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

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                                    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.

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                                    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.

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                                   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
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   r,nnn
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                                       "• ^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.
35.
95.
Gn
.3*
95.
,0
,1
, 2
\
_i
5
5
7
3
a
g
0
T
2
3
4
5
5
6
7
8
9
6
T_
i
2
3
4
5
5
6
7
3
g
g
6
i
2
2
3
4
91.
91.
9ll
at
91 .
91.
91.
91.
92.
92.
92.
92.
32.
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.
94.
.2
.3
.4

,6
, 7
,3
,9
,0
,1
,2
,3
4
5
5
7
8
g
0
1
2
3
4
5
^
5
7
3
g
0
i
2
3
3
4
5
6
7
3
g
g
90.
90.
90.
90.
90.
91.
91.
91.
91.
31.
91.
91.
91.
91.
91.
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.
,4
5
,5
3
g
0
1
2
3
A
*T
5
5
7
8
g
1
7
3
4
5
6
7
8
g
6
i
2
3
4
5
6
6
7
8
g
6
1
2
i
^
4
5
89.
39.
89.
90,
90.
90.
90.
90.
90.
90.
90.
90.
91.
91.
91.
91.
91.
91.
91.
91.
92.
92.
92.
92.
32.
92.
92.
92.
92.
92.
93.
S3.
S3.
S3.
S3.
93.
93.
S3.
S3.
33.
94.
,6
, 7
,9
,0
,1
,2
,3
5
6
-T
3
g
0
2
3
4
«*
5
7
8
0
1
2
3
4
r-
6
7
8
g
0
.L
2
3
4
5
6
/
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
-r
I
9
0
1
2
4
5
5
7
g
0
1
2
3
H
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 f€AN 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.

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3-16

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                                   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.

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                                    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

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                                  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

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                                    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

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                                   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.

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