Coconomography
Ray Madachy
rjmadach@nps.edu
25th International Forum on COCOMO and Systems/Software Cost Modeling
November 2, 2010
Agenda
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Coconomography Introduction
Computation Method
Project and Instructional Examples
Instruments
References
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Introduction
• Coconomography is the graphical computation of constructive
cost models for systems and software engineering using
nomographs.
• They are the most rapid and simple method of calculating the
models by drawing lines. No computers, calculators or
manual calculations are needed.
• The graphs are printed on paper or used on a flat screen
• Nomographs are used for very fast calculations when
approximate answers are appropriate and useful
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COCOMO Calculator
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A typical cost model nomograph for three
variables computes effort in Person-Months (PM)
by drawing a line between size in Kilo Source
Lines of Code (KSLOC) and the Effort
Adjustment Factor (EAF).
The graph layout encapsulates all the constants
and variables in the formula PM = 2.94 *
KSLOC^1.1 * EAF. It is plotted in logarithmic
space so linear movement executes the
multiplications.
Can be extended to four variables using a single
calculation line.
Scale factors an be included with a contour “net
diagram” replacing the straight line for PM. The
contours that vary as a function of the scale factor
ratings.
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Possible Uses
• Nomographs are the most concise representation to visualize and quantify
model relationships. A sensitivity analysis is conducted by drawing
multiple lines.
• The input and output variables are easily switched to use effort or schedule
as targets, and graphically visualize the feasible regions of the project
factors.
– Suppose there is a fixed target cost or timeframe. How much functionality can
be incorporated with the given budget? The feasible size range is shown as the
spread on the left axis from changing project factors represented on the EAF
line.
• The constrained ranges of organizations and their options can be visualized
and easily discussed between stakeholders at a sitdown meeting. Anyone
can mark them up instantly without waiting for specialists to perform a
computer run.
• Visual preface and summary for more detailed analyses.
• The graphs can be used as crosschecks of other estimation methods and
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tools, or help flag their erroneous inputs.
Agenda
•
•
•
•
•
Coconomography Introduction
Computation Method
Project and Instructional Examples
Instruments
References
6
Basic Nomograph Construction
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Transform the COCOMO II effort equation into logarithmic space:
PM = 2.94 * KSLOC1.0997 * EAF
PM / 2.94 = KSLOC1.0997 * EAF
log(PM) - log(2.94) = 1.0997 * log(KSLOC) + log(EAF)
The nomograph equation for three parallel lines is:
F1(u1) + F2(u2) + F3(u3) = 0
To construct the graph set the functions to:
F1(u1) = 1.0997 * log(KSLOC)
F2(u2) = log(PM) - log(2.94)
F3(u3) = log(EAF)
F1
F2
F3
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Agenda
•
•
•
•
Coconomography Introduction
Computation Method
Project and Instructional Examples
Instruments
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Sensitivity Analysis
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COSYSMO Effort
Poster size
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Effort and Schedule Ratio
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Compound graphs are created by aligning common axes in relationships.
Schedule is determined from effort by drawing a line through the schedule ratio.
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Note this example needs additions to calculate the cost increases when the ratio is less than unity.
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Effort with Scale Factor
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Solving for the Scale Factor is of the form F1(u1) = F2(u2) * F3(u3) = 0 (a diagonal
line)
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Visualizing Scale Factor Effects
100 K Range
10 K Range
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Scale Factor and EAF
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Decision Analysis Illustration
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Agenda
•
•
•
•
•
Coconomography Introduction
Computation Method
Project and Instructional Examples
Instruments
References
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Instruments
• Desktop and poster size nomographs
• Circular and linear slide rules
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Aviation Usage
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The slide rule still is in widespread use in
aviation.
The E6B Flight Computer, or"whiz wheel", is a
circular slide rule mostly used in flight training
but many professional and airline pilots carry
and use them.
• During flight planning on the ground they
aid in calculating fuel burn, wind
correction, time en route, and other items.
• In the air, they can be used to calculate
ground speed and the back is designed for
wind correction calculations.
Manual E6Bs remain far more popular than
electronic ones because they are lighter,
smaller, less prone to break, easy to use with
one hand, quicker, and do not require electrical
power. (Wikipedia)
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COCOMO Slide Rule Cutout
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Failed Design Goal
• Five foot slide rule for conference room.
• Groove mechanical tolerance became an issue
due to imperfect wood warp
– Two foot breadboard did not scale up
– Did not check the important interfaces before
applying fancy GUI (paint)
• At this size the fine-grained tickmarks are
precise enough to create recordable estimates
in a group meeting
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Agenda
•
•
•
•
•
Coconomography Introduction
Computation Method
Project and Educational Examples
Instruments
References
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References
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Boehm B., Abts C., Brown W., Chulani S., Clark B., Horowitz E., Madachy R., Reifer
D., Steece B., Software Cost Estimation with COCOMO II, Prentice-Hall, 2000
Doerfler R., “Creating Nomograms with the Pynomo Software”,
http://www.myreckonings.com, 2009
Levens A.S., Nomography, Fearon Publishers, 1971
Madachy R., “Coconomography”, http://diana.nps.edu/~madachy/coconomography/,
2010
Pynomo, http:/pynomo.org, accessed October 2010
Valerdi R., Systems Engineering Cost Estimation with COSYSMO, Wiley, 2011
Wikipedia, “E6B”, accessed October 2010
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