Research and application of estimation method for software cost estimation based on Putnam model

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1 Available online Journal of Cheical an Pharaceuical Research, 014, 6(7: Research Aricle ISSN : COEN(USA : JCPRC5 Research an applicaion of esiaion eho for sofware cos esiaion base on Puna oel Ning Jingfeng 1, Jiang Yan an Yu Honglei 1 1 Changchun Universiy of Technology, Changchun, China Changchun Finance College, Changchun, China ABSTRACT Effecive sofware esiae is he os challenging an he os iporan aciviy in a sofware evelopen projec anageen. Only when using scienific ehos o reasonably an reliably esiae he scale, he aoun of work an cos of he sofware projec, o he people ipleen goo plan an conrol. The paper inrouces several ypical ways of sofware cos esiae, eeply analyses he oel of Puna, uses he exaples o research he scale, he nuber of labors a he peak an he ie of he projec o provie inforaion for anagers o ake posiive ecisions. ey wors: cos of sofware; esiaion; he oel of Puna INTROUCTION Esiaion an cos buge are always ae ogeher, for cos buge is he purpose of esiae, wihou esiae, here is no possible o ake cos buge. In sofware inusry, sofware cos esiae is always an aruous ask[1].esiae of sofware evelopen inclues boh scale an cos esiae. Accoring o he reasonable esiae resul, he paper ses ou feasible objecive, an weighs he cos, scheule an qualiy of sofware, ipleen effecive risk anageen, an provies powerful basis for anagers o ake invesen ecisions[]. The sofware projec esiae runs hrough he whole sofware life evelopen cycle, an also nees coninuous iproveen, planning, review an follow-up[ 4]. Wih he inforaion accuulae, copare he acual aa wih he esiae aa, an iprove he nex esiaion[5]. CLASSIFICATION OF SOFTWARE COST ESTIMATION The earlies sofware cos esiae can be race back o SC (Syse evelopen Corporaion linear oel in he 1960s, wen hrough 40 years of evelopen [6]. Mr.Boeh, he Professor of Souhern California, poine ou, unersaning an conrolling of sofware cos bring us no only ore sofware bu also beer sofware [7]. A presen, soe oesic sofware enerprises also graually pay aenion o he hough an ehos of sofware engineering, an pu hese echnology an ehos ino pracice. China s sofware projec anageen is China's sofware projec anageen is also oving owars sanarizaion an noralizaion, bu sar lae in ers of sofware projec esiaion,for esiaion ehos such as various sofware cos esiaion, esiaion of he aoun of work, an esiaion of funcion poins are only in he saring sage. So i is relaively ifficul o esiae he sofware projec in he sofware inusry, an he esiaion eho of sofware engineering base on experience is sill being aope. The oesic sofware projec esiaion echniques are sill on he original sae o a grea exen. There are any classificaion oels for sofware cos esiaion ehos [8,9], which can be classifie hree ypes fro he poin of wheher using algorih oel: base on algorih oel, no base on algorih oel an he cobinaion of boh ehos. The basic iea of eho base on algorih oel is[10]: o fin he cos affece facors for sofware aoun of work, an juge how i influences on he workloa, o be 617

2 Ning Jingfeng e al J. Che. Phar. Res., 014, 6(7: aiive, uliple or exponenial, in orer o ge opiize oel algorih expression for. The ypical ehosno base on he algorih oel are expers esiaion, analogy esiaion an regression analysis.the cobinaion eho of sofware cos esiaion obviously applies various echniques an analysis ehos in esiaion echniques, which is he ren of sofware cos esiaion, an also he beer selecion ha cobines various esiaion ehos avanages an isavanages, an aaps o ifferen esiaion siuaions an eans. Puna esiaion oel is he ynaic an ulivariable esiaion oel of workloa, which is euce fro anpower isribuion of large projec. Puna furher suies he original oel an iproves ehos, an explores he poenial relaions aong various facors by collecing aa. I uses aa ienificaion facor an oel o explain he perforance of sofware projec, an give enough inforaion for he ainisraor o ake ecisions for seeking ore profi. Puna oel cobines any conceps, such as anpower srucure, echniques, environen an process prouciviy. ESTABLISHMENT OF PUTNAM MOEL uring he sofware evelopen projec, alhough he quaniy of probles is unknown an liie, i also nees anpower o solve he probles. Take inicarix of quaniy of probles as oal labor cos. The accuulaive labor cos involve in he projec C (, expresse as an year. C ( is null a he beginning of he projec, an onoonously increases owars he oal labor cos. The change rae of accuulaive labor cos, shows he nuber of en pu ino a rano ie uring evelopen. So he accuulaive cos a ie is shown as: C( 0 ( ζ ζ (1 Suppose a any given ie, he opiize nuber of en pu ino he projec ea is in irec proporion o he nuber of probles o be solve, an hen ge he following equaion: C( k[ C( ] ( Aong which k is proporionaliy coefficien. Because uring he life cycle of he projec, one group of engineers are graually increase heir efficiency, he concep of projec ea suy is inrouce. The growh ren of solving probles abiliy is also a favorable facor for iproving work efficiency, which is shown as funcion p (. So he change rae of accuulaive labor cos can be suppose o be in irec proporion o p (. This assupion is escribe hrough he following ifferenial equaion of firs orer. C( p( [ C( ] ( For his equaion fro he beginning of he projec, i.e., 0 following equaion: C( 1 exp p( τ τ 0 (4 Separae variables an ake replaceen of u( C( hen: C Log 0 P( τ τ Furher assupion on he learning funcion irec proporion o ie, his linear relaionship ay be expresse as follow: P( a (5 C o ge any given ie inegraion, ge he, hen ge u C(, when u 0 (, p(, os of he expression of learning funcions are linear, i.e., in Suppose paraeer a is a posiive nuber. By inegraion on he equaion (4, a any given ie, he forula of 618

3 Ning Jingfeng e al J. Che. Phar. Res., 014, 6(7: accuulaive labor cos C( becoes: C( [1 exp( a ] (6 By accuulaive cos funcion By accuulaive cos funcion agains ie ifferenial, he nuber of labor of he projec can be calculae, naely, anpower funcion: ( a exp( a (7 This funcion represens Rayleigh curve, a he beginning of he projec ( 0, is value is 0. Then increase owar he eployen peak irecion, afer he peak, graually reuce o zero. See Figure 1 Fig. 1: Paraeer a s effec on he labor isribuion Fro he above Figure we can see: paraeer a has he iension of inverse square of ie, which plays an iporan role in eerining of labor peak. The larger a value is, he earlier he occurrence ie of peak, an he seeper he labor curve is. erive anpower funcion agains ie, o ge is zero value, hen he relaion beween peak hour 1 a an a can be foun. (8 ESTIMATION OF LABOR PEA uring easureen of large sofware evelopen projec, he anpower isribuion curve has axiu value, which occurs a he ie very near elivery ie, before ha ie, anpower use in specificaion escripion, esign, coing, es an qualifie verificaion; afer ha, anpower ean is use in ainenance, oificaion an oher sie work. Accoring o equaion (8, he labor peak ie is relae o a. Accoringly, acan be obaine fro he peak ie as follows: a 1 So he nuber of en pu ino he projec a peak ie is eerine by using Noren/Rayleigh oel. By replaceen, equaion (7becoes: (9 1 o replace a in 619

4 Ning Jingfeng e al J. Che. Phar. Res., 014, 6(7: ( exp( (10 When, labor peak can be obaine, which is also expresse in 0. So he expression on labor peak of projec is expresse in: 0 e (11 Aong which is he oal projec cos in he uni of an year, he base nuber of naural logarih, 0 is he nuber of en eploye a he peak. is he elivery ie in he uni of year, e is IFFICULTY ESTIMATION A ifficul projec ainly refers o a very urgen ask which nees o arrange a nuber of persons o work concurrenly, hus resuling in he evelopen plans ifficul o conrol. Copare wih he projec no quie ifficul, ifficul projec is ore sensiive o isurbance. Generally for he projec wih relaively longer ie lii, he anpower isribuion curve is relaively fla. The Noren/Rayleigh funcion agains ifferenial of ie ges he following equaion: ' ( a(1 a exp( a When 0 ( a ' The rae of is calle he egree of ifficuly (also known as he coefficien of ifficuly, expresse in : ( uni: an/ year This relaional expression shows, when here are ore labor eans or aybe ie arrangeen is igh(he value of is sall, he evelopen of projec is ore ifficul. Accoring o forula (11 0 e Fro egree of ifficuly, we can see he ifficul projec norally ean he relaively higher labor peak nuber in given evelopen ie. LABOR INCREMENT ESTIMATION The labor increen is also calle labor accelerae spee. I shows he projec s bearable an progressive anpower applie axiu allowable growh rae. relaive o he erivaive of ' ( ' ( ( 年 In fac 1 ' ( an : is always uch saller han ' (. (1 (14 The egree of ifficuly relaive o he erivaive of ie plays an iporan role in escribing sofware evelopen If he projec scale increases,he evelopen ie also increases o such exen,hus aking (1 60

5 Ning Jingfeng e al J. Che. Phar. Res., 014, 6(7: paraeer focuses on a value an reain he value,which igh be 8, 15 or 7. This paraeer is expresse in 0 as: ( an 0 /year (an/year (15 The value of 0 an he evelope sofware propery have he following relaions: new sofware has any inerfaces an is ineracive wih oher sofware syses. new an inepenen syse. sofware re-esablishe fro he exising sofware. Paraeer 0 is calle labor increen, which is also calle labor accelerae spee. 0 he shape of he labor isribuion curve. The bigger 0 labor growh accelerae. ACCUMULATIVE LABOR COST ESTIMATION efine accuulaive labor cos: C( [1 exp( a ] has grea influence on is, he seeper he labor isribuion curve is, he faser he Accoring o forula (6 Aong which C (wih an year as uni gives he labor cos fro he beginning of he projec o ie, is he oal labor cos of sofware life cycle (wih an year as he uni, while a is Noren coefficien efine by Puna, i equals 1 C [1 exp( (see equaion 9, so he accuulaive labor cos in he whole cycle is expresse as: ( ] (16 While he accuulaive labor cos in evelopen sub-cycle is expresse as: C ( 1 exp( ] [ 0 uring he perio of sofware projec, he accuulaive cos increases fro zero, hen one well known S-curve (see Figure labor coss in elivery ie in he anageen of he projec can be obaine in equaion (6 by replaceen of 1 C 9 e ( 1 0. : (17 (18 Fro his equaion we can see, he evelope sofware syse once elivere o he arge processor, on he iniial operae sage, i only spens 9% of he oal cos, he res labor aoun uses in accepance es, ainenance an oificaion aspecs, ec. EFINE SOFTWARE EQUATION The efiniion of wo iporan paraeers of Sofware projecs an see how labor change wih he ie, now iscuss he relaions beween an fin he relaions beween labor cos an evelopen ie, an by eans of Rayleigh funcion, an sofware proucs, i.e., o an he elivere sofware scale S. Fro he relaions beween prouciviy an egree of ifficuly, i woul ge he following equaion: 61

6 Ning Jingfeng e al J. Che. Phar. Res., 014, 6(7: Pr C n (19 Pr is prouciviy, is he efine egree of ifficuly, echnical coniion in he aa collecing environen. Cn is a proporional consan, which epens on he Cos Fig. : Accuulaive labor cos While he egree of prouciviy is he rae of inpu o oupu: Inpu Pr Oupu Se prouciviy Pr is he proporion of he oal elivere source coes consiue prouc an he oal labor neee o prouce hese source coes: Pr The size of elivere source The oal labor of coe coe Toal labor inclues labor cos spen fro he beginning of he projec o he elivery ie we ge: ( 0. C 9 (0. Fro equaion (18, Thus, a ie, he elivere sofware size is S, use he source progra saeen nuber as he uni expresse in: S Pr 0. 9 (1 Fro equaions (19an(1, we ge: S n 0.9C Accoring o equaion(1,we ge: S 0.9C n afer syseizing, we ge: 1 4 S 0.9Cn ( Use coefficien E o replace 0.9C n, we ge he sofware equaion as follows: 6

7 Ning Jingfeng e al J. Che. Phar. Res., 014, 6(7: S E 1 4 ( E becoes environen facor, i eerine by he echnical coniion in he proucion environen. The ore efficien of he eho an ool of sofware evelopen, he ore skillful he analyss an prograers an heir ainisraors, he higher he environen facory E is. is he labor cos in he coplee perio (wih an year as he uni, uni. is evelopen ie (wih year as he uni, S is he scale of he sofware (wih NCSS as he APPLICATION CASE Take secon-han car raing syse as he exaple. riven by he sae secon-han car policies an logisic prooion policies, he secon-han car arkes also have increase graually, in orer o grasp an conrol he sae secon-han car price ren an he region ifferences, he eans for he secon-han car service plafor facing he whole counry an wih coplee funcions are also increasing. Because he secon-han car arke is characerize as one car one price, one place one price, one person one price, an one ie one price, how o juge a car s acual qualiy ruly an correcly is he inheren proble o increase he secon-han car arke close rae o be solve, seconly, how o coplee car ransacion in ifferen places convenienly, fas, an wih high qualiy o increase he secon-han car arke close rae is he key proble o be solve. This projec is a projec of a cerain Changchun secon-han car raing copany, ainly realizing he funcions such as he anageen of secon-han car, iniviual user s anageen, enerprise user s anageen, an websie anageen. For is cos esiaion, relaively aure Puna oel esiaion eho is use. Accoring o he previous projec experience, he esiae scale of his projec is 9000NCSS, no ore han 18000NCSS (Non-coen source saeen, so i belongs o sall projec, which is evelope uner he coniion of environen facor 100. This sofware is an inepenen aa processing ype progra, an is labor acceleraion evelopen sub-cycle: The sofware equaion given by equaion ( over E an he hir power of which ge: S E 4 The righ sie uliplies an ivies equaion: S E 7 0 To solve he evelopen ie 1 7, i woul ge: an replaces eerine he by labor acceleraion 0, we ge he following 1 S 0 E This 0 value correspons o he shores evelopen ie, for he above given value, i woul ge he shores evelopen ie: (in 1. 6year,his value also approxiaely equals o 1 year an 7 onhs. Esiae he labor neee in he coplee perio. Fro equaion (15 o solve, i woul ge: 0 6.7an year Fro he egree of ifficuly efine by equaion (1, i woul esiae: 4.5an/ year an/year Seen fro he above, accoring o he curren pracical experience of our ea, prograing asks iniially increase 6

8 Ning Jingfeng e al J. Che. Phar. Res., 014, 6(7: a he growh rae of wo persons onhly. Huan isribuion of sofware evelopen is a sub cycle of he coplee cycle, i is also Rayleigh funcion, accoring o equaion (10, escribe again as follows: (..exp( 0 0 In he forula, 0 is labor peak hour (uni: year, is he labor cos (uni: an year relevan o he sub-cycle of he prouc evelopen, he anpower spen on he evelopen aciviies of he proucs, sars afer he iniial esign recheck an sops a he syse es an is accepe. Thus i covers he subsyse esign, oule specificaions, esign, coing, es, subsyse es, syse es an accepance. an 0 have he following specific value relaion: k (5 (6 ( an year. 95% of which woul spen on he evelopen perio of Thus i woul ge. Accoring o he accuulaive labor cos expression of he ie given by equaion (17, i is escribe again as follows: C ( Subsiue C ( 1 exp 0 1 exp 0 ino equaion, an ivie by Then base on equaion (6, i woul ge: C ( hus ge: C ( 1 exp( 100% 95% This eans wihin he elivery ie of (7 on boh sies of he equaion, hen i woul ge: (8, 95% of he oal evelopen/projec labor cos has consue away, 5% leaves for he sie insallaion an qualificaion esing expenses. So C ( 9. 9 an year. The res 0.6 any year (7. an onhswoul spen on afer-sales services. Accoring o he above aa, he labor characers use in he evelopen peak hour is calculae. The peak labor ie is given fro equaion (6, so we have: year 6 Subsiue 0 or 7.8 onhs. ino equaion (4, i woul ge: 1 0 ( 0 exp( 0 64

9 Ning Jingfeng e al J. Che. Phar. Res., 014, 6(7: e i.e. 0 So nuber of en in peak labor ie an. Fro he obvious acual consieraion, we hink he nuber of en in he evelopen ea woul increase o 10 wihin 7 onhs afer he projec begins. Fro he above resul,we fin, if he ie perio is shor, firs, he higher he Noren coefficien α value is, he seeper he labor isribuion curve is; seconly, labor peak value forula 0 gives higher value, which is confore wih he forer poin. This eans he ore ifficul he projec is, he ore ean o concenrae ore persons, an he earlier he concenrae ie is. The iplici eaning is, a very urgen ask woul nee o arrange ore persons o work concurrenly, an aking he evelopen plan no easy o conrol. Copare wih no very ifficul projec, ifficul projec is ore sensiive o he inerrupion, he slighes eans change or α 1 response resul in anageen will cause he ecrease of, i.e., for he projec wih relaively longer ie lii, he anpower isribuion curve is relaively fla. Naurally, if he anpower ean is higher, his effec is ore obvious. ESTIMATION RESULT AN COMPARATIVE ANALYSIS Copare he esiaion resul wih he acual resul of he case using Puan oel as follow, he accuulaive labor cos of he evelopen sub-cycle is 9.9 an year, while he acual one is 1 an year; he esiaion resul of labor ie a he peak is 7.8 onhs, while he acual ie sars in he 10h onh afer he projec begins; he esiaion resul of he labor nuber of people a he peak is 10, he acual resul is 8. The acual value is basically near he esiae value. In he exising sofware esiaion ehos, using he aforeenione expers esiaion ehos an analogy an oher ehos, can also esiae he sofware projec. Bu he exper esiaion ehos ainly epen on he exper o ake he iniviual jugen by preicing he objec fuure evelopen ren an coniion; esiaion is able o be ae accoring o he specific sofware projec saus, wih sronger perinence, i only epens on he esiaion expers knowlege an experience, wih ore subjeciviy an lack of objeciviy, in acual work, for sofware projec of he sae ype or even he sae sofware projec, ifferen expers igh evaluae obvious ifferen resuls. While uring he esiaion of sofware by analogy eho, i is he scale esiaion by he coparison beween new projec an hisory projec, which is suiable o evaluae soe projecs of equivalen applicaion fiels, environen an coplexiy wih hisory projec, he precision of is esiaion resuls epen on he inegriy an correcness of he hisory projec aa. CONCLUSION Puna fin ha he resuls ge fro projecs of he sae ype basically obey he noral isribuion, hen ake linear reaen, hen ge relevan benchark graph, using hese graphs, evelopen capaciy of ifferen sofware enerprises can be copare, which is very useful for he biing an progress esiaion of projec. The paper collecs relevan aa, akes eeper analysis on Puna oel, an esiaes he acual projec in secon-han car inusry. uring using he oel esiaion, he paper reveals he relaions aong he source progra coe lengh of sofware projec, he evelopen ie of sofware an he workloa, wih very iporan heoreical eaning, can help he sofware ainisraor o ipleen effecive risk anageen an ecision. The sofware projec esiaion ehos researche in he paper have verifie in any sofware projec, an he resuls show ha hese ehos have higher reliabiliy an beer applicaion poenial. Bu Puna oel also has he properies such as a relaively low correcness, no reflecing he sofware prouc, projec, paricipans, an sofware an harware resources. In he fuure esiaion process of sofware projec using Puna oel, collecing an accuulaing ifferen hisorical aa relae o cos esiaion, cobine by he saisics an analysis of he aa o ge he oel paraeer suiable o he organizaion iself. Sofware cos esiaion is base on probabiliy oel, hus i is very ifficul o prouce precision, bu if proviing goo hisorical aa an using syseaic echnology, beer resul can be obaine, copleely correc esiaion of sofware cos sill nees he coninuous effors fro he broa science researchers. Acknowlegens The auhors wish o hank he Jilin Provincial Eucaion eparen The 1h Five Year Plan science an echnology research projec Research an applicaion base on sofware cos esiaion (Projec No.: JJHZi [014] No.144, uner which he presen work was possible. e 65

10 Ning Jingfeng e al J. Che. Phar. Res., 014, 6(7: REFERENCES [1]T. C. Jones.Esiaing Sofware Coss, New York:McGraw Hill, []B. W. Boeh, R. E. Fairley. Sofware esiaion perspecives, IEEE sofware,v.17, n.6, pp.-6, 000. []B. Loneix Cos Esiaion for Sofware evelopen.reaing, MA:AiSon Wesley, [4]R. E. Fairle. Recen avances in Sofware esiaion echniques, In:Proc.199 In l Conf.Sofware Engineering, New York, ACM Press, pp.8-91, 199. [5]B. W. Boeh. Sofware cos esiaion wih COCOMO.Englewoo Cliffs, NJ:Prenice_Hall, 000. [6]Boeh BW, Valeri R. Achieveens an challenges in sofware resource esiaion.technical Repor, No.USC-CSE , 005. hp://sunse.usc.eu/publicaions/techrpts/005/usccse005-51/usccse pf [7]Boeh BW. Unersaning an conrolling sofware coss. IEEE Trans. on Sofware Engineering,v.14, n.10, pp , [8]R.Agarwal, M.uar, Yogesh, e al.esiaing sofware projecs.acm SIGSOT Sofware Engineering Noes, v.6, n.14, pp.60-67, 001. [9]B. W. Boeh. Sofware Engineering Econoics, Englewoo C1iffs,NJ:Prenice-Hall, [10]Boeh BW, Valeri R. Achieveens an challenges in sofware resource esiaion, Technical Repor, No.USC-CSE , 005. hp://sunse.usc.eu/publicaions/techrpts/005/usccse005-51/usccse pf 66