How To Improve Software Reliability

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1 2 Iteratioal Joural of Computer Applicatios ( ) A Software Reliability Growth Model for Three-Tier Cliet Server System Pradeep Kumar Iformatio Techology Departmet ABES Egieerig College, Ghaziabad Affiliated to UPTU Luckow, Idia Yogesh Sigh Professor, Uiversity School of IT Guru Gobid Sigh Idraprastha Uiversity Delhi 6, Idia, ABSTRACT With the ever-icreasig role that software is playig i our reallife systems, cocer has steadily grow over the quality of the software products. I today s life the computers are beig used to moitor ad cotrol safety critical ad civilia systems with a great demad for high-quality software products. So reliability is a primary cocer for both software developers ad software users. I literature may software reliability growth models have bee proposed over the years to estimate ad predict reliability of software products. But it is ofte very difficult for project maagers ad practitioers to determie which model is more useful i a particular domai ad up to what extet. I this paper we propose a NHPP based software reliability growth model for three-tier cliet server systems. The preset model composed of three layers of cliet-server architecture related to presetatio logic, busiess logic ad database stored at backed. Presetatio layer cotais forms or server pages which presets the user iterface for the applicatio, displays the data, collects the user iputs ad seds the requests to ext layer. Busiess layer, which provides the support services to receive the requests for data from user tier, evaluates agaist busiess rules, passes them to the data tier ad icorporates the busiess rules for the applicatio. Data layer icludes data access logic, database driver(s), query egies used for commuicatig directly with the data store of a database. The model has bee validated through stadard dataset cosists of software failure data o various projects released from the software reliability dataset ad applyig to a live commercial applicatio. Categories ad Subject Descriptors Software reliability egieerig, cliet-server models, distributed applicatios, software metrics, ohomogeeous Poisso process, failure rate. Geeral Terms Reliability, Measuremet, Performace, Experimetatio Keywords Applicatio server, database server, presetatio layer, reliability growth factor. INTRODUCTION The preset sceario of software developmet life cycle has emerged ito a distributed eviromet because of the developmet of etwork techology & ever icreased demad of sharig the resources to optimize the cost. Therefore to improve the process of reliability estimatio ad predictio of software products we idetify ad remove the remaiig faults durig the testig phase i a three-tier cliet server based systems. Reliability ca be grow through various meas such as improvig the process of desigig, effectiveess of testig, maual & automated ispectios, familiarizatio with developers, users & product, ad improvig the maagemet processes & decisios [, 2]. The rate at which reliability grows depeds o the factors related to how rapidly defects are discovered, how fast corrective actio ca be idetified ad implemeted & how soo the impact of the chages take place ad make operatioal i the field. I three-tier cliet server architecture the presetatio logic ad busiess logic are split off ito separate compoets resultig ito three-tier system show as i figure. Level Level 2 Level Sedig request sedig request SQL Query Presetatio Cotais Presetatio Logic Cliet Sedig reply Busiess Cotais Busiess Logic Data Cotais Data Access Logic sedig reply Applicatio Server Database Server Database Figure. A three-tier cliet-server architecture view 2. SRGM SPECIFICATION I a multi ode cliet-server system cosistig of various compoets of software that execute o differet odes it becomes almost madatory to model the system i such a clietserver computig eviromet if realistic reliability predictio ad assessmet are to be made. Also i three-tier architecture whe there are umber of cliets ad umber of servers i a cliet-server system, it is ot always ecessarily the case that a software failure i ay of the cliets or servers will cause the system to fail. There are various factors related to the failure of a system such as trasmissio failure, etworkig failure, database-likig failure, query egie failure icludig software developmet life cycle (SDLC) failure [4,5]. To address some of these vital issues related to software failure we decompose the 9

2 2 Iteratioal Joural of Computer Applicatios ( ) preset model ito three differet layers ad discuss each layer to idetify the causes of errors, level of severity ad its impact to improve the reliability of the software durig the testig phase. Fially we compute the failure itesity fuctio, probability distributio fuctio, cumulative distributio fuctio, mea time to failure, ad reliability of the system as a whole usig a real life software reliability dataset [6,7]. The preset model facilitates project maagers ad the practitioers to assess the reliability of a software system based o the amout of efforts put i testig, how accurately parameters are estimated, how efficietly the relevat & updated failure data of moder computer system is collected ad to the possible extet the model has bee validated usig curret real life software. This model further ca be used to determie the quality of developmet processes i terms of the umber of remaiig faults, mea time to failure, time betwee failure, ext expected failure ad failure itesity of the software at the begiig of a system test. Table. Causes of Errors at Differet of the Model Model s Possible Causes of Error(s) Presetatio layer Busiess Database Ivalid iput(s), o-formatted data such as eterig characters i place of a o egative iteger value, User autheticatio ad authorizatio error such as ivalid logi or password ad Lack of security measures such as damagig & mishadlig of the system Logical error such as busiess logic is ot beig coded as per the software requiremet specificatios, Exceptios are ot beig hadled properly, Less tolerace power (degree to which hadle the uexpected behavior of the system) ad Security measures such as poor ecryptio / decryptio algorithm(s) No homogeeous data formats, database coectivity error or itermittet coectivity, ODBC driver failure, query egie failure to execute the query or large amout of data to process ad retrieve, availability of low badwidth to fetch the data, etwork cogestio ad security measures such as fire, floods, earthquake or ay other mishap. The mai advatage of three-tier cliet server SRGM is that all busiess logic has bee cetralized i oe layer. A compoet i the busiess layer ca be accessed by ay umber of compoets i the presetatio layer, therefore ay chages to busiess logic ca be made i oe place ad be automatically iherited by all other compoets without havig to duplicate the chage i those other compoets. Also the presetatio layer compoets do ot access the database all data is provided by the busiess layer i the form of XML streams. Ay chages made i the presetatio layer eed to be passed back to the busiess layer before they ca be applied to the database. 2. Severity of Errors We categorize the severity level of error(s) durig the executio & operatio of preset model as follows: Catastrophic: The system failures may cause to loss of life or heavy damage to the system wherever it is istalled. Gradual: The severity level of this kid of error(s), which may further be critical, margial or egligible depedig upo the kid of applicatio ad operatioal eviromet. Critical: may cause complete loss of system such as disaster ad applicable to all three layers presetatio, applicatio ad database of the model. Margial: may degrade the system gradually such as ifected by viruses, worms or etwork cogestio ad heavy load of data to be processed. Negligible: may lead to mior failure of the system ad applicable to the presetatio & database layer such as icorrect userame & password, ivalid user s iput, database ot foud or does ot exist, ODBC driver failure or rebootig the system i worst case. Termiology Node: A hardware elemet o a etwork geerally a computer \PC \desktop\ laptop that is istalled with a NIC card. Cliet: A ode that makes request of services i a etwork or that uses resources available through the servers. Server: A ode that provides some type of services to the cliets such as etwork resources/ files or distributed services. Cliet-Server computig: defied as processig capability or available iformatio distributed across multiple odes. Software Defect: Ay udesirable deviatio i operatio of the software from its iteded operatio, as defied i the software requiremet specificatios. Errors: are huma actios that result i the software cotaiig a fault. Examples of such faults are the omissio or misiterpretatio of the user s requiremets, a codig error etc. Faults: are maifestatios of a error i the software. If ecoutered the it may cause a failure of the software. Failure: is the iability of the software to perform its missio for fuctio withi specified limits. Failures are observed durig testig ad operatio. Failure rate: refers to the rate of occurrece of Failure (ROCOF) depedig upo the cotext. The ROCOF is the ucoditioal rate of occurrece of a failure at a poit i time. Software failure: a failure caused by a software fault. It is to be oticed that software itself does ot fail. Faults already preset i the software lead to failure of the system uder certai coditios. NHPP: The o-homogeeous Poisso process model (NHPP) represets the umber of failures experieced up to time t is a o-homogeeous Poisso process {N (t), t }. The NHPP based model provides a aalytical framework for describig the software failure pheomeo durig testig. The mai issue i the NHPP model is to estimate the mea value fuctio of the cumulative umber of failures experieced up to a certai poit i time. Assumptios:

3 2 Iteratioal Joural of Computer Applicatios ( ) The software failure-occurrece pheomeo is described by a NHPP. The software faults detected durig the testig phase are corrected certaily ad completely, that is o ew faults are itroduced ito the software systems durig the debuggig phase. O a failure observatio a immediate effort takes place to locate the causes of the failure & the error removal takes very small amout of time, which is early egligible. Software is subject to failures durig executio caused by faults remaiig i the software. The software is developed for three-tier cliet server based systems. A fiite umber of test cases are prepared to esure that the software works accordig to the requiremets ad specificatios. Each test case is desiged to execute a fiite umber of istructios. The error removal itesity per executio is proportioal to the remaiig errors i the software at ay poit of time. Notatios: a total umber of errors i the software N(t) umber of errors corrected up to time t m(t) the mea value fuctio or expected o. of faults detected or removed by time t b error correctio rate durig the iitial testig phase of presetatio layer b 2 error correctio rate durig the testig phase of busiess layer b error correctio rate durig the fial testig phase of database layer r error geeratio factor due to correctio of errors i iitial testig phase of presetatio layer r 2 error geeratio factor due to correctio of errors i testig phase of busiess layer r error geeratio factor due to correctio of errors i testig phase of database layer t time spet i iitial testig phase at presetatio layer t 2 time spet i testig of busiess layer t time spet i testig at database layer t total time spet i all the three phases of testig λ(t) itesity fuctio for NHPP models or fault detectio rate per uit time T k software life cycle legth R(t) reliability of the software developed F(t) cumulative distributio fuctio (cdf) f(t) probability distributio fuctio (pdf) MTTF mea time to failure. MATHEMATICAL MODEL We cosider a software i which failures are caused by software errors. Let {N (t), t } be the total umber of errors corrected up to time t durig the total testig phase. A stochastic process {N (t), t } is a o egative process where N(t) is a radom variable which represets the cumulative o of faults detected up to a testig time t. The fault detectio process is described by NHPP with the mea value fuctio m(t) as follows: {m (t)} exp [- m(t)]} Pr {N (t) = } =! where =,, 2 m (t) = t λ (x) dx () where Pr{N(t)} deotes the probability of evet N(t) ad m(t) is the mea value fuctio, which represets the expected cumulative o. of faults detected i the testig time iterval (,t] ad λ(t) is a itesity fuctio which represets the fault-detectio rate per fault. The NHPP model is characterized by its mea value fuctio defied as follows: m(t) = a ( e bt ) a>, b> (2) where a, is the expected o of iitial iheret fault before testig ad b is the software failure occurrece rate per iheret fault.i three-tier cliet server based model there are three type of faults ad some faults are easier to detect the others based upo the efforts required to detect the cause of failure i order to fix ad remove it. I the preset model these faults are associated with presetatio layer, busiess layer ad database layer durig the total testig phases. Also we cosider that error correctio rate ad error geeratio factor is differet for both these phases, i.e. durig the iitial testig phase more errors are likely to occur which cosequetly decreases as the testig progresses. Durig the process of error correctio at presetatio layer, a few errors may be geerated at busiess layer ad database layer, which will affect the total performace of the system. Thus m(t) for the proposed model ca be writte as: m(t) = a ( exp[-b i t i ] )*(- r i ) () where t + t 2 + t t, a >, < b < b 2 < b <, < r i < For three types of fault at each layer the itesity fuctio ca be writte as dm(t) / dt that is λ(t) = a {b i exp[-b i t i ]-r i exp[-b i t i ]b i } = a b i exp [-b i t i ] (- r i ) (4) This is the istataeous error detectio rate, i.e. the expected umber of detected errors per uit time at time t. Also we ca derive the expressios for various software reliability assessmet measures from this ew model give by eq. (). The expected o. of faults remaiig at the system testig time t which is obtaied by takig expectatios of radom variables {N( ) N(t)}i.e. (t) = E [N( ) N(t) ] (5) The error detectio rate per error (per uit time) at time t is defied by dp(t) as follows: λ(t) dp(t)= [a m(t) ] a ( exp [-b i t i ] ( - r i ) =

4 2 Iteratioal Joural of Computer Applicatios ( ) a- a ( exp [-b i t i ] ( - r i ) a b i exp [-b i t i ] (- r i ) = r i + exp [-b i t i ] - r i exp [-b i t i ] (6) Applyig the boudary coditios whe t= ad t= we get dp() = b i (- r i ) ad dp( )= (7) The expected o. of errors remaiig i the software at time t is give by N(t)=a m(t) i.e., N(t)= a [ ( - r i ) exp(- b i t i ) + r i ] (8) The probability that a software failure does ot occur durig (s, s + x), give that the last occurrece time of a software failure was s, is give by R( x / s)=exp(-a [{exp[-b i s] exp[-b i (s + x)]} (( - r i ) j= + r i ]) (9) The coditioal probability fuctio R p (x /s) is kow as software reliability of NHPP model with m(t). The mea value fuctio m (t) represets the umber of errors actually corrected. 4. DATA COLLECTION The sactity of collected failure data depeds o how accurately & efficietly we observe failure data from real life software products of moder computer systems which is very complex procedure ad that eed to be addressed further separately for better validatio of the model by the commuity of researchers ad practitioers. I this paper we have take software failure data o various projects from the Software Life Cycle Empirical/Experiece Database (SLED) published by Data & Aalysis Ceter for Software (DACS). Further to validate our model for estimatig reliability growth of three-tier cliet server system we have applied the model to the data set of O-lie Data Etry Software Package test data (Obha 984a) ad Real-Time Cotrol Systems (Hou et al., 997) assumig that the o. of failures-detectio data set is observed from the system-testig phase after cofirmatio of the itegratio of all modules\ software compoets. The observatio of failure ad repair times ca be represeted by t,t 2.,. t where t i represets the time of failure of i th uit. It is assumed that each failure represets a idepedet sample from the same populatio. The populatio is the distributio of all possible failure times ad may be represeted by f(t), R(t), F(t) or λ(t). Therefore the basic problem reduces to determie the best failure distributio implied by the failure times comprised i the sample. I all cases the sample is assumed to be a simple radom or probability sample. A simple radom sample is oe i which the failure or repair times are idepedet observatios from a commo populatio. If f(t) is the probability desity fuctio of the uderlyig populatio the f(t i ) is the probability desity fuctio of the i th sample value. Sice the sample comprises of idepedet values therefore the joit probability distributio of the sample is the product of idetical ad idepedet distributios i.e. ft,t 2 t (t,t 2 t )=f(t )f(t 2 ).,f(t ) () S.No. Table 2. Failure Datasets applied to the model Project Descriptio Real Time Commad & Cotrol Real Time 2 Commad & Cotrol Real Time Commad & Cotrol Real Time 4 Commad & Cotrol Commercial 5 Subsystem O-lie Data 6 Etry Software Package Real-Time 7 Cotrol Systems Number of Failures Source # 6 DACS 54 DACS 58 DACS 5 DACS Method of Parameter Estimatio DACS Obha 984 (Hou et al., 997) The value of six ukow parameters of the proposed model give i equatios () ad (4) are obtaied by the method of Maximum Likelihood Estimatio (MLE). Let X be the discrete variable represetig the o. of trials ecessary to obtai the first failure. Here we assume that the probability of failure remais a costat p ad each trial is idepedet the Pr{X = x } = f(x) = (- p) x -. p () where x=,2,. ad which is the probability of (x-) successes i.e. probability =(- p) x - followed by a failure probability ( probability = p).if x, x 2.,. x represets a sample of size from this distributio the from equatio () the joit distributio may be writte as: fx, x 2 x (x, x 2 x ) = f(x )f(x 2 ).,f(x ). =(-p) x-.p(-p) x2-.p (-p) x-.p,(-p) x-.p =p.(-p) exp[ ( x i - ) ] (2) Equatio (2) is called likelihood fuctio ad represets the probability of obtaiig the observed sample. Sice equatio (2) cotais the ukow parameter p we fid a value of p cosistet with the observed sample. If a value of p is foud that maximize the likelihood fuctio the it also maximize the probability of obtaiig the observed sample. max g(p) = p.(-p) exp[ ( x i - ) ] for <=p<= 2

5 2 Iteratioal Joural of Computer Applicatios ( ) Therefore we solve this equatio to get maximum of a fuctio by fidig the poit at which the first derivative is equal to zero as follows: max log g(p) = log[ p.(-p) exp[ ( x i - ) ]] = log p + ( x i - ) log( p) () Now puttig first derivative of max log g(p) = we get i.e. d/dp [max log g(p)] = d/dp [ log p + + log ( p ) ] = / p + ( x i - ) ( ) / (-p) = / p ( p) = ( x i - ) max (p) = / x i (4) where max (p) is defied as the Maximum Likelihood Estimator of the give distributio. 4.2 Model Validatio Based o the data available give i table (2) the performace aalysis of the proposed model is measured by the four commo criteria SSE as the sum of squared errors, R-square, Adjust R- square & RMSE for the model compariso of goodess of-fit as follows: Sum of square of Error (SSE): This statistic measures the deviatio of the resposes from the values of resposes. A value closer to idicates a better estimatio. It is calculated as: k SSE = [ y ij - m j (t i )] 2 (5) j= where y ij is total umber of type j failures observed at time t i accordig to the actual data m j (t i ),the estimated cumulative umber of type j failures at time t i for i =,2,, ad j =,2,, k. Mea Square of fittig Error (MSE): It is calculated as: [ m j (t i ) - y ij ] 2 (6) MSE = where y ij (m j (t i )) is the actual estimated value of the total umber of errors removed i iterval (, t]. The MSE measures the distace of a model estimate from the actual data with the cosideratio of the umber of observatios ad the umber of parameters (N) i the model. RMSE is defied as the root of mea squared error ad for a computed value closer to it idicates a better approximatio & estimatio. That is, RMSE = MSE (7) R-square: This statistic measures how successful the model is i explaiig the variatio of the data, which may be defied as the square of the correlatio betwee the respose values ad the predicted respose values. It is also called the square of the multiple correlatio coefficiets ad the coefficiet of multiple determiatios. R-square ca take o ay value betwee ad, with a value closer to idicatig a better estimatio of the model. For example if R-square =.824 meas that the estimatio explais 82.4% of the total variatio i the data about the average. Adjusted R-Square: The degrees of freedom uses the R-square statistic ad adjusts it based o the residual degrees of freedom. The residual degree of freedom is defied as the umber of respose values mius the umber of fitted coefficiets m estimated from the respose values. v = -m (8) where v idicates the umber of idepedet pieces of iformatio ivolvig the data poits that are required to calculate the sum of squares. A value closer to idicates a better estimatio of the model. 5. RESULT ANALYSIS I this sectio we show the result of our model applied to a set of failure data extracted from various projects listed i table2. Figure (2) to figure (2) exhibits the result of various computed quality attributes usig equatios () ad (4) such as failure itesity λ(t), reliability of the software at ay istace of time durig testig phase R(t), cumulative distributio fuctio (CDF), probability distributio fuctio (PDF), mea time to failure (MTTF) & variace factor. Here we have modeled the daily defect arrival data durig the testig phase of system based o the cumulative failures, legth of failure iterval ad the day of failure it was reported whereas trackig of the data for software reliability estimatio has bee doe o a caledar-time basis ad the testig effort is homogeeous throughout the testig phase. We have simulated the seve failure datasets take as oe-dimesioal data with the help of o-liear fittig fuctios usig Matlab 7.. uder Widows XP eviromet. Goodess of fitess criteria Table. Goodess of fitess for differet projects SSE R_ Square Adj. R- Square RMSE Project Project Project Project Project Project Project OBSERVATIONS Typically software reliability growth model estimate the time to ext failure or the expected umber of remaiig failures or whe to stop the testig ad release the product to the customer.

6 2 Iteratioal Joural of Computer Applicatios ( ) Time is measured i terms of test time icludig CPU executio time, lies of code tested, system operatig time as a calader time i.e. the duratio of testig such as o. of hours \days\weeks & moths.as a result the probabilistic models are used i describig software reliability ad ormally a decreasig failure rate is observed if software failures are fixed as they occur ad the fix does ot geerate ay ew failures. Thus software testig ca be likeed to reliability growth testig i which the software is executed i a attempt to discover failure, aalyze the causes of failure mechaism ad iitiate the corrective measures. Followig are the observatios made from applyig the model o seve projects listed i table (2) ad table (). The differet reliability attributes computed usig datasets of project (6) ad (7) are show i figures (9) to figure () with sigificat ad improved results. The preset model exhibits costat failure rates ad the expoetial distributio i may respects, which is the simplest reliability distributio to aalyze ad reveals from the observatios that if the failure rates of all failure modes of a compoet are costat & idepedet the the overall failure rate of the compoet is also costat. There are several iterestig physical processes that give rise to the cause why have we chose expoetial probability distributio for implemetig our model. A costat failure rate implies completely radom ad idepedet failures over time ad hece results i lack of memory. I fact these three characteristics related to radomess, costat failure rates ad memorylessess more or less exhibit differet form of same pheomeo. Failure Itesity F a i l u r e i t e s i t y vs T e s t i g t i m e : a p p l i e d t o p r o j e c t fi t t e d d a t a A c t u a l d a t a Reliability fuctio Failure itesity Reliability fuctio R(t) R e lia b ilit y fu c t io vs t e s t i g F it t e d d a t a A c t u a l d a t a T e s t i g t im e (i d a y s ) Figure 4. Reliability fuctio vs. testig time T e s t i g T im e (d a y s ) F ailure Ites ity vs Tes tig period Figure 5. Failure itesity vs. testig time Reliability fuctio vs testig time Fitted Data Actual data fit R e l vs. t im e failure rate T e s t i g t i m e ( d a y s ) Figure 2. Failure itesity vs. testig time F a ilu re R a t e vs t e s t i g p e rio d 2 F it t e d d a t a 8 A c t u a l d a t a T e s t i g t i m e (d a y s ) Figure. Failure itesity vs. testig time Testig time (days ) Failure Rate Lambda(t) Figure 6. Reliability fuctio vs. testig time Failure rate vs Testig time Fitted data Actual data Testig time (days) Figure 7. Failure itesity vs. testig time 4

7 2 Iteratioal Joural of Computer Applicatios ( ).8 R e lia b ility V s Te s ti g Reliability & MTTF.7 F itte d d a ta A c tua l data Reliability fuctio.4..2 MTTF.6.4 MTTF Reliability Testig tim e (days) Figure 8. Reliability fuctio vs. testig time Testig period (days) Figure 2. Cumulative distributio fuctio vs. testig time R(t) Reliability fuctio observed data Reliability fuctio Probability distributio fuctio 7 x PDF observed data PDF Testig period (days) Figure 9. Reliability fuctio vs. testig time Reliability & CDF Testig time (days) Figure. Probability distributio fuctio vs. testig time Cummulative distributio fuctio (CDF) Variace factor CDF Reliability fuctio Testig period (days) Figure. Reliability & CDF vs. testig time Variace factor Variace factor Cummulative o of errors Cummulative o of errors Figure. Cumulative errors vs. Variace factor 6. CONCLUSION & FUTURE WORK Based o the above approach it seems to be quite feasible to develop such a software reliability growth model for a three-tier cliet-server system. However, i order to implemet the preset model it is ecessary to partitio the failures ad defects ito three categories associated with each presetatio, applicatio & database layer of the preset model. I this paper we have desiged a software reliability growth model for three-tier cliet-server system based o ohomogeeous Poisso process, which icorporates the expoetial software reliability growth model for estimatio ad predictio of software reliability. We have discussed various aspect related to the severity level of errors ad its impact o the respective layer of the proposed model. The model also has bee validated usig failure data of seve real life datasets of various projects released by software reliability dataset DACS. Further if we are able to estimate the values of the parameters more precisely the we ca ehace software reliability assessmet measures more accurately with the help of our model i compariso with the covetioal existig models. However we have assumed a perfect debuggig eviromet to validate ad implemet the preset model, which may ot be realistic i may real life developmet processes that is the removal of all software error(s) or faults is performed perfectly at each particular layer of the model durig the testig phase. Therefore to overcome this kid of deficiecy we eed to collect more realistic data little bit more precisely from real life projects 5

8 2 Iteratioal Joural of Computer Applicatios ( ) released uder the imperfect debuggig eviromet of moder computer systems with the possibility of itroducig ew faults at differet layers of the model. Sice the software testig cosumes a large amout of efforts required to locate ad fix the error durig the testig phase of a software system, which cosequetly icrease the allocated budget for the developmet of the system. Therefore, i the future it is very much essetial ad required to develop a mechaism of whe to stop the testig process ad release the products to the ed user with higher quality, withi budget ad without ay delay. REFERENCES [] A Software Reliability Growth Model for a Distributed Developmet Eviromet Electroics ad Commuicatios i Japa, Part, Vol. 8. No. 2, 2, Shigeru Yamada, Yoshiobu Tamura ad Mitsuhiro Kimura. [2] Determiatio of software release istat usig a ohomogeeous error detectio rate model Microelectro Reliability, Vol.. No. 6. pp. 8-87, 99, prited i Great Britai, K.K. Aggarwal ad Yogesh Sigh. [] Software Reliability Egieerig: more reliable software faster ad cheaper secod editio published by TMH publicatios 27, Musa J D. [4] Software reliability model for modular structure IEEE Trasactios o Reliability, R-28, No. 979, Littlewood B. [5] Topics i safety, reliability ad quality Reliability Egieerig published by Kluwer publicatios 99, K.K. Aggarwal. [6] Software reliability modelig published by World Scietific publicatios 99, Mi Xie. [7] System Software Reliability published by Spriger Series i Reliability Egieerig 26, Hoag Pham. [8] Hadbook of Software reliability egieerig edited ad published by IEEE computer society press ad TMH publicatios 27, Michael R Lyu. [9] Operatioal profile i software reliability egieerig IEEE software 99, Musa J D. [] Software Reliability Egieerig for Cliet-Server Systems Proceedigs of the Seveth Iteratioal Symposium o Software Reliability Egieerig (ISSRE 96), /96, 996 IEEE, Norma F Scheidewid. [] A Architecture-Based Software Reliability Model Computer Sciece Departmet, SUNY Albay 2, We- Li Wag, Ye Wu, Mei-Hwa Che. [2] Software Egieerig: programs, documetatio & operatig Procedures published by New Age Iteratioal publicatios 27, K.K. Aggarwal ad Yogesh Sigh. [] Post-Release reliability Growth i Software Products ACM Trasactios o Software egieerig ad Methodology, Vol. 7, No.4, Article 7, pub. Date: August 28, Pakaj Jalote, B Murphy, Vibhu Saujaya Sharma. [4] Cotributios to Hardware & Software Reliability published by World Scietific publicatios 999, P K Kapur, R B Garg, S K Kumar. [5] Software Reliability Caregie Mello Uiversity 8-849b Depedable Embedded Systems Sprig 999 Authors: Jiatao Pa,jpa@cmu.edu, Jiatao Pa. [6] Probability ad Statistics with Reliability, Queuig ad Computer Sciece Applicatios, secod editio published by Joh-Wiley publicatios 27, Kishore S Trivedi. [7] Software Metrics ad Reliability Software Reliability Egieerig the 9th Iteratioal Symposium, 998, Germay, Roseberg, L., Hammer, T., Jack S. [8] Metrics ad Models i Software Quality Egieerig published by Pearso educatio 28, Stepha H Ka. [9] Reliability ad maitaiability egieerig published by TMH publicatios by Charles E. Ebelig 27. [2] A Assessmet of Testig-Effort Depedet Software Reliability Growth Model, IEEE Trasactios o Reliability, Vol, 56,No,2, Jue 27 by Chi-Yu Huag, Sy-Ye Kuo, Michel R. Lyu. 6