U.S. patent application number 11/732037 was filed with the patent office on 2008-08-21 for system and method for determining equivalency factors for use in comparative performance analysis of industrial facilities.
This patent application is currently assigned to HSB Solomon Associates, LLC. Invention is credited to Robert Broadfoot, Michael J. Hileman, Richard B. Jones.
Application Number | 20080201181 11/732037 |
Document ID | / |
Family ID | 34135205 |
Filed Date | 2008-08-21 |
United States Patent
Application |
20080201181 |
Kind Code |
A1 |
Hileman; Michael J. ; et
al. |
August 21, 2008 |
System and method for determining equivalency factors for use in
comparative performance analysis of industrial facilities
Abstract
The present invention provides a system and method for
determining equivalency factors for use in comparative performance
analysis of industrial facilities by determining a target variable
and a plurality of characteristics of the target variable. Each of
the plurality of characterstics is ranked according to value. Based
on ranking value, the characteristics are divided into categories.
Based on the sorted and ranked characteristics, a data collection
classification system is developed. Data is collected according to
the data collection classification system. The data is validated,
and based on the data, an analysis model is developed. The analysis
model then calculates the equivalency factors.
Inventors: |
Hileman; Michael J.;
(McKinney, TX) ; Broadfoot; Robert; (Richardson,
TX) ; Jones; Richard B.; (The Woodlands, TX) |
Correspondence
Address: |
AKIN GUMP STRAUSS HAUER & FELD LLP
1111 Louisiana Street, 44th Floor
Houston
TX
77002
US
|
Assignee: |
HSB Solomon Associates, LLC
Dallas
TX
|
Family ID: |
34135205 |
Appl. No.: |
11/732037 |
Filed: |
April 2, 2007 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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11488266 |
Jul 18, 2006 |
7233910 |
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11732037 |
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10913728 |
Aug 9, 2004 |
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11488266 |
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60493150 |
Aug 7, 2003 |
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Current U.S.
Class: |
705/7.39 ; 703/2;
705/7.11 |
Current CPC
Class: |
G06Q 10/06398 20130101;
G06Q 10/04 20130101; G06Q 10/06393 20130101; G06Q 10/063 20130101;
G06Q 10/0639 20130101; Y02P 90/845 20151101 |
Class at
Publication: |
705/7 ;
703/2 |
International
Class: |
G06Q 10/00 20060101
G06Q010/00; G06F 17/10 20060101 G06F017/10 |
Claims
1. A method for determining equivalency factors in an industrial
facility, comprising: determining a target variable; determining a
plurality of characteristics of the target variable; classifying
the plurality of characteristics; collecting data with respect to
the characteristics; determining an equivalency factor for each of
the plurality of characteristics using an optimization model.
2. The method of claim 1, wherein the optimization model is any
non-linear optimization method.
3. The method of claim 1, wherein the optimization model is a
linear optimization method.
4. The method of claim 1, further comprising: determining a
percentage variation value for each of the plurality of
characteristics; dividing the plurality of characteristics into at
least two categories based on the percentage variation value; and
grouping characteristics in one of the at least two categories
based on a relationship of the characteristics.
5. The method of claim 1, further comprising: dividing the
plurality of characteristics into a first category, a second
category and a thir category; determining a relationship between
the characteristics in the first category; and grouping the
characteristics in the first category that have a common
relationship.
6. The method of claim 1, further comprising: creating a developed
characteristic by determining a mathematical relationship between a
first one of the plurality of characteristics and a second one of
the plurality of characteristics.
7. The method of claim 1, further comprising: using the equivalency
factor to compare a first facility and a second facility.
8. The method of claim 1, further comprising: adjusting a target
variable of a first facility using the equivalency factor;
adjusting a target variable of a second facility using the
equivalency factor; and comparing the adjusted target variable of
the first facility against the adjusted target variable of the
second facility.
9. The method of claim 1, further comprising: selecting a benchmark
facility.
10. The method of claim 9, further comprising: calculating a
performance gap value between a first facility and the benchmark
facility.
11. The method of claim 1, further comprising: calculating a
performance gap value between a first facility and a second
facility using the equivalency factor.
12. The method of claim 1, further comprising: classifying a first
facility into a performance subgroup in accordance with the ratio
of the first facility's actual target variable to the first
facility's actual target variable adjusted using the equivalency
factor.
13. The method of claim 1, further comprising: ranking a first
facility and a second facility in accordance with the first
facility's actual target variable adjusted using the equivalency
factor and the second facility's actual target variable adjusted
using the equivalency factor.
14. The method of claim 1, further comprising: calcuating
performance gaps using subgroups derived through the use of the
equivalency factor.
15. A method for determining equivalency factors, comprising:
determing a target variable; determing a plurality of
characteristics of the target variable; determining a percentage
variation value for each of the plurality of characteristics;
dividing the plurality of characteristics based on the percentage
variation value into a first category, a second categaory and a
third category; determining a relationship between the
characteristics in the first category; grouping the characteristics
in the first category that have a common relationship; classifying
the characteristics in the second category and the grouped
characteristics; combining the grouped characteristics and the
characteristics in the second category; collecting data with
respect to the combined characteristics; creating at least one
developed characteristic by determining a mathematical relationship
between a first one of the combined characteristics and a second
one combined characteristics; and using a non-linear optimization
model to determine equivalency factors by reducing an error value
between an actual value of the target variable and a predicted
value of the target variable using collected data of the combined
characteristics and the at least one developed characteristic.
16. A system for determining equivalency factors, comprising: a
target variable for an industrial facility; a plurality of
characteristics of the target variable; data for each of the
plurality of characteristics; and a computer-readable medium
comprising a plurality of instructions for execution by at least
one computer processor, the instructions for: determing a
mathematical relationship between a first one of the combined
characteristics and a second one combined characteristics; and
reducing an error value between an actual value of the target
variable and a predicted value of the target variable using the
data of the combined characteristics and the at least one developed
characteristic.
Description
[0001] This application claims the benefit of U.S. Provisional
Application No. 60/493,150, filed Aug. 7, 2003.
[0002] The present invention relates to comparing the performance
of manufacturing, refining, petrochemical, pipeline, power
generating, distribution, and other industrial facilities. More
specifically, the invention relates to determining the equivalency
factors that enable the conversion of production and other data
from a facility to a form that can be directly compared to the
production and other data from a another facility that has
different characteristics.
SUMMARY
[0003] The present invention provides a new and unique system and
method for determining equivalency factors for use in comparative
performance analysis of industrial facilities by determining a
target variable, and a plurality of characteristics of the target
variable. The characteristics are sorted and a data collection
classification system is developed. The data classification system
is used to quantitatively measure the differences in
characteristics. Data is collected according to the data collection
classification system. The data is validated, and based on the
data, an analysis model is developed to compare predicted target
variable to actual target variable for a set of industrial
facilities. The model is used to then find the best set of
complexity factors to minimize the difference in predicted versus
actual target variable values in the model.
BRIEF DESCRIPTION OF THE DRAWINGS
[0004] FIG. 1 is a flowchart illustrating the operation of an
embodiment of the invention.
[0005] FIG. 2 is a flowchart illustrating the operation of another
embodiment of the invention.
[0006] FIG. 3 is a flowchart illustrating the operation of another
embodiment of the invention.
[0007] FIG. 4 is an example implementation of an embodiment of the
invention.
[0008] FIG. 5 is another example implementation of an embodiment of
the invention using example data.
[0009] FIG. 6 is another example implementation of an embodiment of
the invention using example data.
[0010] FIG. 7 is a flowchart illustrating an example implementation
of an embodiment of the invention.
[0011] FIG. 8 is a graph depicting an example use of equivalency
factors to compare performance of facilities using equivalency
factors.
[0012] FIG. 9 is an illustrative node for implementing a method of
the invention.
DETAILED DESCRIPTION
[0013] The following disclosure provides many different
embodiments, or examples, for implementing different features of a
system and method for accessing and managing structured content.
Specific examples of components, processes, and implementations are
described to help clarify the invention. These are, of course,
merely examples and are not intended to limit the invention from
that described in the claims. Well-known elements are presented
without detailed description in order not to obscure the present
invention in unnecessary detail. For the most part, details
unnecessary to obtain a complete understanding of the present
invention have been omitted inasmuch as such details are within the
skills of persons of ordinary skill in the relevant art.
[0014] Referring now to FIG. 1, an example 100 of the operation of
one embodiment of a method for determining equivalency factors for
use in comparative performance analysis of industrial facilities is
shown. At step 102, a target variable ("Target Variable") is
selected. The target variable is a quantifiable attribute (such as
total operating expense, financial result, capital cost, operating
cost, staffing, product yield, emissions, energy consumption, or
any other quantifiable attribute of performance). Target Variables
could be in manufacturing, refining, chemical (including
(petrochemicals, organic and inorganic chemicals, plastics,
agricultural chemicals, and pharmaceuticals), Olefins plant,
chemical manufacturing, pipeline, power generating, distribution,
and other industrial facilities. The Target Variables could also be
for different environmental aspects. Target Variables could also be
in other forms and types of industrial and commercial
industries.
[0015] At step 104, the first principle characteristics are
identified. First principle characteristics are the physical or
fundamental characteristics of a facility or process that are
expected to determine the Target Variable. Common brainstorming or
team knowledge management techniques can be used to develop the
first list of possible characteristics for the Target Variable. In
one embodiment, all of the characteristics of an industrial
facility that may cause variation in the Target Variable when
comparing different manufacturing facilities are identified as
first principle characteristics.
[0016] At step 106, the primary first principle characteristics are
determined. As will be understood by those skilled in the art, many
different options are available to determine the primary first
principle characteristics. One such option is shown in FIG. 2.
[0017] At step 108, the primary characteristics are classified.
Potential classifications include discrete, continuous, or ordinal.
Discrete characteristics are those characteristics that can be
measured using a selection between two or more states, for example
a binary determination, such as "yes" or "no." An example discrete
characteristic could be "Duplicate Equipment." The determination of
"Duplicate Equipment" is "yes, the facility has duplicate
equipment" or "no, there is no duplicate equipment." Continuous
characteristics are directly measurable. An example of a continuous
characteristic could be the "Feed Capacity," since it is directly
measured as a continuous variable. Ordinal characteristics are
characteristics that are not readily measurable. Instead, ordinal
characteristics can be scored along an ordinal scale reflecting
physical differences that are not directly measurable. It is also
possible to create ordinal characteristics for variables that are
measurable or binary. An example of an ordinal characteristic would
be refinery configuration between three typical major industry
options. These are presented in ordinal scale by unit
complexity:
[0018] 1.0 Atmospheric Distillation
[0019] 2.0 Catalytic Cracking Unit
[0020] 3.0 Coking Unit
Ordinal variables are in rank order, and generally do not contain
information about any useful quality of measurement. In the above
example, the difference between the complexity of the 1.0 unit and
the 2.0 unit, does not necessarily equal the complexity difference
between the 3.0 unit and the 2.0 unit.
[0021] Variables placed in an ordinal scale may be converted to an
interval scale for development of equivalency factors. To convert
ordinal variables to interval variables requires the development of
a scale upon which the differences between units are on a
measurable scale. The process to develop an interval scale for
ordinal characteristic data can rely on the understanding of a team
of experts of the characteristic's scientific drivers. The team of
experts can first determine, based on their understanding of the
process being measured and scientific principle, the type of
relationship between different physical characteristics and the
Target Variable. The relationship may be linear, logarithmic, a
power function, a quadratic function or any other mathematical
relationship. Then the experts can optionally estimate a complexity
factor to reflect the relationship between characteristics and
variation in Target Variable. Complexity factors are the
exponential power used to make the relationship linear between the
ordinal variable to the target variable resulting in an interval
variable scale.
[0022] At step 110, a data collection classification system is
developed. For those characteristics categorized as continuous, a
data collection system that allows a quantification of the
characteristics is needed. A system of definitions will need to be
developed to ensure data is collected in a consistent manner. For
characteristics categorized as binary, a simple yes/no
questionnaire is used to collect data. A system of definitions may
need to be developed to ensure data is collected in a consistent
manner. For characteristics categorized as ordinal, a measurement
scale can be developed as described above.
[0023] To develop a measurement scale for ordinal characteristics,
at least four methods to develop a consensus function can be
employed. In one embodiment, an expert or team of experts can be
used to determine the type of relationship that exists between the
characteristics and the variation in Target Variable. In another
embodiment, the ordinal characteristics can be scaled (for example
1, 2, 3 . . . n for n configurations). By plotting the target value
versus the configuration, the configurations are placed in
progressive order of influence. In utilizing the arbitrary scaling
method, the determination of the Target Variable value relationship
to the ordinal characteristic is forced into the optimization
analysis, as described in more detail below. In this case, the
general optimization model described in Equation 1.0 can be
modified to accommodate a potential non-linear relationship.
[0024] In yet another embodiment, the ordinal measurement can be
scaled as discussed above, and then regressed against the data to
make a plot of Target Variable versus the ordinal characteristic to
be as nearly linear as possible. In a further embodiment, a
combination of the foregoing embodiments can be utilized to make
use of the available expert experience, and available data quality
and data quantity of data.
[0025] Once a relationship is agreed, a measurement scale is
developed. For instance, a single characteristic may take the form
of five different physical configurations. The characteristics with
the physical characteristics resulting in the lowest impact on
variation in Target Variable will be given a scale setting score.
This value may be assigned to any non-zero value. In this example,
the value assigned is 1.0. The characteristics with the second
largest impact on variation in Target Variable will be a function
of the scale setting value, as determined by a consensus function.
The consensus function is arrived at by using the measurement scale
for ordinal characteristics as described above. This is repeated
until a scale for the applicable physical configurations is
developed.
[0026] At step 112, the classification system is used to collect
data. The data collection process can begin with the development of
data input forms and instructions. In many cases, data collection
training seminars are conducted to assist in data collection.
Training seminars may improve the consistency and accuracy of data
submissions. A consideration in data collection is the definition
of the industrial facility boundaries being analyzed. Data input
instructions will provide definitions of what facilities, costs and
staffing are to be included in data collection. The data collection
input forms may provide worksheets for many of the reporting
categories to aid in the preparation of data for entry.
[0027] The data that is collected can come for several sources,
including existing historical data, newly gathered historical data
from existing facilities and processes, simulation data from
model(s), or synthesized experiential data derived from experts in
the field. Additionally, no data at all can be used, in which case
the determination of primary characteristics may be based on expert
experience.
[0028] At step 114, the data is validated. Many data checks can be
programmed into an interactive data collection system. The
interactive data collection system should only accept data that
passes the validation check or the check is over-ridden with
appropriate authority. Validation routines may be developed to
validate the data as it is collected. The validation routines can
take many forms, including: [0029] Range of acceptable data is
specified [0030] Ratio of one data point to another is specified
where applicable [0031] Data is cross checked against all other
similar data submitted to determine outlier data points for further
investigation [0032] Data is cross referenced to any previous data
submission [0033] Judgment of experts
[0034] After all input data validation is satisfied, the data is
examined relative to all the data collected in a broad
"cross-study" validation. This "cross-study" validation may
highlight further areas requiring examination and may result in
changes to input data.
[0035] At step 116, constraints may be developed for use in solving
the analysis model. These constraints could include constraints on
the equivalence factor values. These can be minimum or maximum
values, or constraints on groupings of values, or any other
mathematical constraint forms. One method of determining the
constraints is shown in FIG. 3.
[0036] At step 118, the analysis model is solved by applying
optimization methods of choice with the collected data to determine
the optimum set of complexity factors relating the Target Variable
to the characteristics. In one embodiment, the generalized reduced
gradient non-linear optimization method can be used. However, many
other optimization methods could be utilized.
[0037] At step 120, developed characteristics may be determined.
Developed characteristics are the result of any mathematical
relationship that exists between one or more first principle
characteristics and may be used to express the information
represented by that mathematical relationship. In addition, if a
linear general optimization model is utilized, then nonlinear
information in the characteristics can be captured in developed
characteristics. Determination of the developed characteristics
form is accomplished by discussion with experts, modeling
expertise, and by trial and refinement.
[0038] At step 122, the optimization model is applied to the
primary first principle characteristics and the developed
characteristics to determine the equivalency factors. In one
embodiment, if developed characteristics are utilized, step 116
through step 122 may be repeated in an iterative fashion until the
level of model accuracy desired is achieved.
[0039] Referring now to FIG. 2, one embodiment 200 of determining
primary first principle characteristics 106 is shown. At step 202,
the effect of each characteristic on the variation in the Target
Variable between industrial facilities is determined. In one
embodiment, the method is iteratively repeated, and an analysis
model can be used to determine the effect of each characteristic.
In another embodiment, a correlation matrix can be used. The effect
of each characteristic may be expressed as a percentage of the
total variation in the Target Variable in the initial data set. At
step 204, each characteristic is ranked from highest to lowest
based on its effect on the Target Variable. It will be understood
by those skilled in the art that other ranking criteria could be
used.
[0040] At step 206, the characteristics may be grouped into one or
more categories. In one embodiment, the characteristics are grouped
into three categories. The first category contains characteristics
that effect a Target Variable at a percentage less than a lower
threshold (for example, 5%). The second category are those
characteristics with a percentage between the lower percentage and
a second threshold (for example, 5% and 20%). The third category
are those characteristics with a percentage over the second
threshold (for example, 20%). Additional or fewer categories and
different ranges are also possible.
[0041] At step 208, those characteristics with Target Variable
average variation below a specific threshold may be removed from
the list of characteristics. For example, this could include those
characteristics in the first category (e.g., those characteristics
with a percentage of less than 5%). It will be understood by those
skilled in the art that other thresholds could be used, and
multiple categories could be removed from the list of
characteristics. In one embodiment, if characteristics are removed,
the process is repeated starting at step 202 above. In another
embodiment, no characteristics are removed from the list until
determining whether another co-variant relationships exist, as
described in step 212 below.
[0042] At step 210, the relationships between the mid-level
characteristics are determined. Mid-level characteristics are
characteristics that have a certain level of effect on the Target
Variable, but individually do not influence the Target Variable in
a significant manner. Using the illustrative categories, those
characteristics in the second category are mid-level
characteristics. Example relationships between the characteristics
are co-variant, dependent, and independent. A co-variant
relationship occurs when modifying one characteristic causes the
Target Variable to vary, but only when another characteristic is
present. For instance, in the scenario where characteristic "A" is
varied, which causes the Target Variable to vary, but only when
characteristic "B" is present, then "A" and "B" have a co-variant
relationship. A dependent relationship occurs when a characteristic
is a derivative of or directly related to another characteristic.
For instance, when the characteristic "A" is only present when
characteristic "B" is present, then A and B have a dependent
relationship. For those characteristics that are not co-variant or
dependent, they are categorized as having independent
relationships.
[0043] At step 212, characteristics displaying dependence on each
other may be resolved to remove dependencies and high correlations.
There are several potential methods for resolving dependencies.
Some examples include: (i) grouping multiple dependent
characteristics into a single characteristic, (ii) removing all but
one of the dependent characteristics, and (iii) keeping one of the
dependent characteristics, and creating a new characteristic that
is the difference between the kept characteristic and the other
characteristics. After the dependencies are removed, the process
may be repeated from step 202. In one embodiment, if the difference
variable is insignificant it can be removed from the analysis in
the repeated step 208.
[0044] At step 214, the characteristics are analyzed to determine
the extent of the inter-relationships. In one embodiment, if any of
the previous steps resulted in repeating the process, the
repetition should be conducted prior to step 214. In some
embodiments, the process may be repeated multiple times before
continuing to step 214.
[0045] At 216, the characteristics that result in less than a
minimum threshold change in the impact on Target Variable variation
caused by another characteristic are dropped from the list of
potential characteristics. An illustrative threshold could be 10%.
For instance, if the variation in Target Variable caused by
characteristic "A" is increased when characteristic "B" is present;
the percent increase in the Target Variable variation caused by the
presence of characteristic "B" must be estimated. If the variation
of characteristic "B" is estimated to increase the variation in the
Target Variable by less than 10% of the increase caused by
characteristic "A" alone, characteristic "B" can be eliminated from
the list of potential characteristics. Characteristic "A" can also
be deemed then to have an insignificant impact on the Target
Variable. The remaining characteristics are deemed to be the
primary characteristics.
[0046] Referring now to FIG. 3, an example embodiment 300 for
developing constraints for equivalency factors is shown.
Constraints are developed on the equivalency factors, step 302. The
objective function, as described below, is optimized to determine
an initial set of equivalency factors, step 304.
[0047] At step 306 the percent contribution of each characteristic
to the target variable is calculated. There are several methods of
calculating the percent contribution of each characteristic. One
method is the "Average Method," which is a two step process where
the Total Average Impact is calculated and then the percent
contribution of each characteristic is calculated. To calculate the
Total Average Impact, the absolute values of the equivalency
factors times the average value of each characteristic are summed
as shown below:
Average Method Equation:
TAI=.SIGMA..sub.j|.alpha..sub.j*avg.sub.j(F.sub.ij)| [0048]
TAI=Total Average Impact [0049] i=individual record referring to
the facility [0050] j=individual first principle or developed
characteristic [0051] .alpha..sub.j=equivalency faction for the jth
characteristic [0052] F=is a function of the measured first
principle characteristics or developed characteristic for a
facility. In the case where the first principle characteristic is
used directly, F may be 1 * characteristics. In the case of a
developed characteristic, F can be any function of the first
principle characteristic(s) and other developed characteristic(s).
[0053] avg.sub.j (F.sub.ij)=the average value of the measured first
principle characteristics or developed characteristic over all
facilities (over all j) in the analysis dataset
[0054] Following the calculation of the Total Average Impact, the
percent contribution of each characteristic is then calculated as
shown below:
Percent Contribution Equation : ##EQU00001## AI j = .alpha. j * avg
i ( F ij ) TAI ##EQU00001.2## AI j = Average Impact of jth first
principle or developed characteristic ##EQU00001.3##
[0055] An alternate method is the "Summation of Records Method,"
which calculates the percent contribution of each characteristic by
calculating the individual impacts from a summation of the impacts
at each individual data record in the analysis dataset of
facilities as shown below:
Summation of Records Equation: AI.sub.j=average over all
i[|.alpha..sub.j*F.sub.ij|/.SIGMA..sub.k|.alpha..sub.k*F.sub.ik|)
[0056] AI.sub.j=Average Impact of jth first principle or developed
characteristic [0057] i=the individual record referring to the
facility [0058] j=individual first principle or developed
characteristic [0059] k=individual first principle or developed
characteristic [0060] .alpha..sub.j=equivalency faction for the jth
characteristic [0061] F=is a function of the measured first
principle characteristics or developed characteristic for a
facility.
[0062] The Summation of Records Method may be used if non-linearity
exists in the impacts. It is contemplated that other methods to
calculate impacts may be used.
[0063] With the individual percent contributions developed, the
method proceeds to step 308, where each percent contribution is
compared against expert knowledge. Domain experts will have an
intuitive or empirical feel for the relative impacts of key
characteristics to the overall target value. The contribution of
each characteristic is judged against this expert knowledge.
[0064] At step 310 a decision is made about the acceptability of
the individual contributions. If the contribution are found to be
unacceptable the process continues to step 312. If they are found
to be acceptable the process continues to step 316.
[0065] At step 312, a decision is made to address how the
unacceptable results of the individual contributions are to be
handled. The options are to adjust the constraints on the
equivalency factors to affect a solution, or to decide that the
characteristic set chosen can not be helped through constraint
adjustment. If the developer gives up on constraint adjustment then
the process proceeds to step 316. If the decision is made to
achieve acceptable results through constraint adjustment then the
process continues to step 314.
[0066] At step 314, the constraints are adjusted to increase or
decrease the impact of individual characteristics in an effort to
obtain acceptable results from the individual contributions. The
process continues to step 302 with the revised constraints.
[0067] At step 316, peer and expert review of the equivalency
factors developed may be performed to determine the acceptability
of the equivalency factors developed. If the factors pass the
expert and peer review, the process continues to step 326. If the
equivalency factors are found to be unacceptable, the process
continues to step 318.
[0068] At step 318, new approaches and suggestions for modification
of the characteristics are developed by working with experts in the
particular domain. This may include the creation of new developed
characteristics, or the addition of new first principle to the
analysis data set. At step 320, a determination is made as to
whether data exists to support the investigation of the approaches
and suggestions for modification of the characteristics. If the
data exists, the process proceeds to step 324. If the data does not
exist, the process proceeds to step 322.
[0069] At step 322, additional data is collected and obtained in an
effort to attempt the corrections required to obtain a satisfactory
solution. At step 324, the set of characteristics are revised in
view of the new approaches and suggestions.
[0070] At step 326, the reasoning behind the selection of
characteristics used is documented. This documentation can be used
in explaining results for use of the equivalency factors.
[0071] Referring to FIG. 4, an example matrix 10 of a system for
determining equivalency factors is illustrated. While matrix 10 can
be expressed in many configurations, in this particular example,
matrix 10 is constructed with the first principle characteristics
12 and developed characteristics 14 on one axis, and the different
facilities 16 for which data has been collected on the other axis.
For each first principle characteristic 12 at each facility 16,
there is the actual data value 18. For each first principle
characteristic 12 and developed characteristic 14, there is the
equivalency factor 22 that will be computed with the optimization
model. The constraints 20 limit the range of the equivalency
factors 22. Constraints can be minimum or maximum values, or other
mathematical functions or algebraic relationships. Moreover,
constraints can be grouped and further constrained. Additional
constraints on facility data, and relationships between data points
similar to those used in the data validation step, and constraints
of any mathematical relationship on the input data can also be
employed. In one embodiment, the constraints to be satisfied during
optimization apply only to the equivalency factors.
[0072] The target variable (actual) column 24 are the actual values
of the target variable as measured for each facility. The target
variable (predicted) column 26 are the values for the target value
as calculated using the determined equivalency factors. The error
column 28 are the error values for each facility as determined by
the optimization model. The error sum 30 is the summation of the
errors in error column 28. The optimization analysis, which
comprises the Target Variable equation and an objection function,
solves for the equivalency factors to minimize the error sum 30. In
the optimization analysis, the equivalency factors (.alpha..sub.j)
are computed to minimize the error (.epsilon..sub.i) over all
facilities. The non-linear optimization process determines the set
of equivalency factors that minimizes this equation for a given set
of first principle characteristics, constraints, and a selected
value.
[0073] The Target Variable is computed as a function of the
characteristics and the yet to be determined equivalency factors.
The Target Variable equation is expressed as:
Target Variable equation : ##EQU00002## TV i = j .alpha. j f (
characteristic ) ij + i ##EQU00002.2## [0074] TV.sub.i is the
measured Target Variable for facility i [0075] characteristic is a
first principle characteristic [0076] i is the facility number
[0077] j is the characteristic number [0078] .alpha..sub.j is the
jth equivalency factor [0079] .epsilon..sub.i is the error of the
model's TV prediction as defined by: Actual TV value-Predicted TV
value for facility i
[0080] The objective function has the general form:
Objective Function : ##EQU00003## Min [ i = 1 m i p ] 1 / p , p
.gtoreq. 1 ##EQU00003.2## [0081] i is the facility [0082] m is the
total number of facilities [0083] p is a selected value
[0084] One common usage of the general form of objective function
is for minimization of the absolute sum of error by using p=1 as
shown below:
Objective Function : ##EQU00004## Min [ i = 1 m i ]
##EQU00004.2##
[0085] Another common usage of the general form of objective
function is using the least squares version corresponding to p=2 as
shown below:
Objective Function : ##EQU00005## Min [ i = 1 m i 2 ] 1 / 2
##EQU00005.2##
[0086] Since the analysis involves a finite number of first
principle characteristics and the objective function form
corresponds to a mathematical norm, the analysis results are not
dependent on the specific value of p. The analyst can select a
value based on the specific problem being solved or for additional
statistical applications of the objective function. For example,
p=2 is often used due to its statistical application in measuring
data and target variable variation and target variable prediction
error.
[0087] A third form of the objective function is to solve for the
simple sum of errors squared as given in Equation 5 below.
Objective Function : ##EQU00006## Min [ i = 1 m i 2 ]
##EQU00006.2##
[0088] While several forms of the objective function have been
shown, other forms of the objective function for use in specialized
purposes could also be used. Under the optimization analysis, the
determined equivalency factors are those equivalency factors that
result in the least difference between the summation and the actual
value of the Target Variable after the model iteratively moves
through each facility and characteristic such that each potential
equivalency factor, subject to the constraints, is multiplied
against the data value for the corresponding characteristic and
summed for the particular facility.
[0089] For illustrative purposes, a more specific example of the
system and method for determining equivalency factors for use in
comparative performance analysis as illustrated in FIGS. 1-3 is
shown. The example will be shown with respect to a major process
unit in most petroleum refineries, known as a Fluidized Catalytic
Cracking Unit (Cat Cracker). A Cat Cracker cracks long molecules
into shorter molecules in the gasoline boiling range and lighter.
The process in conducted at very high temperatures in the presence
of a catalyst. In the process of cracking the feed, coke is
produced and deposited on the catalyst. The coke is burned off the
catalyst to recover heat and to reactivate the catalyst. The Cat
Cracker has several main sections: Reactor, Regenerator, Main
Fractionator, and Emission Control Equipment. Refiners desire to
compare the performance of their Cat Crackers to the performance of
Cat Crackers operated by their competition. This Cat Cracker
example is for illustrative purposes and may not represent the
actual results of applying this methodology to Cat Crackers, or any
other industrial facility. Moreover, the Cat Cracker example is but
one example of many potential applications of the used of this
invention in the refining industry.
[0090] First, at step 102, the desired Target Variable will be
"Cash Operating Costs" or "Cash OPEX" in a Cat Cracker facility. At
step 104, the first principle characteristics that may affect Cash
Operating Costs for a Cat Cracker might be:
TABLE-US-00001 Feed Quality Regenerator Design Staff Experience
Location Age of Unit Catalyst Type Feed Capacity Staff Training
Trade Union Reactor Temperature Duplicate Equipment Reactor Design
Emission Control Equipment Main Fractionator Design Maintenance
Practices Regenerator Temperature Degree of Feed Preheat
[0091] To determine the primary characteristics, step 106, this
example has determined the effect of the first characteristics. For
this example, the embodiment for determining primary
characteristics as shown in FIG. 2 will be used. Moving to FIG. 2,
at step 202, each characteristic is given an variation percentage.
At step 204, the characteristics from the Cat Cracker Example are
rated and ranked. The following chart shows the relative influence
and ranking for the example characteristics:
TABLE-US-00002 Characteristics Category Comment Feed Quality 3
Several aspects of feed quality are key Catalyst Type 3 Little
effect on costs, large impact on yields Reactor Design 1 Several
key design factors are key Regenerator 3 Several design factors are
key Design Staffing Levels 2 Feed Capacity 1 Probably single-most
highest impact Emission Control 2 Wet versus dry is a key
difference Equipment Staff Experience 3 Little effect on costs
Staff Training 2 Little effect on costs Main Fractionator 3 Little
effect on costs, large impact on Design yields Location 3 Previous
data analysis shows this characteristic has little effect on costs
Trade Union 3 Previous data analysis shows this characteristic has
little effect on costs Maintenance 2 Effect on reliability and
"lost Practices opportunity cost" Age of Unit 2 Previous data
analysis shows this characteristic has little effect on costs
Reactor 3 Little effect on costs Temperature Regenerator 3 Little
effect on costs Temperature Duplicate 3 Little effect on costs
Equipment
[0092] In this embodiment, the categories are as follows:
TABLE-US-00003 Percent of Average Variation in the Target Variable
Between Facilities Category 1 (Major Characteristics) >20%
Category 2 (Midlevel Characteristics) 5-20% Category 3 (Minor
Characteristics) <5%
[0093] It is understood that other embodiments could have any
number of categories and that the percentage values that delineate
between the categories may be altered in any manner.
[0094] Based on the above example rankings, the characteristics are
grouped according to category, step 206. At step 208, those
characteristics in Category 3 are discarded as being minor.
Characteristics in Category 2 must be analyzed further to determine
the type of relationship they exhibit with other characteristics,
step 210. Each is classified as exhibiting either co-variance,
dependence or independence, step 212. As an example:
TABLE-US-00004 Classification of Category 2 Characteristics Based
on Type of Relationship Type of If Co-variant or Category 2
characteristics Relationship Dependent, Related Partner(s) Staffing
Levels Independent Emission Equipment Co-variant Maintenance
Practice Maintenance Practices Co-variant Staff Experience Age of
Unit Dependent Staff Training Staff Training Co-variant Maintenance
Practice
[0095] At step 214, the degree of the relationship of these
characteristics is analyzed. Using this embodiment for the Cat
Cracker example: Staffing levels, classified as having an
Independent relationship, stays in the analysis process. Age of
Unit is classified as having a dependent relationship with Staff
Training. A dependent relationship means Age of Unit is a
derivative of Staff Experience or vice versa. After further
consideration, it is decided Age of Unit can be dropped from the
analysis and the broader characteristic of Staff Training will
remain in the analysis process. The three characteristics
classified as having a co-variant relationship, Staff Training,
Emission Equipment, Maintenance Practices, must be examined to
determine the degree of co-variance.
[0096] It is determined that the change in Cash Operating Costs
caused by the variation in Staff Training is modified by more than
30% by the variation in Maintenance Practices. Along the same
lines, the change in Cash Operating Costs caused by the variation
in Emission Equipment is modified by more than 30% by the variation
in Maintenance Practices. Therefore, Maintenance Practices, Staff
Training and Emission Equipment are retained in the analysis
process.
[0097] It is also determined that the change in Cash Operating
Costs caused by the variation in Maintenance Practice is not
modified by more than the selected threshold of 30% by the
variation in Staff Experience. Therefore, Staff Experience can be
dropped from the analysis.
[0098] Continuing with the Cat Cracker example, and returning to
FIG. 1, the remaining characteristics are categorized as
continuous, ordinal or binary type measurement, step 108.
TABLE-US-00005 Classification of Remaining characteristics Based on
Measurement Type Remaining characteristics Measurement Type
Staffing Levels Continuous Emission Equipment Binary Maintenance
Practices Ordinal Staff Training Continuous
In this Cat Cracker example: Maintenance Practices have an "economy
of scale" relationship with Cash Operating Costs (which is the
Target Variable). So the improvement in Target Variable improves at
a decreasing rate as Maintenance Practices Improve. Based on
historical data and experience, a complexity factor is assigned to
reflect the economy of scale. In this particular example, a factor
of 0.6 is selected.
[0099] As an example of coefficients, the complexity factor is
often estimated to follow a power curve relationship. Using Cash
Operating Costs as an example of a characteristic that typically
exhibits an "economy of scale;" the effect of Maintenance Practices
can be described with the following:
Target Variable facility A = ( Capacity facilityA Capacity
facilityB ) ComplexityFactor * Target Variable facilityB
##EQU00007##
[0100] At step 110, a data collection classification system is
developed. In this example, a questionnaire is developed to measure
how many of ten key Maintenance Practices are in regular use at
each facility. A system of definitions are used so that data is
collected in a consistent manner. The data in terms of number of
Maintenance Practices in regular use is converted to a Maintenance
Practices Score using the 0.6 factor and "economy of scale"
relationship as illustrated in the following table.
TABLE-US-00006 Maintenance Practices Score Number Maintenance
Practices In Regular Use Maintenance Practices Score 1 1.00 2 1.52
3 1.93 4 2.30 5 2.63 6 2.93 7 3.21 8 3.48 9 3.74 10 3.98
[0101] For illustrative purposes with respect to the Cat Cracker
example, at step 112, data was collected and, at step 114,
validated as follows:
TABLE-US-00007 Cat Cracker Data Cash Staff Staffing Emission Feed
Operating Reactor Training Levels Equipment Capacity Maintenance
Cost Unit of Design Man Number Yes = 1 Barrels Practices Dollars
Measurement Score Weeks People No = 0 per Day Score per Barrel
Facility #1 1.50 30 50 1 45 3.74 3.20 Facility #2 1.35 25 28 1 40
2.30 3.33 Facility #3 1.10 60 8 0 30 1.93 2.75 Facility #4 2.10 35
23 1 50 3.74 4.26 Facility #5 1.00 25 5 0 25 2.63 2.32
[0102] Constraint ranges were developed for each characteristics by
the expert team to control the model so that the results are within
a reasonable range of solutions.
TABLE-US-00008 Cat Cracker Model Constraint Ranges Reactor Staff
Staffing Emission Maintenance Feed Design Training Levels Equipment
Practices Capacity Minimum -3.00 -3.00 -1.0 -1.0 0.0 0.0 Maximum
0.00 1.00 40 0.0 4.0 4.0
[0103] At step 116, the results of the model optimization runs are
shown below.
TABLE-US-00009 Model Results Characteristics Equivalency Factors
Reactor Design -0.9245 Staff Training -0.0021 Staffing Levels
-0.0313 Emission Equipment 0.0000 Maintenance Practices 0.0000 Feed
Capacity 0.1382
[0104] The model indicates Emission Equipment and Maintenance
Practices are not significant drivers of variations in Cash
Operating Costs between different Cat Crackers. This is indicated
by the model finding zero values for equivalency factors for these
two characteristics. Reactor Design, Staff Training, and Emission
Equipment are found to be significant drivers.
[0105] In the case of both Emission Equipment and Maintenance
Practices, the experts agree it is reasonable that these
characteristics are not significant in driving variation in Cash
Operating Cost. The experts feel there is a dependence effect not
previously identified that fully compensates for the impact of
Emission Equipment and Maintenance Practices.
[0106] A sample model configuration for the illustrative Cat
Cracker example is shown in FIG. 5. The data 18, actual values 24,
and the resulting equivalency factors 22 are shown. In this
example, the error sum 30 is minimal, so developed characteristics
are not necessary in this instance. In other examples, an error sum
of differing values may be significant, and result in having to
determine developed characteristics.
[0107] For additional illustrative purposes, a more specific
example of the system and method for determining equivalency
factors for use in comparative performance analysis as illustrated
in FIGS. 1-3 is shown. The example will be shown with respect to
pipelines and tank farms terminals. Pipelines and tank farms are
assets used by industry to store and distribute liquid and gaseous
feedstocks and products. The example is illustrative for
development of equivalence factors for:
[0108] a. pipelines and pipeline systems alone
[0109] b. tank farm terminals alone
[0110] c. any combination of pipelines, pipeline systems and tank
farm terminals.
This example is for illustrative purposes and may not represent the
actual results of applying this methodology to any particular
pipeline and tank farm terminal, or any other industrial
facility.
[0111] First, at step 102, the desired Target Variable will be
"Cash Operating Costs" or "Cash OPEX" in a pipeline asset. At step
104, the first principle characteristics that may affect Cash
Operating Costs might be:
TABLE-US-00010 Pipeline Related Characteristics Tank Terminal
Characteristics Type of Fluid Transported Fluid Class Average Fluid
Density Number of Tanks Number of Input and Output Total Number of
Valves in Terminal Stations Total Nominal Tank Capacity Total
Installed Capacity Annual Number of Tank Turnovers Total main pump
driver KW Tank Terminal Replacement Value Length of pipeline
Altitude change in pipeline Total Utilized Capacity Pipeline
Replacement Value Pump Station Replacement Value
[0112] To determine the primary first principle characteristics,
step 106, this example has determined the effect of the first
characteristics. For this example, the embodiment for determining
primary characteristics as shown in FIG. 2 will be used. Moving to
FIG. 2, at step 202, each characteristic is given an impact
percentage. This analysis shows that the pipeline replacement value
and tank terminal replacement value that are used widely in the
industry are characteristics that are dependent on more fundamental
characteristics. Accordingly, in this instance, those values are
removed from consideration for primary first principle
characteristics. At step 204, the characteristics from are rated
and ranked. The following chart shows the relative impact and
ranking for the example characteristics:
TABLE-US-00011 Characteristics Category Comment Type of Fluid
Transported 2 products and crude Average Fluid Density 3 affects
power consumption Number of Input and Output 1 more stations means
more Stations cost Total Installed Capacity 3 surprisingly minor
affect Total Main Pump Driver KW 1 power consumption Length of
pipeline 3 no affect Altitude change in pipeline 3 small affect by
related to KW Total Utilized Capacity 3 no effect Pipeline
Replacement Value 3 industry standard has no effect Pump Station
Replacement 3 industry standard has little Value effect Fluid Class
3 no effect Number of Tanks 2 important tank farm parameter Total
Number of Valves in 3 no effect Terminal Total Nominal Tank
Capacity 2 important tank farm parameter Annual Number of Tank 3 no
effect Turnovers Tank Terminal Replacement 3 industry standard has
little Value effect
[0113] In this embodiment, the categories are as follows:
TABLE-US-00012 Per Cent of Average Variation in the Target Variable
Between Facilities Category 1 (Major Characteristics) >15%
Category 2 (Midlevel Characteristics) 7-15% Category 3 (Minor
Characteristics) <7%
It is understood that other embodiments could have any number of
categories and that the percentage values that delineate between
the categories may be altered in any manner.
[0114] Based on the above example rankings, the characteristics are
grouped according to category, step 206. At step 208, those
characteristics in Category 3 are discarded as being minor.
Characteristics in Category 2 must be analyzed further to determine
the type of relationship they exhibit with other characteristics,
step 210. Each is classified as exhibiting either co-variance,
dependence or independence as show below:
TABLE-US-00013 Classification of Category 2 Characteristics Based
on Type of Relationship If Co-variant or Type of Dependent,
Category 2 characteristics Relationship Related Partner(s) Type of
Fluid Transported Independent Number of Input and Output Stations
Independent Total Main Pump Driver KW Independent Number of Tanks
Independent Total Nominal Tank Capacity Independent
[0115] At step 212 the dependent characteristics are resolved. In
this example, there are no dependent characteristics that need to
be resolved. At step 214, the degree of the co-variance of the
remaining characteristics are analyzed and no characteristics are
dropped.
[0116] The remaining variables were deemed to be primary
characteristics in step 218.
[0117] Continuing with the Pipeline and Tank Farm example, and
returning to FIG. 1, the remaining characteristics are categorized
as continuous, ordinal or binary type measurement, step 108.
TABLE-US-00014 Classification of Remaining characteristics Based on
Measurement Type Remaining characteristics Measurement Type Type of
Fluid Transported Binary Number of Input and Output Stations
Continuous Total Main Pump Driver KW Continuous Number of Tanks
Continuous Total Nominal Tank Capacity Continuous
[0118] At step 110, a data collection classification system is
developed. In this example a questionnaire is developed to collect
information from participating facilities on the measurements
above.
[0119] At step 112, data was collected and, at step 114, validated
as follows:
TABLE-US-00015 Pipe Line and Tank Farm Data Type Number of Input
Characteristic of Fluid and Output Total Main Number Total Nominal
Measurement 1 = Product Stations Pump Driver of Tanks Tank Capacity
Units 2 = Crude Count KW Count KMT Facility 1 1 8 74.0 34 1,158
Facility 2 2 16 29.0 0 0 Facility 3 1 2 5.8 7 300 Facility 4 1 5
4.9 6 490 Facility 5 1 2 5.4 8 320 Facility 6 2 2 2.5 33 191
Facility 7 1 3 8.2 0 0 Facility 8 2 2 8.7 0 0 Facility 9 1 3 15.0
10 180 Facility 10 1 9 12.0 22 860 Facility 11 1 4 20.0 5 206
Facility 12 2 9 9.3 0 0 Facility 13 2 12 6.2 0 0 Facility 14 1 5
41.4 19 430 Facility 15 2 8 8.2 0 0 Facility 16 1 8 96.8 31 1,720
Facility 17 1 2 15.0 8 294
[0120] In Step 116, constraints were also developed on the
equivalency factors by the expert as given below.
TABLE-US-00016 Equivalency Factor Constraints Number of Input Type
and Output Total Main Number Total Nominal of Fluid Stations Pump
Driver of Tanks Tank Capacity Minimum 0 0 0 134 0 Maximum 2000 700
500 500 100
[0121] At step 116, the results of the model optimization runs are
shown below.
TABLE-US-00017 Model Results Characteristics Equivalency Factors
Type of Fluid Transported 1301.1 Number of Input and Output
Stations 435.4 Total Main Pump Driver KW 170.8 Number of Tanks
134.0 Total Nominal Tank Capacity 6.11
[0122] In step 118 it was determined that there was no need for
developed characteristics for this example. Thus the final
equivalency factors are those determined in the analysis model step
above.
[0123] FIG. 6 shows the analysis performed on the pipeline and tank
farm example. This example shows but one of many potential
applications of this invention to the pipeline and tank farm
industry.
[0124] It is understood that this methodology could be applied to
many different industries and facilities. For example, this
methodology could be applied to the power generation industry (such
as developing equivalency factors for predicting operating expense
for single cycle and combined cycle generating stations that
generate electrical power from any combination of boilers, steam
turbine generators, combustion turbine generators and heat recovery
steam generators). In another example, this methodology could be
applied to develop equivalency factors for predicting the annual
cost for ethylene manufacturers of compliance with environmental
regulations associated with continuous emissions monitoring and
reporting from ethylene furnaces. In one embodiment, the
equivalency factors would apply to both environmental applications
and chemical industry applications.
[0125] Once equivalency factors have been developed, the factors
can be utilized to allow comparison of any one facility's data to
another or to compare data across multiple facilities in an
industry segment. Referring now to FIG. 7, an example embodiment
700 for using equivalency factors to establish a standard to be
used for comparison between facilities is shown.
[0126] At step 702, the gap for all facilities are calculated. The
gap is calculated by first determining the predicted value using
the equivalency factors. This predicted value may be referred to as
the "Equivalent Value" or "EV". The different between the actual
Target Value and the Equivalent value is the gap for a particular
facility as calculated in accordance with the following
equations:
EV i = j = 1 .alpha. j F ij ##EQU00008## Gap i = TV i - EV i
##EQU00008.2##
[0127] At step 704, the ratio of target variable to equivalent is
calculated and plotted. In one embodiment, a piano chart can be
used for analysis of comparative performance. An example piano
chart for the generation example is given in FIG. 8. The equations
below are used to develop this information.
PR.sub.i=TV.sub.i/EV.sub.i [0128] PR.sub.i=Performance Ratio of
facility i [0129] TV.sub.i=Actual Target Value of facility i [0130]
EV.sub.i=Equivalent Value of facility i The set of performance
ratios in the analysis are then rank ordered from low to high and
plotted on the piano chart for discussion with individual
participant's facilities.
[0131] It is recognized that the actual gap could be used in a
similar manner and use of gap rather than ratio is included in this
disclosure. Using a ratio permits the "hiding" of gap information
while still providing to peers in the study a qualitative value for
comparative performance.
[0132] At step 706, the rank ordered list of ratios is used to
determine membership in performance subgroups. Subgroups can be
established as any fraction of the total participants. Typical
subgroups include:
[0133] a. Halves (top and bottom)
[0134] b. Quartiles (1.sup.st, 2.sup.nd, 3.sup.rd and 4.sup.th
quartiles)
[0135] c. Deciles (1.sup.st through 10.sup.th deciles)
Participants are advised of the rank membership, and their actual
position on the piano chart is indicated.
[0136] At step 708, a customized set of one or more facilities can
optionally be selected as the standard for a comparison of all
records to be included in the analysis. At this point the
facilities to be selected for the measurement standard group for
this analysis are arbitrary. Typical value selections include:
[0137] the predicted equivalent value EV [0138] the average of all
values for each characteristic [0139] the combined average for a
set of one or more facilities demonstrating the maximum performance
ratio [0140] the combined average for a set of one or more
facilities demonstrating a minimum performance ratio [0141] the
combined average for a set of one or more facilities contained in
any of the performance subgroups [0142] the combined average for a
set of one or more facilities demonstrating the lowest performance
ratio or most positive gap [0143] the combined average of a set
from a geographic or economic subset [0144] a set of facilities
that the customer considers to be their competitors [0145] a set of
facilities of equal size and complexity [0146] any criteria
selected to achieve the desired comparison
[0147] At step 710, the set of facilities selected as the benchmark
are combined into one single benchmark point. In one embodiment,
this can be accomplished by taking the average of the target value
of the facilities selected as the benchmark and the average of each
characteristic as the single benchmark facility.
[0148] At step 712, for each facility, the benchmark is adjusted to
the actual characteristic values of each individual facility as
shown below:
Equiv.sub.2-1=TV.sub.2*EV.sub.1/EV.sub.2
[0149] At step 714, the gap between the performance of each
individual facility in the peer group is calculated from the
performance of the adjusted benchmark, and the actual performance
of the target facility as shown below:
GAP.sub.i=Equiv.sub.2-1-TV(actual).sub.i
[0150] For illustrative purposes, two facilities will be compared
using the equivalency factors developed in the power generation
industry. First, the equivalency factors must be developed. The
following data will be used for determining the equivalency
factors.
TABLE-US-00018 Initial Characteristics HRSG count of heat recovery
steam generators CTG count of combustion turbine generators STG
count of steam turbine generators BOIL count of combustion boilers
NDC net dependable capacity SVC Factor fraction of hours in the
year that the facility is operated NetMWH megawatts generated in a
year PurGas yearly economic value of purge gas PurLiquid yearly
economic value of purge liquid ACTStarts actual count of starts in
a year NCF Net Capacity Factor NOF Net Operating Factor
[0151] The primary characteristics for use were determined to be
the following:
TABLE-US-00019 Primary Characteristics C2 (a developed
characteristic) HRSG + STG + BOIL NDC net dependable capacity SVC
Factor fraction of hours in the year that the facility is operated
C3 (a developed characteristic) NCF-NOF
[0152] The equivalency factors are developed using the collected
data, which results in the following:
TABLE-US-00020 Equivalancy Factors C2 674.3 NDC 10.4 SVC Factor
440.7 C3 -46.0
[0153] Below is the example data for two facilities to be
compared.
TABLE-US-00021 Target Variable C2 NDC SVC Factor C3 Facility 1
$6,690 7.0 470 1.00 0.0 Facility 2 $2,082 1.0 97 0.979 -1.92
[0154] The first step is to pick one of the facilities as the
standard. For this example, Facility 1 will be used.
[0155] Using the developed equivalency factors, Facility 2's values
are modified to place it on the same basis as Facility 1. This is
done by multiplying the Facility 2 data by the ratio of predicted
target variable values.
EV.sub.1=(674.3)(7)+(10.4)(470)+(440.7)(1.000)+(-46.0)(0.00)=10,048.8
EV.sub.2=(674.3)(1)+(10.4)(97)+(440.7)(0.979)+(-46.0)(-1.92)=2,202.9
Now converting Facility 2 Target Value to compare with Facility,
the ratio of the Equivalent values as shown below is used.
Equiv.sub.2-1=$2,202*10,048.8/2,202.9=$9,497.5
[0156] Facility 1's target value can now be compared to that of
Facility 2. The difference is $9,497.5-$6,690=$2,807.5. Facility 1
is operating at a lower OPEX than Facility 2. The difference may
represent a gap closure opportunity for Facility 2, if the reasons
for the lower OPEX in Facility 1 can be determined.
[0157] The gap of each facility to the analysis set average
performance can also be determined from the equation below. For the
current example the gap can be calculated as shown below:
GAP.sub.1=$10,048.8-$6,690=+$3,358.8
GAP.sub.2=$2,202.9-$2,082=+$120.9
[0158] This procedure can be expanded to the entire population of 2
or more facilities to be included in the study.
[0159] Referring to FIG. 9, an illustrative node 40 for
implementing the method is depicted. Node 40 can be any form of
computing device, including computers, workstations, hand helds,
mainframes, embedded computing device, holographic computing
device, biological computing device, nanotechnology computing
device, virtual computing device and or distributed systems. Node
40 includes a microprocessor 42, an input device 44, a storage
device 46, a video controller 48, a system memory 50, and a display
54, and a communication device 56 all interconnected by one or more
buses or wires or other communications pathway 52. The storage
device 46 could be a floppy drive, hard drive, CD-ROM, optical
drive, bubble memory or any other form of storage device. In
addition, the storage device 42 may be capable of receiving a
floppy disk, CD-ROM, DVD-ROM, memory stick, or any other form of
computer-readable medium that may contain computer-executable
instructions or data. Further communication device 56 could be a
modem, network card, or any other device to enable the node to
communicate with humans or other nodes.
[0160] While the invention has been shown and described with
reference to the preferred embodiment thereof, it will be
understood by those skilled in the art that various changes in form
and detail may be made therein without departing from the spirit
and scope of the invention.
* * * * *