Software testing effort estimation with cobb douglas function- a practical application
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This paper discusses a Cobb-Douglas function model for estimating software testing effort, highlighting its accuracy based on historical data from 13 project releases. The model demonstrated a statistical accuracy of 93.42%, outperforming expert judgments and traditional estimation techniques. Conclusions emphasize the model's robustness and its potential to enhance software project planning and budgeting.
![IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163
__________________________________________________________________________________________
Volume: 02 Issue: 05 | May-2013, Available @ http://www.ijret.org 750
SOFTWARE TESTING EFFORT ESTIMATION WITH COBB-DOUGLAS
FUNCTION: A PRACTICAL APPLICATION
Shaik Nafeez Umar
Lead-industry consultant, Test Management Consultant, AppLabs – a CSC Company, Hyderabad, India
nshaik5@csc.com, nafishaik123@gmail.com
Abstract
Effort estimation is one of the critical challenges in Software Testing Life Cycle (STLC). It is the basis for the project’s effort
estimation, planning, scheduling and budget planning. This paper illustrates model with an objective to depict the accuracy and bias
variation of an organization’s estimates of software testing effort through Cobb-Douglas function (CDF). Data variables selected for
building the model were believed to be vital and have significant impact on the accuracy of estimates. Data gathered for the
completed projects in the organization for about 13 releases.
Statistically, all variables in this model were statistically significant at p<0.05 and p<0.01 levels. The Cobb-Douglas function was
selected and used for the software testing effort estimation. The results achieved with CDF were compared with the estimates provided
by the area expert. The model’s estimation figures are more accurate than the expert judgment. CDF has one of the appropriate
techniques for estimating effort for software testing. CDF model accuracy is 93.42%.
Index Terms: Effort estimation, software testing, Cobb-Douglas function, STLC and SDLC
-----------------------------------------------------------------------***------------------------------------------------------------------
1. INTRODUCTION
Effort estimation in software industry is highly based on human
judgment, Most of the IT organizations fail to deliver the
projects on time. Most of the IT organizations use traditional and
composite techniques effort estimation. There are different
models available in market that is discussed below in brief.
Singh, Bhatia et al. [1] gave a more detailed classification of
effort estimation empirical techniques, model/theory, expertise
techniques, regression techniques, composite techniques and
machine learning languages.
Empirical techniques correspond to the analogy-based
techniques which estimations are based on the practice and
previous experience.
Model/Theory based techniques are the algorithm based
techniques that include Function Point Analysis, SLIM,
Checkpoints and COCOMO model.
Expertise techniques are equivalent to the expert judgment
when a person carries out estimation based on non-explicit
and non-recoverable reasoning [1];
Regression based models are used to infer how the Y-
variables are related to X-variable(s), requiring data from
previous projects;
Composite techniques combine both approaches - expert
judgment and project data - in a consistent way in order to
obtain the effort estimation [2, 3].
In the Software engineering literature there are many of the
traditional models used to estimate the effort. Typically, the
most common effort model used in testing field is COCOMO
basic model [4, 5], SEL model, Walston –Felix model [6, 5],
Bailey-Basil model [7], Halstead model [8], Doty model. From
the existing effort prediction models no one indentify the right
model to use in test effort estimation. These are all just about
prediction models.
Advantages
Help to effort prediction for each release
Help to plan for preventive actions for effort estimation
Improves the overall quality of the software product
Streamlining the SDLC/STLC
Insure users next to the costs of field defect occurrence
Determine the reliability
2. OBJECTIVES AND METHODOLOGY
The main objective of this paper is to predict test effort in
different test phases like Requirements Analysis, Test case
design, Test execution, Test Automation, Test Governance and
Project management. The proposed Cobb-Douglas model was
implemented in excel sheet. The foremost step is to identify
independent parameters of the testing effort model. These
parameters should have impact or any relationship between
effort and their corresponding independent parameters.](https://image.slidesharecdn.com/softwaretestingeffortestimationwithcobb-douglasfunction-apracticalapplication-160801115548/85/Software-testing-effort-estimation-with-cobb-douglas-function-a-practical-application-1-320.jpg)
![IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163
__________________________________________________________________________________________
Volume: 02 Issue: 05 | May-2013, Available @ http://www.ijret.org 751
Before deployment of CMMI practices, organizations estimates
were based on the judgment of only one expert. But, this is not
considered to be a valid method and also not validated
statistically. Two possible solutions were identified to meet the
requirements of CMMI. One of the methods was Delphi method
[9] with participation of at least three algorithmic models for the
testing effort prediction. The other solution was implementation
of algorithm model for the effort estimation based on the
historical data of organization [9].
Model specifications includes input parameters like number of
requirements, number of test cases, complexity of the release,
number of resources, domain experience, requirements, test case
design, test execution, test automation, test governance and
project management. It predicts individual effort of testing
phases and total effort. This model has analyzed the data of 14
software releases with parameters that are derived from the
project dataset. The next step is to normalize the data. Next,
check the correlation between the parameters and multi-
collinerity crisis within the independent parameters. Then
transform the data into logarithmic using the method of least
squares to find coefficient values. Eventually, multiple linear
regressions is used. The Cobb-Douglas function is given by
Y= β0+X1β1+ X2 β2+ X3 β3+ …………+ Xn βn
Where Y=Effort, β0=Constant, β1, β2, β3…… βn are coefficient
values and X1, X2, X3…, Xn are independent parameters.
Accuracy of the model
In statistical modeling, accuracy is the one of the important
criteria for measuring the performance of the model. After
building the model, performance and precision of the model is
evaluated. In this model, we used Theil’s statistics to find out
model performance. The Theil’s statistical values lies between 0
and 1, the accuracy of the model is determined based on how
close the value is to 1.
3. RESULTS AND DISCUSSION
Due to organization security and policy names of the projects are
not disclosed. The Table#1 shows the distribution of release
wise test data of different testing phases collected for 13
releases. The test data is depicted for both dependent and
independent parameters.
The most significant R-squares (Table#2) of the dependent
parameters of the model are Requirements (0.66), Test case
design (0.75), Automated testing (0.68), Test governance (0.75)
and Project management (0.85) which is highly statistically
significant at 0.01 levels. This shows the selected dependent
parameters selected for this model has significant impact on
estimating the effort for software testing.
The standard error is comparatively less for requirement
(6.58%), test case design (7.2%) and automated testing (5.69%).
This shows statistically error of the model is very less for these
variables when compared to other parameters. This indicates that
these parameters are reliable and has significant impact in
estimating the effort for software testing. In software testing
organization most of the parameters are not associated with the
effort due to frequent changes in the business requirements.
Apparently, test execution is not statistically significant in
model, it may be poorly correlated with effort and also its
standard error is 11.52%, which is high in the model. The
proposed Cobb-Douglas model gave 93.42% of accuracy of the
actual and predicted values.
The variation between actual and predicted values using this
model is significantly very low. When comparison of each every
independent Cobb-Douglas model for testing phase it was good
prediction actual vs predicted values. It was shows (Table#4)
predicted values close to actual values. Finally in Cobb-Douglas
model putting the actual independent parameters we will get
predicted effort values.](https://image.slidesharecdn.com/softwaretestingeffortestimationwithcobb-douglasfunction-apracticalapplication-160801115548/85/Software-testing-effort-estimation-with-cobb-douglas-function-a-practical-application-2-320.jpg)
![IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163
__________________________________________________________________________________________
Volume: 02 Issue: 05 | May-2013, Available @ http://www.ijret.org 753
Table3: Predicted Effort (Hrs) of testing phases-using Cobb-Douglass function
CONCLUSIONS
Based on the objective of the study Cobb-Douglas testing effort
estimation model proposed is statistically and scientifically
significant. Using the model the accuracy of effort estimation
calculated is93.42%.It clearly states Cobb-Douglas model is
more robust than other models as the model is blend of using
historical data and scientific approach. With this level of
accuracy, this model brings in huge relief for the software
industry by helping them in estimating the testing efforts
required for executing the project and thereby increasing the
accuracy levels of the overall project effort estimates..
ACKNOWLEDGEMENTS
I want to thank Narendra singh Rajput, Lead Associate Manager,
for his valuable feedback and guidance and Prof Balasiddamuni,
Department of Statistics, S V University, Tirupati and Raghav
Beeram, Global Head - Test Management Consulting,
Independent Testing Services, CSC, Hyderabad for guiding me
and supporting me in my research paper.
I would like to express my love affection to my mother Smt.
Shaik Zaibunnisa, My Father Sri. Late S. Mahaboob Basha,
Brothers and Sisters, My spouse Ballary Ameen, Children’s
Shaik Mohammed Wafeeq, Shaik Waneeya, my Niece Samreen
Aaleia for enthusing me throughout the work
REFERENCES
[1]. Y. Singh, P.K. Bhatia, A. Kaur, and O. Sangwan, A Review
of Studies on Effort Estimation Techniques of Software
Development, in Proc. Conference Mathematical Techniques:
Emerging Paradigms for Electronics and IT Industries, New
Delhi, 2008, pp. 188-196.
[2]. B. Boehm, C. Abts and S. Chulani, Software development
cost estimation approaches - A survey, Annal of Software
Engineering, vol. 10, pp. 177-205, 2000.
[3]. L.C. Briand and I. Wieczorek, Resource Estimation in
Software Engineering, Encyclopedia of Software Eng., J.J.
Marcinak, ed., pp. 1160-1196, John Wiley & Sons, 2002.
[4]. M.V. Deshpande and S.G. Bhirud, “Analysis of Combining
Software Estimation Techniques,” International
Journal of Computer Applications (0975 – 8887) Volume 5 –
No.3.
[5]. Y. Singh, K.K.Aggarwal. Software Engineering Third
edition, New Age International Publisher Limited New Delhi.
[6]. Pressman. Software Engineering - a Practitioner’s
Approach. 6th Eddition Mc Graw Hill international Edition,
Pearson education, ISBN 007 - 124083 – 7.
Predicted effort (Hrs)-Testing phases
Release
Requirements
Testcasedesign
Testexecution
Automatedtesting
Testgovernance
Product/Project
management
Totaleffort
1 19 40 16 51 45 51 221
2 18 41 15 47 50 47 218
3 18 36 14 47 50 47 212
4 19 25 15 42 30 42 172
5 17 38 19 43 36 43 196
6 18 26 13 48 34 48 187
7 18 27 18 44 31 44 182
8 20 24 15 39 30 39 166
9 19 23 14 40 29 40 166
10 17 19 12 40 27 40 154
11(Assumed) 18 17 17 32 18 32 134
12(Assumed) 18 29 19 38 28 38 170
13(Assumed) 18 33 16 44 38 44 192](https://image.slidesharecdn.com/softwaretestingeffortestimationwithcobb-douglasfunction-apracticalapplication-160801115548/85/Software-testing-effort-estimation-with-cobb-douglas-function-a-practical-application-4-320.jpg)
![IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163
__________________________________________________________________________________________
Volume: 02 Issue: 05 | May-2013, Available @ http://www.ijret.org 754
[7]. S. Devnani-Chulani, "Bayesian Analysis of Software Cost
and Quality Models”. Faculty of the Graduate School,
University Of Southern California May 1999.
[8]. O. Benediktsson and D. Dalcher, “Effort Estimation in
incremental Software Development,” IEEE Proc. Software, Vol.
150, no. 6, December 2003, pp. 351-
[9] H. Leung and Z. Fan, Software Cost Estimation, in
Handbook of Software Engineering and Knowledge
Engineering, Hong Kong Polytechnic University, 2002
BIOGRAPHIES
Working as Lead Industry Consultant in Test
Management Consulting group, AppLabs – a
Computer Science Corporation Company,
Hyderabad, India. He has 9 years in IT
experience as Statistician and Statistical
modeler. He has published 14 papers in
National/International journals. He is expert
in Statistical and Econometric modeling](https://image.slidesharecdn.com/softwaretestingeffortestimationwithcobb-douglasfunction-apracticalapplication-160801115548/85/Software-testing-effort-estimation-with-cobb-douglas-function-a-practical-application-5-320.jpg)
Software testing effort estimation with cobb douglas function- a practical application
- 1. IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 05 | May-2013, Available @ http://www.ijret.org 750 SOFTWARE TESTING EFFORT ESTIMATION WITH COBB-DOUGLAS FUNCTION: A PRACTICAL APPLICATION Shaik Nafeez Umar Lead-industry consultant, Test Management Consultant, AppLabs – a CSC Company, Hyderabad, India nshaik5@csc.com, nafishaik123@gmail.com Abstract Effort estimation is one of the critical challenges in Software Testing Life Cycle (STLC). It is the basis for the project’s effort estimation, planning, scheduling and budget planning. This paper illustrates model with an objective to depict the accuracy and bias variation of an organization’s estimates of software testing effort through Cobb-Douglas function (CDF). Data variables selected for building the model were believed to be vital and have significant impact on the accuracy of estimates. Data gathered for the completed projects in the organization for about 13 releases. Statistically, all variables in this model were statistically significant at p<0.05 and p<0.01 levels. The Cobb-Douglas function was selected and used for the software testing effort estimation. The results achieved with CDF were compared with the estimates provided by the area expert. The model’s estimation figures are more accurate than the expert judgment. CDF has one of the appropriate techniques for estimating effort for software testing. CDF model accuracy is 93.42%. Index Terms: Effort estimation, software testing, Cobb-Douglas function, STLC and SDLC -----------------------------------------------------------------------***------------------------------------------------------------------ 1. INTRODUCTION Effort estimation in software industry is highly based on human judgment, Most of the IT organizations fail to deliver the projects on time. Most of the IT organizations use traditional and composite techniques effort estimation. There are different models available in market that is discussed below in brief. Singh, Bhatia et al. [1] gave a more detailed classification of effort estimation empirical techniques, model/theory, expertise techniques, regression techniques, composite techniques and machine learning languages. Empirical techniques correspond to the analogy-based techniques which estimations are based on the practice and previous experience. Model/Theory based techniques are the algorithm based techniques that include Function Point Analysis, SLIM, Checkpoints and COCOMO model. Expertise techniques are equivalent to the expert judgment when a person carries out estimation based on non-explicit and non-recoverable reasoning [1]; Regression based models are used to infer how the Y- variables are related to X-variable(s), requiring data from previous projects; Composite techniques combine both approaches - expert judgment and project data - in a consistent way in order to obtain the effort estimation [2, 3]. In the Software engineering literature there are many of the traditional models used to estimate the effort. Typically, the most common effort model used in testing field is COCOMO basic model [4, 5], SEL model, Walston –Felix model [6, 5], Bailey-Basil model [7], Halstead model [8], Doty model. From the existing effort prediction models no one indentify the right model to use in test effort estimation. These are all just about prediction models. Advantages Help to effort prediction for each release Help to plan for preventive actions for effort estimation Improves the overall quality of the software product Streamlining the SDLC/STLC Insure users next to the costs of field defect occurrence Determine the reliability 2. OBJECTIVES AND METHODOLOGY The main objective of this paper is to predict test effort in different test phases like Requirements Analysis, Test case design, Test execution, Test Automation, Test Governance and Project management. The proposed Cobb-Douglas model was implemented in excel sheet. The foremost step is to identify independent parameters of the testing effort model. These parameters should have impact or any relationship between effort and their corresponding independent parameters.
- 2. IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 05 | May-2013, Available @ http://www.ijret.org 751 Before deployment of CMMI practices, organizations estimates were based on the judgment of only one expert. But, this is not considered to be a valid method and also not validated statistically. Two possible solutions were identified to meet the requirements of CMMI. One of the methods was Delphi method [9] with participation of at least three algorithmic models for the testing effort prediction. The other solution was implementation of algorithm model for the effort estimation based on the historical data of organization [9]. Model specifications includes input parameters like number of requirements, number of test cases, complexity of the release, number of resources, domain experience, requirements, test case design, test execution, test automation, test governance and project management. It predicts individual effort of testing phases and total effort. This model has analyzed the data of 14 software releases with parameters that are derived from the project dataset. The next step is to normalize the data. Next, check the correlation between the parameters and multi- collinerity crisis within the independent parameters. Then transform the data into logarithmic using the method of least squares to find coefficient values. Eventually, multiple linear regressions is used. The Cobb-Douglas function is given by Y= β0+X1β1+ X2 β2+ X3 β3+ …………+ Xn βn Where Y=Effort, β0=Constant, β1, β2, β3…… βn are coefficient values and X1, X2, X3…, Xn are independent parameters. Accuracy of the model In statistical modeling, accuracy is the one of the important criteria for measuring the performance of the model. After building the model, performance and precision of the model is evaluated. In this model, we used Theil’s statistics to find out model performance. The Theil’s statistical values lies between 0 and 1, the accuracy of the model is determined based on how close the value is to 1. 3. RESULTS AND DISCUSSION Due to organization security and policy names of the projects are not disclosed. The Table#1 shows the distribution of release wise test data of different testing phases collected for 13 releases. The test data is depicted for both dependent and independent parameters. The most significant R-squares (Table#2) of the dependent parameters of the model are Requirements (0.66), Test case design (0.75), Automated testing (0.68), Test governance (0.75) and Project management (0.85) which is highly statistically significant at 0.01 levels. This shows the selected dependent parameters selected for this model has significant impact on estimating the effort for software testing. The standard error is comparatively less for requirement (6.58%), test case design (7.2%) and automated testing (5.69%). This shows statistically error of the model is very less for these variables when compared to other parameters. This indicates that these parameters are reliable and has significant impact in estimating the effort for software testing. In software testing organization most of the parameters are not associated with the effort due to frequent changes in the business requirements. Apparently, test execution is not statistically significant in model, it may be poorly correlated with effort and also its standard error is 11.52%, which is high in the model. The proposed Cobb-Douglas model gave 93.42% of accuracy of the actual and predicted values. The variation between actual and predicted values using this model is significantly very low. When comparison of each every independent Cobb-Douglas model for testing phase it was good prediction actual vs predicted values. It was shows (Table#4) predicted values close to actual values. Finally in Cobb-Douglas model putting the actual independent parameters we will get predicted effort values.
- 3. IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 05 | May-2013, Available @ http://www.ijret.org 752 Table1: Distribution of release wise data of different testing phases Independent parameters Actual effort (Hrs)-Dependent parameters Release Numberofrequirements(#) Numberoftestcases(#) Complexityoftherelease(Scale) Numberofresources(#) Domainexperience(#) Requirements Testcasedesign Testexecution Automatedtesting Testgovernance Projectmanagement Totaleffort 1 15 420 3 3 2 16 32 13 48 46 21 176 2 62 1240 2 5 2 15 43 14 52 56 20 200 3 65 1560 1 4 3 21 38 16 45 47 26 193 4 26 728 2 3 4 21 39 14 50 45 20 189 5 45 810 3 2 2 19 39 21 42 33 23 177 6 14 210 2 2 2 23 31 16 47 30 34 181 7 15 525 1 1 5 16 23 18 43 28 29 157 8 65 2600 2 8 6 23 25 16 37 28 24 153 9 48 1344 3 8 4 16 18 15 38 25 35 147 10 52 520 1 2 3 15 16 10 39 28 20 128 11(Assumed) 100 1800 3 4 5 12(Assumed) 75 2400 4 6 4 13(Assumed) 50 1250 2 4 3 Table2: Descriptive statistics and R-square values of the testing parameters Testing phases Mean Standard deviation R-square Standard error (%) Requirements (Hrs) 18.50 3.27 0.66 (p<0.01) 6.58 Test case design (Hrs) 30.40 9.50 0.75 (p<0.01) 7.2 Test execution (Hrs) 15.30 2.95 0.48 (p>0.05) 11.52 Automated testing (Hrs) 44.10 5.17 0.68 (p<0.05) 5.69 Test governance (Hrs) 36.60 10.83 0.75 (p<0.01) 14.59 Project management (Hrs) 25.20 5.71 0.85 (p<0.01) 12.59
- 4. IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 05 | May-2013, Available @ http://www.ijret.org 753 Table3: Predicted Effort (Hrs) of testing phases-using Cobb-Douglass function CONCLUSIONS Based on the objective of the study Cobb-Douglas testing effort estimation model proposed is statistically and scientifically significant. Using the model the accuracy of effort estimation calculated is93.42%.It clearly states Cobb-Douglas model is more robust than other models as the model is blend of using historical data and scientific approach. With this level of accuracy, this model brings in huge relief for the software industry by helping them in estimating the testing efforts required for executing the project and thereby increasing the accuracy levels of the overall project effort estimates.. ACKNOWLEDGEMENTS I want to thank Narendra singh Rajput, Lead Associate Manager, for his valuable feedback and guidance and Prof Balasiddamuni, Department of Statistics, S V University, Tirupati and Raghav Beeram, Global Head - Test Management Consulting, Independent Testing Services, CSC, Hyderabad for guiding me and supporting me in my research paper. I would like to express my love affection to my mother Smt. Shaik Zaibunnisa, My Father Sri. Late S. Mahaboob Basha, Brothers and Sisters, My spouse Ballary Ameen, Children’s Shaik Mohammed Wafeeq, Shaik Waneeya, my Niece Samreen Aaleia for enthusing me throughout the work REFERENCES [1]. Y. Singh, P.K. Bhatia, A. Kaur, and O. Sangwan, A Review of Studies on Effort Estimation Techniques of Software Development, in Proc. Conference Mathematical Techniques: Emerging Paradigms for Electronics and IT Industries, New Delhi, 2008, pp. 188-196. [2]. B. Boehm, C. Abts and S. Chulani, Software development cost estimation approaches - A survey, Annal of Software Engineering, vol. 10, pp. 177-205, 2000. [3]. L.C. Briand and I. Wieczorek, Resource Estimation in Software Engineering, Encyclopedia of Software Eng., J.J. Marcinak, ed., pp. 1160-1196, John Wiley & Sons, 2002. [4]. M.V. Deshpande and S.G. Bhirud, “Analysis of Combining Software Estimation Techniques,” International Journal of Computer Applications (0975 – 8887) Volume 5 – No.3. [5]. Y. Singh, K.K.Aggarwal. Software Engineering Third edition, New Age International Publisher Limited New Delhi. [6]. Pressman. Software Engineering - a Practitioner’s Approach. 6th Eddition Mc Graw Hill international Edition, Pearson education, ISBN 007 - 124083 – 7. Predicted effort (Hrs)-Testing phases Release Requirements Testcasedesign Testexecution Automatedtesting Testgovernance Product/Project management Totaleffort 1 19 40 16 51 45 51 221 2 18 41 15 47 50 47 218 3 18 36 14 47 50 47 212 4 19 25 15 42 30 42 172 5 17 38 19 43 36 43 196 6 18 26 13 48 34 48 187 7 18 27 18 44 31 44 182 8 20 24 15 39 30 39 166 9 19 23 14 40 29 40 166 10 17 19 12 40 27 40 154 11(Assumed) 18 17 17 32 18 32 134 12(Assumed) 18 29 19 38 28 38 170 13(Assumed) 18 33 16 44 38 44 192
- 5. IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 05 | May-2013, Available @ http://www.ijret.org 754 [7]. S. Devnani-Chulani, "Bayesian Analysis of Software Cost and Quality Models”. Faculty of the Graduate School, University Of Southern California May 1999. [8]. O. Benediktsson and D. Dalcher, “Effort Estimation in incremental Software Development,” IEEE Proc. Software, Vol. 150, no. 6, December 2003, pp. 351- [9] H. Leung and Z. Fan, Software Cost Estimation, in Handbook of Software Engineering and Knowledge Engineering, Hong Kong Polytechnic University, 2002 BIOGRAPHIES Working as Lead Industry Consultant in Test Management Consulting group, AppLabs – a Computer Science Corporation Company, Hyderabad, India. He has 9 years in IT experience as Statistician and Statistical modeler. He has published 14 papers in National/International journals. He is expert in Statistical and Econometric modeling