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Analysis of Empirical Software Effort Estimation Models

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  • Mazoon University College, Oman

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Reliable effort estimation remains an ongoing challenge to software engineers. Accurate effort estimation is the state of art of software engineering, effort estimation of software is the preliminary phase between the client and the business enterprise. The relationship between the client and the business enterprise begins with the estimation of the software. The credibility of the client to the business enterprise increases with the accurate estimation. Effort estimation often requires generalizing from a small number of historical projects. Generalization from such limited experience is an inherently under constrained problem. Accurate estimation is a complex process because it can be visualized as software effort prediction, as the term indicates prediction never becomes an actual. This work follows the basics of the empirical software effort estimation models. The goal of this paper is to study the empirical software effort estimation. The primary conclusion is that no single technique is best for all situations, and that a careful comparison of the results of several approaches is most likely to produce realistic estimates.
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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 7, No. 3, 2010
Analysis of Empirical Software Effort Estimation
Models
Saleem Basha
Department of Computer Science
Pondicherry University
Puducherry, India
smartsaleem1979@gmail.com
Dhavachelvan P
Department of Computer Science
Pondicherry University
Puducherry, India
dhavachelvan@gmail.com
Abstract Reliable effort estimation remains an ongoing
challenge to software engineers. Accurate effort estimation is the
state of art of software engineering, effort estimation of software
is the preliminary phase between the client and the business
enterprise. The relationship between the client and the business
enterprise begins with the estimation of the software. The
credibility of the client to the business enterprise increases with
the accurate estimation. Effort estimation often requires
generalizing from a small number of historical projects.
Generalization from such limited experience is an inherently
under constrained problem. Accurate estimation is a complex
process because it can be visualized as software effort prediction,
as the term indicates prediction never becomes an actual. This
work follows the basics of the empirical software effort
estimation models. The goal of this paper is to study the empirical
software effort estimation. The primary conclusion is that no
single technique is best for all situations, and that a careful
comparison of the results of several approaches is most likely to
produce realistic estimates.
Keywords-Software Estimation Models, Conte’s Criteria,
Wilcoxon Signed-Rank Test.
I. INTRODUCTION
Software effort estimation is one of the most critical and
complex, but an inevitable activity in the software development
processes. Over the last three decades, a growing trend has
been observed in using variety of software effort estimation
models in diversified software development processes. Along
with this tremendous growth, it is also realized the essentiality
of all these models in estimating the software development
costs and preparing the schedules more quickly and easily in
the anticipated environments. Although a great amount of
research time, and money have been devoted to improving
accuracy of the various estimation models, due to the inherent
uncertainty in software development projects as like complex
and dynamic interaction factors, intrinsic software complexity,
pressure on standardization and lack of software data, it is
unrealistic to expect very accurate effort estimation of software
development processes [1]. Though there is no proof on
software cost estimation models to perform consistently
accurate within 25% of the actual cost and 75% of the time
[30], still the available cost estimation models extending their
support for intended activities to the possible extents. The
accuracy of the individual models decides their applicability in
the projected environments, whereas the accuracy can be
defined based on understanding the calibration of the software
data. Since the precision and reliability of the effort estimation
is very important for the competitiveness of software
companies, the enterprises and researchers have put their
maximum effort to develop the accurate models to estimate
effort near to accurate levels. There are many estimation
models have been proposed and can be categorized based on
their basic formulation schemes; estimation by expert [5],
analogy based estimation schemes [6], algorithmic methods
including empirical methods [7], rule induction methods [8],
artificial neural network based approaches [9] [17] [18],
Bayesian network approaches [19], decision tree based
methods [21] and fuzzy logic based estimation schemes [10]
[20].
Among these diversified models, empirical estimation
models are found to be possibly accurate compared to other
estimation schemes and COCOMO, SLIM, SEER-SEM and FP
analysis schemes are popular in practice in the empirical
category [24] [25]. In case of empirical estimation models, the
estimation parameters are commonly derived from empirical
data that are usually collected from various sources of
historical or passed projects. Accurate effort and cost
estimation of software applications continues to be a critical
issue for software project managers [23]. There are many
introductions, modifications and updates on empirical
estimation models. A common modification among most of the
models is to increase the number of input parameters and to
assign appropriate values to them. Though some models have
been inundated with more number of inputs and output features
and thereby the complexity of the estimation schemes is
increased, but also the accuracy of these models has shown
with little improvement. Although they are diversified, they are
not generalized well for all types of environments [13]. Hence
there is no silver bullet estimation scheme for different
environments and the available models are environment
specific.
II. COCOMO ESTIMATION MODEL
A. COCOMO 81
COCOMO 81 (Constructive Cost Model) is an empirical
estimation scheme proposed in 1981 [29] as a model for
estimating effort, cost, and schedule for software projects. It
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was derived from the large data sets from 63 software projects
ranging in size from 2,000 to 100,000 lines of code, and
programming languages ranging from assembly to PL/I. These
data were analyzed to discover a set of formulae that were the
best fit to the observations. These formulae link the size of the
system and Effort Multipliers (EM) to find the effort to develop
a software system. In COCOMO 81, effort is expressed as
Person Months (PM) and it can be calculated as
15
1
** ii
bEMSizeaPM  
where,
“a” and “b” are the domain constants in the model. It
contains 15 effort multipliers. This estimation scheme accounts
the experience and data of the past projects, which is extremely
complex to understand and apply the same.
Cost drives have a rating level that expresses the impact of
the driver on development effort, PM. These rating can range
from Extra Low to Extra High. For the purpose of quantitative
analysis, each rating level of each cost driver has a weight
associated with it. The weight is called Effort Multiplier. The
average EM assigned to a cost driver is 1.0 and the rating level
associated with that weight is called Nominal.
B. COCOMO II
In 1997, an enhanced scheme for estimating the effort for
software development activities, which is called as COCOMO
II. In COCOMO II, the effort requirement can be calculated as
17
1
** ii
EEMSizeaPM  
where SF
BE j
j
5
1
*01.0
COCOMO II is associated with 31 factors; LOC measure as
the estimation variable, 17 cost drives, 5 scale factors, 3
adaptation percentage of modification, 3 adaptation cost drives
and requirements & volatility. Cost drives are used to capture
characteristics of the software development that affect the
effort to complete the project.
COCOMO II used 31 parameters to predict effort and time
[11] [12] and this larger number of parameters resulted in
having strong co-linearity and highly variable prediction
accuracy. Besides these meritorious claims, COCOMO II
estimation schemes are having some disadvantages. The
underlying concepts and ideas are not publicly defined and the
model has been provided as a black box to the users [26]. This
model uses LOC (Lines of Code) as one of the estimation
variables, whereas Fenton et. al [27] explored the shortfalls of
the LOC measure as an estimation variable. The COCOMO
also uses FP (Function Point) as one of the estimation
variables, which is highly dependent on development the
uncertainty at the input level of the COCOMO yields
uncertainty at the output, which leads to gross estimation error
in the effort estimation [33]. Irrespective of these drawbacks,
COCOMO II models are still influencing in the effort
estimation activities due to their better accuracy compared to
other estimation schemes.
III. SEER-SEM ESTIMATION MODEL
SEER (System Evaluation and Estimation of Resources) is
a proprietary model owned by Galorath Associates, Inc. In
1988, Galorath Incorporated began work on the initial version
of SEER-SEM which resulted in an initial solution of 22,000
lines of code. SEER (SEER-SEM) is an algorithmic project
management software application designed specifically to
estimate, plan and monitor the effort and resources required for
any type of software development and/or maintenance project.
SEER, which comes from the noun, referring to one having the
ability to foresee the future, relies on parametric algorithms,
knowledge bases, simulation-based probability, and historical
precedents to allow project managers, engineers, and cost
analysts to accurately estimate a project's cost schedule, risk
and effort before the project is started. Galorath chose
Windows due to the ability to provide a more graphical user
environment, allowing more robust management tradeoffs and
understanding of what drives software projects.[4]
This model is based upon the initial work of Dr. Randall
Jensen. The mathematical equations used in SEER are not
available to the public, but the writings of Dr. Jensen make the
basic equations available for review. The basic equation, Dr.
Jensen calls it the "software equation" is:
5.0
)( dtee KtCS  
where,
‘S’ is the effective lines of code, ‘ct’ is the effective
developer technology constant, ‘k’ is the total life cycle cost in
man-years, and ‘td’ is the development time in years.
This equation relates the effective size of the system and the
technology being applied by the developer to the
implementation of the system. The technology factor is used to
calibrate the model to a particular environment. This factor
considers two aspects of the production technology -- technical
and environmental. The technical aspects include those dealing
with the basic development capability: Organization
capabilities, experience of the developers, development
practices and tools etc. The environmental aspects address the
specific software target environment: CPU time constraints,
system reliability, real-time operation, etc.
The SEER-SEM developers have taken the approach to
include over 30 input parameters, including the ability to run
Monte Carlo simulation to compensate for risk [2].
Development modes covered include object oriented, reuse,
COTS, spiral, waterfall, prototype and incremental
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development. Languages covered are 3rd and 4th generation
languages (C++, FORTRAN, COBOL, Ada, etc.), as well as
application generators. It allows staff capability, required
design and process standards, and levels of acceptable
development risk to be input as constraints [15]. Figure 1 is
adapted from a Galorath illustration and shows gross categories
of model inputs and outputs, but each of these represents
dozens of specific input and output possibilities and
parameters.
Figure 1. SEER-SEM I/O Parameters
Features of the model include the following:
Allows probability level of estimates, staffing and
schedule constraints to be input as independent
variables.
Facilitates extensive sensitivity and trade-off analyses
on model input parameters.
Organizes project elements into work breakdown
structures for convenient planning and control.
Displays project cost drivers.
Allows the interactive scheduling of project elements
on Gantt charts.
Builds estimates upon a sizable knowledge base of
existing projects.
Model specifications include these:
Parameters: size, personnel, complexity, environment
and constraints - each with many individual
parameters; knowledge base categories for platform &
application, development & acquisition method,
applicable standards, plus a user customizable
knowledge base.
Predictions: effort, schedule, staffing, defects and cost
estimates; estimates can be schedule or effort driven;
constraints can be specified on schedule and staffing.
Risk Analysis: sensitivity analysis available on all
least/likely/most values of output parameters;
probability settings for individual WBS elements
adjustable, allowing for sorting of estimates by degree
of WBS element criticality.
Sizing Methods: function points, both IFPUG
sanctioned plus an augmented set; lines of code, both
new and existing.
Outputs and Interfaces: many capability metrics, plus
hundreds of reports and charts; trade-off analyses with
side-byside comparison of alternatives; integration
with other Windows applications plus user
customizable interfaces.
Aside from SEER-SEM, Galorath, Inc. offers a suite of
many tools addressing hardware as well as software concerns.
One of particular interest to software estimators might be
SEER-SEM, a tool designed to perform sizing of software
projects.
The study done by Thibodeau in 1981 and a study done by
IIT Research Institute (IITRI) in 1989 states that they
calibrated SEER-SEM model using three databases. The
significance of this study is as follows:
1. Results greatly improved with calibration, in fact, as high
as a factor of five.
2. Models consistently obtained better results when used
with certain types of applications.
The IITRI study was significant because it analyzed the
results of seven cost models (PRICE-S, two variants of
COCOMO, System-3, SPQR/20, SASET, SoftCost-Ada) to
eight Ada specific programs. Ada was specifically designed for
and is the principal language used in military applications, and
more specifically, weapons system software. Weapons system
software is different then the normal corporate type of
software, commonly known as Management Information
System (MIS) software. The major differences between
weapons system and MIS software are that weapons system
software is real time and uses a high proportion of complex
mathematical coding. Up to 1997, DOD mandated Ada as the
required language to be used unless a waiver was approved.
Lloyd Mosemann stated: The results of this study, like other
studies, showed estimating accuracy improved with calibration.
The best results were achieved by SEER-SEM model were
accurate within 30 percent, 62 percent of the time.
IV. SLIM ESTIAMTION MODEL
SLIM Software Life-Cycle Model was developed by Larry
Putnam [3]. SLIM hires the probabilistic principle called
Rayleigh distribution between personnel level and time. SLIM
is basically applicable for large projects exceeding 70,000 lines
of code. [4].
Figure 2. The Rayleigh Model
Percentage of Total Effort
T=0
D
td
Time
2
2
2at
Kate
dt
dy
Reliability
Maintenance
Risk
Schedule
Cost
Effort
SEER-SEM
Size
Personnel
Environment
Complexity
Constraints
Input Parameters Output Parameters
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It makes use of Rayleigh curve referred from [14] as shown
in figure 2 for effort prediction. This curve represents
manpower measured in person per time as a function of time. It
is usually expressed in personyear/ year (PY/YR). It can be
expressed as
2
2
2at
Kate
dt
dy
 
where,
dy/dt is the manpower utilization per unit time, “ t”
is the elapsed time, “a” is the parameter that affects the shape
of the curve and “K” is the area under the curve. There are two
important terms associated with this curve:
1) Manpower Build up given by D0=K/td3
2) Productivity = Lines of Code/ Cumulative Manpower i.e.
P=S/E and S= CK1/3td4/3,where C is the technology factor which
reflects the effects of various factors on productivity such as
hardware constraints, program complexity, programming
environment and personal experience.
The SLIM model uses two equations: the software the
manpower equation and software productivity level equation
The SLIM model uses Rayleigh distribution to estimate to
estimate project schedule and defect rate. Two key attributes
used in SLIM method are productivity Index (PI) and
Manpower Buildup Index (MBI). The PI is measure of process
efficiency (cost-effectiveness of assets), and the MBI
determines the effects on total project effort that result from
variations in the development schedule [A Probabilistic
Model].
Inputs Required: To use the SLIM method, it is necessary
to estimate system size, to determine the technology factor, and
appropriate values of the manpower acceleration. Technology
factor and manpower acceleration can be calculated using
similar past projects. System size in terms of KDSI is to be
subjectively estimated. This is a disadvantage, because of the
difficulty of estimating KDSI at the beginning of a project and
the dependence of the measure on the programming language.
Completeness of Estimate: The SLIM model provides
estimates for effort, duration, and staffing information for the
total life cycle and the development part of the life cycle.
COCOMO I provides equations to estimate effort, duration,
and handles the effect of re-using code from previously
developed software. COCOMO II provides cost, effort, and
schedule estimation, depending on the model used (i.e.,
depending on the degree of product understanding and
marketplace of the project). It handles the effect of reuse, re-
engineering, and maintenance adjusting the used size measures
using parameters such as percentage of code modification, or
percentage of design modification
Assumptions: SLIM assumes the Rayleigh curve
distribution of staff loading. The underlying Rayleigh curve
assumption does not hold for small and medium sized projects.
Cost estimation is only expected to take place at the start of the
design and coding, because requirement and specification
engineering is not included in the model.
Complexity: The SLIM model’s complexity is relatively
low. For COCOMO the complexity increases with the level of
detail of the model. For COCOMO I the increasing levels of
detail and complexity are the three model types: basic,
intermediate, and detailed. For COCOMO II the level of
complexity increases according to the following order:
Application Composition, Early Design, Post Architecture.
Automation of Model Development: The Putnam method is
supported by a tool called SLIM (Software Life-Cycle
Management). The tool incorporates an estimation of the
required parameter technology factor from the description of
the project. SLIM determines the minimum time to develop a
given software system. Several commercial tools exist to use
COCOMO models.
Application Coverage: SLIM aims at investigating
relationships among staffing levels, schedule, and effort. The
SLIM tool provides facilities to investigate trade-offs among
cost drivers and the effects of uncertainty in the size estimate.
Generalizability: The SLIM model is claimed to be
generally valid for large systems. COCOMO I was developed
within a traditional development process, and was a priori not
suitable for incremental development. Different development
modes are distinguished (organic, semidetached, embedded).
COCOMO II is adapted to feed the needs of new development
practices such as development processes tailored to COTS, or
reusable software availability. No empirical results are
currently available regarding the investigation these
capabilities.
Comprehensiveness: Putnam’s method does not consider
phase or activity work breakdown. The SLIM tool provides
information in terms of the effort per major activity per month
throughout development. In addition, the tool provides error
estimates and feasibility analyses. As the model does not
consider the requirement phase, estimation before design or
coding is not possible. Both COCOMO I and II are extremely
comprehensive. They provide detailed activity distributions of
effort and schedule. They also include estimates for
maintenance effort, and an adjustment for code re-use.
COCOMO II provides prototyping effort when using the
Application Composition model. The Architectural Design
model involves estimation of the actual development and
maintenance phase. The granularity is about the same as for
COCOMO I.
V. REVIC ESTIMATION MODEL
REVIC (REVised version of Intermediate COCOMO) is a
direct descendent of COCOMO. Ourada [16] was one of the
first to analyze validation, using a large Air Force database for
calibration of the REVIC model. There are several key
differences between REVIC and the 1981 version of
COCOMO, however.
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REVIC adds an Ada development mode to the three
original COCOMO modes; Organic, Semi-detached,
and Embedded.
REVIC includes Systems Engineering as a starting
phase as opposed to Preliminary Design for
COCOMO.
REVIC includes Development, Test, and Evaluation as
the ending phase, as opposed to COCOMO ending
with Integration and Test.
The REVIC basic coefficients and exponents were
derived from the analysis of a database of completed
DoD projects. On the average, the estimates obtained
with REVIC will be greater than the comparable
estimates obtained with COCOMO.
REVIC uses PERT (Program Evaluation and Review
Technique) statistical techniques to determine the
lines-of-code input value, Low, high, and most
probable estimates for each program component are
used to calculate the effective lines-of-code and the
standard deviation. The effective lines-of-code and
standard deviation are then used in the estimation
equations rather than the linear sum of the line-of-code
estimates.
REVIC includes more cost multipliers than COCOMO.
Requirements volatility, security, management reserve,
and an Ada mode are added.
VI. SASET ESTIMATIN MODEL
SASET (Software Architecture, Sizing and Estimating
Tool) is a forward chaining, rule-based expert system using a
hierarchically structured knowledge database of normalized
parameters to provide derived software sizing values. These
values can be presented in many formats to include
functionality, optimal development schedule, and man-loading
charts. SASET was developed by Martin Marietta Denver
Aerospace Corp. on contract to the Naval Center for Cost
Analysis. To use SASET, the user must first perform a
software decomposition of the system and define the
functionalities associated with the given software system [22].
SASET uses a tiered approach for system decomposition;
Tier 1 addresses software developmental and environmental
issues. These issues include che class of the software to be
developed, programming language, developmental, schedule,
security, etc. Tier 1 output values represent preliminary budget
and schedule multipliers. Tier II specifies the functional aspects
of the software system, specifically the total lines-of-code
(LOC). The total LOC estimate is then translated into a
preliminary budget estimate and preliminary schedule estimate.
The preliminary budget and schedule estimates are derived by
applying the multipliers from Tier I to the total LOC estimate.
Tier III develops the software complexity issues of the system
under study. These issues include: level of system definition,
system timing and criticality, documentation, etc. A complexity
multiplier is then derived and used to alter the preliminary
budget and schedule estimates from Tier II. The software
system effort estimation is then calculated. Tier IV and V are
not necessary for an effort estimation. Tier IV addresses the in-
scope maintenance associated with the project.
The output of Tier IV is the monthly man-loading for the
maintenance life-cycle. Tier V provides the user with a
capability to perform risk analysis on the sizing, schedule and
budget data. The actual mathematical expressions used in
SASET are published in the User's Guide, but the Guide is very
unclear as to what they mean and how to use them
VII. COSTMODL ESTIMATION MODEL
COSTMODL (Cost MODeL) is a COCOMO based
estimation model developed by the NASA Johnson Space
Center. The program delivered on computer disk for
COSTMODL includes several versions of the original
COCOMO and a NASA developed estimation model KISS
(Keep It Simple, Stupid). The KISS model will not be
evaluated here, but it is very simple to understand and easy to
use; however, the calibration environment is unknown. The
COSTMODL model includes the basic COCOMO equations
and modes, along with some modifications to include an Ada
mode and other cost multipliers.
The COSTMODL as delivered includes several calibrations
based upon different data sets. The user can choose one of
these calibrations or enter user specified values. The model also
includes a capability to perform a self-calibration. The user
enters the necessary information and the model will "reverse"
calculate and derive the coefficient and exponent or a
coefficient only for the input environment data. The model uses
the COCOMO cost multipliers and does not include more as
does REVIC. This model includes all the phases of a software
life cycle. PERT techniques are used to estimate the input
lines-of-code in both the development and maintenance
calculations
VIII. STUDY OF EMPIRICAL MODELS
Empirical estimation models were studied for the past
couple of decades, out of these studies many came with the
result of accuracy and performance. Table I summaries the
brief study of the most relevant empirical models. Studies are
listed in chronological order. For each study, estimation
methods are ranked according to their performance. A “1”
indicates the best model, “2” the second best, and so on.
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TABLE I. SUMMARY OF EMPIRICAL ESTIMATION STUDY
A. Impact of Cost Drivers
Empirical Software estimation models mainly stands over
the cost drivers and scale factors. These model reveals the
problem of instability due to values of the cost drivers and
scale factors, thus affects the sensitivity of the effort. Also,
most of the model depends on the size of the project, a change
in the size leads to the proportionate change in the effort.
Miscalculations of the cost drives have even more vivid change
in the result too. For example, a misjudgment in personnel
capability in COCOMO or REVIC from ‘very high to very
low’ will result in 300% increase in effort. Similarly in SEER-
SEM changing security requirements from ‘low’ to ‘high’ will
result in 400% increase in effort. In PRICE-S, 20% change in
effort will occur due to small change in the value of the
Productivity factor. All models have one or more inputs for
which small changes will result in large changes in effort and,
perhaps, schedule.
The input data problem is further compounded in that some
inputs are difficult to obtain, especially early in a program. The
size must be estimated early in a program using one or more
sizing models. These models usually have not been validated
for a wide range of projects. Some sensitive inputs, such as
analyst and programmer capability, are subjective and often
difficult to determine. Studies like one performed by Brent L.
Barber, Investigative Search of Quality Historical Software
Support Cost Data and Software Support Cost-Related Data,
show that personnel parameter data are difficult to collect.
Figure 3, extended from the SEER-SEM User’s Manual shows
Figure 3. Relative Cost Driver Impact[32]
Sl No.
Author Regression
COCOMO
Analogy
SLIM
CART ANN Stepwise
ANOVA OSR Expert
Judgment Other
Methods
1 Luciana Q, 2009 1
2 Yeong-Seok Seo, 2009 1
3
Jianfeng Wen, 2009
2
1
4
Petrônio L. Braga, 2007
2
1
5
Jingzhou Li, 2007
2
1
6
Iris Fabiana de Barcelos Tronto,
2007 3 4 5 2 1
7 Chao-Jung Hsu, 2007 1
8 Kristian M Furulund, 2007 1
9 Bilge Başkeleş, 2007 2 1
10 Da Deng, 2007 2 1
11 Simon, 2006 2 1
12 Tim Menzies, 2005 2 1
13 Bente Anda, 2005 2 1
14 Cuauhtémoc López Martín, 2005 1
15
Parag C, 2005
2
3
1
16 Randy K. Smith, 2001 2 1
17
Myrtveit, Stensrud, 1999
2
3
18 Walkerden, Jeffery, 1999 2 1
19 Kitchenham, 1998 2 1
20 Finnie et al., 1997 2 1 1
21 Shepperd, Schofield, 1997 2 1
22 Jorgensen, 1995 1 2 1
23 Srinivasan, Fischer, 1995 2 4 5 3 1
24 Bisio, Malabocchia, 1995 2 1
25 Subramanian, Breslawski 1993 1 2
26 Mukhopadhyay, Kerke 1992 1-3 2
27 Mukhopadhyay et al., 1992 3 4 2 1
28 Briand et al. 1992 2 3 1
29
Vicinanza et al., 1991
2
3
1
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the relative impact on cost/effort of the different input
parameters for that model. Even "objective" inputs like
Security Requirements in SEER-SEM may be difficult to
confirm early in a program, and later changes may result in
substantially different cost and schedule estimates. Some
sensitive inputs such as the PRICE-S Productivity Factor and
the SLIM PI should be calibrated from past data. If data are not
available, or if consistent values of these parameters cannot be
calibrated, the model’s usefulness may be questionable.
IX. ANALYSIS OF STUDY
A. Accuracy Estimatos
The field of cost estimation suffers a lack of clarity about
the interpretation of a cost estimate. Jørgensen reports different
application of the term ‘cost estimate’ being “the most likely
cost, the planned cost, the budget, the price, or, something
else”. Consequently there is also disagreement about how to
measure the accuracy of estimates. Various indicators for
accuracy relative and absolute – have been introduced
throughout the cost estimation literature such as mean squared
error (MSE), absolute residuals (AR) or balanced residual error
(BRE). Our literature review indicated that the most commonly
used by far are the mean magnitude relative error or MMRE,
and prediction within x or PRED(x). Of these two, the MMRE
is the most widely used, yet both are based on the same basic
value of magnitude relative error (MRE) which is defined as
The first step will be to apply Conte’s criteria to determine the
accuracy of the calibrated and uncalibrated model. This will be
achieved using the following equations.
Conte’s Criteria:
The performance of model generating continuous output
can be assesses in many ways including PRED(30), MMRE,
correlation etc., PRED(30) is a measure calculated from the
relative error, or RE, which is the relative size of the difference
between the actual and estimated value. One way to view these
measures is to say that training data contains records with
variables 1,2,3,……N and performance measures and
additional new variables N+1, N+2,….
MRE(Magnitude of Relative Error): First, calculate the
Magnitude of Relative Error (degree of estimating error in an
individual estimate) for each data point. This step is a
precedent to the next step and is also used to calculate
PRED(n). Satisfactory results are indicated by a value of 25
percent or less [30].
actualactualpredictedMRE / 
MMRE(mean magnitude of the relative error): The mean
magnitude of the relative error, or MMRE, is the average
percentage of the absolute values of the relative errors over an
entire data set.
iii actualactualpredicted
N
MMRE /
100
where, N = total number of estimates
RMS (Root Mean Square): Now, calculate the Root Mean
Square (model’s ability to accurately forecast the individual
actual effort) for each data set. This step is a precedent to the
next step only. Again, satisfactory results are indicated by a
value of 25 percent or less[30].
 
2
*/1 ii actualpredictednRMS
RRMS(Relative Root Mean Square): Lastly, calculate the
Relative Root Mean Square (model’s ability to accurately
forecast the average actual effort) for each data set. According
to Conte, the RRMS should have a value of 25 percent or
less[30].
)//( TactualRMSRRMS
PRED(n): A model should also be within 25 percent
accuracy, 75 percent of the time [30]. To find this accuracy rate
PRED(n), divide the total number of points within a data set
that have an MRE = 0.25 or less (represented by k) by the total
number of data points within the data set (represented by n).
The equation then is: PRED(n) = k/n where n equals 0.25 [30].
In general, PRED(n) reports the average percentage of
estimates that were within n percent of the actual values. Given
N datasets, then
For example, PRED(30) = 50% means that half the
estimates are within 30 percent of the actual.
Wilcoxon Signed-Rank Test.
The next step will be to test the estimates for bias. The
Wilcoxon signed-rank test is a simple, nonparametric test that
determines level of bias. A nonparametric test may be thought
of as a distribution-free test; i.e. no assumptions about the
distribution are made. The best results that can be achieved by
the model estimates is to show no difference between the
number of estimates that over estimated versus those that under
estimated. The Wilcoxon signed-rank test is accomplished
using the following steps [31],
1. Divide each validated subset into two groups based on
whether the estimated effort was greater (T+) or less (T-) than
the actual effort.
2. Sum the absolute value of the differences for the T+ and
T-groups. The closer the sums of these values for each group
are to each other, the lower the bias.
(9)
(8)
(7)
(6)
N
i=1
PRED(n)=
Σ
100
N
1 i
f MRE
i
<=n/100
0 otherwise
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3. Any significant difference indicates a bias to over or
under estimate.
Another performance measure of a model predicting
numeric values is the correlation between predicted and actual
values. Correlation ranges from +1 to -1 and a correlation of +1
means that there is a perfect positive linear relationship
between variables. And can be calculates as follows
The correlation coefficient for COCOMO II is 0.6952 and
the correlation coefficient for proposed model is 0.9985
All these performance measures (correlation, MMRE, and
PRED) address subtly different issues. Overall, PRED
measures how well an effort model performs, while MMRE
measures poor performance.
A single large mistake can skew the MMREs and not effect
the PREDs. Sheppard and Schofield comment that MMRE is
fairly conservative with a bias against overestimate while
PRED(30) will identify those prediction systems that are
generally accurate but occasionally wildly inaccurate[28]
B. Model Accuracy
There is no proof on software cost estimation models
to perform consistently accurate within 25% of the cost and
75% of the time[30]. In general model fails to produce
accurate result with perfect input data. The above studies have
compared empirical estimation models with known input data
and actual cost and schedule information, and have not found
the accuracy to be scintillating. Most model were accurate
within 30% of the actual cost and 57% of the time.
The Ourada study showed even worse results for SEER-SEM,
SASET, and REVIC for the 28 military ground programs in an
early edition of the Space and Missiles Center database. A
1981 study by Robert Thibodeau entitled An Evaluation of
Software Cost Estimating Models showed that calibration
could improve model accuracy by up to 400%. However, the
average accuracy was still only 30% for an early version of
SLIM and 25% for an early version of PRICE-S. PRICE-S and
System-3 are within 30%, 62% of the time. An Air Force
study performed by Ferens in 1983 and published in the ISPA
Journal of Parametrics, concluded that no software support
cost models could be shown to be accurate. The software
support estimation problem is further convoluted by lack of
quality software support cost data for model development,
calibration, and validation. Even if models can be shown to be
accurate, another effect must be considered.
Table III summarizes the parameters used and activities
covered by the models discussed. Overall, model based
techniques are good for budgeting, tradeoff analysis, planning
and control, and investment analysis. As they are calibrated to
past experience, their primary difficulty is with unprecedented
situations.
TABLE II. ANALYSIS OF EMPIRICAL ESTIMATION MODELS
Study Model Application Type
Validated Accuracy
MMRE /
MRE RRMS Pred
Karen
Lum, 2002
COCOMO Flight Software 34.4 - -
SEER 140.7 - -
COCOMO Ground Software
88.22 - -
SEER 552.33 - -
Karen
Lum, 2006
COSEEKMO
Kind:min 31 - 60(0.3)
Lang:ftn 44 - 42(0.3)
Kind:max 38 - 52(0.3)
All 40 - 60(0.3)
Mode:org 32 - 62(0.3)
Lang:mol
36
-
56(0.3)
Project:Y
22
-
78(0.3)
Mission Planning
36 - 50(0.3)
Avioicsmonitoring
38
-
53(0.3)
Mode:sd 33 - 62(0.3)
Project:X 42 - 42(0.3)
Fg:g 32 - 65(0.3)
Center:5 57 - 43(0.3)
All 48 - 43(0.3)
Mode:e 64 - 42(0.3)
Cemter:2 22 - 83(0.3)
Gerald L
Ourada,
1992
REVIC
Aero Space
0.373 0.776 42(0.25)
SASET 5.95 -0.733 3.5(0.25)
SEER
3.55
-
1.696
10.7(0.25)
Cost Model 0.46 0.53 29(0.25)
Chris F
Kemour,
1987
SLIM
ABC Software
771.87
-
-
COCOMO 610.09 - -
FP 102 - -
Estimac 85.48 - -
SLIM
Business:App
772 - -
COCOMO 601 - -
FP 102.74 - -
Estimac 85 - -
Jeremiah
D Deng,
2009
Machine
Learning Random 0.61 - 0.4(30)
De Tran-
Cao, 2007
Cosmic B-1 39 - 50(0.25)
In Table II, Summary of the analysis of the study, the result
of a collaborative effort of the authors, which includes author
name, cost model name, application type, validated accuracy
(MMRE, RRMS, Pred) is the percentage of estimates that fall
within the specified prediction level of 25 or 30 percent. In this
Chris F Kemour validated SLIM and obtained the result of
highest MRE of 772, COCOMO obtained the result of highest
Sp=
Σ
i
T
(Predicted
i
p)
2
,
T-1
P=
Σ
i
T
Predicted
i ,
T a=
Σ
i
T
Actual
i
,
T
Sa=
Σ
i
T
(Actual
i
a)
2
,
T-1
Corr= Spa/ Sp * Sa
(10)
Spa=
Σ
1
T
(Predicted
i
p)
(Actual
i
a)
,
T-1
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Vol. 7, No. 3, 2010
TABLE III. ACT IVITIES COVERED/FACTORS EXPLICITLY CONSIDERED BY VARIOUS MODELS[33]
MRE rate of 610.09. Karen Lum has validated SEER-
SEM and found to be 552.33. the validation of COSEEKMO
in Mode:e has an enormous MRE of 64 evaluated by Karen
Lum. Ourada study showed REVIC has MMRE of 0.373
and SASET even worse result of 5.95.
X. CONCLUSION
Based upon the background readings, this paper states
that the existing models were highly credible; however, this
survey found this not to be so based upon the research
performed. All the models could not predict the actual
against either the calibration data or validation data to any
level of accuracy or consistency. Surprisingly, SEER and
machine learning techniques were reliable good at predicting
the effort. But however they are not accurate because all the
model lies in the term prediction, prediction never comes
true is proved in this estimation models. In all the models,
the two key factors that influenced the estimate were project
size either in terms of LOC or FP and the capabilities of the
development team personnel. This paper is not convinced
that no model is so sensitive to the abilities of the
development team can be applied across the board to any
software development effort. Finally this paper concludes
that the no model is best for all situations and environment.
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O II
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ted Metrics
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Yes
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!
Yes
Yes
Yes
Program Attributes
Type/Domain
Yes
Yes
Yes
Yes
Yes
Yes
No
Complexity
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Language Yes Yes Yes ! Yes Yes Yes
Reuse Yes Yes Yes ! Yes Yes Yes
Required Reliability ! ! Yes Yes Yes No Yes
Computer
Attributes Resource Constraints Yes Yes Yes Yes Yes No Yes
Platform Volatility ! ! ! ! Yes No Yes
Personnel
Attributes
Personnel Capability Yes Yes Yes Yes Yes Yes Yes
Personnel Continuity ! ! ! ! ! No Yes
Personnel Experience Yes Yes Yes Yes Yes No Yes
Project Attributes
Tools and Techniques Yes Yes Yes Yes Yes Yes Yes
Breakage Yes Yes Yes ! Yes Yes Yes
Schedule Constraints
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Process Maturity Yes Yes ! ! Yes No Yes
Team Cohesion
!
Yes
Yes
!
Yes
Yes
Yes
Security Issues ! ! ! ! Yes No No
Multi Site Development ! Yes Yes Yes Yes No Yes
Activity Covered
Inception Yes Yes Yes Yes Yes Yes Yes
Elaboration Yes Yes Yes Yes Yes Yes Yes
Construction Yes Yes Yes Yes Yes Yes Yes
Transition and Maintenance Yes Yes Yes No Yes No Yes
76
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ISSN 1947-5500
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AUTHORS PROFILE
Saleem Basha is a Ph.D research scholar in the Department
of Computer Science, Pondicherry University. He has
obtained B.E in the field of Electrical and Electronics
Engineering, Bangalore University, Bangalore, India and
M.E in the field of Computer Science and Engineering,
Anna University, Chennai, India. He is currently working in
the area of SDLC specific effort estimation models and web
service modelling systems.
Dr. Dhavachelvan Ponnurangam is working as Associate
Professor, Department of Computer Science, Pondicherry
University, India. He has obtained his M.E. and Ph.D. in the
field of Computer Science and Engineering in Anna
University, Chennai, India. He is having more than a decade
of experience as an academician and his research areas
include Software Engineering and Standards, web service
computing and technologies. He has published around 75
research papers in National and International Journals and
Conferences. He is collaborating and coordinating with the
research groups working towards to develop the standards
for Attributes Specific SDLC Models & Web Services
computing and technologies.
77
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