Journal of Software Engineering and Applications, 2011, 4, 497-511
doi:10.4236/jsea.2011.48058 Published Online August 2011 (
Copyright © 2011 SciRes. JSEA
Temporal Patterns of Software Evolution Defects:
A Comparative Analysis of Open Source and
Closed Source Projects
Uzma Raja, Joanne Elaine Hale, David Peter Hale
Department of Information Systems, Statistics, and Management Science, The University of Alabama, Tuscaloosa, Alabama, USA.
Received January 22nd, 2011, revised March 30th, 2011, accepted A pr i l 10 th, 2011.
This study examines temporal patterns of software systems defects using the Autoregressive Integrated Moving Average
(ARIMA) approach. Defect reports from ten software application projects are analyzed; five of these projects are open
source and five are closed source from two software vendors. Across all samp led projects, the ARIMA time series mod-
eling technique provides accurate estimates of reported defects during software maintenance, with organizationally
dependent parameterization. In contrast to causal models that require extraction of source-code level metrics, this ap-
proach is based on readily available defect report data and is less computation intensive. This approach can be used to
improve software maintenance and evolution resource allocation decisions and to identify outlier projects—that is, to
provide evidence of unexpected defect reporting patterns that may indicate troubled projects.
Keywords: Op en Source Software, Software Defects, Software Maintenance, Time Series Analysis
1. Introduction
Today’s software systems are fragile [1], particularly
when new software releases are deployed [2]. The falli-
bility of software applications and their underlying op-
eration systems is seemingly inevitable [3]. As a result,
sixty to eighty percent of the typical firm’s total software
budget is allocated to software maintenance [4,5]. In ad-
dition, an entire business function and support industry
has grown up to handle the problems as they occur [6].
Operational planning within such organizations may take
several forms. Some organizations attempt to ramp up
and down maintenance staff and related resources (such
as test harnesses, software maintenance tools, and testing
environments) in response to task arrival rate fluctuations.
Other organizations respond by keeping resources stable
which results in oscillation between resource over-utili-
zation (and the resulting increased wait time for software
patches, decreased user satisfaction and business value)
and resource under-utilizatio n (and the resulting resource
idling and increased cost).
Stark and Oman [7] provide alternative staffing and
release schedule strategies responding to user detected
software defect reports. Anchored at one extreme, a fixed
capacity staff can be assigned to respond to defect re ports
as received, with upgrade releases occurring at fixed in-
tervals. At the other extreme, staff augmentation can be
used to provide resources as needed and upgrade release
times adjusted to aggregate related changes. Between
these extremes, additional strategies are implemented in
practice that provide for variable staffing, but fixed
schedule periods; or fixed staffing with variable lengths
of time between upgrades. To evaluate the potential fu-
ture benefit of any of these strategy alternatives requires
knowledge of the potential distribution pattern of the
reported defe cts.
The manager’s choice in resource planning approaches
is critical. In recent work, Chulani et al. [8] identified the
interval between reporting and fixing defects as the
dominate factor in user satisfaction; this dominance out-
strips even the number of defects. To maintain user sat-
isfaction, resources must be available to resolve defects
and promptly make the system operate as expected. This
result is necessary to the use of information systems as a
vital component in business operations. These observa-
tions lead naturally to the operational planning question:
Is there a model to aid in predicting when resources
will be needed?
Temporal Patterns of Software Evolution Defects: A Comparative Analysis of Open Source and Closed Source Projects
Secondarily, if such a predictive model for software
maintenance resources can be derived:
Is such a predictive model computationally and eco-
nomically practi cal?
These questions have yet to be adequately addressed,
as according to Pelayo and Dick [9] “no parametric
model has ever been developed that accurately forecasts
the number or occurrence of faults [defects] in a software
module.” To meet this research challenge, this study
seeks to develop an accurate predictive model of soft-
ware defect patterns that can be applied to the larger
problem of software maintenance resource allocation and
alignment, while using readily available defect report
data and computational resources.
2. Background
During peak shopping times, retailers increase their staff
of floor professionals and cashiers. When few truckloads
are expected to arrive, a distribution center manager
schedules fewer fork lift operators. Software mainte-
nance managers are faced with similar arrival rate fluc-
tuations that impact resource requirements. Software
maintenance managers must ensure product quality and
required service levels, while simultaneously minimizing
costs associated with defect resolution and penalties for
non-performance [10,11]. Faced with this challenge,
formal predictive models are not common in resource
planning; instead maintenance planning methods in prac-
tice continue to be largely ad hoc [12], with recent per-
sonal experience weighing heavily on practitioner pre-
dictions of change requests and staffing needs [10,12].
As a result, maintenance project managers too often ei-
ther overstaff (causing resources to idle and costs to in-
crease) or understaff (causing delays in defect resolution
and a decline in user satisfaction and business value).
Previous work is reviewed regarding predicting soft-
ware defects, where a defect is defined as a reported error
that is encountered in an operational software applicatio n.
The predominance of prior research does not focus on
patterns of discovered defects once the application is in
use. Instead, a strong body of research exists that predicts
software defects during the development of new systems.
Both areas are explored and fall into three classes of
forecasting approaches: causal, learning and time-series.
2.1. Causal Models
Many researchers have constructed models to predict the
number of defects remaining in completed software
products or identify defect-dense modules within a sys-
tem. Ohlsson et al. [13] use principal components analy-
sis and classification trees to identify fault-prone com-
ponents. Khoshgoftaar and Lanning [14] used a neural
network technique to classify modules as high or low risk
for defects based on quality and complexity metrics in-
cluding the number of fault-correcting and enhancive
changes. El Emam and Laitenberger [15] used a Monte
Carlo simulation to evaluate the accuracy of a capture-
recapture re-inspection de fe c t prediction model.
Khoshgoftaar et al. [16] constructed a nonlinear re-
gression model predicting the number of faults using
lines of code. Fenton and Neil [17] and Adams [18] dis-
covered that post-release defects were more likely in
modules where few defects were discovered pre-release
and that testing effectiveness significantly impacts the
post-release presence of defects. Krishnan and Kellner
[19] found that organizations that consistently followed
Capability Maturity Mo del (CMM) practices ex perienced
significantly fewer reported field defects in the resulting
software. Krishnan [20] found that higher levels of do-
main experience of the software team are associated with
a reduction in the number of field defects in the product.
However, there is no significant association between either
the language or the domain experience of the software
team and the costs incurred in developing the product.
Such causal predictive models of defects identify the
factors that impact software defects, thus serving both
predictive and explanatory roles regarding what factors
could be controlled to manage future defects. Such mod-
els are useful for software development teams, since they
can control these variables and manage the overall qual-
ity of software system. Most of these models however
require access to internal characteristics of software.
Although available for decades for use in staffing and
system quality and defect modeling, these causal models
have not been widely used in practice because of the cost
and complexity of implementation [21]. Further compli-
cating their use during software maintenance, mainte-
nance practitioners have little control over the internal
characteristics commonly modeled to predict defects
(largely set at time of product release), thus rendering
such complex models of little use to maintenance man-
agers who want to manage and allocate budget, time and
resources for future defect occurrences.
2.2. Learning Techniques
A number of authors have investigated the use of ma-
chine-learning techniques for software defect prediction.
Some examples include neural networks [22], genetic
programming [23], fuzzy clustering ([24] and decision
trees [25]. For example, Seliya et al. [26] proposed a
semi-supervised clustering method to detect failures in
software modules. Instead of working with the individual
modules on software, they group modules and label them
as fault prone or not fault prone.
Fenton and Neil [17] used Bayesian belief networks
(BBN) as an effective approach for defect prediction, an
Copyright © 2011 SciRes. JSEA
Temporal Patterns of Software Evolution Defects: A Comparative Analysis of Open Source and Closed Source Projects499
approach that is gaining popular ity [27]. Building on this
work, Menzies et al. [28] showed positive results using a
naïve Bayes classifier with log-filtered static code meas-
Challagulla et al. [29] used simulation to compare
software prediction using stepwise regression, rule in-
duction, case-based reasoning, and artificial neural net-
works. They concluded that stepwise regression per-
formed better with contin uous target functions, while the
other machine learning approaches performed better for
discontinuous target functions. They favored case based
reasoning since it appeared to be the best all round pre-
dictor by a small margin. Song et al. [30] investigated the
above prediction models on real software data, compar-
ing them in terms of accuracy, explanatory value, and
configurability. They concluded that the explanatory
value of case-based reasoning and rule induction gives
them an advantage over neural nets, which have prob-
lems of configuration. Aljahdali et al. [31] compared
regression with neural nets for prediction of software
reliability and concluded that for most cases neural nets
provided fewer errors than regression models.
These adaptive, learning based predictive models have
been found to i mprove on the accuracy of traditional sta-
tistical linear causal models. However, they still fail to
meet the ease of implementation goal of this study, as
they require professionals with specialized model know-
ledge and sophisticated software not typically at the dis-
posal of a maintenance manager.
2.3. Time Series Models
Causal and learning models are both computationally
complex and require significant investments in project
data collection. In response to these challenges, the goal
of this study is to provide a method of predicting patterns
in software defects that is accurate without the cost and
complexity of more traditional predictive methods.
Time series models assume that events are correlated
over time and the impact of other factors is progressively
captured in historical archives [32]. The most commonly
used forecasting method, time series models are fre-
quently used to predict product demand [33], macro-eco-
nomic trends [34], and retail sales [35], but are yet to be
widely adopted in the software maintenance domain [36].
Within the domain of software maintenance, time se-
ries modeling has had limited use. Kemerer and Slaugh-
ter [37] used ARIMA modeling to predict monthly
changes, not reported defects, in software. Kenmei et al.
[38] and Raja et al. [36] created time series models for
defects in open source software (OSS) and found that the
ARIMA models outperform the accuracy of simple mod-
els. Each research team found that time series modeling
was a suitable and accurate method of defect prediction
for large-scale OSS projects. However neither of the lat-
ter studies investigated proprietary closed source soft-
ware applications.
Thus based on results in the literature, time series
analysis potentially provides a method of predicting pat-
terns in software defects that is accurate without the cost
and complexity of causal and learning models. It is left to
this study to determine whether the results found in OSS
projects can be replicated across open and closed source
software (CSS) applications.
3. Methods
This work builds on previous studies that discovered the
accuracy and ease of implementation of time series soft-
ware defect prediction. Specifically this research com-
pares the defect evolution patterns across a diverse set of
projects, providing the opportunity to study projects
within and across organizations. This section describes
the prediction model adopted in this study, the software
maintenance projects examined, the associated data ex-
tracted, and the analytical techniques used.
3.1. Time Series Analysis
As proposed in prior studies [32,36], time series an alysis
offers promise in the field of software defect prediction.
These models are suited for representing situations char-
acterized by frequent variations, such as the pattern of
software defect occurrences. A time series is a collection
of observations made over equal intervals of time that can
be used to predict future values and to identify trends [39] .
A wide variety of time series modeling techniques are
available and their su itability depends upon the nature of
the data. A Moving Average series (MA) explain present
as a mixture of random impulses, while an Autoregres-
sive (AR) model builds the present in terms of past val-
ues. These series are suitable for data that is stationary in
nature i.e. its statistical properties (e.g. mean, variance,
autocorrelation) are constant over time.
For cases in which there is evidence of data being
non-stationary as opposed to stationary, Box and Jenkins
[40] introduced a corresponding generalized model. This
model is called Autoregressive Integrated Moving Aver-
age (ARIMA). T he general form of ARI M A (p,d,q) is:
 
 
Yt = time series of the variable y.
= coefficient associated with Yt, to be estimated
using least squares.
= the defect term, assumed to be independent,
identically distributed variables sampled from a normal
Copyright © 2011 SciRes. JSEA
Temporal Patterns of Software Evolution Defects: A Comparative Analysis of Open Source and Closed Source Projects
distribution with zero mean.
= the coefficient associated with t
to be esti-
mated using least squares.
As detailed in the following subsections, the ARIMA
modeling strategy followed in this study is comprised of
four steps: Identification, Estimation, Diagnostic Testing
and Application .
Model Identification: The first step in model identifi-
cation is often to apply a logarithmic transformation to
stabilize the variance of a series. Then the model is pa-
rameterized as ARIMA (p,d,q), where
p = order of the Autoregressive component.
d = order of the Dif ferenced com ponent.
q = order of the Moving Average component.
During model identification, the time series is ana-
lyzed to assess what values of the parameters p, d, and q
are most appropriate. The value of d is set taking into
account whether the series is stationary (d = 0) or non-
stationary (d > 0).
Estimation: The original or transformed time series is
then modeled using the parameters and identified in the
previous step to estimate the coefficients
in Equation
(1). The different candidate values of p and q are used to
compute the respective coefficient. The final model is
selected using goodness of fit tests. Where goodness of
fit is equivalent, t he m ost parsim onious m odel i s selected.
Diagnostic Testing: The residuals are computed as the
difference of the actual and predicted values (using the
identified mode). These residuals are then analyzed using
known techniques to determine the adequacy of the
model. The residuals of a good model are expected to be
small and random.
Model Application: The predictive model accuracy on
unseen data is estimated using a hold-out data sample
[41]. Using this approach, a subset of the time series data
is withheld from use in parameter estimation, and is in-
stead used to test the model’s accuracy.
3.2. Site Selection and Data Description
To study patterns in defect arrival rates, projects from a
diverse set of organizations, problem domains, teams,
and development methodologies were selected. The
closed source software data was acquired from two or-
ganizations. Organization A is a large diversified interna-
tional software consulting firm, with a mature method-
ology environment; all Organization A development
groups are currently assessed at Capability Maturity
Model Integration (CMMI) Level 3 or higher. Data for
three Organization A projects was obtained, denoted in
this study as Project A1, Project A2, and Project A3.
Organization B is a small (30 employee) privately
owned provider of financial transaction automation soft-
ware using agile methodologies. Data for two Organiza-
tion B projects was obtained, denoted in this study as
Project B1 and Project B2.
In addition to the five CSS projects (three from Or-
ganization A and two from Organization B) five projects
not included in Raja et al. [36] study were randomly se-
lected from the list of the top twenty most active OSS
projects within the SourceForge repository. Inclusion of
these five projects provides process replication and ex-
tends the sample set coverage by more than 50% to the
OSS projects as evaluated by Raja et al. [36]. Descrip-
tions of the OSS and CSS projects included in this study
are presented in Table 1.
Each of the ten studied projects has one or more arti-
fact repositories that store information regarding various
artifact types e.g. defects, patches, and feature requests.
Defects of an individual project can be extracted using
the unique defect repository identifier, available in each
artifact. The defect data also includes the time of defect
submission. The data is then aggregated to compute
monthly defects for each project. Table 1 shows the st art
date, number of months of available data and the total
number of defects for each of the sampled projects.
3.3. Variable Specification and Data Extraction
Time series modeling requires that data are gathered
across equally spaced time intervals. Consistent with the
commonly used resource planning interval, a monthly
count of software defects was computed for each project.
The model accuracy is sensitive to the length of historical
data available. Therefore projects with a minimum 50
months of data available were used in the analysis. This
also ensures that there is enough data available for hold-
out sampling and testing of the accuracy of the model
For OSS projects, the defect-tracking
repository holds archives of defect reports for the pro-
jects hosted by that community. Organization A and B
host their own internal defect tracking repositories for
trouble resolution. In all three environments, the data
dictionary of the repository was used to identify the arti-
fact repository of defects. SQL queries were used to ex-
tract individual project defect data from the hosting ar-
chive warehouse. Further queries were used to compute
monthly statistics of the defects for each project indi-
vidually. The monthly counts of defects were computed
using the time stamps of each defect report. The resulting
dataset contained the monthly defects for all OSS and
CSS projects.
4. Analysis and Results
4.1. Model Identification
The first step in model identification is to stabilize the
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Temporal Patterns of Software Evolution Defects: A Comparative Analysis of Open Source and Closed Source Projects
Copyright © 2011 SciRes. JSEA
Table 1. Sample description.
Projects Description Months Total Defects
wxWidgets wxWidgetsis a free C++ framework that facilitates cross platform soft-
ware development, including GUIs, threads, sockets, database, file system
access, etc 90 4843
Firewall Builder Object Oriented GUI and set of compliers for various firewall platform.
Currently implemented compilers for iptables, ipfiler, OpenBSD, ipfw,
Cisco PIC firewall routers access lists 93 1067
Netatalk is a freely-available Open Source AFP fileserver. It also provides
a kernel level implementation of the AppleTalk Protocol Suite. A
*NIX/*BSD system running Netatalk is capable of serving many Macin-
tosh clients simultaneously as an AppleShare file server (AFP), Apple-
Talk router, *NIX/*BSD print server, and for accessing AppleTalk print-
69 347
PhpWiki is a WikiWikiWeb clone in PHP. A WikiWikiWeb is a site
where anyone can edit the pages through an HTML form. Multiple stor-
age backends, dynamic hyperlinking, themeable, scriptable by plugins,
full authentication, ACL's.
99 627
Open Source Projects
Exult Exuit is a game engine for running Ultima7 on modern operating systems,
plus a map editor and other tools for creating your own mods and games. 102 1675
Org A#1 A1 is an n-tier web-enabled wholesale billing application using J2EE and
interfacing with an Oracle database. 58 3539
Org A#2 A2 is an object oriented service rating, pricing and discounting applica-
tion using J2EE and interfacing with Oracle database. 60 1214
Org A#3 A3 is a performance management system providing KPI dashboards and
analytics for monitoring and forecasting, built using a SOA and interfac-
ing with most industry stan dard databases. 58 377
Org B#1 B1 is a payment processing application built on Microsoft platform that
includes check scanning, image and data archival, courtesy amount rec-
ognition and legal amount r ec og ni t io n. 54 1842
Closed Source Projects
Org B#2 B2 is a merchant capture application that allows for the remote digital
capture of check and payment data at the point of presentment and the
bundled transmission for depo s i t i n to multiple accounts 54 582
means and variances by applying a logarithmic transfor-
mation to the time series data. The next step is to plot:
the autocorrelation factors (ACF), the correlation, at spe-
cific lags, between the residuals of the data; and the par-
tial autocorrelation factors (PACF). For each studied
project the values of p (the autoregressive component)
and q (the moving average component) are determined
by examining the trends in the ACF and PACF plots. If
ACF plots die out (i.e., disappear gradually) and PACF
plots cut-off (i.e., disappear abruptly), this suggests that
an autoregressive model is suitable (p > 0, q = 0). If the
opposite is true, i.e. the ACF plots cut-off and PACF
plots die-out, a Moving Average model is suitable (p = 0,
q > 0). If both ACF and PACF die out, then the most
appropriate model contains both a p and q parameter (i.e.
a mixed model is called for). The ACF and the PACF
plots are shown in Figures 1-3. The differencing term is
obtained by examining if the series is stationary or not. In
most software evolution studies, a simple differencing
(i.e., d = 1), transforms the data to a near-linear series
4.2. Model Estimation
For all five of the studied OSS projects the best fitting
model was ARIMA (0,1,1). Though the OSS project set
used in this study did not overlap with the project set
used by Raja et al., [36] the best fitting model is consis-
tent with their findings. It can be seen that for each OSS
project the p value of the t-statistic is significant for MA1.
The plots of the residual ACF and PACF indicate that the
model provides suitable fit and there are no significant
correlations in the residuals. The final estimates of the
model parameter are shown in Table 2 and the ACF and
PACF plots of the residuals are shown in Figure 4.
The best model for all the three projects in Organiza-
tion A was ARIMA (2,1,0). Several competing models
were evaluated, but based on fit statistics and the residual
analysis the same autoregressive model was the best fit
for all three projects. The final estimates of the model pa-
rameters for each of the sampled Organization A projects
Temporal Patterns of Software Evolution Defects: A Comparative Analysis of Open Source and Closed Source Projects
Figure 1. ACF and PACF plots of the original time series for OSS projects.
Copyright © 2011 SciRes. JSEA
Temporal Patterns of Software Evolution Defects: A Comparative Analysis of Open Source and Closed Source Projects503
Figure 2. ACF and PACF plots of the original time series for Organization A projects.
Figure 3. ACF and PACF Plots of the original time series for Organization B projects.
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Temporal Patterns of Software Evolution Defects: A Comparative Analysis of Open Source and Closed Source Projects
Copyright © 2011 SciRes. JSEA
Table 2. Best fitting model specifications for each project.
Project Type Coefficient SE Coefficient t p
OSS #1 MA1
Constant 0.5761
0.17 0.0873
0.6827 6.6
0.25 0
OSS #2 MA1
Constant 0.5606
–0.1085 0.0872
0.3075 6.43
–0.35 0
OSS #3 MA1
Constant 0.5693
–0.0854 0.1072
0.178 5.31
–0.48 0
OSS #4 MA1
Constant 0.6991
0.0005 0.0734
0.0242 9.53
0.02 0
OSS #5 MA1
Constant 0.6827
–0.0138 0.0743
0.0266 9.19
–0.52 0
Org A #1 AR1
Org A #2 AR1
Org A #3 AR1
Org B #1 MA1
Constant 0.4163
–0.05461 0.128
0.05364 3.25
–1.02 0.002
Org B #2 MA1
Constant 0.3088
0.02648 0.151
0.07185 2.05
0.37 0.046
are shown in Table 2. The ACF and PACF plots of the
residuals are shown in Figure 5.
t model for both of the projects from Organization B
was an ARIMA (0,1,1). Several competing models were
evaluated, but based on fit statistics and the residual
analysis the same Moving Average model was the best fit
for both the projects. The final specifications of the
model parameters for each of the sampled Organization
B projects are shown in Table 2 and the ACF and PACF
plots for Organization B are shown in Figure 6.
4.3. Diagnostic Testing
After estimating the series for all the sample projects,
they are individually tested ag ainst the competing models.
The best model is selected using the t statistics and
goodness of fit tests. The residuals are also analyzed to
ensure that autocorrelation has been removed. We used
the Ljung-Box [43] test for the residual analysis. The null
hypothesis for this test is that ACFs for lag 1 through m
are all 0. If H0 is rejected, it implies that there is signifi-
cant autocorrelation in the residuals. Failure to reject the
null hypothesis means that the co rrelation in the residuals
is insignificant.
The results of the diagno stic testing for all the projects
are shown in Table 3. Across all 10 projects, diagnostic
results show that the selected model fully captures the
behavior of the series and there are no significant missing
elements in the model.
4.4. Model Application
Because the ultimate goal of the research is to develop
models that can be useful for forecasting future defects,
the accuracy of model predictions on unseen data is a
critical factor. We therefore used the hold-out cross-
validation technique for comparing model predictions
[41]. In this method, some data is withheld and not used
during parameter estimation. The selected model is then
used to generate a forecast, which is compared to the
withheld (ac t u a l ) values.
We used a holdout sample of 4 months data for each
project. This number was selected keeping in view the
amount of data available for all projects. Results indicate
the best-fit models identified in the Model Estimation
section were all stable over the sample sets’ holdout se-
ries for each of the 10 studied projects. Across all 10
sampled projects, the mean square error (MSE), mean
absolute percentage error (MAPE), and mean absolute
deviation (MAD) for the previously identified best-fit
models (ARIMA (0,1,1) for OSS and Organization B;
ARIMA (2,1,0) for Organization A) are all lower than
competing models.
5. Discussions
The purpose of this study is o determine whether a time t
Temporal Patterns of Software Evolution Defects: A Comparative Analysis of Open Source and Closed Source Projects505
Figure 4. ACF and PACF plots of theresiduals for OSS pr ojec ts.
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Temporal Patterns of Software Evolution Defects: A Comparative Analysis of Open Source and Closed Source Projects
Figure 5. ACF and PACF plots of the residuals for organization a projects.
Figure 6. ACF and PACF Plots of the residuals for Organization B projects.
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Temporal Patterns of Software Evolution Defects: A Comparative Analysis of Open Source and Closed Source Projects
Copyright © 2011 SciRes. JSEA
Table 3. Lijung-Box fit statistics for sampled projects.
Ljung-Box Chi-Square Project Statistic at Lags
Project 12 24 36 48
OSS #1 5.4
(–0.866) 16.9
(0.768) 26.8
(0.807) 32.1
OSS #2 9.2
(–0.514) 25.4
(0.276) 32.9
(0.522) 39.7
OSS #3 14.3
(–0.162) 36
(0.03) 32.94
(0.061) 54.1
OSS #4 9.1
(–0.26) 19
(0.648) 25.2
(0.864) 33.9
OSS #5 12.4
(–0.26) 21.8
(0.475) 26.4
(0.82) 41.6
Org A #1 7.9
(0.545) 16.6
(0.736) 26.1
(0.799) 33.5
Org A #2 9.8
(0.369) 21.3
(0.44) 29
(0.668) 37.9
Org A #3 11.7
(0.228) 21.1
(0.454) 30.3
(0.601) 39.5
Org B #1 6.9
(0.734) 14.1
(0.897) 26.2
(0.827) 34.7
Org B #2 13.6
(0.191) 21.5
(0.491) 34.6
(0.437) 44.8
Note: Chi-Square Statistic with p values in parenthesis.
series approach (which requires no data collection in-
vestment beyond what normally resides in most defect
tracking databases) could be used to accurately predict
patterns in software defects discovered during software
maintenance, the extent to which this approach holds
across a diverse set of projects, organizations, and main-
tenance teams, and whether variations in model parame-
ters can be identified a priori. The evidence from ten
projects is shown in Table 4, and supports study goals.
Across all ten projects examined in this study, reported
defects are accurately predicted using a form of the
ARIMA model (as evidenced by measures including
MSE, MAPE, MAD, and Ljung-Box).
Five of the ten projects are independently developed,
maintained, and managed open source projects. Across
all five OSS projects, the ARIMA (0,1,1) model—a first
order moving average with one order of non-seasonal
differencing—accurately predicts the number of monthly
reported defe cts.
Two of the ten projects are developed and maintained
by a small (30 people, 4 developers) privately held soft-
ware firm using agile methods in a single geographic
location. In this environment, the same ARIMA (0,1,1)
model—best fitting for all five open source projects—
was found to perform best. Because the same team de-
veloped and maintained both products, it is not possible
to explore cross-team differences within this organiza-
Three of the ten projects are developed by different
teams within a large international software firm using a
mature waterfall-based methodology. Two of these three
projects are maintained by (different) joint North Ameri-
can-Indian teams, and the third by a solely North Ameri-
can team dispersed across two offices in the Southeast.
In this organizational environment, more accurate results
are obtained using a competing second order auto-re-
gressive model with a constant and one order of non-
seasonal differencing i.e., ARIMA (2,1,0). This model
held for all three projects, regardless of team size or geo-
graphic scope.
These results demonstrate promise for the use of the
ARIMA model to predict software defect patterns during
maintenance. This model held across a diverse set of
organizations, teams, geographic collaboration models,
and development approaches. Comparison of the model
fit results across project and team demographics indicates
that parameters may be dependent on factors related to
organization or development approach.
5.1. Implications for Research
Within the maintenance stage, this research responds to
the challenge by Pelayo and Dick [9] for the develop-
ment of models that accurately forecast the occurrence of
defects in software. Results obtained across multiple
Temporal Patterns of Software Evolution Defects: A Comparative Analysis of Open Source and Closed Source Projects
Table 4. Results summary.
Project Best Fitting Model MSE MAPE MAD
OSS #1 ARIMA (0,1,1) 0.099 0.049 0.049
OSS #2 ARIMA (0,1,1) 1.435 2.163 0.717
OSS #3 ARIMA (0,1,1) 0.007 0.028 0.003
OSS #4 ARIMA (0,1,1) 0.362 0.801 0.181
OSS #5 ARIMA (0,1,1) 0.636 0.798 0.318
Org A #1 ARIMA (2,1,0) 0.173 0.038 0.087
Org A #2 ARIMA (2,1,0) 0.212 0.125 0.106
Org A #3 ARIMA (2,1,0) 1.595 0.917 0.797
Org B #1 ARIMA (0,1,1) 1.015 0.630 0.507
Org B #2 ARIMA (0,1,1) 1.624 0.813 0.812
teams, organizations, and development environments
confirm that the ARIMA modeling approach accurately
predicts the pattern of software defects reported during
This project addresses several important research
questions and raises another: what organizational factors
impact the form of the defect reporting time series? One
form of the ARIMA model held for all OSS projects and
all projects developed and maintained by a small pri-
vately held software firm with a self-described "informal,
geek" culture located in a single office and using agile
methods. In contrast, another ARIMA model form held
for all projects developed and maintained by a large in-
ternational software firm characterized by a formal, hier-
archical culture and using a mature waterfall-based
methodology to structure the efforts of globally distrib-
uted teams. These findings suggest that the significant
factors focus on development approach and organiza-
tional culture rather than team distribution. Future re-
search is needed to further explore this idea.
Exploring the differences in patterns of reported de-
fects from a cultural perspective will build on the work
of Gregory [44] who discovered that Silicon Valley
software developers shared the same occupational sub-
culture, regardless of firm or role. Several researchers
have labeled the OSS community a hacker culture that
values and rewards pushing the boundaries of what are
considered doable [45]. This work will add to the under-
standing of the linkages, commonalities and similarities
between the CSS and OSS subcultures.
Exploring the differences in patterns of reported de-
fects from a development approach perspective will al-
low researchers to integrate the strengths and reduce the
weakness of the CSS and OSS development processes.
Crowston and Scozzi [46] characterize free and open
source projects as predominately self-organizing and self-
assigning, often without the formality of appointed lead-
ers or specified roles. This characterization may play an
important role in setting the pattern of software defect
reports and aid in building a more unified model of CSS
and OSS defect management.
5.2. Implications for Practice
In contrast to learning or causal predictive approaches
that require complex models difficult to implement (in-
cluding for example the extraction of source-code level
metrics), the ARIMA time series modeling technique
provides a computationally tractable approach that can be
used by practitioners. Commonly available statistical
packages such as Minitab™, SPSS™, and RATS™ pro-
vide this functionality, which can be implemented with
readily available professional training. In addition the
evidence from the analysis of the sampled projects indi-
cates that the resulting pattern is stable once established
as well as consistent across projects within a particular
organization. Thus, once the pattern is established from
existing defect data, project managers can begin to use
the organizationally-specific model to build staffing and
resource estimates for upcoming planning periods. Main-
tenance staff assignments, testing tool licenses and test-
ing technology environments can be adjusted to be in
alignment with predicted workloads, ensuring that ser-
vice level agreements are met and organizational re-
sources are not idle during slack demand periods.
Based on the robust nature of the results thus far, any
project that does not fit the temporal defect reporting
pattern of the other projects in the organization is a can-
didate for outlier analysis. A pattern shift may be caused
by a number of factors—from changes in user adoption
rates, to changes in business tasks supported, to changes
in the software development, evolution and maintenance
processes. In any even t, a shift in defect reporting pattern
is an indicator that can trigger a root cause inquiry.
5.3. Threats to Validity
We discuss four types of threats to validity: Construct,
content, internal and external [47]. Construct validity
applies to the relationship between theory and observa-
tion and addresses the question: Do the measures quan-
tify what they are expected to? In this study, the major
threat to construct validity is the fact that the project
software defects are not classified by criticality level.
Content valid ity refers to the sampling adequacy of th e
measurement instrument [48]. In this study, the sole
source of software defects gathered is the centrally
maintained defect tracking repository. To the extent that
other sources of reported defects exist (such as message
boards, emails, and direct communication with develop-
Copyright © 2011 SciRes. JSEA
Temporal Patterns of Software Evolution Defects: A Comparative Analysis of Open Source and Closed Source Projects509
ers), the study’s content validity is threaten ed.
Internal validity is related to the extent to which infer-
ences can be made regarding cause and effect relation-
ships. As is the case with any univariate time series
model where only one variable is considered, this study
is limited in this regard. The impact of other causal vari-
ables is not included in the model.
External validity deals with the generalizability of the
study. Since there has been previous research on tempo-
ral patterns of softwa re maintena nce in OSS projects and
this study confirms the uniformity of the previously dis-
covered patterns, external validity is less a threat in that
domain. For CSS projects, because of the small conven-
ience sample size and limited range of organizations,
teams, and development environments, the gen eralizabil-
ity of the discoveries of this study is not certain. Analysis
of additional CSS projects and the associated defect pat-
terns will help establish generalizability.
There are other additional threats to validity as well.
The mechanism for defect reporting is homogenous
within organizations and within the SourgeForge defect
repository. However, across these sets, the defect report-
ing mechanism is not unifo rm. Issues associated with the
process of defect reporting are not considered in this
Future research can reduce the threats to validity.
Studies that include additional causal v ariab les to contro l
for organizational processes and contract management
will increase the robustness of the model. Replication of
this study using other CSS and OSS projects and organi-
zations will be used to establish the external validity.
6. Conclusions
The introduction section posed two questions important
to software maintenance resource management:
Is there a model to aid in predicting when software
maintenance resources will be needed? If so, is it com-
putationally and economically practical?
This study points to an affirmative answer to both
In answer to the first question, across all ten projects
evaluated in this study the ARIMA time series modeling
technique was found to provide accurate estimates of
reported defects during software maintenance. ARIMA
model parameters were found to be organizationally de-
pendent. Future research will explore the proposition that
predictive model parameters are dependent on the organ-
izational factors of methodology formalism and organ-
izational culture.
In answer to the second question, the data and compu-
tational needs of the ARIMA models are compared to
alternative prediction techniques. Causal models require
the consistent ongoing extraction and analysis of source-
code level metrics. In addition to this shortcoming,
learning models require relatively sophisticated statistical
and computational expertise and software tools. In con-
trast to these approaches, the ARIMA time series method
is based on readily available defect report data and is less
computationally intensive. Thus, by employing the
ARIMA modeling technique to predict the arrival rates
of the inevitable software defects, maintenance managers
can begin to align their staff and technical resources to
balance the competing demands of cost minimization and
meeting service level expectations..
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