Journal of Software Engineering and Applications, 2012, 5, 737-742 Published Online September 2012 ( 737
Role of Software Reliability Models in Performance
Improvement and Management
Padmanabha Aital1, P. Sashikala2
1SIOM, Nashik, India; 2IBS, Hyderabad, India.
Received May 23rd, 2012; revised June 26th, 2012; accepted July 9th, 2012
Software reliability models describe th e failure behavior of the software. The models are used to evaluate the software
quantitatively. They assess the reliab ility of the software by predictin g fau lts or failures for a software. Reliability is one
of important quality attributes of the software in which software end user is more interested rather than the software
developer. Hence, the performance of a software can be improved by incorporating important quality attributes like
reliability, maintainability and availability of the software along with performance attributes like response time and
throughput. The paper discusses abou t the role played by important software reliability models in analyzing th e failure
prediction of the software. It also explores the stro ng relatio nship that ex ists between quality a ttributes an d perfo rmance
attributes. With some illustrations highlighting the necessity of in-depth understanding of the link that exists between
reliability and performance of the software, th e derived knowledge helps in improving the perfo rmance of the software
sustainably over a period of time and manage the software more effectively.
Keywords: Software Reliability; Software Reliability Models; Software Availability Software Performance;
Performance Management
1. Introduction
Software reliability is an important aspect of functioning
of a software system which may be a combination of
different software sub systems or embedded in a com-
puting environment that provides inputs to the software
system [1]. Software reliability is the probability that th e
system will function without failure for a specified pe-
riod of time under stated conditions. Due to error in
software by human action or discrepancy between com-
puted, observed, or measured value and specified value
of some important reliability parameter may lead to fault
in the software. The fault, if unchecked may or may not
result in software failure depending on the operating
conditions. The software reliability is similar to hardware
reliability in some aspects. Most of the reliability quan ti-
ties are defined in terms of time. The execution time of
software (CPU time) is the actual time spent by the
computer in executing the software. The clock time is the
time elapsed between starting of computer and shutting it
down including idle ti me [2]. All these times can be con-
verted into calendar time which will be useful for system
development personnel to calculate human effort re-
quired to develop software. Some of the reliability meas-
ures are cumulative failure function, failure intensity
function, failure rate function and mean time to failure
function [1,3].
The operational profile of a system is defined as the
set of operations that the software can execute along with
probability with which they will occur. It will help us to
identify operations which are failure prone and also af-
fect reliability and performance of the software [2].
The software reliability measurement involves use of
failure data by software reliability models to estimate and
predict software reliability. The type of failure data used
by number of software reliability models belongs to two
types—Failure count data and ti me between failures [2].
Software reliability model specifies the general form
of the dependence of the failure process on the principal
factors that affect it—fault introduction, fault removal
and operational environment [1].
Fault prevention is by construction to avoid fault oc-
currences. The fault removal talks about detection by
testing and removal of fault. Fault to lerancehighlig hts the
issues of redundancy to accommodate any failure in op-
eration. Fault/failure forecasting predictsthe presence of
faults and o c currence and consequen ces of failure [4,5].
2. Software Reliability Models
Software reliability models consist of a wide variety of
models base d on statist ical theory and Baye sian ap proach.
Copyright © 2012 SciRes. JSEA
Role of Software Reliability Models in Performance Improvement and Management
The paper presents some of the popular models and their
model forms. Though the time domain based models
overcast the other type of models in terms of usability and
wider application, other type of models also find their
place depending on suitability and operational environ-
ment [2]. Combination of models can also be used to
improve reliability measurement. Time domain based
model is integrated with input domain based model to
form a tree based model which finds its application in
large commercial software [1].
2.1. Time between Failures (TBF) Models
The common approach is to assume that time between ith
and (i – 1) failure will follow a certain distribution whose
parameters will depend on number of faults remaining in
the program during the given interval. From this, the es-
timates of the parameters are calculated which give reli-
ability and other parameters of interest on subsequent
calculations. Another approach is to treat the failure
times as realizations of a stochastic process and an ap-
propriate time-series model to describe the underlying
failure process [1 ,2] .
Example-Jelinski-Moranda mo del
One of the earliest models proposed which is still be-
ing applied today is the de-eutrophication model devel-
oped by Jelinski and Moranda, The elapsed time between
failure is taken to follow an exponen tial distribution with
a parameter that is proportional to the number of re-
maining faults in the software, i.e. Mean time between
failures (MTBF) is
1. Here t is any point
in time between the occurrence of the (i – 1)th & ith fault
occurrence.The quantity
is the proportionality constant
and N is the total number of faults in the software from
the initial point in which the software is observed [1].
Model Form: Hazard Function
1ZtiN i
where N = Number of errors present in the software at
the beginning of the test phase
= Proportional constant.
Mean failure value function,
1exptN t
 
exptN t
and Failure intensity function,
2.2. Fault/Failure Count (FC) Models
Number of faults or failures in a time interval is taken
into consideration rather than times between failures. The
failure counts are assumed to follow a known stochastic
process with a time dependent discrete or continuous
failure rate. The useful reliability parameters are calcu-
lated from the estimates obtained from the observed
Musa’s Basic Execution Time Model
This model has had the widest distribution among the
software reliability models. This model was one of the
first to use the actual execution time of software compo-
nent on computer for modeling process. Musa feels that
execution time is more reflective of the actual stress in-
duced on the software system than the amount of the
calendar time that has been elapsed [2]. This model can
even use time between failures (tbf) as input f ailure data.
Hence, the categorization of models under TBF Models
and FC Models is not rigid. It is entirely depends on what
type of failure data is fed to the model and failure data
can be converted from one form to the other to suit the
model failure data requirement.
Model Form: Mean failure value function,
 
and Failure intensity function,
 
 where βo = Total number of
faults that would be detected in the time limit,
1 = a
constant & failure intensity decay parameter. The prod-
uct of
o and β1 =
0 where
0 is initial failure intensity at
the start of execution.
Illustration 1:
Assume that initial failure intensity is 5 failures per
execution hour and the failure intensity decay parameter
is 0.01 per failure. Let the failure experienced or the fault
detected in a time limit is 100 (mean failure value func-
tion), Then current failure intensity is
exp5exp0.01 100
5exp11.84perexecution hour.
 
A similar illustration can be worked out for Jelinski-
Moranda Model which is a TBF Model.
The software faults predicted by these models have to
be removed to enhance the reliability of the software [1].
The software faults may not directly affect the function-
ing and performan ce of the software unless they result as
software failures. Hence, sufficient care should be taken
and resources be allotted to remove software faults. The
current failure intensity function of these models help in
knowing impending failures in the software. The soft-
ware models help in predicting the performance of the
software by showing failure behavior of the software
over a time. Depending on the performance level ex-
pected out of software in terms of timely response and
throughput, failure behavior of the software has to be
studied in depth and non-testing methods like Formal
Technical Reviews (FTRs), informal reviews, walk-
throughs and inspections have to be deployed to find
faults. It is advisable to use these methods during analy-
sis and design phases of the software development. If
sufficient faults are not found or removed, then extensive
testing has to be carried out to raise reliability of soft-
ware by reducing the number of faults in the software.
The reliable software without fau lts o r mini mum n umb er
of faults will assure good performance of software.
Hence, reliability of the software directly affects the
functioning and performance of the software.
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Role of Software Reliability Models in Performance Improvement and Management 739
3. Software Dependability and Its Attributes
Software Reliability is one of the attributes to define de-
pendability (trustworthiness) of the software. The other
important attributes are availability, maintainability,
safety, confidentiality and integrity [1]. The availability
is the preparedness of the software for use. Unless the
software is available or fit for use, it is directly affecting
reliability and proper functioning of the software and
indirectly the performance of the software. The main-
tainability of the software deals with “down time” or
minimum Mean Time to Repair (MTTR) of a software/
system and ease with services are restored. This is one of
the important attribute which affects performance of the
system. Hence, both reliability and maintainability are
important to assure proper availability of the software
system to carry out stated functions or operations in
stipulated time. The functional failure or sub-optimal
functional behavior affects the performance and per-
formance improvement initiatives for the software.
The availability of a software system can be measured
in 3 different ways depending on the time elements taken
into consideration. They are Inherent availability, Achi-
eved availability and Operational availability [6].
Inherent availability is the probability that a software
system will operate satisfactorily when used under stated
conditions in an ideal support environment without any
scheduled or preventive maintenance [6]. The software
system includes both software and hardware. Hence, in-
herent availability is system availability which is given
as below
Inherent Availability, Ai = MTBF/(MTBF +MTTR)
where MTBF is Mean time between failures and MTTR
is mean time to repair [6]. It is obvious from above rela-
tion that in order to have higher inherent availability, the
MTTR should be as low as possible [7].
Illustration 2:
Let us assume a system is having MTBF of 10 execu-
tion hours (CPU Hrs) and MTTR which is equivalent to
1.6 execution hours (CPU Hrs), then
Inherent availability10101.60.8620
Achieved availability is taking into consideration ac-
tive maintenance down time resulting from both preven-
tive and corrective maintenance. Hence, achieved avail-
ability is given by following relationship [6].
Achieved availability, Aa = MTBM/(MTBM + M)
where MTBM is mean time between maintenance and M
is the mean active down time resulting from both preven-
tive and corrective maintenance. If preventive mainte-
nance and corrective maintenance are ignored, then
MTBM becomes MTBF. The achieved availability is
usually less than inherent availability of the system.
Illustration 3:
Let us assume a system with MTBM value of 8 execu-
tion hours (CPU Hrs) and M value equivalent to 4 execu-
tion hours (CPU Hrs ), t hen
Achieved availability is 8840.66
The operational availability considers supply down
time and administrative downtime which is given as fol-
lows [6].
Operational availability, Ao = MTBM/(MTBM +
MDT) where MTBM is mean time between maintenance
and MDT is supply downtime and administrative down-
time. Hence, operational availability is usually less than
inherent availability and achieved availability.
Illustration 4:
Consider the previous illustration with same value for
MTBM. But by assuming a MDTvalue equivalent to 6
execution hours, then
Operational availability = 8/(8 + 6) = 0.5714
The system availability (As) of a software system
which comprises both software and hardware compo-
nents is usually expressed as a complex function of reli-
ability (Rs), maintainability (Ms) and supply effectiveness
System Availability, As = f(Rs, Ms , Ss)
Hence, system availability is a function of tradeoff
between reliability and maintainability of the system with
stated value of supply effectiveness. As far as the system
is functioning properly without any failure, maintainabil-
ity will be low and all performance related issues and
performance improvement may be worked out according
to a stated plan. However, for a failed system in terms of
functions and performance which is under maintenance,
the maintainability issues of the system should be taken
into consideration along with changed reliability to work
out availability of the system. Hence, performance im-
provement and management should be addressed with
altered perspective.
The other attributes of dependability are safety, confi-
dentiality and integrity. The absence of serious conse-
quences to the environment is safety. The non-occur-
rence of unauthorized disclosure of information is called
confidentiality and absence of alteration of information is
called integrity [1]. These three attributes are very im-
portant to place highest trust on the functioning of soft-
ware. The functioning of the software and its improve-
ment in performance will not be useful unless the safety,
confidentiality and integrity is achieved for the software.
Hence, it is very essential to ensure dependability
(trustworthiness) of the software before launching on any
performance enhancement and management program.
The software should be built from requirements stage to
installation stage taking all six important dependability
attributes into account. Ignoring any of these attributes
will cost the organization to pay the customer in terms of
penalties and other types of compensation.
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Role of Software Reliability Models in Performance Improvement and Management
A tradeoff may be worked out with objective reliabil-
ity and other attributes like maintain ability and avail-
ability to cater to application as far as performance pa-
rameters are not sacrificed. Since reliability is most im-
portant attribute which directly deals with functioning of
software and the user is more interested to have higher
reliability for any given software, it is advisable to have
most of the performance improvement and management
initiatives geared towards ensuring higher reliability and
optimal performance of the software.
The organization should have comprehensive plan to
address dependability and performance related issues on
a broader perspective. It should not be limited to Soft-
ware Quality Assurance (SQA) group or Software Engi-
neering Process Group (SEPG). All other important
groups which are directly or indirectly related to de-
pendability and performance of the software should be
involved to strive for developing highly dependable, and
robust soft ware in terms of performance. Hence, proper
personnel and resources should be allocated throughout
the software development cycle (SDLC) to ensure higher
dependability and performance of the software.
4. Software Performance and Its
Software performance is an indicator of how well a
software system or component meets its requirements for
timeliness. This is measured in terms of response time
and throughput. Th e response time is the time requ ired to
respond to a request. It may be the time required for sin-
gle transaction or end to end time for user task. In em-
bedded systems, it is the time required to respond to the
events or number of events processed in a time interval.
Throughput of a system is number of requests that can be
processed in some specified time interval [8,9].
When failure intensity function increases indicating
presence of more faults to be removed to enhance reli-
ability of the software, response time of software in-
creases and throughput decreases. As indicated in earlier
two software reliability models, either time between fail-
ures should be extended in case of TBF models or fault
count in a time interval has to be reduced to achieve
higher reliability which may contribute to higher per-
formance with improved response time and throughputs.
Responsiveness is the ability of a system to meet its
objectives for response time or throughput. Scalability is
the ability of the system to meet its response time or
throughput objectives as demand for new software func-
tion increases [8,9].
Illustration 5:
From Illustration 1, the number of faults is 1.8 per
execution hour (CPU hr). As the time advances, more
faults are uncovered and with improved testing efficiency,
number of faults uncovered usually decreases. It may not
be the case always.
If we assume that second set of faults are detected
during 3rd execution hour of the software, then we can
take MTBF as 2 execution hours (CPU Hr) between first
and third hour of execution.
MTBF indicates failure free operation of software.
The performance parameter response time is indirectly
related to MTBF.
If R indicates the response time of a software for a task,
then R = K/(MTBF) where K is a constant. As MTBF
increases response time decreases. In our illustration, R =
K/2 (assuming a linear relationship between R and
MTBF which may not be true always).
The second performance parameter, throughput in a
time interval is directly dependent on MTBF. As MTBF
increases, number of transactions in the time interval
(MTBF) increases. In our illustration MTBF is 2 execu-
tion hours. If 10 transactions occur in 2 execution hours,
then it would be 20 transactions if MTBF is improved to
4 execution hours. In this case, through put is constant.
Even the number of transactions in a time interval (im-
proved MTBF) can be increased to improve throughput
of the software.
Hence, reliability parameter MTBF has impact on
performance parameters response time and throughput.
These facts may be corroborated with failure data
taken from Reference [2] which gives number of illustra-
tions to calculate MTBF and other reliability parameters
using specific software reliability model.
The reference [9] gives illustrations to calculate per-
formance parameters response time and throughput with
the support of data. The guiding principle for good re-
sponse time and throughput is failure free operation of
software (higher reliability with higher MTBF values).
Hence, it is just the logical extension to establish the
relationship between reliability parameter MTBF and
performance parameters response time & throughput
since both of these parameters are independently sup-
ported by data and illustration in references [2,8].
It may look exploratory in nature as far as exact rela-
tionship between these parameters. Nevertheless, it holds
true for simple & general applications. The exact rela-
tionship can be worked out in a new or subsequent re-
search paper as future work.
The higher reliability of the software ensures higher
scalability for a new function without much difficulty as
far as other performance parameters are addressed in
The following are the consequences of performance
failures—damaged customer relations, business failures,
additional resources and reduced competitiveness [9].
The causes which hinder the optimum performance of
software may be due to internal and external conditions.
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Role of Software Reliability Models in Performance Improvement and Management 741
The internal conditions may be defective computer sys-
tem with presence of faults in the system (both hardware
and software). The external conditions may be environ-
ment in which computer system operates. Hardware
faults may be due to imperfect material or manufacturing
process to build computer system. But most of the soft-
ware faults are design fault which are difficult to identify
and rectify.
5. Software Performance Management
The software performance has to be managed to deliver
optimum performance. There are basically two different
methods to manage software performance [10].
5.1. Reactive Performance Management
Reactive performance management focuses on actions or
remedies that will be taken, once the software perform-
ance problem is encountered. It may be for any of the
reasons like not meeting optimal performance require-
ments with presence of faults or malfunctioning of some
critical components or non-functioning due to exhausted
resources or system overloading. Reactive performance
management has the risk of cost overrun, delayed project
and poor product/serv ice delivery [9].
5.2. Proactive Performance Management
(with Inputs from Software Reliability
It anticipates potential software performance problems
and steps to detect and removal of those problems early
in process. The characteristics of performance manage-
ment are as follows [1,10].
1) Quantify product usage by specifying reliability and
performance level so that failure free functioning and
optimum performance is possible.
2) A performance engineer does track and communi-
cate the issues related to performance and everyone is
informed about his role in performance management. He
should closely work with Reliability Engineer to check
the product trustworthiness (Reliability, availability and
maintainability). Performance is not possible without
reliable product or service.
3) An organization wide standard business processes
and best practices in software reliability engineering
(SRE) should be established to meet any unforeseen
outcome related to reliability and performance problems.
4) Analyze, manage and improve the reliability of the
software predicted by software reliability models and
match the outcome reliability with reliability assured to
the customers. Improvement in reliability with presence
of very few faults will improve the performance of the
5) Team members should be trained in processes re-
lated to Software performance engineering (SPE) and
software reliability engineering (SRE).
6) A performance risk management plan will be put in
place to provide contingencies for pe rformance risk.
7) The important SPE strategies like simple modeling
strategy, Best and worst case strategy and adoption to
precision strategy for modeling with suitable estimates
should be chosen. Failure behavior of the software pre-
dicted by software reliability models along with resource
requirements needed for the performance of the software
are used to formulate these estimates.
8) The software performance models involve construc-
tion of software execution model followed by building
the system execution models by studying and measuring
execution patterns of computer systems. In addition,
workloads are characterized and input parameters are
developed. The developed model is validated by com-
paring model results with observed and measured data
for the computer system. The model is calibrated until its
results match measured data. [10]
9) The software reliability models can be used in con-
junction with SPE models, while designing software exe-
cution models and subsequent system execution models.
The execution patterns of software will reveal failure
behavior and reliability of the software. The software
performance engineer can work on these issues before
characterizing work loads and developing inputs for the
model. The workloads may be varied and inputs may be
changed or altered according to the behavior of the soft-
ware. If a higher reliability is achieved by removing de-
fects of software during execution, greater workload and
more/selective inputs can be chosen for higher perform-
ance while carrying out SPE.
6. Conclusions and Inferences
1) An overview of concepts related to software reli-
ability, software reliability models along with two im-
portant models are discussed to highlight their impor-
tance in analyzing the failure behavio r of s oft ware.
2) Failure behavior of the software as predicted by
software reliability models has important implication in
understanding the performance of the software and its
3) Resources can be allocated and optimized by se-
lecting suitable non-testing methods and also testing
methods by targeting objective software reliability and
optimal performance of the software.
4) The dependability of software with six attributes are
discussed, highlighting the importance of each of them.
But reliability and maintainability are found to be more
dominating attributes among other attributes. Nonethe-
less, other attributes are equally important to form overall
Copyright © 2012 SciRes. JSEA
Role of Software Reliability Models in Performance Improvement and Management
Copyright © 2012 SciRes. JSEA
dependability perspective.
5) The different definitions related to availability of
software are discussed along with formulation and illus-
trations. The availability as function of reliability, main-
tainability and supply effectiveness are discussed. Hence,
reliability emerges as an important attribute directly af-
fecting the performance of the software.
6) Software performance management with two dif-
ferent approaches (Reactive and Proactive Performance
Management) are discussed in detail with inputs from
SRE to Proactive performance m a nagement.
7) The guidelines given in proactive performance man-
agement can be followed for good results in reliability
and performance by combinin g best practices in both the
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