 Open Access
 Total Downloads : 558
 Authors : Chhavi Gautam, Sandeep Singh Kang
 Paper ID : IJERTV1IS6391
 Volume & Issue : Volume 01, Issue 06 (August 2012)
 Published (First Online): 30082012
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Comparison And Implementation Of Software Maintenance Models
Chhavi Gautam
R.B.C.E.N.T.W, India
Sandeep Singh Kang
C.E.C Landran, India
Abstract
Measurement of the maintainability of the software system is very important as it will help in the better maintenance of the software system. Measurement of the software maintainability early in the development life cycle, especially at the design phase is important, it may help designers to incorporate required enhancement and corrections at design phase for improving maintainability of the final software. Earlier MEMOOD model was developed which finds the maintainability of the class diagrams on the basis of Understandability and Modifiability of software system on the basis of object oriented metrics of class diagrams of software system. This paper has proposed a multivariate linear model Compound MEMOOD, which estimates the maintainability of class diagrams of software systems in terms of their understandability, modifiability, Scalability and Level of Complexity. The paper further developed three more multivariate models for maintainability, scalability and level of complexity. These three models use design level objectoriented metrics of software systems, to quantify maintainability, Scalability and Level of Complexity of class diagram. The models for Understandability and modifiability are taken from the previous MEMOOD model. Then, we make a comparison of MEMOOD model and Compound MEMOOD model through regression analysis and it is found that Compound MEMOOD Model gives better results with the given dataset. All these models have been validated through appropriate statistical measures.

Introduction
The everchanging world makes maintainability a strong quality requirement for the majority of software systems. The maintainability measurement during the development phases of objectoriented system estimates the maintenance effort, and also evaluates the
likelihood that the software product will be easy to maintain [1]. The maintainability is defined by IEEE standard glossary of Software Engineering as the ease with which a software system or component can be modified to correct faults, improve performance or other attributes, or adapt to a changed environment. Despite the fact that software maintenance is an expensive and challenging task, it is not properly managed and often ignored. As class diagrams play a key role in the design phase of objectoriented software therefore early estimation of their maintainability may help designers to incorporate required enhancements and corrections in order to improve their maintainability and consequently the maintainability of the final software to be delivered in future. Hence, there is a need of developing a maintainability estimation model, which quantifies the maintainability of object oriented software at the design stage.

Literature Survey
Wide range of maintainability prediction models have been proposed in the literature within last two decades. Some of the models are predicting maintainability using the metrics from coding as well as design phase, while some are focusing only on design level metrics [3]. Anton Ellis et al. [4], proposed a method of mapping object oriented source code metrics onto the subcharacteristics of maintainability mentioned in ISO 9126. Oman and Hagemeister [5], proposed the Maintainability Index (MI) that objectively determines the maintainability of software system based upon the status of the source code. Welker and Oman [6], suggested measuring maintainability in terms of cyclomatic complexity, lines of code(LOC) and lines of comments. Hayes et al. [7], proposed a model that estimates Adaptive software maintenance effort in terms of difference lines of code (DLOC) i.e. number of added, deleted and updated lines. Polo et al. [8], used number of modification requests, mean effort per
modification request and type of correction to examine maintainability. In another study Hayes and Zhao [9], proposed a maintainability model that categorizes software modules as easy to maintain and not easy to maintain. The model helps the developers to identify the modules those are not easy to maintain, before integrating them. From the survey of literature it has been observed that various researchers proposed several models for maintainability estimation, but in most of these studies, maintainability estimation depends on the measures taken after the coding phase. Because of this, maintainability predictions are made in the latter stages of SDLC, and it became very difficult to improve the maintainability at that stage. Muthanna et al. [10], developed a maintainability model using polynomial linear regressions. But this model could be applied only for procedural software and not suitable for objectoriented software. Genero et al. [11], developed four models that relate size and structural complexity metrics of UML class diagrams with maintainability measures like understandability time, modifiability correctness and modifiability completeness. But none of the four models quantify the maintainability of class diagrams itself. Earlier MEMOOD model was developed which finds the maintainability of the class diagrams on the basis of Understandability and Modifiability on the basis of object oriented metrics of class diagrams [12].
3 Metrics Selection
Metric Selection is very objective in nature. There are several ways in which these metrics can be picked up based on which a particular model can be developed. The goal of metric selection is to select such metrics which are statistically significant, relevant in coherent context of Object Oriented Programming for developing following models:
Maintainability Model Understandability Model Modifiability Model Scalability Model Complexity Model
For each model, we have to do extensive research to find out which metric or which measure of attribute of software will be highly relevant for the above said models. For this purpose, recent literature survey as well as cross and within company data set was chosen with help of experts and their performance, measurable expects for developing such model were studied. Here is list of matrices for each model.
Table 1 Modifiability Model
Metric Name 
Metric Definition 
Number of classes 
The total number of classes 
Number of Generalizations (NGen) 
The total number of generalization relationship within a class diagram 
Number Of Generalizations Hierarchies (NGenH) 
The total number of generalization hierarchies within a class diagram 
Maximum DIT 
It is the maximum DIT value obtained for each class diagram. The DIT value for class is the longest path from the class to the root of the tree. value obtained for each class diagram. The DIT value for class is the longest path from the class to the root of the tree. 
Number Of Aggregation Hierarchies (NAggH) 
The total number of aggregation hierarchies within a class diagram 
Metric Name 
Metric Definition 
Number of classes 
The total number of classes 
Number Of Aggregation Hierarchies (NAggH) 
The total number of aggregation hierarchies within a class diagram 
Table 2.Understandability Model
Metric Nme 
Metric Definition 
Affarent Coupling (Ca) 
The number of types inside this assembly that depends upon types inside this assembly. 
Effernt Coupling (Ce) 
The number of types inside this assembly that depends upon types outside this assembly. 
% Coverage(PC) 
The percentage of code coverage by tests. 
Distance From Main sequence 
It is the predictor of balance between abstractness and stability. 
Nesting Depth 
It is the maximum number of encapsulated scopes inside the body of the method. 
Table 3. Scalability Model
Table 4. Level of Complexity Model
Metric Name 
Metric Definition 
Coupling 
The number of types inside this assembly that depends upon types inside this assembly. 
Cohesion 
The number of types inside this assembly that depends upon types outside this assembly. 
Cyclomatic Complexity 
Number of decisions that can be taken in procedure. 
ILCC 
It is the predictor of balance between abstractness and stability. 

Models Development
Quantification of class diagrams understandability andmodifiability is prerequisite for the maintainability estimation model. Therefore before developing MEMOOD, the paper has developed two models for understandability and modifiability. In order to establish all the three models following multivariate linear model (1) has been selected.
Y=+1*X1+2*X2++ n*Xn+
(1)

Modifiability Model
In order to establish a multivariate model for modifiability of class diagram, metrics listed in Table 1, will play the role of independent variables while modifiability will be taken as dependent variable. To identify metrics those are effectively contributing in the prediction of modifiability, the technique of backward stepwise multiple regression has been used. This procedure starts with a model, which initially includes all the independent variables and gradually eliminates those, one after another, that does not explain much of the variation in the dependent variable, until it ends with an optimal set of independent variables. Now applying backward stepwise regression, on the available data has resulted into the following modifiability model (2). This model has been taken from MEMOOD Model [13].
Modifiability=0.629+0.471*NC0.173*NGen
0.616*NAggH0.696*NGenH+0.396*MaxDIT (2)
Where, NC is the Number of Classes, NGen is
Number of Generalizations, NAggH is Number of Aggregation Hierarchies, NGenH is Number of Generalization Hierarchies andMaxDIT is Maximum DIT. From the model it can be interpreted that modifiability of class diagram is DIT, while NGen and Number of directly proportional to Number of Classes and Maximum Generalization and Aggregation Hierarchies are inversely proportional to modifiability of class diagram.

Undersatandability Model
After establishing a model for modifiability the next task is to build a similar model for understandability also. Applying the same technique of stepwise backward multiple regressions on the available data resulted into the following understandability model (3).
Understandability= 1.166+0.256*NC
.0.394*NGenH (3)
Where, NC is the Number of Classes and NGenH is
Number of Generalization Hierarchies. From (3) it could be interpreted that understandability of class diagram is directly proportional to NC, while
NGenH is inversely proportional to the understandability of class diagram.
4.3 Scalability Model
In order to establish a multivariate model for Scalability of class diagram, metrics listed in Table 3, will play the role of independent variables while Scalability will be taken as dependent variable.
Scalability=2.182+.099*AC+.100*EC+.O97*ND
.036*PC+.068*DMS (4)
Where AC is Afferent Coupling, EC is efferent Coupling, ND is Nesting depth, PC is % Coverage and DMS is Distance from main sequence.
4.3.1 Statistical Significance of the Model
Observing the significance for the Ftest in the last column of Analysis of Variance (Table 5), it can be concluded that the Scalability model (4) is statistically significant at a confidence level of more than 99%.
Table 5. Anova for Scalability Model
Sum Of
Squares
DF
Mean
Square
F
Significan
ce
Regressi on
211.772
5
42.354
5.005E5
.000a
Residual
.002
22
.000
Total
211.774
27
Predictors: (Constant), DMS, PC, AC, EC, ND
Also the value of R2 (Coefficient of Determination) and Adjusted R2 in the Table 6, is also very encouraging. As, it refers to the percentage or proportion of the total variance in modifiability by all the five metrics (independent variables) participating in the model (4).
Table 6. Model Summary For Scalability Model
4.4 Level of Complexity Model
In order to establish a multivariate model for Complexity of class diagram, metrics listed in Table 3, will play the role of independent variables while Scalability will be taken as dependent variable.
LOC=.269+.008*Coupling+.181*cohesion+.119*CC
+.084*ILCC (5)
Where ILCC is IL Cyclomatic Complexity and CC iscyclomatic Complexity.
4.4.1 Statistical Significance of the Model
Observing the significance for the Ftest in the last column of Analysis of Variance (Table 5), it can be concluded that the modifiability model (5) is statistically significant at a confidence level of more than 99%.
R
R Square
Adjusted R Square
Std. Error of the Estimate
1.000a
1.000
1.000
.009
Sum Of
Squares
DF
Mean
square
F
Sig
Regression
147.022
4
36.755
1.296
.000
Residual
.027
23
.001
Total
147.049
27
Table 8.Anova For Loc Model
4.3.2 Statistical significance of the Independent Variables
As long as statistical significance and relevance of individual independent variables in the Scalability model (4) is concern. It can be noticed from the last column of Table 7, that each of the five metrics participating in the model is statistically significant at a significance level of 0.05 (equivalent to a confidence level of 95%).
Table 7. Coefficients and Statistical Significance of Independent variables
B
Std. Error
Beta
Significance
(Constant)
2.182
.030
73.089
.000
AC
.099
.001
76.290
.000
EC
.100
.001
84.038
.000
ND
.097
.004
25.379
.000
PC
.036
.032
1.138
.267
DMS
.068
.009
7.733
.000
Dependent Variable: Scalability
Also the value of R2 (Coefficient of Determination) and Adjusted R2 in the Table 9, is also very encouraging. As, it refers to the percentage or proportion of the total variancein modifiability by all the five metrics (independent variables) participating in the model (5).
Table 9. Model Summary
R Square
Adjusted R Square
Std. Error of the Estimate
1.000a
1.000
1.000
.0340099
4.4.2 Statistical Significance of Independent Variables
As long as statistical significance and relevance of individual independent variables in the Level Of Complexity model (5) is concern. It can be noticed from the last column of Table 10, that each of the five metrics participating in the model is statistically significant at a significance level of 0.05 (equivalent to a confidence level of 95%).
Table 10. Coefficients and Statistical Significance Of Independent variables
B
Std. Error
Beta
Significance
(Constant)
.269
.025
10.744
.000
Coupling
.008
.032
.251
.804
Cohesion
.181
.032
5.725
.000
CC
.119
.029
4.169
.000
ILCC
.084
.026
3.268
.003
Dependent variable: Level Of complexity

Compound MEMOOD Model
In order to establish a multivariate model for Maintainability of class diagram, Scalability, Level Of Complexity, Understandability and Modifiability of class diagrams becomes in dependent variables while maintainability will be taken as dependent variable.
Maintenance=2.399+.493*Modifiability+.474*Under standability+.524*scalability+.507*LOC (6)

Statistical significance of the Model
Observing the significance for the Ftest in the last column of Analysis of Variance (Table 11), it can be concluded that the compound MEMOOD model (6) is statistically significant at a confidence level of more than 99%.
Table 11. Anova For Compound MEMOOD Model
Sum Of
Squares
DF
Mean
square
F
Sig
Regression
356.331
4
89.083
1.296E
.0000
Residual
.158
23
.007
Total
356.489
27
Also the value of R2 (Coefficient of Determination) and Adjusted R2 in the Table 12, is also very encouraging. As, it refers to the percentage or proportion of the total variance in modifiability by all the five metrics (independent variables) participating in the model (6).
Table 12. Model Summary For Compound MEMOOD Model
R
R
Square
Adjusted R Square
Std. Error of the Estimate
DurbinWatson
1.000
1.000
.999
.08291
1.570

Statistical Significance of Independent Variables

As long as statistical significance and relevance of individual independent variables in the compound MEMOOD model (6) is concern. It can be noticed from the last column of Table13, that each of the five metrics participating in the model is statistically significant at a significance level of 0.05 (equivalent to a confidence level of 95%)
Table 13. Coefficients and statistical Significance of independent variables
B
Std. Error
Beta
Significance
(Constant)
2.399
.048
.000
Modifiability
.493
.018
.250
.000
Understandability
.474
.047
.136
.000
Scalability
.524
.014
.404
.000
LOC
.507
.012
.325
.000
4.6 MEMOOD MODEL
In order to establish a multivariate model for Maintainability of class diagram, Scalability, Level of Complexity, Understandability and Modifiability of class diagrams becomes independent variables while maintainability will be taken as dependent variable
Maintainability = 0.126 + 0.645* Understandability
+0.502*Modifiability (7)
R
R Square
Adjusted R Square
Std. Error of the Estimate
Durbin Watson
.982
.965
.962
.2947681
1.895
TABLE 14: Model Summary For MEMOOD Model
Also the value of R2 (Coefficient of Determination) and Adjusted R2 in the Table, is also very encouraging. As, it refers to the percentage or proportion of the total variance in modifiability by all the five metrics (independent variables) participating in the model (7).



Results And Discussion
With Comparison of MEMOOD Model and Compound MEMOOD Model, it is found that Compound MEMOOD Model have R Square value equals to 1 which states that it best fits the data. MEMOOD Model doesnt have R Square value equals 1. Also the value of Durbin Watson variable of compound MEMOOD has value less than that of MEMOOD Model which is considered good. Thus Compound MEMOOD Model has better results than MEMOOD Model. Hence it is better.
Table 15. Performance Results of MEMOOD Model and Compound MEMOOD Model
COMPOUND MEMOOD MODEL
MEMOOD MODEL
Maintenance value of R Square
1.00
.962
Durbin Watson
1.570
1.895
Fig. 5.1. Comparison of models on the basis of RSquare value
Fig. 5.2. Comparison of models on the basis of DurbinWatson value

Comparison of Models on attribute basis
A comparison between models is done on the basis of attributes of models. A comparison is made on the basis of modifiability, Understandability, Scalability and Level of Complexity which shows that compound MEMOOD Model gives better results.
Fig. 5.3 Comparison of MEMOOD Model and compound MEMOOD Model on modifiability
The above Fig. 3 shows the comparison of MEMOOD MODEL and Compound MEMOOD Model on the basis of modifiability which shows that Compound MEMOOD Model has higher chances of modifiability. Thus it is easy to modify and there are more chances of maintenance.
Fig. 5.3 Comparison of MEMOOD Model and compound MEMOOD Model on understandability
The above Fig. 2 shows the comparison of MEMOOD MODEL and Compound MEMOOD Model on the basis of understandability which shows that Compound MEMOOD Model has higher chances of understandability. Thus it is easy to modify and here are more chances of maintenance.
Fig. 5.4 Comparison of MEMOOD Model and compound MEMOOD Model on Level of Complexity
The above Fig. 3 shows the comparison of MEMOOD MODEL and Compound MEMOOD Model on the basis of level Of Complexity.
Fig.5.5 Comparison of MEMOOD Model and compound MEMOOD Model on Scalability
The above Fig. 4 shows the comparison of MEMOOD MODEL and Compound MEMOOD Model on the basis of scalability.


Conclusion
The paper has developed three models to quantify understandability, modifiability, scalability, Level of Complexity and maintainability of the class diagrams. Maintainability model (Compound MEMOOD) estimates the maintainability of class diagrams in terms of their understandability, modifiability, scalability and
Level of Complexity. In [12], MEMOOD Model is introduced. With Comparison of MEMOOD Model and Compound MEMOOD Model, it is found that Compound MEMOOD Model have R Square value equals to 1 which states that it best fits the data. Also the value of Durbin Watson variable of compound MEMOOD has value less than that of MEMOOD Model which is considered good. From the diagrammatical analysis it is found that all the attributes of maintainability has better results for Compound MEMOOD Model than MEMOOD Model. Thus Compound MEMOOD Model has better results than MEMOOD Model. Hence it is better.
6. References

V.S. Alagar, L.Qiaoyum, and O.S. Ormandjieva, Assessment of Maintainability in ObjectOriented Software, Proc. 39th International Conference and Exhibition on Technology of ObjectOriented Languages andSystems (TOOLS39), 29 July 03 Aug. 2001, vol. 19, pp. 194 204, Santa Barbara, Callifornia, USA, 2001.

M. Dagpinar and J. Jahnke, Predicting Maintainability with ObjectOriented Metrics an Empirical Comparison, Proc10th Working Conference on Reverse Engineering (WCRE03),13 – 17 Nov. 2003, pp. 155164, 2003.

S.W.A. Rizvi and R.A. Khan, A Critical Review on Software Maintainability Models, Proc. of the National Conference on Cutting Edge Computer and Electronics Technologies, 14 – 16 Feb. 2009, pp. 144 148,Pantnagar, India, 2009.

P. Antonellis, D. Antoniou, Y. Kanellopoulos, C. Makris,
E. Theodoridis, C. Tjortjis, and N. Tsirakis, A Data Mining Methodology for Evaluating Maintainability According toISO/IEC9126 Software Engineering Product Quality.Standard, Proc. 11th IEEE Conference onSoftware Maintenance and Reengineering (CSMR2007), 21 23 Mar.2007, Amsterdam, Netherlands, 2007.

P.W. Oman and J.R. Hagemeister, Construction and Testing of Polynomials Predicting Software Maintainability, Journal of Systems and Software, vol. 24, no. 3, pp. 251 266, 1994.

K.D. Welker and P.W. Oman, Software Maintainability Metrics Models in Practice, Journal of Defense Software Engineering, vol. 8, no. 11, pp. 19 – 23, 1995.

J.H. Hayes, S.C. Patel, and L. Zhao, A MetricsBased Software Maintenance Effort Model, Proc. 8th European Conference on Software Maintenanceand Reengineering
(CSMR'04), 24 26 Mar. 2004, pp. 254 258,IEEE
Computer Society, 2004.

M. Polo, M. Piattini, and F. Ruiz, Using Code Metrics to Predict Maintenance of Legacy Programs: a Case Study, Proc. of InternationalConference on Software Maintenance, ICSM 2001, pp. 202208, IEEE Computer Society, Florence Italy, 2001.

J.H. Hayes and L Zhao, Maintainability Prediction: a Regression Analysis of Measures of Evolving Systems, Proc. 21st IEEE InternationalConference on Software Maintenance, 26 – 29 Sept. 2005, pp. 601 604, 2005.

S. Muthanna, K. Kontogiannis, K. Ponnambalam, and B. Stacey, A Maintainability Model for Industrial Software Systems Using Design Level Metrics, Proc. 7th Working Conference on Reverse Engineering(WCRE00), 23 – 25 Nov., 2000, pp. 248 256, Brisbane, Australia, 2000.
11] M. Genero, E. Manso, and G. Cantone, Building UML Class Diagram Maintainability Prediction Models Based on Early Metrics, Proc. 9th International Symposium on Software Metrics (METRICS'03), 3 – 5 Sept., 2003, pp.
263 – 275, 2003.
[12] S.W.A. Rizvi and R.A. Khan Maintainability Estimation Model for Object Oriented Software in Design Phase (MEMOOD).