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  • Marian Jureczko and Diomidis Spinellis. Using object-oriented design metrics to predict software defects. In Models and Methodology of System Dependability. Proceedings of RELCOMEX 2010: Fifth International Conference on Dependability of Computer Systems DepCoS, Monographs of System Dependability, pages 69–81, Wroclaw, Poland, 2010. Oficyna Wydawnicza Politechniki Wroclawskiej.

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Diomidis Spinellis Publications

Using Object-Oriented Design Metrics to Predict Software Defects*

Marian JURECZKO[1], Diomidis D. SPINELLIS[2]

1. Introduction

Many object-oriented design metrics have been developed [1,3,8,17,24] to help in predict software defects or evaluate design quality. Since a defect prediction model may give crucial clues about the distribution and location of defects and, thereby, test prioritization, accurate prediction can save costs in the testing process. Considerable research has been performed on defect prediction methods; see the surveys by Purao and Vaishnavi [22] and by Wahyudin et al. [25], unfortunately few results appear at statistically significant level. Therefore, further empirical validation is necessary to prove the usefulness of the metrics and software prediction models in industrial practice.

Our study was made possible through the creation of a new metric calculation tool[3].  There are many tools that calculate object-oriented metrics. What is the reason to create another one? In fact the situation is not so perfect. The available programs are either extremely inefficient (sometimes they do not work with big software projects at all), not available as open source and therefore difficult to reason about their results, or incomplete — the set of calculated metrics is not wide enough. It is extremely hard to find a tool that calculates all metrics from the Chidamber and Kemerer (C&K) metrics suite [3]. Having both, C&K and QMOOD metrics suites [1] in one tool is even rarer, and according to the authors' knowledge there is no other tool, that calculates metrics suggested by Tang et al. [24]. Ckjm calculates metrics that have been recommended as good quality indicators. There are several works that investigate the C&K metric suite and that have empirically proven their usability in quality or defect prediction [2, 10, 11, 20]. There are recommendations about QMOOD metrics suite [1, 20] and the quality oriented extension of C&K [24] too. Ckjm does not offer a GUI and its focus is not on elaborate diagrams but on efficient calculation of metrics. Ckjm is an open source project, thus it is free of charge. Finally, Ckjm is a mature tool. This paper presents a new version of the tool substantially expanding a previous version (v 1.8[4]) which evaluated a smaller set of metrics. The new version is a quality oriented extension and calculates many additional metrics that have been recommended as good quality indicators.

The paper is organized as follows: In Section 2 the motivation and goals are provided. In Section 3 related works are described. Section 4 presents the suite of OO metrics that are calculated by ckjm. The experiment is shown in Section 5. This includes description of investigated projects and methods of data acquiring in Section 5.1, conducted statistical analysis in Section 5.2 and potential threats in Section 5.3. Section 6 contains results of the experiment. Conclusions and future research are in Section 7.

2. Motivation and goals

Testing of software systems is an activity that consumes time and resources. Applying the same testing effort to all modules of a system is not the optimal approach, because the distribution of bugs among individual parts of a software system is not uniform. Therefore, testers should be able to identify fault-prone classes. With such knowledge they would be able to prioritize the tests and therefore, work more efficiently. The availability of adequate software defect prediction models is, thus, vital.  This task can be performed by tools, like ckjm, which is designed to help in quality assurance by calculating metrics that can be used to predict software defects.

The main goal of this research is to construct software defect prediction models. The metrics calculated by ckjm are used as the model input. Therefore, the model constructing process allows deciding whether the calculated metrics are usable as defect predictors. The estimated number of defects for a Java class is the model output. The model output may be used to select classes where the estimated number of defects is on high level. According to Weyuker et al. [21,26,27,28] typically 20% of files contain upwards of 80% of defects. Testers with a good defect predicator should be able to reduce their test effort by testing only 20% of files (Java classes) and they still should be able to find most of the defects (80%). Models constructed in this research are evaluated by counting the percentage of Java classes that must be tested in order to find 80% of the defects.

The collecting of data, that was required to construct the software defect prediction models, gave an opportunity to investigate a hypothesis about factors that influence at defect prediction mechanism. There are works [5,6,13,14,19] where class or module size has been pointed as an important factor in defect prediction. 44 models, that ignore the class size factor and 88 models that use the class size factor have been created in order to test if the class size factor has statistically significant influence on defect prediction accuracy. There are so many models and only 16 software projects because several versions of each project have been investigated.

3. Related work

Considerable research has been performed on software metrics; see Kan's monograph [12], survey by Purao and Vaishnavi [22], and the references therein. Some of the metrics has been shown to be useful for predicting the fault-proneness of classes and for building the software defect prediction models [1,2,4,9,10,11,15,19,20,21,23,24,26,27, 28,29]. There are also several papers where the Pareto analysis has been used to evaluate the models ability of identifying the fault-prone classes, modules or files. Weyuker et al. found 76-93% of the faults in 20% of the files that had been selected by defect prediction model, by using the negative binomial regression [21] and 68-85% of the faults by using the recursive partitioning [26]. Further, the models were simplified in order to make them more generic, what resulted in founding 50-92% of the fault in 20% of the files. Denaro and Pezze [4] used logistic regression models to identify fault-prone modules. They reported that their best model required about 50% of the modules to be investigated in order to find 80% of the software faults. They used data collected from Apache v. 1.3 and they assessed the model on Apache v. 2.0. Succi et al. [23] used C&K metrics suite as well as software size to find fault-prone classes. They have investigated two software projects, both written in C++. They reported, that their required 43-48% of classes to be analyzed in order to cover 80% of the defects.

According to the authors' knowledge, few works has been done on the use of class size for defect prediction. Some interesting observations are the followings. Fenton and Neil [6] described the phenomenon, that larger modules may have lower defect densities. Koru and Liu [13] discovered that the predictability was worse for subsets that included many small components and they gave some practical hints that explain how the defect prediction models should be constructed with respect to their findings [14]. Their advice is that data sets are stratified according to the module size in order to facilitate prediction of defects on these data subsets. Mende and Koschke [19] created defect prediction models, that were based only on the module size measured in Line of Code (LoC). The results were surprisingly well. The outputs of their models were strongly correlated with the actually data. The Spearman's correlation coefficient varied between 0.41 and 0.9. El Emam et al. [5] investigated whether there is a confounding effect of class size measured in Line of Code (LoC). They considered the C&K metrics, and a subset of the Lorenz and Kidd [16] metrics. Their findings indicate that the class size should be considered in the defect prediction models. However El Emam et al. investigated only one software project.

4. The metrics

The set of metrics that ckjm is able to calculate are listed in Table 1 and have been defined according to the metric importance in defect prediction. All metrics, except McCabe's Cyclomatic Complexity (CC), are class size metrics.

Table 1. Metrics definitions.

Metric Name



Weighted methods per class (WMC)

The value of the WMC is equal to the number of methods in the class (assuming unity weights for all methods).

C&K [3]

Depth of Inheritance Tree (DIT)

The DIT metric provides for each class a measure of the inheritance levels from the object hierarchy top.

C&K [3]

Number of Children (NOC)

The NOC metric simply measures the number of immediate descendants of the class.

C&K [3]

Coupling between object classes (CBO)

The CBO metric represents the number of classes coupled to a given class (efferent couplings and afferent couplings). This couplings can occur through method calls, field accesses, inheritance, method arguments, return types, and exceptions.

C&K [3]

Response for a Class (RFC)

The RFC metric measures the number of different methods that can be executed when an object of that class receives a message. Ideally, we would want to find for each method of the class, the methods that class will call, and repeat this for each called method, calculating what is called the transitive closure of the method call graph. This process can however be both expensive and quite inaccurate. Ckjm calculates a rough approximation to the response set by simply inspecting method calls within the class method bodies. The value of RFC is the sum of number of methods called within the class method bodies and the number of class methods. This simplification was also used in the Chidamber and Kemerer's [3] description of the metric.

C&K [3]

Lack of cohesion in methods (LCOM)

The LCOM metric counts the sets of methods in a class that are not related through the sharing of some of the class fields. The original definition of this metric (which is the one used in ckjm) considers all pairs of class methods. In some of these pairs both methods access at least one common field of the class, while in other pairs the two methods do not share any common field accesses. The lack of cohesion in methods is then calculated by subtracting from the number of method pairs that do not share a field access the number of method pairs that do.

C&K [3]

Lack of cohesion in methods (LCOM3)

m - number of methods in a class

a - number of attributes in a class

µ(A) - number of methods that access the attribute A

Henderson-Sellers [8]

Afferent couplings (Ca)

The Ca metric represents the number of classes that depend upon the measured class.

Martin [17]

Efferent couplings (Ce)

The Ca metric represents the number of classes that the measured class is depended upon.

Martin [17]

Number of Public Methods (NPM)

The NPM metric simply counts all the methods in a class that are declared as public. The metric is known also as Class Interface Size (CIS)


Data Access Metric  (DAM)

This metric is the ratio of the number of private (protected) attributes to the total number of attributes declared in the class.


Measure of Aggregation (MOA)

This metric measures the extent of the part-whole relationship, realized by using attributes. The metric is a count of the number of class fields whose types are user defined classes.


Measure of Functional Abstraction  (MFA)

This metric is the ratio of the number of methods inherited by a class to the total number of methods accessible by the member methods of the class. The constructors and the java.lang.Object (as parent) are ignored.


Cohesion Among Methods of Class (CAM)

This metric computes the relatedness among methods of a class based upon the parameter list of the methods. The metric is computed using the summation of number of different types of method parameters in every method divided by a multiplication of number of different method parameter types in whole class and number of methods.


Inheritance Coupling  (IC)

This metric provides the number of parent classes to which a given class is coupled. A class is coupled to its parent class if one of its inherited methods functionally dependent on the new or redefined methods in the class. A class is coupled to its parent class if one of the following conditions is satisfied:

· One of its inherited methods uses an attribute that is defined in a new/redefined method.

· One of its inherited methods calls a redefined method.

· One of its inherited methods is called by a redefined method and uses a parameter that is defined in the redefined method.

Tang [24]

Coupling Between Methods (CBM)

The metric measures the total number of new/redefined methods to which all the inherited methods are coupled. There is a coupling when at least one of the given in the IC metric definition conditions is held.

Tang [24]

Average Method Complexity (AMC)

This metric measures the average method size for each class. Size of a method is equal to the number of Java binary codes in the method.

Tang [24]

McCabe's cyclomatic complexity (CC)

CC is equal to number of different paths in a method (function) plus one. The cyclomatic complexity is defined as:


  CC = E – N + P

E - the number of edges of the graph

N - the number of nodes of the graph

P - the number of connected components

CC is the only method size metric. The constructed models make the class size predictions. Therefore, the metric had to be converted to a class size metric. Two metrics has been derived:

· Max(CC) - the greatest value of CC among methods of the investigated class.

· Avg(CC) - the arithmetic mean of the CC value in the investigated class.

McCabe [18]

Lines of Code (LOC)

The LOC metric based on Java binary code. It is the sum of number of fields, number of methods and number of instructions in every method of the investigated class.


5. Study design

There are many guidelines for constructing defect prediction models [6,7,25]. The approach that has been used in this paper does not follow all the recommendations found in the literature. Some simplifications have been made. According to Lessmann et al. [15] simple algorithms are not significantly worse than the sophisticated data processing techniques. Thus the models output may be not as accurate as it is possible but still usable and helpful in the testing process.

5.1 Data sourceS

The data about software projects metrics and defects has been collected from source code repositories. The ckjm tool has been used to calculate the metrics. Another tool, called BugInfo, has been prepared to identify defects. BugInfo analyses the logs from source code repositories (Subversion or CVS) and according to the log content decides if a commit is a bugfix. Each of the projects had been investigated in order to identify bugfixes commenting guidelines that were used in the source code repository. The guidelines were formalized in regular expressions. Buginfo compares the regular expressions with comments of the commits. When a comment fits to a regular expression, BugInfo increments the defect count for all classes that have been modified in the commit.

The following projects have been investigated (project size is the average number of classes):

Forrest ( The Forrest software is a publishing framework that transforms input from various sources into a unified presentation in one or more output formats. Size = 34.

POI ( The POI project consists of APIs for manipulating various file formats based upon Microsoft's OLE 2 Compound Document format, and Office OpenXML format, using pure Java. Size = 421.

Synapse ( Synapse is a simple, lightweight and high performance Enterprise Service Bus (ESB) from Apache. Synapse has support for HTTP, SOAP, SMTP, JMS, FTP and file system transports, Financial Information eXchange (FIX) and Hessian protocols for message exchange as well as first class support for standards such as WS-Addressing, Web Services Security (WSS), Web Services Reliable Messaging (WSRM), efficient binary attachments (MTOM/XOP). Size = 220.

Xalan-Java ( Xalan is an XSLT processor for transforming XML documents into HTML, text, or other XML document types. It implements XSL Transformations (XSLT) Version 1.0 and XML Path Language (XPath) Version 1.0. Size = 1043.

PBeans ( pBeans is a Java persistence layer and an object/relational database mapping (ORM) framework. Size = 48.

Xerces ( Xerces is a Parser that supports the XML 1.0 recommendation and contains advanced parser functionality, such as support for XML Schema 1.0, DOM level 2 and SAX version 2. Size = 484.

Ant ( Ant is a well known Java-based, shell independent build tool. Size = 488.

Ivy ( Ivy is a dependency manager focusing on flexibility and simplicity. Size = 311.

Camel ( Apache Camel is a powerful open source integration framework based on known Enterprise Integration Patterns with powerful Bean Integration. Size = 894.

Log4j ( Log4j is a well known logging framework. Size = 187.

Lucene ( Lucene provides Java-based indexing and search technology, as well as spellchecking, hit highlighting and advanced analysis/tokenization capabilities. Size = 402.

There are five proprietary software projects too. All of them are custom build solutions and all of them were successfully installed in the customer environment. Their sizes are as follows: prop-1 size = 3954; prop-2 size = 2138; prop3 size = 2218; prop-4 size = 2860; prop-5 size = 3574.

5.3 Data analysis method

The main goal of this study is to empirically validate metrics calculated by the ckjm tool whether those metrics are useful for predicting fault-prone classes. A class is said to be fault-prone if it has at least one defect. The defect is identifying according to the history from the source version control system. When a class has been changed and the change has been marked as defect (bug) fix, the count of the defects for the class will be incremented.

The second goal of this study is to investigate whether class size is a relevant factor in the defect prediction models. This lead to the formulation of the following quantifiable hypothesis to be tested:

· H0 WMC – There is no difference in the accuracy of the defect prediction models between model using the WMC metric as the class size factor and model ignoring the class size factor.

· HA WMC – There is a difference in the accuracy of the defect prediction models between model using the WMC metric as the class size factor and model ignoring the class size factor.

· H0 LOC – There is no difference in the accuracy of the defect prediction models between model using the LOC metric as the class size factor and model ignoring the class size factor.

· HA LOC – There is a difference in the accuracy of the defect prediction models between model using the LOC metric as the class size factor and model ignoring the class size factor.

Model accuracy is the percentage of classes that have to be investigated in order to find 80% of the defects. The classes are investigated in the order of decreasing estimated number of defect. The estimation is made by the defect prediction model. Each of the investigated software projects has at least two versions (external releases). The model constructed on the project version i-1 is always assessed on the version i. The data about version i-1 is always available during version i development.  Therefore, the assessment method suits very well to the software development practice.

The following steps are performed in order to construct a defect prediction model:

1. Correlation matrix with all metrics and the number of defects is created. The Pearson correlation coefficient (r) is used.

2. Highly Correlated metrics are identified (r>0.8 and correlation statistically significant with a=0.05). The highly correlated metrics that are lower correlated with the number of defects are eliminated from further calculations. Example: rRFC,CBO=0.9, rRFC,Defect=0.69, rCBO,Defect=0.77 – the RFC metric will be eliminated.

3. Stepwise linear regression is used to construct the model. All no eliminated metrics are used as independent variables. The number of defects is used as the dependent variable.

For models using the class size factor, the input data is divided into two sets according to the value of the class size factor. We assign small classes in the first set and big classes in the second set. The above steps are performed for each set separately.

The hypotheses are evaluated by the parametric t-test. Following general assumptions should be checked in order to use a parametric test: level of measurement (the variables must be measured at the interval or ratio level scale), independence of observations, homogeneity of variance and the normal distribution of the sample. The homogeneity of variance is checked by Levene's test. The assumption that the sample came from a normally distributed population is tested by the Shapiro-Wilk and Kolmogorov-Smirnov tests.

5.4 Threats to validity

A number of limitations that may compromise to some extent the quality of the results of this study are listed below.

· It is possible that there are mistakes in the defect identification. The comments in the source code version control system are not always well written and, therefore, it was sometimes very hard to decide whether a change is connected with a defect or not.

· Metrics from the revision r1 and defects fixed in revisions (r1;r2) are taken to build the defect prediction model. Subsequently, the model takes (as input) metrics from the revision r2 and the model is used to predict defects in (r2;r3). Therefore, all information about the classes (and their defect), that have been created in the period (r1;r2) are ignored during model creation because those classes did not exist in the r1  revision.

· Text Box:  
Fig. 1. Accuracy of the defect prediction models. 

The defects are assigned to versions according to the bugfix date. It could be probably better to assign a defect to the version, where the defect has been found, but unfortunately, the source code version control system does not contain such information.

· We were not able to track operations like changing class name or moving class between packages. Therefore, after such a change, the class is interpreted as a new class.

6. Results

Text Box: Tab. 3. T-test statistics
Hypothesis	t	Degrees of freedom	Probability level
H0 WMC	1.071	86	0.287
H0 LOC	1.654	86	0.102

The details of creating the defect prediction models would be impossible to present in the space provided. The results of applying models are described on Figure 1. 8.57-62.27% of classes (mean (m) = 39.216; standard deviation (s) = 11.568) have to be investigate in order to find 80% of defects when the simple models (Ms) are used. For the models with the class size factor the results are as follows: 7.57-58.93% (m=37.433; s=10.258) of classes have to be investigated according to the WMC based models (MWMC), and 10,56%-54,93% (m=36.086; s=10,435) according to the LOC based models (MLOC). Please notice that the Forrest project has been investigated only with the simple model and the result, which has been obtained for this project, is below the mean value. The project was too small to be investigated with more sophisticated models. The Forrest project has been removed from the sample before hypotheses testing.

The assumptions that variables are measured at the interval or ratio level and that the observations are independent of one another are met. The assumption of homogeneity of variance has been tested using Levelene's test. The test was not significant in both cases (pS,WMC=0.768, pS,LOC=0.952), so we accept the null hypothesis, that the population variances are equal. The assumption of normality has been tested using the Kolmogorov-Smirnov and the Shapiro-Wilk tests. The assumption of normality has not been violated: MS - S-W (W=0.983, p=0.767), K-S (d=0.094, p=0.2); MWMC - S-W (W=0.981, p=0.693), K-S (d=0.081, p=0.2); MLOC - S-W (W=0.976, p=0.482), K-S (d=0.097, p=0.2).

       Since p>0.05 (probability level in tab. 3), there are no reasons to reject the H0 WMC or the H0 LOC hypothesis. So we can conclude that the size factor did not significantly affect the defect prediction model accuracy. According to fig. 1 models with the size factor give better predictions, but the size factor based improvements are not statistically significant.

7. Conclusions and future research

An analysis of the calculated metrics has been used to construct defect prediction models. The models have been assessed on five proprietary and eleven open source projects. Each time, a model constructed according to the data from version i of a project has been assessed by predicting the defects in version i+1 of the project. The analysis showed that by applying simple regression models with the class size factor we were able to find 80% of defects in 10.56% to 54.93% (m=36.086; s=10.435) of the classes. Therefore, one could be able to save considerable costs in the testing process by testing only 36% of the classes (the mean value) and still finding most of the defects (80%). Using more sophisticated regression models may lead to even better results; see Weyuker et al. [26,27,28] and the negative binomial model. This is the primary contribution of the research. Another contribution of the paper is an empirical study of usefulness of the class size factor in the defect prediction models. Two metrics have been considered as the class size factors: WMC (Weighted Methods per Class) and LOC (Lines of Code). The WMC based models were slightly and the LOC based models were clearly better as the simple models (without  class size factor), but the difference was statistically significant neither in the case of WMC based models, nor in the case of LOC based models.

There are a number of factors (except the class size) that may be relevant in defect prediction. The collected metrics will be used in further researches, where we would like to try to identify the factors and investigate whether they have statistically significant influence on defect prediction. The number of investigated projects may be to small to perform some of the analyses, especially increasing the sample size may show statistically significance of the class size factor. Therefore data about further software projects will be collected.

A simple regression model has been used in the presented research. Using more sophisticated regression models, like the negative binomial regression model, may be a better alternative. There are plans to evaluate more sophisticated models to see how they will work, especially in comparison wit the simple models.

We finish by noting the importance of conducting reproducible empirical research studies. The researchers typically make many decisions in order to study the software metrics. Therefore, the main way to make research on software metrics reproducible is to make the collected metrics publicly accessible. Therefore, we are going to place the collected metrics online at


The authors are very grateful to the Capgemini Polska Company that allowed analyzsing five of their proprietary projects. Thus, the research has been better validated - authors could use not only open source, but also industrial projects.


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*  Fellowship co-financed by European Union within European Social Fund

[1] Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław - Poland,

[2] Department of Management Science and Technology, Athens University of Economics and Business, Patission 76, GR-104 34 Athens - Greece