Published by: PIONEER RESEARCH & DEVELOPMENT GROUP ( 1

Transcription

1 Cpturing The Combined Effect Of Testing Time And Testing Coverge Using Two Dimensionl Softwre Relibility Growth Models B.Anniprincy 1, Dr. S. Sridhr 2 1 Reserch Scholr, Sthybm University, Chenni. 2 Den-Cognitive & Centrl Computing Fcility, RV College of Engineering, Bnglore Abstrct Softwre Relibility is the likelihood of brekdown free opertion of softwre in provided time period under specified conditions. Softwre testing is process to detect fults in the totlity nd worth of developed computer softwre. Testing is very essentil tool in ssuring the qulity of the softwre by identifying different fults in softwre, nd possibly removing them. But testing of this softwre for long time my not ensure bug free softwre nd high relibility. Best possible mount of code lso needs to be covered to mke sure tht the softwre is of good qulity. Testing time lone my not give the correct preview of the number of fults removed in the softwre. Therefore to cpture the combined effect of testing time nd testing coverge we propose two dimensionl softwre relibility growth models. We will ssume tht the number of fults detched in the softwre by fixed time is dependent on the totl testing resources ccessible to the testing tem. This testing resource will be fusion of both testing time nd testing coverge. We hve used cobb-dougls production function to develop the two dimensionl model incorporting the effect of testing time nd testing coverge on the number of fults removed in the softwre system. Keywords Two-dimensionl model, Cobb-dougls production function, Testing time nd Testing Coverge. I. INTRODUCTION Testing coverge plys one of the most promising roles while predicting the softwre relibility. Testing Coverge cn be defined s structurl testing technique in which the softwre performnce cn be judged with respect to specifiction of the different source codes nd the extent or the degree to which softwre is executed by the test cses. TC cn help softwre developers to clculte the qulity of the tested softwre nd to determine the mount of dditionl effort needed to improve the relibility of the softwre besides providing customers with quntittive confidence criterion while plnning for using softwre product. Hence, sfety of the criticl system hs high coverge objective. The bsic testing coverge mesures which includes different criteri such s Sttement Coverge, Decision / Condition Coverge, Pth Coverge nd Function Coverge. Sttement Coverge is defined s the proportion of lines executed in the single progrm. If we suppose tht the different fults re uniformly distributed throughout the code, then percentge of executble sttements covered shows the percentge of fults discovered[14][15]. Decision / Condition Coverge indictes whether Boolen expressions tested in control structures evluted to both true nd flse. Pth Coverge shows the percentge of ll possible pths existing in the code exercised by the test cses. Function Coverge indictes the different proportion of functions/ procedures influenced by the softwre testing. II SOFTWARE RELIABILITY GROWTH MODELS WITH TWO TYPES OF IMPERFECT DEBUGGING The fults in the softwre my not be removed perfectly. When the fults re not removed perfectly nd led to further genertion of fults. In this pper, we develop n S shped model with imperfect debugging nd fult genertion[16][17]. The proposed method is implemented using JAVA nd it is vlidted on rel dt sets. Time dependent model The time dependent behvior of fult removl process is explined by Softwre Relibility Growth Model (SRGM). Most of the softwre relibility models cn be ctegorized under Non Homogeneous Poisson Process (NHPP) models[12][13]. The ssumption tht governs these models is softwre filure occurs t rndom times during testing cused by fults lying dormnt in softwre. And, for modeling the softwre Published by: PIONEER RESEARCH & DEVELOPMENT GROUP ( 1

2 fult detection phenomenon, counting process { N ( ; t 0} is defined which represents the cumultive number of softwre fults detected by testing timet. The SRGM bsed on NHPP is formulted s: Pr{ N( m( n} n exp( m( ) n! (1) Where n 0, 1, 2, 3. m ( is the men vlue function of the counting process N ( III TESTING COVERAGE BASED MODELING The testing coverge bsed softwre relibility growth model cn be formulted s follows: dm c' dt 1 t ct ( (2) N m t Where, m ( is the expected number of fults identified in the time intervl ( 0, t ] c ( is the testing coverge s function of time t. N is the constnt, representing the number of fults lying dormnt in the softwre t the beginning of testing. Here c ( defines the percentge of the coded sttements tht hs been observed till time t. So, 1 c( defines the percentge of the coded sttements which hs not yet been covered till timet. Then, the first order derivtive of c (, denoted by c '(, represents the testing coverge rte. Therefore, function c 1 ' t ct cn be tken s mesure of the fult detection rte. In one dimensionl SRGM with testing coverge we need to define coverge function c ( lthough in two dimensionl modeling pproch we need not define coverge function nd it cn be estimted directly from the dt. S-Shped Flexible Model In 1992 Kpur nd Grg developed n S-shped model with ssuming tht when we remove the different fults in the softwre some dditionl fults in the softwre re removed without ctully ffecting the system[18]. The revised Kpur grg model is derived by using logistic rte s the detection rte to cpture the effect of imperfect debugging nd fult genertion[11]. This model ws bsed on the ssumption of Non- Homogeneous Poisson Process. The bsic ssumptions of the model re s follows: 1. Filure /fult removl phenomenon is modeled by NHPP. 2. Softwre is subject to filures during execution cused by fults remining in the softwre. 3. Filure rte is eqully ffected by ll the fults remining in the softwre. 4. Fult detection / removl rte my chnge t ny time moment. The differentil eqution of the representing the rte of chnge of cumultive number of fults detected in time t is given s Eq. (3) m' t b 1 exp N m ( t ) bt The below Eq. (4) gives the men vlue function of the number of fults detected in time t Where, Published by: PIONEER RESEARCH & DEVELOPMENT GROUP ( 2 m N 1 exp( b 1 exp b ) (3) (4) b is the rte t which fult is detected/removed in the softwre. m is the men number of fults detected/ Corrected corresponding to testing timet. is the constnt. x is the rte of error genertion. p is the probbility of imperfect debugging. IV TWO-DIMENSIONAL MODELING Lter two dimensionl softwre relibility model ws developed to ccess the softwre quntittively. The need of development of two dimensionl model is one of the idel solution to the problem regrding softwre relibility in the hnds of softwre engineers [6][7]. In one dimensionl nlysis the object vrible usully depends upon one bsic vrible lthough the object tkes on mny different roles bsed upon its dependence on vrious other fctors. Two dimensionl models re used to cpture the joint effect of testing time nd testing coverge on the number of fults removed in the softwre. Trditionlly used one dimensionl model ws depending upon the

3 testing time, testing effort or testing coverge. However if the relibility of softwre is mesured on the bsis on the number of hours spent while testing the softwre or the percentge of softwre tht ws covered then the results re not conclusive. To hndle the need of high precision softwre relibility we hve the requirement of softwre relibility growth model which does not only solve the issues relted to the testing time but lso the testing coverge of the softwre i.e. the percentge of code covered of the softwre. For this we hve developed two dimensionl softwre relibility growth model which tkes into ccount the joint effect of testing time nd testing effort on the number of fults removed in the softwre. The two dimensionl model developed in this pper is bsed on the Cobb Dougls production function. Cobb Dougls Production Function The Cobb Dougls functionl form of production functions is brodly used to represent the reltionship of n output to inputs[3]. It ws proposed by Knut Wicksell ( ), nd tested ginst sttisticl evidence by Chrles Cobb nd Pul Dougls in The Cobb-Dougls function considered simplified view of the economy in which production output is determined by the mount of lbor involved nd the mount of cpitl invested[4][5]. Even if there re mny fctors ffecting economic performnce, still their model proved to be remrkbly ccurte. The mthemticl form of the production function is given s follows 1 Where, Y AL K (5) Y is the totl production per yer. L is the lbor input. K is the cpitl input. A is the totl fctor productivity. is the elsticity of lbor which is constnt nd determined by vilble technology. Two-Dimensionl S-Shped Model b m' N m (6) 1 exp b The men vlue function of the number of fults detected with testing resources x using the initil is given s x 0 condition 0 m N 1 exp( b 1 exp b ) (7) Now we extend the testing resource of one dimensionl S-shped model to two dimensionl problem. Using the cobb-dougls production the corresponding men vlue function is given s 1 N 1 exp bs u m 1 (8) 1 exp bs In the bove two-dimensionl men vlue function, if 1, then the bove men vlue function cn be regrded s trditionl one dimensionl time dependent SRGM nd if 0 it becomes testing coverge dependent SRGM. Two-Dimensionl S-Shped Model with Imperfect Debugging Mostly, the debugging process in rel life won t be much perfect. While during the fult removl process two possibilities cn occur. It my hppen tht the fult, which ws considered to be perfectly fixed, hd been improperly repired nd resulted in sme type of filure gin. There is lso fine chnce tht some new fults might get introduced during the course of correcting[2]. This sitution is much dngerous thn the former one, becuse in the first cse the totl fult content is not ltered, wheres in ltter, error genertion resulted in incresed fult content. The effects of both type of imperfect debugging during testing phse re incorported in our proposed model. The rte eqution of flexible model with imperfect debugging nd error genertion cn be written s follows u In this proposed method, we develop two dimension S- shped model determining the combined effect of testing time nd testing coverge[9][10]. The differentil eqution of the representing the rte of chnge of cumultive number of fults detected with respect to the totl testing resources is given s d dt m bp 1 exp N xm m Published by: PIONEER RESEARCH & DEVELOPMENT GROUP ( 3 b (9) We use logistic function to incorporte the effect of imperfect debugging nd error genertion. By solving the bove eqution using initil condition N ( 0) 0,

4 we get N t N x 1 exp bp p 1 x exp bp 1 x (10) Relibility Evlution Softwre evlution is very significnt phenomenon in quntittive softwre relibility ssessment. The softwre relibility function signifies the probbility tht softwre filure does not occur in time-intervl t, t xt 0, x 0given tht the testing tem or the user opertion hs been going up to time t [8].In two dimensionl SRGM, we cn ssess softwre relibility in n opertion phse where we ssume tht the testing coverge is not expnded. We cn derive the probbility tht the softwre filure does not occur in time- tht testing hs intervls, s s 0, 0 been going up to hs been ttined up to s s: s nd the vlue of testing coverge u by testing termintion time s, u exp m s, u / k ms, u k R / / (11) Where k indictes the set of prmeter estimtes of two dimension SRGM V. RESULTS AND DISCUSSION An SRGM is defined s tool tht cn be used to evlute the softwre quntittively, develop test sttus, schedule sttus, nd monitor the chnges in relibility performnce. Softwre relibility ssessment nd prediction is importnt to evlute the performnce of softwre system[1].in this pper, n effective softwre relibility growth model is developed with two types of imperfect debugging. In this section, the smple outputs re explined which is obtined during the execution of progrm. Here the relibility of the softwre is identified by using S-shped Cobb-Dougls function. In this pper, testing time nd testing coverge ws considered to identify the relibility of the softwre. A dt set with filure number, filure intervl nd lso dy of filure is given s the input to the SRGM tool. The tool identifies the fults nd gives the relibility prmeters s output s shown in the figure below. Fig. 1 Smple output of the SRGM Tool Comprtive Anlysis Using the proposed imperfect-debugging model, we now show rel numericl illustrtion for softwre relibility mesurement. Here, in order to vlidte the imperfect-debugging model, the AE nd MSF re selected s the evlution criteri. The Accurcy of Estimte (AE) is defined s (12) Published by: PIONEER RESEARCH & DEVELOPMENT GROUP ( 4 AE M M Where M is the ctul cumultive number of is detected errors fter the test, nd is the estimted number of initil errors. For prcticl purposes, M is obtined from softwre error trcking fter softwre testing. The men of Squred Errors (Long-term predictions) is defined s 1 MSE k Where t i k mt i m i i1 2 (13) m is the expected number of errors t time ti estimted by model, nd mi is the observed number of errors t time t. MSE gives the qulittive i comprison for long-term predictions. A smller MSE indictes minimum fitting error nd better performnce. The proposed method is compred with Ymnd Ryleigh Model nd Hung Logistic Model. The comprison vlues of the proposed method, nd Ymnd Ryleigh model nd Hung Logistic Model re given in the below tble.

5 Tble I. Comprtive results of different SRGM Model r AE(%) MSE Proposed Model Ymnd Ryleigh Model Hung Logistic Model The grphicl representtion of AE nd MSE for the proposed method, Ymd Ryleigh model nd Hung Logistic Model re shown in the below grphs Fig.3 Comprision of MSE From the bove tble nd grphs, AE is very high nd MSE is low thn previous methods. Thus the proposed method is very effective. VI CONCLUSION Softwre relibility engineering uses quntittive mesurement to increse the efficiency of the testing effort. By developing opertionl profiles of the systems use, SRE requires tht trde-offs between time, cost, nd qulity be mde explicitly for the project. In this pper we hve developed generl pproch in deriving more generl models bsed on simple ssumptions, constnt with the bsic softwre relibility growth modeling bsed on NHPP. The proposed models implnt broder theoreticl frmework which ccounts for interction between different dimensions of softwre relibility metrics. Incorporting the dynmics of testing time of the softwre nd the testing coverge hs llowed us the model to be two dimensionl frmework. The proposed models use the Cobb Dougls production function to cpture the combined effect of testing time nd testing coverge. The proposed models re vlidted on rel dt sets nd nlyses re done using goodness of fit criterion. We lso conclude tht the proposed SRGM hs better performnce s compre to the other SRGM nd gives resonble predictive cpbility for the ctul softwre filure dt. Therefore, this model cn be pplied to wide rnge of softwre. Fig.2 Comprision of AE REFERENCES 1. Chin-Yu Hung, Sy-Yen Kuo nd Michel R. Lyu, "An Assessment of Testing-Effort Dependent Softwre Relibility Growth Models," IEEE Trnsctions on Relibility, Vol. 56, No. 2, pp , Jun P. K. Kpur, H. Phm, Smeer Annd nd Klpn Ydv, "A Unified Approch for Developing Softwre Relibility Growth Models in the Presence of Imperfect Debugging nd Error Genertion," IEEE Trnsctions on Relibility, Vol. 60, No. 1, pp , Mr Khurshid Ahmd Mir, "A Softwre Relibility Growth Model," Journl of Modern Mthemtics nd Sttistics, Vol. 5, No. 1, pp , N. Ahmd, S. M. K Qudri nd Rzeef Mohd, "Comprison of Predictive Cpbility of Softwre Relibility Growth Models with Exponentited Weibull Distribution," Interntionl Journl of Computer Applictions, Vol. 15, No. 6, pp , Feb Shinji Inoue nd Shigeru Ymd, "A Bivrite Softwre Relibility Model with Chnge-Point nd Its Applictions," Americn Journl of Opertions Reserch, Vol. 1, No. 1, pp. 1-7, Mr S. M. K. Qudri, N. Ahmd nd Sheikh Umr Frooq, "Softwre Relibility Growth modeling with Generlized Exponentil testing effort nd optiml Softwre Relese Published by: PIONEER RESEARCH & DEVELOPMENT GROUP ( 5

6 policy," Globl Journl of Computer Science nd Technology, Vol. 11, No. 2, pp , Feb Crin Andersson, "A replicted empiricl study of selection method for softwre relibility growth models," Journl of Empiricl Softwre Engineering, Vol. 12, No. 2, pp , Apr Hn Seong Son, Hyun Gook Kng nd Seung Cheol Chng, "Procedure for Appliction of Softwre Relibility Growth Models to NPP PSA," Journl of Nucler Engineering nd Technology, Vol. 41 No. 8,pp , Oct V. B. Singh1; Klpn Ydv, Reech Kpur nd V. S. S. Ydvlli, "Considering the Fult Dependency Concept with Debugging Time Lg in Softwre Relibility Growth Modeling Using Power Function of Testing Time," Interntionl Journl of Automtion nd Computing, Vol. 4, No. 4, pp , Oct Lev V. Utkin, Svetln I. Ztenko nd Frnk P.A. Coolen, "Combining imprecise Byesin nd mximum likelihood estimtion for relibility growth models," In Proc. of the Sixth Interntionl Symposium on Imprecise Probbility: Theories nd Applictions, Durhm, UK, Dr. R. Sty Prsd, K. Rmchnd H Ro nd Dr. R.R.L. Knth, "Softwre Relibility Mesuring using Modified Mximum Likelihood Estimtion nd SPC," Interntionl Journl of Computer Applictions, Vol. 21, No.7, pp. 1-5, My Andy Ozment, "Softwre Security Growth Modeling: Exmining Vulnerbilities with Relibility Growth Models," Journl of Advnces in Informtion Security, Vol. 23, No. 2, pp , Mrtin Bumer, Ptrick Seidler, Richrd Torkr nd Robert Feldt, "Predicting Fult Inflow in Highly Itertive Softwre Development Processes: An Industril Evlution," In Proc. of the 19th IEEE Interntionl Symposium on Softwre Relibility Engineering, Settle, USA, Mn Cheol Kim, Seung Cheol Jng nd Je Joo H, "Possibilities And Limittions of Applying Softwre Relibility Growth Models To Sfetycriticl Softwre," Journl of Nucler Engineering nd Technology, Vol. 39, No. 2, pp , Apr Chin-Yu Hung, Jung-Hu Lo, Sy-Yen Kuo nd Michel R. Lyu, "Softwre Relibility Modeling nd Cost Estimtion Incorporting Testing-Effort nd Efficiency," In Proc. of the 10th Interntionl Symposium on Softwre Relibility Engineering, Boc Rton, FL, pp , Nov Swpn S. Gokhle, Michel R. Lyu, nd Kishor S. Trivedi, "Incorporting Fult Debugging Activities Into Softwre RelibilityModels: A Simultion Approch," IEEE Trnsctions on Relibility, Vol. 55, No. 2, pp , Jun Kterin Gosev-Popstojnov, nd Kishor S. Trivedi, "Filure Correltion in Softwre Relibility Models," IEEE Trnsctions on Relibility, Vol. 49, No. 1, pp , Mr Swpn S. Gokhle, Michel R. Lyu nd Kishor S. Trivedi, "Softwre Relibility Anlysis Incorporting Fult Detection nd Debugging Activities," In Proc. of the Ninth Interntionl Symposium on Softwre Relibility Engineering, Pderborn, Germny, pp , Nov Published by: PIONEER RESEARCH & DEVELOPMENT GROUP ( 6