Int. Journal of Electrical & Electronics Engg.
Vol. 2, Spl. Issue 1 (2015)
e-ISSN: 1694-2310 | p-ISSN: 1694-2426
Optimal Selection of Software Reliability Growth Model-A Study 1
Monika Sharma, 2Dalbir Kaur 1
1,2
Asst. Professor, 2Student UIET Panjab University, Chandigarh
monikahsp@gmail.com, dalbir1209614@gmail.com
Abstract—People use software and sometime software fails.so they try to quantify software reliability and try to understand how and why it fails.For this purpose so many software Reliability models have been developed to estimate the defects in the software while delivering it to the customer.Till now so many software Reliability models have been developed,but main issue is that it remain largely unsolved that how to calculate software reliability efficiently.In everycircumstance we cannotuse one model because no single model can completely represent all features.This paper describes the circumstances and criteria under which particular model can be selected. Keywords—software reliability; SRGM; model criteria;survey;comparative analysis; performance evaluation.
INTRODUCTION Software Reliability is an important concept in the field of Software engineering.Software Reliability helps to attribute software maintainability together with performance,quality and functionality of software etc.Software Reliability is defined as a probability at which a system would operate without failure under the conditions in a given environment for a given period of time. In other words we can say, Software Reliability can be defined as a measure of how well the users think the system operates according to its specifications. There are followingtwo uncertainties which render any inaccurate reliability measurement: (a)Uncertainty: Some time the customer doesn’t know about the proper usability of system. (b)Uncertainty: Some time we don’t know about the fault removal effects. Much time we are not able to sure about the corrections that may or may not be complete and successful after the fixing of a fault.Some time it introduced other faults. Some time we have lack of knowledge about the improvement to IFT(inter failure time) that will be occur after the faults are properly fixed. Software Reliability Model is based mostly on data from the testing phase, after development is virtually complete. The basic “goal” of Reliability Theory is to predict when the system will fail. e.g. How can we use the existing data of time between failures {t1, t2, - - - -, tn} used for next failure to predict time, ti , where i>n? (The data from testing provide a fairly good indication of reliability) Due to the nature of software, no general accepted mechanisms exist to predict software reliability.We need importantempirical observation and experience.Good engineering methods can largely improve software reliability.To improve and measure software reliability,software testing plays an important role. Databases with software failure rates are available but NITTTR, Chandigarh
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numbers should be used with caution and adjusted based on observationand experience.The testing teams or programmer used so many software fault removal and detection methods and techniques so that highly reliable software system can be achieve. SGRM (Software Reliability Growth Model) play an important role for applying these methods and techniques because SGRM help in providing useful knowledge and information for tester and developers during the debugging phase for predict and estimate software reliability of system under test and they also help during software operational phase for measure the failure data.For a software to operate accurately and reliability it should undergo testing and debugging.It can be consuming as well as costly process and the manager want to know accurate knowledge about the process result that how it help in grow software reliability so that their budgets and projects are effectively manage. If their budget and projects are effectively managed,then the manager is hoped that reliability of software will grow very well.Various SGRM can be used to make more reliable software. THE CONCEPT OF RELIABILITY GROWTH When the system is tested so that faults can be removed to change the reliability of system, we can use a mathematical natured model that is called growth model.It is used for measure reliability of system by extrapolating from used current data which is depending on the testing procedure.The improvement in software reliability is thatit gives results from correcting faults in the software. No single model is universally applicable.Applications are not independent on reliability growth. Various growth models fit on different observed data.so that the model is selected according to data that is best fit on. SGRM By the study of software reliability Models we can say that failure which is a random process are result of two processes-first is fault introduction and second is fault activation which is occur after input state selection. By nature it is random process. Various Software Reliability Growth models have been developed and the most appropriate model should be chosen by fitting observed reliability may be described as a form of probability distribution of random process value in time at each point. Failureof probability distribution measurement of one of these models plays an important role in the development of SGRMs.So we can say that when we select the input state SRGM is activated and this is random natured process. In this paper we will describe following software reliability Models which will be explain below. Goel-Okumoto Imperfect Debugging Model 100
Int. Journal of Electrical & Electronics Engg.
Vol. 2, Spl. Issue 1 (2015)
Goel –Okumoto Nonhomogeneous Poisson Model Musa–Okumoto Logarithmic Poisson Execution Jelinski Moranda Model Delayed S Model Inflection S Model Goel-Okumoto Imperfect Debugging model If weassume perfect debugging, then in this model if we fix a defect, it may inject new defects. So it is called errorprone because in this process activation of fix defect occurs. Goel-Okumotoovercomes the limitations of this assumption because they purposed it as a debugging model which is imperfect. The hazard function of the GoelOkumoto model during time interval from the (m-1)st and the nth failures is given( ) = [ − ( − 1)] (1) where X is Fault number at time when testing start. pis probability function of imperfect debugging. λ- Rate of failure at each fault. Mean value Function( ) = (1 – [ − ]) k> 0, λ > 0 (2) Goel-Okumoto Nonhomogeneous Poisson Model When the more concerned are given to the modeling of the observation to calculate how much failure in a given interval during testing is called NHPP(Non Homogeneous Poisson process) model. SoGoel and okumoto purpose the observation of the number of failure in a cumulative manner at time t,so X(t) can be modeled as a nonhomogenous Poisson process(NHPP), because in which Poisson with failure rate are time dependent. So Goel and okumoto called it is a type of exponential distribution of the failure rate which is time dependent in nature. Mean value function( ) = (1– [ −〖 〗 ]) (3) k> 0, λ> 0, > 0 Where m(t) is observed failure which is expected at time t.Lambda density of failure function, k is the expected failure number and c is the detection rate of fault at each fault. So we can say that NHPP(non-homogenous Poisson process) is a straightforward application of the exponential form of model. Musa–Okumoto Logarithmic Poisson Execution Time Model Similar to the NHPP modelthe Musa-Okumoto model is also assumed as a nonhomogeneous Poisson process because in this model at a certain time the number of failures is observed. So it has a different value of MVF (mean value function). In musa-okumoto model one assumption is present that is earlier fixes have greater effect on the reliability of software than later ones. Two main components exist in this model: Calendar time Execution time The mean value function( ) = ∗ (1 + ) (4) k> 0, λ> 0 λ is failure rate initially k is reduction rate of each failure in the normalized intensity.
e-ISSN: 1694-2310 | p-ISSN: 1694-2426
Jelinski Moranda Model Many times we see that if we repair an error, it does not give satisfactory performance. It means to say that reliability of software does not improve to a specified level and by a constant amount. So we can say that umber of error present in a system is assumed to be proportional to fixing of an error due to which there is an improvement in the reliability. In software reliability research J-M model is earliest one. So it is type of a model in which time between failure exist. So whenever testing start it assumes X software faults .The nature of failure is random and for cause testing failure, the contribution of all faults is equal. It considers that for each failure there is perfect fix and time for fix is negligible. Each fi increase software failure rate by same amount. The hazard function at time mi, the time between the (m-1)st and nth failure is given by ( ) = ℎ[ − ( − 1)] (5) Where X - defect number of software when testing start h is constant of proportionality Mean value function- ( ) = 0 [1 − (– ℎ )] (6) The Delayed Model In 1983, Yamada argue about defect detection nature of testing process. According to him, it is also defect isolation with defect detection. So Delayed S shaped RG model is developed for such a process in which growth curve is observed. It is observed by cumulative number of the defects which is detected is S shaped. It is also a form of NHPP with having different value of mean function. Mean value function( ) = (1 − (1 + ) ∗ [− ]) (7) k>0, λ>0 Where time is t λ is rate of error detection K is the number of total defects
Inflection S Model After the development of delayed S shaped Model Ohba in 1984 proposed one more S shaped Model that is called as inflection S reliability GM.He describe that this model have mutual dependency between detected defects which explain the phenomena of failure detection.So in this model if it detects more failure, it will cause more and more undetected failure.Based on the NHPP its mean value function is ( )= (
)
∗
(
(
ψ( r) = k> 0, λ> 0, > 0
( )∗
[–
]) ) [
(9)
]
(8)
Where time is t Lambdais rateof error detection m is the inflection factor k is number oftotal defects At the beginning of period when testing is start at that time testing is start because at that time tester become familiar with the system that time the inflection model and delayed model consider as accounting for the period of learning. There are following Models assumptions-
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Int. Journal of Electrical & Electronics Engg.
Vol. 2, Spl. Issue 1 (2015)
When testing is start there are X software faults which is unknown. The failure is Random in nature –There is independent time in between failure. For cause a failure the contribution of all faults are equal. There is negligible time for fix. For each failure fixes are perfect; during correction no new faults are introduced. CRITERIA FOR MODEL EVALUTION
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accurate which is needed by software engineer, manager and user. AssumptionsQuality:From the viewpoint of consistency which is logically follow the plausibility of assumptions and model can easily met assumptions. Predictive validity: For the specified period of time model is capable to predict the failure behaves and total number of defects which is based on Model’s current data. Simplicity : In following aspects model should be simple that isFor collect data it should be inexpensive and simple Concept wise simple and doesn’t need background with extensive mathematical form for development of the software.
Applicability: For software product which are all different, there is applicability of Model’s degree for e.g.- structure, function, size. Capability: In the planning s/w project which is under development model is able to estimate the satisfactory
V.COMPARISION OF SGRM MODELS COMPARISIONSUMMARYTABLE FOR SGRM MODELS
Name of Model 1.Goel-Okumoto Imperfect Debugging model-
Type Model
of
Concave
( ) =
(1 –
K > 0, λ> 0
2.Goel-Okumoto Nonhomogeneous Poisson Model-
Concave
3.Musa–Okumoto Logarithmic Poisson Execution Time Model
Concave
4.Jelinski Moranda Model
Concave
5.The Delayed S Model-
S shaped
6.Inflection S model
MVF (mean value function)
( ) =
(1– [− , k> 0, λ> 0, > 0
( ) =
∗
])
(1 +
S shaped
( ) = ( ) =
0 [1 −
(1 − (1 +
k>0,λ>0
( ) = k∗
(– ℎ )] )∗
( )∗
CONCLUSION This paper has attempted to lay down different SGRMs (softwareReliability Growth models).With the help of SGRMs models a characterization of the software development process is done and practitioners can easily make predictions about the reliability of the software in future which is under development. Some models work better than others depending on the application area and operating characteristics.We discuss about six SGRMs model in this paper.No single model is universally applicable. Models are applied according to different conditions and environment in which they fit. A
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[–
[− ]) [
]
Ifat the beginning the failure intensity of software slightly increases and then start to decrease. If failure rate reduction is due to repair action which is follow early failure.
)
k> 0, λ> 0
, ( ) = k> 0, λ> 0, > 0
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[ − ])
Model selection criteria If failure detection is an exponentially decaying rate function.
]
If the current fault data or content of the program is proportional to the S/W failure. If the failure rate initially increase and later exponentially decays. Ifthe mutual dependency in between faults of a program and due to more detection of failure, it cause more detection of undetected failure.
Limitations Injection of new defect after fixing an old defect. It is an error prone activity. Exponential Distribution followed by rate of failure. Instruction execution time is smaller with respect to execution time in between failure. The failure is random in nature and increment in reliability is in irregular manner. Introduction of new independent faults during debugging Process. Some faults are removed after then other faults are detected.
comparison table is provided for detailed summary about models.In the table, modeltypes,mean value functions (MVF), their selection criteria and limitations are discussed. Every model has some limitations which can be improved.So it can beconcluded that an appropriate model is selected according to some selection criteria under a particular environmental condition. REFERENCES 1) Goel, A.L. “Software Reliability Models: Assumptions,Limitations, and Applicability,” IEEE Trans. Software Engg. Vol SE-11, No 12, 1985 Dec, pp. 1411-1423. 2) Mohd. Anjum et. al. , Analysis and Ranking of Software Reliability Models Based on Weighted Criteria Value, I.J.Information Technology and Computer Science, 2013, 02, pp. 1-14.
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3) Shanmugam, Latha, and Lilly Florence. "A comparison of parameter best estimation method for software reliability models." International Journal of Software Engineering & Applications 3, no. 5 (2012): pp. 91-102. 4) Musa, John D., and Kazuhira Okumoto. "A logarithmic Poisson execution time model for software reliability measurement." In Proceedings of the 7th international conference on Software engineering,. IEEE Press, 1984,pp. 230-238. 5) Asad, Ch Ali, Muhammad Irfan Ullah, and M. J. Ur-Rehman. "An approach for software reliability model selection." In Computer Software and Applications Conference, 2004. COMPSAC 2004. Proceedings of the 28th Annual International,IEEE, 2004, pp. 534539. 6) Ohba, Mitsuru. "Software reliability analysis models." IBM Journal of research and Development 28, no. 4 (1984): pp. 428-443. 7) Schneidewind, Norman F. "Software reliability model with optimal selection of failure data." Software Engineering, IEEE Transactions on 19, no. 11 (1993): pp.1095-1104. 8) Malaiya, Yashawant K., Naixin Li, Jim Bieman, Rick Karcich, and Bob Skibbe. "The relationship between test coverage and reliability." In Software Reliability Engineering, 1994. Proceedings., 5th International Symposium on. IEEE, 1994,, pp. 186-195. 9) Yamada, Shigeru, Mitsuru Ohba, and Shunji Osaki. "S-shaped reliability growth modeling for software error detection." Reliability, IEEE Transactions on 32, no. 5 (1983): pp.475-484. 10) Gupta, Ajay, Digvijay Choudhary, and Suneet Saxena. "Software Reliability Estimation using Yamada Delayed S Shaped Model under Imperfect Debugging and Time Lag‖." International Journal of Computer Applications 23, no. 7 (2011): pp.0975-0982. 11) Lyu, Michael R. Handbook of software reliability engineering. Vol. 222. CA: IEEE computer society press, 1996.
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