
94.0
94.1
94.2
94.3
94.4
94. £
94.5
94.6
94.7
94.8
94.9
94.9
95.0
95.1
95.2
95. 2
a5 "
95.4
95.5
95.5
2C. 0
91.4
91.5
91.6
91.7
91.3
91 °
92.0
92. '
92"! 2
92.3
92.4
92.5
92.5
92.7
92.3
92.9
93.0
93.1
93.2
93.3
93.4
93.5
93.5
93.7
93.3
Ol 0
94.0
94.1
94.2
94.3
94.3
94.4
9^.5
94.6
94.7
94.3
94.9
9^.9
95.0
95.1
95.2
90.5
90.7
90.3
90.9
91.1
01 £
91.3
91.4
91.5
91.6
91.3
91.9
92.0
92.1
92.2
92.3
92.4
92.5
92.5
92.7
92.3
92.9
93.0
93.1
93.2
Q~ 3
93.4
93.5
93.5
93.7
93.8
93.9
94.0
94.1
94.2
94.3
04.4
94.5
94.5
94.7
94.3
89.3
39.9
90.1
90.2
90.3
90.4
90.6
90.7
90.8
90.9
91.1
91.2
91.3
91.4
91.5
91.7
91.3
91.9
92.6
92.1
92.2
92.3
92.5
92.6
92.7
92.3
92.9
93.0
93.1
93.2
93.3
93.4
93.5
93.6
93.7
93.3
G1 Q
94.0
94.1
94.2
94.3
89.0
89.2
39.3
89.4
39.6
39. 7
39.3
90.0
90.1
90.2
90.4
90.5
90.5
90.3
90.9
91.0
91.1
91.3
91.4
91.5
91.5
91.3
91.9
92.0
92.1
92.2
92.3
92.5
92.5
92.7
92.3
92.9
93.0
93.1
93.2
93.3
Q"« 5
33.5
93.7
93.3
93.9
38.2
38.4
38.5
88.7
38.3
39.0
39.1
89.3
39.4
39.5
39.7
39.3
90.0
90.1
90.2
90. 4
SO. 5
90.6
90.3
SO. 9
91.0
91. 2
31. 3
91.4
91.5
91.7
Q: Q
- * . w
91.9
92.0
32.2
92.3
92.4
92.5
92.6
92.3
92.9
G-3 Q
93.1
93.2
93.3
92.4
Facility autocorrelation = 0.60
corrouting the 30-day average variability, a geometric iiean
emission level of 92* was assumed.
-------
2-31
EXHIBIT 2-20:
MINIMUM GEOMETRIC MEAN EFFICIENCIES REQUIRED TO
MAINTAIN NO MORE THAN ONE FAILURE PER FIVE YEARS
Minimum Efficiency
For Threshold Shown
<90"
5
6
7
8
9
0
90.
90.
90.
90.
90.
90.
90.
90.
91.
91.
91.
91.
91.
91.
91.
91
92.
92.
92.
92.
92.
92.
92.
92.
92.
93.
93.
93.
93.
93.
93.
93.
93.
93.
94.
94.
94.
94.
94.
94.
94.
0
I
3
4
5
6
8
9
0
2
3
4
5
7
8
Q
0
1
3
4
5
5
7
8
9
0
2
*^
4
R
6
7
8
Q
0
i
2
3
4
5
6
89.
89.
89.
89.
89.
89.
90.
90.
90.
90.
90.
90.
90.
91.
91.
01
91.
91.
91.
91.
91.
92.
92.
92.
92.
92.
92.
92.
92.
93.
93.
93.
93.
93.
00
w W
93.
93.
93.
94.
94.
94.
2
4
w
5
8
Q
1_
2
3
5
6
8
o
0
I
3
4
5
7
3
Q
6
2
3
^
5
5
7
9
0
1
2
^
^
w
4
5
6
/
9
0
i
2
88.4
88.6
88.3
88.9
89.1
89.2
89.4
39. 5
89.7
89.8
89.9
90.1
90.2
90.4
90.5
90. 7
90.8
90.9
91.1
91.2
91.3
91.5
91.5
91.7
91.8
92.0
92.1
92.2
92.4
92.5
92.6
92.7
92.3
93.0
93.1
93.2
93.3
93.4
93.5
93.5
93.7
Facility autocorrelation = 0.65
!H computing the 30-day average variability, a geometric mean
emission level of 92* was assumed.
-------
2-32
EXHIBIT 2-21: MINIMUM GEOMETRIC MEAN EFFICIENCIES REQUIRED TO
MAINTAIN NO MORE THAN ONE FAILURE PER FIVE YEARS
Daily Std. Dsv. Minimum Efficiency
Std. Dev. of 30-Day For Threshold Shown
(in log) Average^
<90" <89% <88% <87"
5
8
0
Q
^
2
w
1
w
5
88.7
^ O O
OC. 0
39.0
89.2
39.3
89.5
89.6
89.3
39.9
90.1
90.2
90.4
90.5
90.7
90.3
91.0
91.1
91.3
91.4
91.5
91.7
91.8
91. 9
92.1
92.2
92.3
92.5
92.5
92.7
92.3
92.9
93.1
93.2
93.3
93.4
93.5
33.7
C"5 2
^ w . w
93. 9
94.0
94.1
-In computing the 30-day average variability, a geometric mean
emission level of 92* was assumed.
-------
2-33
EXHIBIT 2-22: MINIMUM GEOMETRIC MEAN EFFICIENCIES REQUIRED TO
MAINTAIN NO MORE THAN ONE FAILURE PER TEN YEARS
Daily Std. Dev. Minimun Efficiency
Std. Oev. of 30-Day For Threshold Shown
(in log) Average1
<90% <89% <38% <87% <86%
.20
.21
.22
.23
.24
.25
.25
.27
.28
.29
.30
.31
.32
.33
.34
.35
.36
.37
.38
.39
.40
.41
.42
.43
.44
.45
.46
.47
.48
.49
.50
.51
.52
.53
.54
. 5~
. 56
.57
.58
.59
.60
Facility autocorrelation = Q.55
(.0054)
(.0057)
(.0060)
(.0063)
(.0065)
(.0068)
(.0071)
(.0074)
(.0077)
(.0080)
(.0083)
(.0087)
(.0090)
(.0093)
(.0096)
(.0099)
(.0103)
(.0106)
(.0109)
(.0113)
(.0116)
(.0119)
(.0123)
(.0127)
(.0130)
(.0134)
(.0138)
(.0141)
(.0145)
(.0149)
(.0153)
(.0157)
(.0161)
(.0165)
(.0159)
(.0174)
(.0173)
(.0182)
(.0187)
(.0192)
(.0196)
92
92
92
92
92
92
92
92
92
93
93
93
.1
.2
.3
.4
. 5
.6
.7
.8
.9
.0
.1
.2
93.3
93
93
93
93
93
93
93
94
94
94
94
94
94
94
94
94
94
94
94
95
95
95
95
95
95
95
95
95
.4
.5
. 5
.6
.7
.8
.9
.0
.1
.2
.2
.3
.4
. 5
.6
.7
.7
.8
.9
.0
.1
.1
.2
.3
.4
.4
. 5
w
91.
91.
91.
91.
91.
91.
92.
92.
92.
92.
92.
92.
92.
92.
92.
92.
93.
93.
93.
93.
93.
93.
93.
93.
93.
93.
93.
94.
94.
94.
94.
94.
94.
94.
94.
94.
94.
94.
95.
95.
95.
2
5
6
7
8
Q
6
i
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
9
0
1
2
3
4
5
6
5
7
8
Q
0
1
I
1
90.
90.
90.
90.
91.
91.
91.
91.
91.
91.
91.
91.
91.
92.
92.
82.
92.
92.
92.
92.
92.
92.
93.
93.
93.
93.
93.
93.
93.
93.
93.
93.
94.
94.
94.
94.
94.
94.
94.
94.
94.
6
7
8
Q
0
1
3
4
5
6
7
8
9
0
2
3
4
5
5
7
8
9
0
1
2
3
T
5
5
7
8
9
0
1
2
3
3
4
5
5
7
39.
89.
90.
90.
90.
90.
90.
90.
90.
90.
91.
91.
91.
91<.
91.
91.
91.
91.
92.
92.
92.
92.
92.
92.
92.
92.
92.
93.
93.
93.
93.
93.
93.
93.
93.
93.
93.
94.
94.
94.
94.
8
9
0
2
3
t
5
7
g
9
6
i
3
4
5
6
7
8
0
1
2
3
4
5
6
7
8
0
I
2
3
4
5
6
7
8
9
0
I
2
3
89.
39.
89.
89.
89.
89.
89.
39.
90.
90.
90.
90.
90.
90.
90.
91.
91.
91.
91.
91.
91.
91.
91.
91.
92.
92.
92.
92.
92.
92.
92.
92.
93.
93.
93.
93.
93.
93.
93.
93.
93.
0
1
3
4
5
7
8
Q
1
2
3
5
6
7
8
0
1
2
3
5
6
7
8
9
1
2
3
4
5
6
7
9
0
1
2
3
4
5
5
7
8
38.2
83.3
88.5
88.5
88.3
88.9
89.1
39.2
89.4
89.5
39.6
89.3
89.9
90.1
90.2
90.3
90.5
90.6
90.7
90.9
91.0
91.1
91.2
91.4
91.5
91.6
91.7
91.9
92.0
92.1
92.2
92.3
92.5
92.5
92.7
92. 3
92.9
93.0
93.2
93.3
93.4
!H comouting the 30-day average variability, -a geometric mean
emission level of 92% was assumed.
-------
2-34
EXHIBIT 2-23: MINIMUM GEOMETRIC MEAN EFFICIENCIES REQUIRED TO
MAINTAIN NO MORE THAN ONE FAILURE PER TEN YEARS
Daily
Std. Dev.
(in log)
.20
.21
.22
.23
.24
.25
.25
.27
.28
.29
.30
.31
.32
.33
.34
.35-
.36
.37
.38
.39
.40
.41
.42
.43
.44
.45
.46
.47
.48
.49
.50
.51
.52
.53
.54
« ~
.56
.57
.53
.59
.50
Std. Dev.
of 30-Day
Average^-
(.0058)
(.OCSU
(.0064)
(.0067)
(.0070)
( . 0073 )
(.0076)
(.0030)
(.0083)
(.0086)
(.0089)
(.0093)
(.0096)
(.0099)
(.0103)
(.0106)
(.0110)
(.0113)
(.0117)
(.0121)
(.0124)
(.0128)
(.0132)
(.0135)
(.0139)
(.0143)
\ wi w /
(.0147}
(.0151)
(.0155)
f.0159)
(.0164)
(.0158)
(.0172)
(.0177)
(.0181)
(.0136)
(.0190)
(.0195)
(.0200)
(.0205)
(.0210)
92.3
92.4
92.5
92.6
92.7
92.8
92,
93.
93.
93.
.9
,0
,1
,2
93.3
93.3
93.
,4
93.5
93.
93.
93.
93.
94.
94.
94.
94.
94.
94.
94.
94.
94.
94.
94.
94.
95.
95.
95.
95.
95.
^s
95.
95.
95.
95.
/> *
y *
,5
7
8
9
0
1
2
3
3
4
5
5
7
3
3
9
0
1
2
2
3
.1
5
5
5
7
3
Mi n i mum E f f i c i ency
For Threshold Shown
91.5 90.7 89.9 39.2
91.6 90.3 90.1 89.3
91.7 91.0 90.2 39.4
91.3 91.1 90.3 39.5
91.9 91.2 90.5 89,7
92.0 91.3 90.6 89.9
92.1
92.3
92.4
92.5
92.5
92.7
92.3
92.9
93.0
93.1
93.2
93.3
93.4
93.5
93.6
93.7
93.3
93.9
94.0
Q4. 1
94.1
94.2
94.3
94.4
94.5
94.5
94.7
94.3
94.9
-4.9
95.0
95. 1
95.2
95.3
95.4
91.
91.
91.
91.
91.
92.
92.
92.
92.
92.
92.
92.
92.
92.
93.
93.
93.
93.
93.
0?
93.
93.
93.
93.
94.
94.
94.
94.
94.
04
94.
94.
94.
94.
94.
4
,6
,7
3
0
0
I
2
4
5
6
7
8
9
0
1
2
o
4
c
5
7
8
g
0
7
2
4
d
;
5
7
3
3
9
90.
90.
i 7
,3
91.0
91.
i
< A
91.2
91.
01 1
91.'
91.
91.
92.
92.
92.
92.
92.
92.
92.
92.
92.
c?
93.
93*.
93.
93.
93.
93.
93.
93.
93.
94.
94.
94.
94.
94.
94.
. 3
5
6
7
3
0
1
2
3
4
3
5
3
Q
n
I
2
3
4
3
5
-r
8
Q
0
7
2
3
*
*4>
5
90.
90.
90.
90.
90.
90.
90.
90.
91.
91.
91.
91.
91.
91.
91.
92.
92.
92.
92.
92.
92.
92.
92.
92.
92.
93.
93.
93.
93.
^ .
93!
93.
93.
94.
94.
0
,1
3
4
5
T
3
0
^
2
3
5
6
7
a
5
1
2
3
4
T
8
0
0
1
^
2
5
-\
-*
w
9
n
1
38.4
88.5
38.7
88.3
39.0
39.1
39.3
39.4
39.5
89.7
89.9
90. 0
90.2
90.3
90.4
90. 6
90.7
90.3
91.0
91.1
91.2
91.4
91.5
91.6
91.3
91.9
92.0
92.1
92.3
92.4
92.5
92.5
92.7
92.9
93.0
a". *
93! 2
0-5 ?
i -J W
G*5 £
93* 5
93.7
Facility autocorrelation =0.50
-In comnuting the 30-day average variability, a geometric mean
emission level of 92" was assumed.
-------
2-35
EXHIBIT 2-24: MINIMUM GEOMETRIC MEAN EFFICIENCIES REQUIRED TO
MAINTAIN NO MORE THAN ONE FAILURE PER TEN YEARS
Daily
Std. Dev.
(in log)
Std. Dev.
of 30-Day
Average^-
Minimum Efficiency
For Threshold Shown
<90% <89%
.20
.21
.22
.23
.24
.25
.26
.27
.28
.29
.30
.31
.32
.33
.34
.35
.36
.37
.38
.39
.40
.41
.42
.43
.44
.45
.46
.47
.48
.49
.50
.51
.52
.53
.54
.55
.56
. 57
.58
,59
.50
(.0062)
(.0066)
(.0069)
(.0072)
(.0076)
(.0079)
(.0082)
(.0086)
(.0089)
(.0093)
(.0096)
(.0100)
(.0104)
(.0107)
f.Olll)
( 0115)
(.0118)
(.0122)
(.0125)
(.0130)
(.0134)
(.0138)
(.0142)
(.0146)
(.0150)
(.0154)
(.0159)
(.0163)
(.0167)
(.0172)
(.0176)
(.0181)
(.0135)
(.0190)
(.0195)
(.0200)
(.0205)
(.0210)
(.0215)
(.0220)
(.0226)
92
92
92
92
92
92
93
93
93
93
93
93
93
93
93
93
94
94
94
94
94
94
94
94
94
94
94
95
95
95
95
.4
. 5
.6
.7
.8
.9
.0
.1
.2
.3
.4
. 5
.6
.7
.8
9
.0
.1
.2
.3
.4
.5
.5
.6
. 7
.8
.9
.0
.1
i
*
.2
95.3
95
95
.4
.5
95.5
95
95
95
95
95
96
.6
. 7
.8
.3
f Q
!o
Q1
91.
91.
92.
92.
92.
92.
92.
92.
92.
92.
92.
93.
93.
93
93,
93.
93.
93.
93.
93.
93.
94.
94.
94.
94.
94.
94.
94.
94.
94.
94.
94.
95.
95.
95.
95.
95.
95.
95.
95.
6
8
9
0
1
2
3
d
6
7
8
9
6
i
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
6
7
8
9
6
1
2
3
3
4
5
6
<88%
90.9
91.0
91.1
91.3
91.4
91.5
91.6
91.8
91.9
92.0
92. 1
92.2
92.3
92.5
92 6
92 7
92.8
92.9
93.0
93.1
93.2
93.3
93.5
93.6
93.7
93.8
93.9
94.0
94.1
94 2
94.3
94.4
94.5
94.5
94.6
94.7
94.8
94.9
95.0
95.1
95.2
/Q 7^ xOC^ xOCT-*1
^O//o ^QOjC ^OO'3
90.
90.
90.
90.
90.
90.
90.
91.
91.
91.
91.
91.
91.
91.
92
92
92.
92.
92.
92.
92.
92.
92.
93.
93.
93.
93.
93.
93.
93.
93.
93.
94.
94.
94.
94.
94.
94.
94.
94.
94.
1
3
4
5
7
3
9
i
2
3
*^
6
7
8
Q
i
2
3
4
6
7
8
g
0
T
±
2
d
5
6
7
8
9
0
1
2
3
4
5
5
7
8
89.
89.
89.
89.
89.
90.
90.
90.
90.
90.
90.
90.
91.
91.
91
91.
91.
91.
91.
92.
92.
92.
92.
92.
92.
92.
92.
93.
93,
93.
93.
93.
93.
93.
93.
93.
94.
94.
94.
94.
94.
4
5
7
8
9
1
2
4
5
7
8
9
I
2
3
5
5
7
9
0
i
2
4
5
6
7
8
0
1
2
3
4
5
6
7
9
0
1
2
3
4
88.6
88.8
88.9
89.1
89.2
89.4
39.5
89.7
89.8
90.0
90.1
90.3
90.4
90.6
90.7
90.9
91.0
91.1
91.3
91.4
91.5
91.7
91.8
91.9
92.1
92.2
92.3
92.5
92.5
92.7
92.8
92.9
93.1
93.2
93.3
93.4
en . 5
93. 5
9sl I
93.9
94.0
Facility autocorrelation = 0.55
In computing the 30-day average variability, a geometric mean
emission level of 92% was assumed.
-------
2-36
EXHIBIT 2-25: MINIMUM GEOMETRIC MEAN EFFICIENCIES REQUIRED TO
MAINTAIN MO MORE THAN ONE FAILURE PER TEN YEARS
Daily
Std. Dev.
(in log)
.20
.21
.22
.23
.24
.25
.26
.27
.28
.29
.30
.31
.32
.33
.34
.35
.35
.37
.33
.39
.40
.41
.42
.43
.44
.45
.46
.47
.48
.49
.50
.51
.52
.53
.54
Std. Oev.
of 30-Day
Average^-
(.0068)
f . 007" )
(
(
(
(
f
(
\
/
(
(
(
t
\
(
(
i
\
}
\
(
(
(
(
(
(
(
(
(
(
(
(
i
I
f
1
\
'.0075)
'.0079)
'.0082)
'.0086)
.0090)
.0093)
.0097)
.0101)
.0105)
.0109)
.0112)
.0116)
.0120)
.0124)
.0128)
.0133)
.0137)
.0141)
.0145)
.0150)
.0154)
.0158)
.0153)
.0157)
.0172)
.0177)
.0132)
.0186)
.0191)
.0196)
.0201)
.0206)
(.0212)
.55 (.0217)
. 56
.57
.58
.59
.60
(
(
.0222)
.0228)
(.0233)
(.0239)
v
.0245)
<90%
92.6
92-7
92
92
93
93
93
93.
93
93
93,
93,
93,
93,
94.
.3
< Q
.'o
% I
'.2
.3
.4
^
» -*
.6
.7
.8
.9
.0
94.1
94.
94.
.2
,3
94.4
94.5
94.6
94.7
94.
3
94.9
95.
95.
95.
95.
95.
95.
95.
95.
95.
95.
95.
95.
95.
96.
96.
95.
96.
0
0
1
2
3
4
5
5
6
7
8
3
9
0
4,
1
2
Minimum Efficiency
For Threshold Shown
-xQoo1 **Q Q^" ** £37^'' ^Q H
^Q_7,o ^00*0 ^O / -o ^O «
91.8 91.1 90.3 39,
91.9 Qi.? 9fi. =5 «
-------
2-37
2.3 METHODOLOGY
Monte-Carlo simulation techniques were used to generate the data in
for the lognormal-distribution processes in exhibits 2-4 through 2-9.
The IBM Scientific Subroutine Packaqe uniform random number generator
RANDU was used to generate the basic pseudo-random number stream for the
analyses. Box and Muller's technique was used for generating
pseudo-random normal random deviates (with an accuracy in the resultant
distribution of at least six digits).! Lognormal deviates were
generated by the exponential function from these normal deviates. All
the estimates were generated using non-overlapping random-number streams
of 720,000 days (2,000 years). The standard errors of the estimates were
estimated by treating the 2,000 years as four replicated experiments of
500 years each. The computations were performed to 32 and 64 bit
accuracy on a Hewlett-Packard Series 1000 Model F computer, and the runs
consumed about 40 CPU hours of computation. The simulation was checked
by comparing statistics for which exact results were known from theory,
and all cases agreed to three or more digit accuracies (with sample
periods of 8,000,000 days in this testing).
The normal-distribution estimates were generated by exact solution
of the mathematical system, to accuracy of five or more decimals.
Completely exact solutions of the lognonnal case were not available,
which led to the use of Monte-Carlo simulation. The critical values
given in exhibits 2-10 through 2-25 could not be found with the required
accuracy by simulation in the two-week term of this analysis, because
This techniaue is significantly more accurate in its results than
those usually used in good statistical practice. It was used because of
the requirement to estimate very small probabilities.
-------
2-38
such a determination by simulating all points necessary to search for the
critical values would have required approximately 2000 hours of comouter
time. Accordingly, mathematical methods were used to compute these
values to within 0.2 oercent. These methods, although derived from
standard techniques, were developed soecifically for this analysis. The
techniaues involve first using series aoproximations to the lognormal
distribution function and to its thirtieth convolution with itself, so as
to obtain accurate estimates of the third and fourth moments and
cumulants of the statistical distribution of the thirty-day averages.
(The first and second moments are known exactly in closed form.) These
estimates are then used in Edgeworth and Cornish-Fisher series expansions
of the distribution of the thirty-day averages, from which expected rates
of threshold failures and critical values can be completed. It was found
that only one non-normal term of the Edgeworth expansion was required to
achieve the desired accuracy. These methods were compared with the
simulation techniques to verify their accuracy (and the accuracy of the
computer implementations used.) All results were within 0.1 percent of
the correct values as determined by simulation, indicating that the
expansions are somewhat more accurate in the region of interest than the
guaranteed bound of 0.2 percent we obtained analytically. The exact
expression used to compute the critical minimum-efficiency values
reported above is given in exhibit 2-26.
-------
EXHIBIT 2-26: FORMULA FOR ESTIMATING THE GEOMETRIC MEAN EFFICIENCY AT WHICH
A LOGNORMAL PROCESS WILL ACHIEVE A RA1
THRESHOLD FAILURES BELOW ONE PER YEAR1
A LOGNORMAL PROCESS WILL ACHIEVE A RATE OF ROLLING-AVERAGE
?1
1 - Z
o 29 i 29
o[GO > /Iff/) + 2f(r) i 4 M30-1)(i-l)r » 0 J:(30-i)
^ ---
' "** M
(2.773 i 1.115 ---------------- ) X f e
10000 [.0333 -f .00222 f(r)]3/2
with
f(r) = r/(l-r) - y(l-r30)/(l-r)2 and similarly for f(r2)
2 ,,2
o?/2
w = e
and
x = [ c"2(e°2-l)(.0333 + .00222 f(r))
where
(t and p are the parameters describing the variability and autocorrelation of the lognormnl process
and Z is the threshold at which the rate of failures is to be < I/year.
Other critical rates involve changes in the constants 2.773 and 1.115.
-------
2-4.0
-------
3-1
3.0 DESCRIPTIVE STATISTICS ON FGD SYSTEM EFFICIENCY DATA
Basic descriptive statistics were required in construction of the
model simulating the variable efficiency of steam generating units. The
appronriate model structure and statistical distribution characteristics
were determined from an examination of observations reoorted from eleven
operating units. In addition, operating system parameters were varied
over ranges determined partly on the basis of parameter estimates made
from the data. This chapter consists of four sections describing the
observations and statistical analyses of them.
Section 3.1 defines the variable analyzed and describes the data
base used. A lognormal description of the analysis variable was used by
EPA and Entropy in previous analysis of this data. Section 3.2 discusses
the appropriateness of such a descriotion. As was shown in the analysis
reported in chapter 2.0, the issue of distributional form has little
influence on the principal results. In section 3.3 the means, standard
deviations, and autocorrelation factors are presented for each of the
eleven units. Differences in these parameters among the eleven units are
also noted. Additionally, the appropriateness of a first-order
autogressive model is discussed. Section 3.4 discusses possible
confounding of results caused by variation in the sulfur content of
untreated emissions.
3.1 DATA SET
Data on the efficiency factor from eleven electric utility steam
generating units were provided to VRI by the EPA. The data which was
received in printed tabular form was believed to be that previously
-------
3-2
analyzed by EPA and Entropy. The eleven units, the number of observa-
tions from each and the time period in which the observations were made
are described in exhibit 3-1. Each observation represents a twenty-four
hour average of FGD system efficiency calculated from the unput and
output emission levels at each unit. (Efficiency was defined as the
percentage of 302 removed from the gas flow through the scrubbing
process.)
As shown in exhibit 3-1, the amount and time frame of the data
differed significantly from one unit to the next. The limited number of
observations from the Philadelphia and Pittsburgh II units make the data
from these two facilities of limited use. The twenty-four data points
from Conesville A and the twenty-one from Conesville 3 represent the only
measurements taken over a six-month period. Further, the data set for
any individual unit was generally characterized by intermittent data
voids. This scattering of data points limits the degree of certainty
with which any inferences concerning the correlation structure of the
process should be reviewed.
3.2 LOGNORMAL TRANSFORMATION
3.2.1 THE UNTRANSFORMED VARIABLE
An analysis of the distribution of the efficiency values for each of
the units indicated that at least four were clearly negatively skewed
(see exhibit 3-2). Skewness, the third moment about the mean, measures
the degree to which a distribution is unbalanced or "off-center". A
negative skewness factor indicates a distribution with a long left-hand
tail. A variable with a normal distribution is balanced and has a
skewness of zero. Two of the units with significant skewness were also
-------
3-3
EXHIBIT 3-1: ANALYSIS DATA BASE DESCRIPTION
Steam Generating
Unit
Louisville North
Louisville South
Pittsburgh I
Pittsburgh II
Philadelphia
Chicago
Shawnee TCA
Shawnee Venturi
Conesville A
Conesville B
Lawrence
Number of
Observations
Time Period During Which
Observations Were Made
66
89
20
11
8
52
42
31
24
21
30
July
July
Sept
Nov.
Sept
Aug.
July
Dec.
Dec.
June
June
Jan.
21,
21,
. 14
10,
. 18
9,
30,
7,
7,
15,
15,
16,
1977
1977
, 1977
1977
, 1977
1977
1978
1978
1978
1978
1978
1979
- Dec.
- Dec.
- Nov.
- Dec.
- Oct.
- Nov.
- Sept
-Jan.
- Jan.
- Dec.
- Dec.
- Feb.
23
23
9,
6,
9,
23
. 8
25
29
13
13
21
, 1977
, 1977
1977
1977
1977
, 1977
, 1978
, 1979
, 1979
, 1978
, 1978
, 1979
(156
(156
(57
(27
(22
(107
(41
(49
(51
(183
(183
(37
days)
days)
days)
days)
days)
days)
days)
days)
days)
days)
days)
days)
-------
EXHIBIT 3-2: SKEWNESS1 AMI) KURTOSIS2 FACTORS AMI) SIGNIFICANCE3
I1NTRANSFORMED VARIABLE (Efficiency)
Unit
Louisville North
Louisville South
Pittsburgh 1
Pittsburgh 11
Philadelphia
Chicago
Shawnee TCA
Shawnee Ventur
Conesville A
Conesville B
Lawrence
Skewness
-.507
-.400
-.467
-1.005
- . 765
-.972
-.629
-.539
-.204
-.351
-1.333
Significant
at .05
Yes
No
No
No
No
Yes
Yes
No
No
No
Yes
Kurtosis
-.167
-.409
.062
.357
.266
3.707
-.015
- . 399
.005
-.574
1.140
Significant
at .05
No
No
No
No
No
Yes
No
No
No
No
Yes
TRANSFORMED VARIABLE Log (1 -
Skewness
-.241
-.302
-.206
.72.5
-.132
.210
.219
-.099
-.5/4
-.654
-.022
Significant
at .05
No
No
No
No
No
No
No
No
No
No
No
Kurtosis
.006
-.110
.120
-.271
-.142
2.173
-.452
-.021
-.660
.115
-.054
efficiency)
Significant
at .05
No
No
No
No
No
Yes£
No
No
No
No
No
^Skewness measures the degree to which the distribution 1s "off-center". A negative skew indicates a long left-hand tail.
This factor is zero fur a normal distribution.
^Kurtosis measures the degree of peakedness in the distribution. A positive value indicates a high peak and a negative
value indicates a flatter peak. This factor is zero for normal distribution.
3"sifin1f leant at .05" indicates 95 percent certainty that the distribution is different from a normal distribution in this
character!stic.
-------
3-5
found to have a significantly non-zero kurtosis. Kurtosis, a function of
the fourth moment about the mean, is often considered to measure the
degree of peakedness in the distribution. A positive value indicates a
higher peak (and longer tails) than in the normal distribution and a
negative value indicates a flatter peak. A variable with a normal
distribution has a kurtosis of zero.
Since the negative skewness was a significant and consistant feature
of the efficiency variable, the loge transformation performed by both
EPA and Entropy in previous analyses of the data might be expected to
produce a variable with a more normal distribution.
3.2.2 THE TRANSFORMED VARIABLE
The transformation variable used is log (1-efficiency). For most of
the units, the transformation improved the normality of the distribution
significantly. This improvement can be seen in the skewness and kurtosis
values for the untransformed and transformed variable, displayed in
exhibit 3-2. The significance column of the display indicates the
certainty with which the sample statistic implies an actual departure
from the normal distribution.
Exhibit 3-3 presents the arithmetic medians, means, and standard
deviations predicted for the observations under the lognormal assumption.
Comparison of these predicted values with the actual sample statistics
provides an intuitive feel for the goodness of fit of the lognormal
distribution. The lognormal assumption results in accurate predictions
except in the estimates of standard deviations at the Conesville and
Lawrence units.
-------
3-6
EXHIBIT 3-3:
Unit
COMPARISON OF ARITHMETIC VALUES PREDICTED BY
THE LOGNQRMAL DISTRIBUTION ASSUMPTION WITH
ESTIMATES FROM THE OBSERVATIONS
Arithmetic Values Predicted
By Lognormal Assumptions
Median
Standard
Mean Deviation
Observed Estimates From
Untransformed Variable
Standard
Median Mean Deviation
Louisville North
Louisville South
Pittsburgh I
Pittsburgh II
Philadelphia
Chicago
Shawnee TCA
Shawnee Venturi
Conesville A
Conesville B
Lawrence
84.4
83.3
80.8
85.4
97.0
89.2
88.5
96.0
86.0
92.5
95.4
83.8
82.2
80.2
85.0
96.8
89.1
88.3
95.8
84.5
91.5
93.4
4.9
6.2
4.5
3.2
1.2
1.2
2.2
1.6
7.3
4.2
5.6
84.6
83.3
81.2
86.1
96.7
88.9
88.5
95.7
84.1
91.9
95.3
83.8
82.3
80.3
85.1
96.3
89.1
88.3
95.8
84.7
91.7
93.6
4.7
5.9
4.6
3.4
1.2
1.3
2.2
1.5
6.1
3.5
5.3
-For lognormal distributions:
distributed).
Median = e"
' -2 >"?
Mean = e~e" ;
Standard Deviation = e'V
!the quantity (1-efficiency) is lognormally
u= mean of logarithmic variable.
z- Standard deviation of log-
arithmic variable.
V2
-------
3-7
In spite of the apparent better agreement between the lognormal
distribution and that data, Kolmogorov-Snn'rnov tests comparing both
normal and lognormal distributions with the data indicated that either
assumption could be accepted.
Overall, then, the lognormal distribution presents a slightly better
characterization of the efficiency data than the normal. However, from
the available data, it is evident that the lognormal description is not
an ideal fit for all cases, and that the distribution is also very nearly
normal in many of the cases.
3.3 ESTIMATED PARAMETERS AND COMPARABILITY AMONG UNITS
3.3.1 MEANS AND STANDARD DEVIATIONS
Exhibit 3-4 presents the medians, means, and standard deviations of
the transformed variable, log (1-efficiency). The differences in the
means and standard deviations among the eleven units can readily be seen
from examination of the exhibit. Statistical tests1 were performed on
the differences in means and variances for each pair of units. (The
variance is the square of the standard deviation.) The results of these
tests are presented in exhibits 3-5 and 3-6. The level of significance
indicates the probability of the observed difference occurring by chance
if, in reality, there was no difference between the two means (or
variances). For example, the significance of the difference in variances
between the Louisville South and Pittsburgh I units is .0305. This means
that if there were really no difference in the variances at these units,
^T-tests were performed on the means and F-tests on the variances.
-------
3-8
EXHIBIT 3-4: ESTIMATED PARAMETERS OF TRANSFORMED VARIABLE
UNIT
Louisville North
Louisville South
i^ittsburgh I
Pittsburgh II
Philadelphia
Chicago
Shawnee TCA
Shawnee Venturi
Conesvilie A
Conesvilie B
Lawrence
MEDIAN
MEAN U) STANDARD DEVIATION (a)
-1.8836
-1.7910
-1.63SS
-1.9729
-3.5143
-2.2047
-2.1840
-3.1353
-1.8798
-2.5170
-3.0791
-1.8608
-1.7863
-1.6492
-1.9223
-3.4927
-2.2217
-2.1608
-3.2270
-1.962S
-2.5884
-3.0714
.295
.343
.234
.212
.359
.118
.132
.368
.447
.474
.835
-------
EXHIBIT 3-5: STATISTICAL SIGNIFICANCE OF DIFFERENCES
IN VARIABILITIES AT DIFFERENT FACILITIES
CAIK:ES OF nJFFEHEHCCS i_i_ SITES
Dull/Unit
Louisville Louisville Pittsburgh Pittsburgh Shawnce Shawnce
North South _ 1 M Philadelphia Ui^S!0.. __KA_ yinJ!Lr-
Concsvlllc Cnncsvllln
A I)
Lawrence
Louisville llorlh
I on I sv I Ho South
Pittsburgh I
Pittsburgh II
I'd 11,nit.'I |ih I a
Chicago
Sh
-------
EXHIBIT 3-6: STATISTICAL SIGNIFICANCE OF DIFFERENCES
IN GEOMETRIC MEAN EMISSIONS AT FACILITIES
Unit/Unit
I (MI I sv I IK- llorth
Louisville South
I'l tlslniKjIi I
mislmigli II
I'll 1 1, idol |ili I a
Shawncp If A
ShilHIICe Vl'Mllll I
Coiwusvllle A
Coiwesvl Del)
I nwi nntc
loulsvlUc loulsvlllc Pittsburgh Mltsbiuyh
llorti
Sliawneo Sluiwricc toiii-'svl Me
O.)
i
rtw < refers In tin- pi ul).il>l I lly that the uhscrvvil illlfcrencc coiihl have occurred liy chanci* even If there were no real
-------
3-11
3.05 percent of random samples drawn from these units would produce a
difference in sample variance of the observed magnitude. A significance
level of .05 or lower is usually considered to be clear evidence of a
difference.
The variances at the Chicago and Shawnee TCA units were signifi-
cantly lower than the variances at almost all of the other units. EPA
officials noted that both of these units are well run and a low
variability in efficiency was expected. The Pittsburgh II unit was
described as being similar to the Shawnee TCA units, but because of the
limited number of observations the results are of less interest. The
significantly high variance at the Lawrence unit is believed by EPA
officials to be the result of an unusually low sulfur content of the
coal.
Because of the highly significant differences in the variances among
the units examined and the inaccurate estimation of variance at the
Conesville and Lawrence units, it is not appropriate to combine these
variances for analysis.
3.3.2 AUTOCORRELATION
The lag-one autocorrelation estimates for each of the eleven units
are presented in exhibit 3-7, along with the number of observations from
which the estimates were drawn and the significance of the factor. (The
observations included were those for which there was also an observation
on the preceding or succeeding day.) The level of significance is
dependent on the number of observations, hence the autocorrelation factor
of 0.6255 at the Conesville B unit is not significant because it is based
on only seven observations while the autocorrelation factor of 0.5995 at
-------
3-12
EXHIBIT 3-7: FIRST-ORDER AUTOCORRELATION FACTORS
ON THE VARIABLE LOG (1 - EFFICIENCY)
UNIT
Autocorrelation
1
Significant at
~05 level
Louisvi lie North
Louisvil le South
Pittsburgh I
Pittsburgh II
Philadelphia
Chicago
Shawnee TCA
Shawnee Venturi
Conesvilie A
Conesvilie 3
Lawrence
49
72
n
7
5
37
37
25
13
7
27
.6955 \
.6949
x
.4683
-.1428
.2524
.6983
.5995
.8897
.7131
.6255
.6386
,r\, yes
) ^>A yes
no
no
no
yes
yes
yes
yes
no
yes
The autocorrelation was determined by comparing day 't' with day 't-1';
the data was not collapsed and missing data was not filled in, so that
only the observation days which were preceded or followed by another
observation day were included.
-------
3-13
Shawnee TCA is significant. It seems almost certain that first-order
autocorrelation does, in fact, exist at most or all units. Entrony used
an estimate of 0.7 in their simulation model. This appears to be an
appropriate value if the model is dealing with a unit similar to one of
the Louisville units. However, for units more similar to the Shawnee TCA
unit, 0.6 would be a more reasonable estimate. Differences in opera-
tional procedures at the units are an unknown but probably relevant
factor.
3.3.3 AUTOREGRESSIVE MODEL
The possibility of autocorrelation factors associated with lags of
two or more was also examined. A first-order autogressive model is one
in which the variable in time "t" is a function of the same variable in
time "t-1". A second-order autogressive model was compared with a
first-order autogressive model. A comparison of the residual led to the
conclusion that the first-order autogressive model is appropriate. A
further examination of partial correlations up to a lag of ten led to the
conclusion that the first-order autogressive model is appropriate.
3.4 POSSIBLE CONFOUNDING FACTORS
It is recognized that many other factors mav be related to the
efficiency variable. It was suspected that the efficiency factor at a
given unit might be related to the level of sulfur in the raw emissions.
Data was available for all but the Lawrence unit on the pounds per
million BTUs of sulfur in the gas before processing. The Pittsburgh I
and Conesville scrubbers processed gas with a significantly higher
averaae sulfur content than the other units (see exhibit 3-8). Mo
-------
3-14
EXHIBIT 3-8: COMPARISON OF MEAN SULFUR CONTENT OF
INPUT EMISSIONS AND fAN EFFICIENCY
MEAN SULFUR CONTENT MEAN OF EFFICIENCY
OF INPUT EMISSIONS (Arithmetic Equivalent
UNIT (Ib/WIBTU) of Transformed Variable)
Louisville North 5.653 82.3
Louisville South 5.637 82.2
Pittsburgh I 6.647 80.2
Pittsburgh II 5.462 S5.0
Philadelphia 5.049 96.8
Chicago 5.643 89.1
Shawnee TCA 5.555 88.3
Shawnee Venturi 5.660 95.3
Conesville A 7.793 84.5
Conesville 3 7.359 91.6
Lawrence NA 93.4
-------
3-15
relationship appeared to exist, however, between mean efficiency at a
unit and the mean level of sulfur before scrubbing.
Within individual units, statistically significant correlations
between efficiency and sulfur content were found at two units, the
Chicago unit and the Shawnee TCA unit. At the Shawnee TCA unit, the
relationship was the expected negative one (-.45) with increasing sulfur
content leading to decreasing efficiency. At the Chicago unit, however,
a positive correlation (.47) was found, with increasing sulfur content
leading to increasing efficiency.
On the basis of the evidence, then, one must conclude that there is
no predictable relation between the actual levels of sulfur emissions
before scrubbing and the efficiency of the scrubbing operation, and that
the analyses reported here are not contaminated by any confounding effect
of this nature.
Many additional factors are of probable relevance in determining the
efficiency levels of scrubbers. Operating procedures can be altered to
compensate for high or low sulfur content as well as high or low electri-
city demands. The location and type of measuring device used can affect
efficiency readings. The age, type, and condition of the scrubber
equipment may also affect efficiency. The present data set does not
offer any evidence of the types or magnitudes of any effects from these
or other sources.
-------
3-16
-------
4-1
4.0 COMPARISON WITH ENTROPY RESULTS
This chapter summarizes the degree to which the findings in the
preceding chapters appear to agree with the results developed by Entropy
Environmentalists, Incorporated. It is organized into two sections which
parallel the material presented in chapters 2.0 and 3.0. In the first
section the number of exceedences predicted by Entropy are compared to
those predicted by YRI, with a potential explanation of the observed
differences. The second sectfon compares the VRI and Entropy descrip-
tions of the statistical structure characterizing the efficiency of
eleven flue gas desulfurization (FGD) units at eight electric utility
sites. The disparities between the Entropy and VRI estimates of process
parameter values are examined, and rationales for these differences are
discussed.
4.1 PREDICTED EXCEEDENCES
Although the details of Entropy's 1,000 year simulation were not
available, VRI believes the material presented in chapter 2.0 nearly
replicates the Entropy approach. Some differences between the VRI and
Entropy simulated data are attributable to the inherent random nature of
the simulation process itself and the slight improvement in confidence
levels of VRI's figures produced as a consequence of the doubling of the
number of simulated years (2,000 instead of 1,000). Where VRI used
parameters comparable to those reported by Entropy, reasonably similar
numbers of exceedences were predicted.
Although these results show generally the same pattern of effects,
there are differences greater than can be explained by chance effects.
-------
4-2
In view of the great care taken in this analysis, including soecial
rechecking of the disparate results, we suspect that the Entrooy results
are probably less accurate where differences exist, possibly due to the
use of less accurate random number generation and transformation tech-
niaues. In this connection, it is worth noting that YRI's estimates were
generated using methods considerably more precise than usually found in
good statistical practice. This extra precision was required in view of
the requirements to make accurate estimates o^ extremely small
probabilities.
Despite these minor differences, VR!1? results substantiate
Entropy's conclusion that the number of exceedences per year is extremely
sensitive to the median (or mean) P"GO system efficiency and the varia-
bility in this efficiency. VRI-simulated values nearly replicate
Entropy's findings that the degree of autocorrelation can affect the
number of exceedences although with less impact than variation in the
mean and variance. VRI's analyses also provide information not provided
by Entropy such as the data in exhibits 2-10 through 2-15; in these
areas, no comparisons are possible.
4.2 PROCESS STRUCTURE
Analysis of the 2^-hour FGD efficiency data indicate that the
measured values of efficiency are not symetrically distributed about
their mean, generally weakening any normal distribution hypothesis.
VRI's analysis agrees with the Entropy and EPA findings that the quantity
(1-efficiency) has a distribution which can be reasonably approximated by
a lognornal distribution. There are many other candidate distributions
-------
4-3
which might equally well be used to describe the observed distribution of
efficiency values. As shown in chapter 2.0, adoption of other distribu-
tions would not significantly influence the analysis results, but instead
might confuse major differences between the Entropy and VRI results with
insignificant discrepancies. Consequently, the above analysis used pri-
marily the lognormal distribution hypothesis proposed by EPA and con-
curred with by Entropy.
Entropy further found that the FGD efficiency data had significant
first-order autocorrelation. VRI's results upheld this finding even
though VRI's estimate of autocorrelation was based on consecutive calen-
dar days rather than the method suggested by Entropy's statistical con-
sultant which collapsed serial data into a string of days for which data
were available. In addition, VRI's negative finding on the presence of
higher order autocorrelation helped to validate the Entropy implicit
assumption that first-order (one day) lags were sufficient to describe
process time dependencies.
VRI used a data base which appeared to be approximately, but not
exactly, the same as that employed in the Entropy analysis. Specific
differences between the data provided are evidenced: (1) by disparities
in the numbers of observations at particular sites; and (2) by differ-
ences in numerical estimates. Disparities in the numbers of observations
occurred for two of the utilities reported, i.e.:
Number of Observations
Site VRI Entropy
Chicago 52 35
Shawnee TCA 42 37
-------
4-4
Entrooy does not report the number of observations from the Lawrence
unit, so comparisons cannot be made. YR!-estimated parameter values for
z and u generally differ from Entrcoy's estimates by no more than two
oercent exceot for the following sites.
loaarithmic Parameter Values
Site
Chicago
Shawnee TCA
Lawrence
h
-2
-2
-3
1 VRI
.222
.161
.071
\.
_2.
-2.
-3.
:E
206
168
437
WVRI
.118
.182
.325
w
t
.106
.186
.676
" YRI
.698
.600
.639
w f*
.86
.65
N/A
As noted above, VRI and Entropy were not using identical data bases for
the Chicago and Shawnee TCA sites. It is expected that the differences
at the Lawrence site may also be the result of a different data base.
Finally, the Entropy data base combined observations from the Louisville
north and south units into a single site (Cane Run) while they were
treated separately in VRI's analysis. Entropy notes that averaging the
results of these two units reduces the overall variability of the com-
bined sites. This effect is illustrated by the difference between the
two YRI logarithmic estimates of for Louisville (0.295 and 0.343) and
the single average Louisville estimate reported by Entrooy (0.239).
4.3 DIFFERENCES AMONG SITES
VRI and Entropy agree in finding that the evidence from existing
utility boiler units shows statistically significant differences in the
levels of variability at different sites. VRI has assumed that at least
some of its variability represents differences in engineering design ana
operating practices, including some designs and/or ooerating practices
-------
4-5
which may not represent the future state of the art for boiler units.
VRI therefore did not combine all the data together to estimate future
site variability. Entropy, in its analysis of these differences, did
combine the data to generate forecasting intervals, discussed in terms of
levels of correctness. In this analysis, Entropy assumed that future
sites would have levels of variability distributed as broadly as the
variabilities observed at existing sites. Thus, Entropy assumed that the
data from each of the existing sites constitutes a sample representating
appropriate state of the art design and operating practices which would
be used in future facilites. Without this assumotion, there is no
justification for using forecasting intervals based on the complete range
of variabilities.
Rather than adopt this strong assumption, VRI has chosen to present
the bulk of its results in parametric form covering the range of
variabilities, leaving er.qipeering analysis (combined with the data from
chapters 2.0 and 3.0) to identify the levels of variability which should
actually be expected at future sites. EPA personnel suggested that
Shawnee TCA and Pittsburgh II might be the best representatives of future
practices. Statistical analysis of these two sites suggests that they
had a common variability. Accordingly, a confidence interval for the
variability at these sites was presented in chanter 2.0. A confidence
interval is also presented there for the Louisville units.
------- |