A Model for Estimation of Efforts in Development of Software Systems

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1 A for Estimatio of Efforts i Developmet of Software Systems Parvider S. Sadhu, Maisha Prashar, Pourush Bassi, ad Atul Bisht Abstract Software effort estimatio is the process of predictig the most realistic use of effort required to develop or maitai software based o icomplete, ucertai ad/or oisy iput. Effort estimates may be used as iput to project plas, iteratio plas, budgets. There are various models like Halstead, Walsto-Felix, Bailey-Basili, Doty ad Based models which have already used to estimate the software effort for projects. I this study Statistical s, Fuzzy- ad Neuro-Fuzzy (NF) Iferece Systems are experimeted to estimate the software effort for projects. The performaces of the developed models were tested o NASA software project datasets ad results are compared with the Halstead, Walsto-Felix, Bailey-Basili, Doty ad Geetic Algorithm Based models metioed i the literature. The result shows that the NF has the lowest MMRE ad RMSE values. The NF shows the best results as compared with the Fuzzy- based hybrid Iferece System ad other estig s that are beig used for the Effort Predictio with lowest MMRE ad RMSE values. Keywords Neuro-Fuzzy, Halstead, Walsto-Felix, Bailey-Basili, Doty, Based, Geetic Algorithm. I. INTRODUCTION N recet years, software has become the most expesive I compoet of computer system projects. Accurate software cost estimates are critical to both developers ad customers. Uderestimatig the costs may result i maagemet approvig proposed systems which ca exceed their budgets, with uderdeveloped fuctios ad poor quality, ad failure to complete o time. Overestimatig may result i too may resources committed to the project, or, durig cotract biddig, result i ot wiig the cotract, which ca lead to loss of jobs. So, accurate cost estimatio is importat. I the last three decades, may quatitative software cost estimatio models have bee developed. They rage from empirical models such as Boehm s COCOMO models [] to aalytical models such as those i [5, 7, ]. A empirical model uses data from previous projects to evaluate the curret project ad derives the basic formulae from aalysis of the particular database available. A aalytical model, o the other had, uses formulae based o global assumptios, such as the rate at which developer solves problems ad the umber of problems Maisha Prashar is workig with Govt. Shivalik College, Naya Nagal, Pujab, Idia. Parvider S. Sadhu, Pourush Bassi ad Atul Bisht are associated with Rayat Bahra Istitute of Egieerig & Bio-Techology, Sahaura, Mohali (Idia). available. Typical major models that are beig used as bechmarks for software effort estimatio are: Halstead, Walsto-Felix Bailey-Basili Doty (for KLOC > 9). These models have bee derived by studyig large umber of completed software projects from various orgaizatios ad applicatios to explore how project sizes mapped ito project effort. But still these models are ot able to predict the Effort Estimatio accurately. As Neuro-fuzzy based system is able to appromate the o-liear fuctio with more precisio ad o of the researcher have explored Neuro-fuzzy approach for the Effort Estimatio ad there is still scope of explorig more statistical modelig approaches. So, i this proposed study, it is tried to use Soft Computig Techiques ad statistical techiques to build a more accurate model that ca improve accuracy estimates of effort required to build a software system. The remaider of this paper ca be described as follows: Sectio II outlies the literature review about the various techiques that are used for the effort ad cost estimatio. Sectio III discusses the methodology adopted for geeratig ad comparig a umber of models. Sectio IV highlights results of implemetatio. It discusses the results of the various models used for the effort estimatio ad Sectio V is all about coclusios of this research work. II. BASIC COST ESTIMATE MODELS There are two major types of cost estimatio methods: A. Algorithmic s These models vary widely i mathematical sophisticatio. Some are based o simple arithmetic formulas usig such summary statistics as meas ad stadard deviatios [5]. Others are based o regressio models [4] ad differetial equatios [7]. To improve the accuracy of algorithmic models, there is a eed to adjust or calibrate the model to local circumstaces. These models caot be used off-the-shelf. Eve with calibratio the accuracy ca be quite mixed. The estig algorithmic methods differ i two aspects: the selectio of cost factors, ad the form of the fuctio. Firstly, the cost factors used i these models are discussed, the characterize the models accordig to the form of the fuctios ad whether the models are aalytical or empirical. The 93

2 followig are algorithmic methods discussed as uder. Liear s have the form: Effort = a + ai () Where, the coefficiets a,,a are chose to best fit the completed project data. The work of Nelso belogs to this type of models [3]. Walsto-Felix [4] used Multiplicative s have the form: = a ai x i Effort () i = Agai the coefficiets a,, a are chose to best fit the completed project data. With each x i takig o oly three possible values equal to: -,, +. Doty model [8] also belogs to this class with each x i takig o oly two possible values either or +. These two models seem to be too restrictive o the cost factor values. Power Fuctio s cotais two of the most popular algorithmic models i use, as follows: COCOMO (Costructive Cost ) Putam s COCOMO (Costructive Cost ) model was proposed by Boehm [, ]. The models have bee widely accepted i practice. I the COCOMO, the code-size S is give i thousad LOC (KLOC) ad Effort is i perso-moth. The followig are the various types of COCOMO models: a) Basic COCOMO: The basic COCOMO model is simple ad easy to use. As may cost factors are ot cosidered, it ca oly be used as a rough estimate. b) Itermediate COCOMO ad Detailed COCOMO: I the itermediate COCOMO, a omial effort estimatio is obtaied usig the power fuctio with three sets of coefficiets, with oe coefficiet beig slightly differet from that of the basic COCOMO. The overall impact factor (M) is obtaied as the product of all idividual factors, ad the estimate is obtaied by multiplyig M to the omial estimate. The detailed COCOMO works o each sub-system separately ad has a obvious advatage for large systems that cotai o-homogeeous subsystems. Putam's is based o Norde/Rayleigh mapower distributio ad his fidig i aalyzig may completed projects [7]. The cetral part of Putam's model is called software equatio as follows: S = E Effort / 3 t 4 d / 3 (3) Where, t d is the software delivery time; E is the eviromet factor that reflects the developmet capability, which ca be derived from historical data usig the software equatio. The size S is i LOC ad the Effort is i perso-year. Aother importat relatio regardig effort estimatio foud by Putam is show below: Effort = D 3 t (4) d Where, D is a parameter called mapower build-up which rages from 8 (etirely ew software with may iterfaces) to 7 (rebuilt software). Combiig the above equatio with the software equatio, we obtai the power fuctio form: Effort D 4 / 7 9 / 7 9 / 7 = ( E ) S (5a) Ad t D / 7 3 / 7 3 / 7 d = ( E ) S Putam's model is also widely used i practice. (5b) B. No-algorithmic Methods The major o-algorithmic methods are discussed as uder: Expert Judgmet method ivolves cosultig oe or more experts. The experts provide estimates usig their ow methods ad experiece. Expert-cosesus mechaisms such as Delphi techique or PERT will be used to resolve the icosistecies i the estimates. A modificatio of the Delphi techique proposed by Boehm ad Fahquhar [] seems to be more effective. Parkiso's priciple work expads to fill the available volume [6], the cost is determied (ot estimated) by the available resources rather tha based o a objective assessmet. This method is ot recommeded as it may provide very urealistic estimates. Also, this method does ot promote good software egieerig practice. May other models such as Price-S [9] ad Rayleigh probability distributio [4] have also bee used i practice. III. METHODOLOGY PROPOSED The followig steps of the methodology are proposed for modelig of effort estimatio: A. Data Collectio First, Survey of the estig s of Effort Estimatio is to be performed ad Secodly, Historical Data beig used by various estig models for the cost estimatio is collected. B. Statistical ig for Effort Estimatio The followig statistical modelig approaches are evaluated for data fittig of effort estimatio data ad the results are compared i terms of RMSE values: Liear icludes costat ad first order terms oly. Let there are sixtee iputs depicted as x to x.the Equatio of Liear ca be writte as: y = b + bi (6) Where y will give the expected values of the respose variable ad b i for i =,.. is the parameters to be estimated. Pure-Quadratic icludes costat, liear ad squared terms. The Equatio of Pure-Quadratic ca be writte as: y = b + bi + bii (7) Where y is output; x to x are iput parameters ad other terms are fittig parameters C. Neuro-Fuzzy, Fuzzy- ad other ig Approaches The followig modelig approaches are used for effort dataset: Neuro-Fuzzy [] 93

3 Fuzzy- Hybrid Halstead Walsto-Felix Bailey-Basili Doty Based [] The based model developed i [] is used for the compariso. I case of the Neuro-fuzzy system the first Sugeo Based Fuzzy Iferece System is desiged that eeds the iitializatio of the Membership Fuctio of the differet attributes ad liear Membership Fuctio for the output ad deducig the fuzzy rules from the data. That Sugeo Based fuzzy iferece system is traied with the eural Network usig the hybrid traiig algorithm. I the forward pass the Backpropagatio learig algorithm ad i the backward pass the LMS learig algorithm is used to update the o-liear ad liear parameters of the Neuro-fuzzy system respectively. The differet estig models: Halstead s, Walsto- Felix, Bailey-Basili ad Doty are also used for the compariso of results. The compariso of the results is made o the basis of: Mea Magitude of Relative Error (MMRE) Root Mea Square Error (RMSE) PRED(3) PRED() RMSE is frequetly used measure of differeces betwee values predicted by a model or estimator ad the values actually observed from the thig beig modeled or estimated. It is just the square root of the mea square error as show i equatio give below: ( ) + ( ) ( ) a c a c a c (8) The mea-squared error is oe of the most commoly used measures of success for umeric predictio. This value is computed by takig the average of the squared differeces betwee each computed value ad its correspodig correct value. The root mea-squared error is simply the square root of the mea-squared-error. The mea magitude of relative error (MMRE) ca be writte as: where y i represets the ith value of the effort ad ˆy i is the estimated effort. PRED(N) is the third criteria used for the compariso ad this reports the average percetage of estimates that were withi N% of the actual values [3]. PRED(N) reports the average percetage of estimates that were withi N% of the actual values, as show i the followig pseudo code: (9) cout = for(;i<=t;i++) do if MRE.i <= N/ the cout++ fi doe PRED(N) = /T * cout For example, e.g. PRED(3)=5% meas that half the estimates are withi 3% of the actual. IV. RESULTS & DISCUSSION Historical NASA s Effort Dataset [3] for the effort estimatio is collected ad the data is polished so that the same data ca be used for the modelig i MATLAB 7.4 eviromet. The attributes are: aalysts capability, programmers capability, applicatio experiece, moder programmig practices, use of software tools, virtual machie experiece, laguage experiece, schedule costrait, mai memory costrait, data base size, time costrait for cpu, turaroud time, machie volatility, process complety, required software reliability ad lies of source code. I the liear fittig the RMSE value is.79e+3 ad coefficiets of the liear model are:.e+4 * (-.379,.75,.6488,.75,.549, -.9,.466, -.868, -.8,.33,.6, -.4, -.57,.497,.7, -.39,.6) The RMSE value for the liear model is:.79e+3. I the Pure Quadratic fittig the RMSE value is.85e+3 ad coefficiets calculated are:.e+5*(.747,.944, -.,.53,.577,.783, -.384, -.67, -.973,.898,.74,.388, , -.588, -.587,.846,., -.397,.55, -.98, -.93,.687,.,.85,.97,.986, -.665, -.66,.966,.83,.486, -.5,-.) This shows that the pure quadratic fittig is better tha the liear fittig meas the data is of o-liear ature. After the statistical fittig the Fuzzy ad Neuro-fuzzy lig approach is experimeted ad the results are compared with the estig modellig approaches. I case of the Neuro-fuzzy approach first the sugeo-based Fuzzy Iferece system is desiged. I order to trai the Sugeo FIS, Adaptive Neuro-Fuzzy system [] is created that makes use of the Sugeo FIS Structure as show i Fig.. The followig the structure parameters of the Neuro-fuzzy system: Number of odes: 55 Number of liear parameters: 68 Number of oliear parameters: 8 Total umber of parameters: 96 Number of traiig data pairs: 63 Number of checkig data pairs: Number of fuzzy rules: 4 The NF system is traied for 5 epoch ad tested. The plot of data idex v/s expected output ad actual output is show i Fig.. 933

4 TABLE I (B) RESULTS OF THE DIFFERENT MODEL USED FOR THE EFFORT DATASET Performace Criteria Fuzzy- Neuro- Fuzzy Halstead s Used Walsto- Felix Bailey- Basili Doty Based MMRE RMSE PRED(3) Fig. Structure of the NF Iferece System for Effort Dataset PRED() Fig. Testig Results of Traied Neuro-Fuzzy System Project-wise Results of the differet used for the Effort dataset is show i Table I (a). The results of Fuzzy- based hybrid model, Neuro-Fuzzy, Halstead, Walsto-Felix, Bailey-Basili, Doty ad based are show i Table I (b). The performace criteria take are MMRE ad RMSE. The results shows that the Neuro-fuzzy have the lowest MMRE ad RMSE values i.e ad.5 respectively for the testig data. The PRED(3) ad PRED() values of Neuro-fuzzy are mamum amog all the models that are beig compared i.e. ad respectively. TABLE I (A) PROJECT-WISE RESULTS OF THE DIFFERENT MODEL USED FOR THE EFFORT DATASET Used Actual Effort Fuzzy- Neuro- Fuzzy Halstead Walsto- Felix Bailey- Basili Doty Based The Neuro-fuzzy shows the best results as compared with the Fuzzy- ad other estig s that are beig used for the Effort Predictio. V. CONCLUSION I this study Statistical s, Fuzzy- ad Neuro- Fuzzy Iferece Systems are experimeted to estimate the software effort for projects. The performaces of the developed models is tested o NASA software project data preseted i [3] ad results are compared with the Halstead, Walsto-Felix, Bailey-Basili, Doty ad Geetic Algorithm Based models as reowed algorithms metioed i the literature. O compariso, the results shows that the Neurofuzzy has the lowest MMRE ad RMSE values as error values of the developed system durig testig i.e ad.5 respectively. Durig testig the PRED(3) ad PRED() values of Neuro-fuzzy are mamum amog all the models that are beig compared i.e. ad respectively. Hybrid Fuzzy- model, Liear Statistical s ad Pure Quadratic Statistical are also developed. But the Neuro-fuzzy shows the better results as compared with the Fuzzy- based hybrid Iferece System, Liear Statistical s ad Pure Quadratic Statistical for the Effort Predictio. Hece, the developed Neuro-Fuzzy model is able to provide good estimatio capabilities. It is suggested to use of Neuro-Fuzzy techique to build suitable model structure for the software effort. REFERENCES [] Alaa F. Sheta, "Estimatio of the COCOMO Parameters Usig Geetic Algorithms for NASA Software Projects", Joural of Computer Sciece (): 8-3, 6. [] B. W. Boehm, Software egieerig ecoomics, Eglewood Cliffs, NJ: Pretice-Hall, 98, pp. 5-. [3] J. W. Bailey ad V. R. Basili, A meta model for software developmet resource expediture, i Proceedigs of the Iteratioal Coferece o Software Egieerig, pp. 7 5, 98. [4] C. E. Walsto, C. P. Felix, A method of programmig measuremet ad estimatio, IBM Systems Joural, vol., o., pp , 977. [5] G. Catoe, A. Cimitile, U. De Carlii, A compariso of models for software cost estimatio ad maagemet of software projects, Computer Systems: Performace ad Simulatio, Elisevier Sciece Publishers. [6] G.N. Parkiso, Parkiso's Law ad Other Studies i Admiistratio, Houghto-Miffi, Bosto, 957. [7] L. H. Putam, A geeral empirical solutio to the macro software sizig ad estimatig problem, IEEE Tras. Soft. Eg., pp , July

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