Computer Scece Systems Bology Reserch Artcle Artcle Ocheg d Mwg, 204, 7:3 http://d.do.org/0.472/csb.0004 Ope Ope Access Softwre Sze Estmto Icremetl Softwre Developmet Bsed O Improved Prwse Comprso Mtrces Peter Ocheg * d Wweru Mwg 2 Deprtmet of Mthemtcs d Iformtcs, Tt Tvet Uversty, Key 2 Isttute of Computer Scece d Iformto Techology, Jomo Keytt Uversty of Agrculture d Techology (JKUAT), Key Abstrct Softwre szg s crucl ctvty mog the tsk of softwre mgemet. Work plg d subsequet estmto of effort requred s bsed o the estmte of the softwre sze requred. Softwre developers re relzg the eed to speed up the developmet process to respod to customers eeds. Ths hs resulted dopto of rpd developmet methods d dopto of gle methodologes. Icremetl method of softwre developmet hs bee dopted s oe of the methods to speed up softwre developmet. Ufortutely there s lttle work tht hs bee doe to develop cler frmework to estmte softwre sze d cost cremetl softwre developmet evromet. Ths reserch work proposes the use of Prwse Comprso mtrces frmework to estmte sze d cost cremetl softwre developmet d evlute the prwse comprso frmework gst Putm s sze estmto model to determe f t produces more ccurte results terms of estmto of sze reltve to ctul sze. Keywords: Prwse; Judgmet mtr; Icremetl estmto Itroducto Before developmet of y softwre, t s vtl for proper plg to be coducted. Proected sze of the softwre to be developed s mportt vrble tht s eeded by softwre proect mgers to estmte the cost of the softwre, umber of people to llocte to the developmet of the softwre d the umber of moths or durto the developmet lfecycle wll tke. Sce softwre sze estmte pror to developmet s o-estece or bstrct, t eeds epereced hum udgmet to estmte the sze of the softwre pror to developmet. The de of usg hum eperece d udgmet fts well the feld of Hum-cetered computg (HCC). I these stges most of the requred formto s ot vlble. To help them ths dffcult tsk, predcto models d the eperece of pst proects re fudmetl. Softwre sze metrcs ply sgfct role to the success of ths tsk. Ufortutely the estg softwre sze estmto models stll produce sze estmtes whch hve bee blmed for softwre developmet flures. The populr computg lterture s wsh wth stores of softwre developmet flures d ther dverse mpcts o dvduls, orgztos, d socetl frstructure. Ideed, cotemporry softwre developmet prctce s regulrly chrcterzed by ruwy proects, lte delvery, eceeded budgets d reduced fuctolty d questoble qulty tht ofte trslte to ccelltos, reduced scope d sgfct rework crcles []. The et result s ccumulto of wste typclly mesured fcl terms (lwys bllos of dollrs) [2]. The Stdsh Group [3] mkes dstcto betwee fled proects d chlleged proects. Fled proects re ccelled before completo, ever mplemeted, or scrpped followg stllto. Chlleged proects re completed d pproved proects tht re over budget, lte, d wth fewer fetures d fuctos th tlly specfed. Most orgztos re costtly serchg for wys to mprove ther proect mgemet prctce d reduce the lkelhood of flures d the degree to whch ther proects re chlleged. Typcl proects etl blcg ct betwee the trple costrts of budget, schedule, d scope. Trdeoffs d dustmets re therefore mde by restrctg, ddg to, or dustg the cost, tme, d scope ssocted wth proect. Ideed the trdtol trgle proect mgemet s sd to be cocered wth fdg blce betwee cost, tme, d scope s show Fgure. For emple, the more tht s requested terms of scope (or rgubly eve the performce or the qulty), the more t s lkely to cost d the loger the epected durto. If the clet eeds to hve cert performce delvered very rpdly, ths wll crese the cost due to the eed to work fster d hve more people volved the developmet. The more fetures epected from system, the hgher the cost d the loger the epected durto. Coversely, f the costs eed to be kept to mmum, oe my eed to cosder the essetl Cost Scope Tme Fgure : Trdtol trgle proect mgemet. *Correspodg uthor: Peter Ocheg, Deprtmet of Mthemtcs d Iformtcs, Tt Tvet Uversty, Key, Tel: 25472096554; E-ml: oepeters@gml.com Receved Mrch 4, 204; Accepted Aprl 5, 204; Publshed Aprl 8, 204 Ctto: Ocheg P, Mwg W (204) Softwre Sze Estmto Icremetl Softwre Developmet Bsed O Improved Prwse Comprso Mtrces. J Comput Sc Syst Bol 7: 079-088. do:0.472/csb.0004 Copyrght: 204 Ocheg P, et l. Ths s ope-ccess rtcle dstrbuted uder the terms of the Cretve Commos Attrbuto Lcese, whch permts urestrcted use, dstrbuto, d reproducto y medum, provded the orgl uthor d source re credted. ISSN: 0974-7230 JCSB, ope ccess ourl Volume 7(3)079-088 (204) - 079
Ctto: Ocheg P, Mwg W (204) Softwre Sze Estmto Icremetl Softwre Developmet Bsed O Improved Prwse Comprso Mtrces. 7: 079-088. do:0.472/csb.0004 performce, or the overll scope, d compromse there. My mgers quckly dscover tht the trgle s ot fleble. I order to ddress the chllege. I order to ddress lck of cler frmework of softwre sze estmto ths pper proposes to develop softwre sze estmto frmework for cremetl developmet evromet usg prwse comprso mtr Lterture Revew I geerl sze estmtes of pplcto s preseted s les of codes (LOC) or fucto pots (FP). There re techques tht c be ppled to covert fucto pots to les of code for specfc lguge, d vce vers. Oe of the best techques used to do ths s clled bckfrg techque [4]. Ths pper wll focus o the methods usg LOC sce our ew methodology lso uses LOC, ths wll mke comprso betwee the methods esy. Lwrece H. Putm LOC Estmto A SLOC estmte of softwre system c be obted from brekg dow the system to smller peces d estmtg the SLOC of ech pece. Putm suggests tht for ech pece, three dstct estmtes should be mde [5]: Smllest possble SLOC Most lkely SLOC m Lrgest possble SLOC b Putm suggested tht three to four eperts mke estmte of, b, c for ech fucto. The the epected SLOC for pece E c be computed by pplyg bet dstrbuto s show equto (.0) + 4m+ b E = (.0) 6 The epected SLOC for the etre softwre system E s smply the sum of the epected SLOC of ech fucto s show equto (.) E = = E (.) where s the totl umber of peces. A estmte of the stdrd devto of ech of the estmtes E c be obted by gettg the rge whch 99% of the estmted vlues re lkely to occur d dvdg by 6 s show equto (.2). b SD = (.2) 6 stdrd devto of the epected SLOC for the etre softwre system SD s clculted by tkg the squre root of the sum of the squres of stdrd devtos of ech estmte SD s show equto (.3) SD = = SD (.3) where s the totl umber of peces. Therefore the totl softwre sze s epected to le the rge epressed equto (.4) E ± SD (.4) Where E s the estmted sze of the etre system computed s show equto (.) Wth rel eperece ths method c yeld ccurte results [6], though t lso fces crtcsm of the llowed rge of the sze estmte s show equto (.3) beg lrge hece the estmte cot be rrowed dow to gve vlue. Developer opo d prevous proect eperece Softwre cost estmtes re typclly requred the erly stges of the lfe-cycle whe requremets d desg specfctos re mmture. Uder these Codtos, the producto of ccurte cost estmte requres etesve use of epert udgmet d the qutfcto of sgfct estmto ucertty. Reserch hs show tht uder the rght codtos, epert udgmet c yeld reltvely ccurte estmtes [5]. Ufortutely, most epert udgmet-bsed estmtes do ot meet these codtos d frequetly degeerte to outrght guessg. At ts best, epert udgmet s dscpled combto of best guess d hstorcl loges. Developer opo s otherwse kow s guessg. If you re epereced developer, you c lkely mke good estmtes due to fmlrty wth the type of softwre beg developed. How well ths estmtes re, deped o the epertse of the perso gvg the estmte hece t cot be emprclly proved but oly to trust the estmtes. But cse of good eperece by the developer t c yeld good estmtes. Lookg t prevous proect eperece serves s more educted guess. By usg the dt stored the metrcs dtbse for smlr proects, you c more ccurtely predct the sze of the ew proect. If possble, the system s broke to compoets, d estmted depedetly. Cout Fucto Blocks The techque of coutg fucto blocks reles o the fct tht most softwre systems decompose to roughly the sme umber of levels [5]. Usg the formto obted bout the proposed system, follow these steps:. Decompose the system utl the mor fuctol compoets hve bee detfed (Cll ths fucto block, or softwre compoet). 2. Multply the umber of fucto blocks by the epected sze of fucto block to get sze estmte. 3. Decompose ech fucto block to sub fuctos. 4. Multply the umber of sub fuctos by the epected sze of sub fucto to get secod sze estmte. 5. Compre the two sze estmtes for cosstecy. Compute the epected sze of fucto block d/or sub fucto wth dt from prevous proects tht use smlr techologes d re of smlr scope. If there re o prevous developmets o whch to bse epected szes, use the vlues 4.6 KSLOC d 4.6 KSLOC for the epected sze of fucto blocks d sub fuctos respectvely. These vlues were preseted by Gffey [4] s resoble szes for erospce proects (rel-tme commd d cotrol systems). It hs the dsdvtge tht t requres tht oe s well kowledgeble o the softwre to be developed order to decompose t to blocks d sub fuctos. Fucto Pot Alyss Fucto pots llow the mesuremet of softwre sze stdrd uts, depedet of the uderlyg lguge whch the softwre s developed. Isted of coutg the les of code tht mke up system, cout the umber of eterls (puts, outputs, qures, d terfces) tht mke up the system. ISSN: 0974-7230 JCSB, ope ccess ourl Volume 7(3)079-088 (204) - 080
Ctto: Ocheg P, Mwg W (204) Softwre Sze Estmto Icremetl Softwre Developmet Bsed O Improved Prwse Comprso Mtrces. 7: 079-088. do:0.472/csb.0004 There re fve types of eterls to cout:. Eterl puts- dt or cotrol puts (put fles, tbles, forms, screes, messges, etc.) to the system 2. Eterl outputs- dt or cotrol outputs from the system 3. eterl qures--i/o queres whch requre respose (prompts, terrupts, clls, etc.) 4. Eterl terfces- lbrres or progrms whch re pssed to d out of the system (I/O routes, sortg procedures, mth lbrres, ru-tme lbrres, etc.) 5. Iterl dt fles-groupgs of dt stored terlly the system (ettes, terl cotrol fles, drectores) Apply these steps to clculte the sze of proect:. Cout or estmte ll the occurreces of ech type of eterl. 2. Assg ech occurrece complety weght 3. Multply ech occurrece by ts complety weght, d totl the results to obt fucto cout (Tble ). 4. Multply the fucto cout by vlue dustmet multpler (VAM) to obt the fucto pot cout. VAM = 4 = v 0.0+ 0.065 Where V s rtg of 0 to 5 for ech of the followg fourtee fctors (). The rtg reflects how ech fctor ffects the softwre sze.. dt commuctos 2. dstrbuted fuctos 3. performce 4. hevly used opertol cofgurto 5. Trscto rte 6. O-le dt etry 7. desg for ed user effcecy 8. O-le updte of logcl terl fles 9. comple processg 0. reusblty of system code. stllto ese 2. opertol ese 3. multple stes 4. ese of chge Assg the rtg of 0 to 5 ccordg to these vlues: 0 - fctor ot preset or hs o fluece - sgfct fluece 2 - moderte fluece Descrpto Low medum Hgh eterl puts 3 4 6 eterl outputs 4 5 7 eterl qures 3 4 6 eterl terfces 5 7 0 terl dt fles 7 0 5 Tble : Complety weghts re. 3 - verge fluece 4 - sgfct fluece 5 - strog fluece Fucto pot lyss s etremely useful for the trscto processg systems tht mke up the morty of MIS proects. However, t does ot provde ccurte estmte whe delg wth commd d cotrol softwre, swtchg softwre, systems softwre or embedded systems. Prwse comprso mtr sze estmto frmework I 977, Sty [7] rgued tht lke physcl mesuremet scle wth zero d ut to pply to obects, we c lso derve ccurte d relble reltve scles tht do ot hve zero or ut by usg our uderstdg d udgmets tht re the most fudmetl determts of why we wt to mesure ythg [7,8]. He showed tht AHP (Alytc Herrchy Process) c be used to solve the Mult Crter Decso Mkg (MCDM) problem. MCDM s referrg to mkg decso the presece of multple crter. Zhed [9] summrzes the orgl AHP procedure by Sty [7,8] to four phses:. Brek the decso problem to herrchy of terrelted problems. 2. Provde the mtr dt for pr wse comprso of the decso elemets. 3. Usg Egevector Method (EV) s prortzto method. 4. Aggregte the reltve weghts of the decso The most tegrl prt of Alytcl Herrchcl Process (AHP) s prwse comprso mtr. A prwse comprso mtr provdes forml, systemtc mes of etrctg, combg, d cpturg epert udgmets d ther reltoshp to logous referece dt (hstorcl dt ) [6]. Bozok gves more detled descrpto of hs pproch hs pper [5]. Usg prwse comprso mtr to estmte softwre sze cremetl developmet requres epert s udgmet o cremets reltve sze compred to oe other. The effectveess of ths pproch s supported by epermets tht dcte tht the hum md s better t detfyg reltve dffereces th t estmtg bsolute vlues [9]. My dustmets hve bee mde to the orgl AHP procedure tht ws proposed by Sty [7] 977 by dfferet uthors. Ths reserch work therefore teds to use some of these modfctos d further dpt t order to ft t the estmto of softwre sze d cost cremetl developmet. Alytcl Herrchy Process (AHP) therefore Step : Rk the cremets Rk the cremets from the lrgest to the smllest. A epert rks the cremets to be developed strtg wth the oe he perceves to be the lrgest to the smllest. Though ths step s ot mdtory t lesses work durg comprso. Step 2: Crete prwse mtr Prwse mtr begs wth cretg udgmet mtr to solve the szg problem cremetl softwre developmet. Cretg udgmet mtr volves cretg mtr ( A = ), where s the umber of cremets to be developed order to delver the whole softwre. Note tht cremetl softwre developmet the totl softwre s delvered seres of cremets d demostrted equto (3.) ISSN: 0974-7230 JCSB, ope ccess ourl Volume 7(3)079-088 (204) - 08
Ctto: Ocheg P, Mwg W (204) Softwre Sze Estmto Icremetl Softwre Developmet Bsed O Improved Prwse Comprso Mtrces. 7: 079-088. do:0.472/csb.0004 Totl softwre= = cremets (3.) (The ssumpto equto (3.) s tht ll the cremets re depedet d the glug code.e. etr code for tegrto hs bee fctored. Ths ssumpto wll be ddressed fully ths thess) Elemet, the mtr s estmte of the reltve sze of cremet wth respect to cremet,.e. = k (3.2) Judgmet mtr should hve two crtcl propertes. = / whch mes tht cremet s tmes bgger th cremet, the cremet s / tmes smller th etty ; 2. A cremet s sme sze s tself meg tht ll dgol elemets =. The mplcto of these propertes s tht epert s oly requred to fll the upper or lower trgle of the udgmet mtr. For emple, see Tble 2, whch s udgmet mtr wth estmtes of the reltve softwre sze of four cremets. The vlues Tble 2 row dcte tht cremet I s s bg s cremet, k bgger th cremet K, d l bgger th cremet L. The remg etres re terpreted the sme mer. Tkg emple of four cremets tht re to be developed to delver the whole softwre mely cremet I, cremet J, cremet K, cremet L we crete prwse comprso mtr of =4 (the mtr s depcted here s tble wth the sole purpose of cresg uderstdg d mkg comprso cocept cler to ll). Crete mtr cosstg of cremets ths cse four cremets d epert flls the elemets ccordg to hs or her perceved reltve sze of oe cremet respect to the other (Tble 2). Note tht the epert whe fllg the udgmet mtr s guded by the scle developed by Sty [7] s show Tble 3. The eplto d defto colum of Tble 8 re dpted to ft ths work s show Tble 3. Applyg codto two of the udgmet mtr.e. cremet compred to tself s the sme terms of sze. The dgol of the mtr represeted Tble 2 s flled mkg the upper prt of the mtr fully flled levg oly the lower prt (Tble 4). Usg the frst codto of the udgmet mtr.e = / whch mes tht etty s tmes bgger th etty, the etty Icremet I Icremet J Icremet K Icremet I Icremet J Icremet K Icremet L k l l kl Icremet L k l Tble 2 represets prtlly flled mtr l kl Tble 2: Prtlly flled prwse comprso mtr showg reltve szes of four cremets. Itesty of Defto mportce Equlsze betwee the cremets 2 Wek or slghtsze dvtge of oe cremet over the other 3 Modertesze dvtge of oe cremet over the other 4 Moderte plus 5 Strogsze dvtge of oe cremet over the other 6 Strog plus 7 Very strog or demostrted mportce 8 Very, very strog Eplto Two cremets re equl sze udgmet slghtly fvor oe cremetover other udgmet modertely fvor oe cremetover other udgmet strogly fvor oe cremetover other A cremet sfvored very strogly over other 9 Etreme mportce The evdece fvorg oe cremet over other s of the hghest possble order.-.9 Whe cremets re very close decml s dded to to show ther dfferece s pproprte Tble 3: Modfed Sty scle. Icremet I Icremet J Icremet K Icremet L Icremet I k l Icremet J Icremet K s / tmes smller th etty ; We c ow fully fll the mtr.e. the lower prt of the mtr s flled by cosderg the recprocl codto (Tble 5). Step 3: Etrct rkg vectors Now we hve fully flled mtr tht gves us reltve szes of the cremets tht we wt to develop order to delver the etre softwre. The udgmet mtr s terpreted tht ech colum yelds dfferet rkg vector for the purpose of determg the reltve sze of the four cremets. Ech vector s ormlzed such tht the cremet tht correspods to t (the dgol elemets) s lwys, d t s the referece cremet gst whch ll comprsos the sme colum re mde. Therefore, colum dctes tht cremet J s / s bg s cremet I; cremet K s / k of the sze of cremet I d cremet L s / l of cremet I. Ech colum c be terpreted ths mer. I ths cse the rkg vectors re k l Icremet L Tble 4 represets prtlly flled mtr l kl k l l k Tble 4: Prtlly flled mtr where codto2 s ppled. ISSN: 0974-7230 JCSB, ope ccess ourl Volume 7(3)079-088 (204) - 082
Ctto: Ocheg P, Mwg W (204) Softwre Sze Estmto Icremetl Softwre Developmet Bsed O Improved Prwse Comprso Mtrces. 7: 079-088. do:0.472/csb.0004 Icremet I Icremet J Icremet K Icremet L Icremet I k l IcremetJ Icremet K k Icremet L l ths s the rkg vector from colum oe the respectve rkg k l vector geerted by colum two, three d four re l k kl l respectvely. A mtr of cremets wll yeld four rkg vectors. If the rkg vectors re dfferet whch s lwys the cse the t mes tht there s more estmto ucertty d etr estmto eeds to be doe order to come up wth oe rkg vector clled Prorty vector. A specl cse ests whe udgmet mtr s perfectly cosstet. Ths occurs whe = k ll for,, k If udgmet mtr s ot cosstet the we eed to go to step 4 otherwse we skp to step 5 Step 4: Compute prorty vector There re some methodologes tht hve bee proposed by dfferet uthors to tckle ths problem. The methods re revewed s follows wthout lookg t the stregths d wekesses of ech. Ege vlue methodology l Let A be mtr. A umber λ s kow s Ege vlue of A f there ests o-zero vector v such tht Av= λ v (3.3) I ths cse, vector v s clled egevector of vector A correspodg to Ege vlue λ Ege vlues d egevectors re defed oly for squre mtrces.e. the umber of rows must be equl to the umber of colums the mtr.e. mtr hece works well wth the comprso mtr whch must be squre mtr. For mtr there re Ege vlues for the mtr. I order to solve for prorty vector usg ths method we must clculte the Egevector correspodg to hghest Ege vlue of the udgmet mtr tht s k l l Tble 5 represets the mtr k k l l Tble 5: Fully flled mtr where the two codtos hve bee ppled. l kl Av= λ m v (3.4) Where λ m s the hghest Ege vlue of the udgmet mtr The et step s to test f the pr wse comprso mtr s cosstet ths s cheved by clcultg cosstecy de (C.I). λm C.I = (3.5) Where λ m s the hghest Ege vlue of the udgmet mtr d s the umber of rows or colum I ccordce wth Sty [7] defed the mtr s cosstet whe C.I<0. If C.I.>0..If C.I flls outsde ths rge he suggested lgorthm bout repetg questos to correct the mtr utl t becme cosstet. Normlzto of the Row Sum (NRS) NRS sums up the elemets ech row d ormlzes by dvdg ech sum by the totl of ll the sums, thus the results ow dd up to uty. NRS hs the form: = =, 2... (3.6) ' = w = =, 2... (3.7) ' = ' Arthmetc Me of Normlzed Colums (AMNC) AMNC ws lso clled the Addtve Normlzto method [4]. The ew me s reltvely cler, tht t descrbes ts clculto process. Ech elemet A s dvded by the sum of ech colum A, d the the me of ech row s tke s the prorty. ' =, =,2... (3.8) = ' = w = =,2... (3.9) Normlzto of Recprocls of Colum Sum (NRCS) NRCS tkes the sum of the elemets ech colum, forms the recprocls of these sums, d the ormlzes so tht these umbers dd up to uty, e.g. to dvde ech recprocl by the sum of the recprocls. It s ths form: = =,2... (3.0) = W = =,2... (3.) ' = ' Wthout lookg t the stregth d wekesses of ech methodology tht s beyod the scope of ths reserch the thess chooses to use Geometrc Me becuse of ts smplcty. Geometrc me method The geometrc me s computed s = = (3.2) Where =umber of cremets d Elemet, the mtr s estmte of the reltve sze of cremet wth respect to cremet Ths whe computed for rows for mtr of wll yeld ISSN: 0974-7230 JCSB, ope ccess ourl Volume 7(3)079-088 (204) - 083
Ctto: Ocheg P, Mwg W (204) Softwre Sze Estmto Icremetl Softwre Developmet Bsed O Improved Prwse Comprso Mtrces. 7: 079-088. do:0.472/csb.0004 2. vector = for the mtr Tble 5 we wll compute the vlues of.. vector s show equto (3.3-3.6) = ( ) 4 (3.3) k l 4 = ( k l ) (3.4) 4 = k ( kl ) (3.5) k 4 = ( ) (3.6) l l Ths wll yeld prorty vector of = k l Step 5: Fctor Hstorcl logy It s t ths pot ths reserch work proposes two dpttos to the methodology to pply to the problem of softwre szg cremetl softwre developmet.. Cse where there s oly oe hstorcl logy (referece). 2. Cse where more th two hstorcl loges est. Cse : Oe Hstorcl Alogy Ths s pplcble whe oly oe referece logy ests.e. oly oe referece hstorcl logy for gve cremet c be foud. The frst step ths cse s to clculte m (multpler) s show szeref m = (3.7) ref where ref s the cremet whch hstorcl referece ests The et step s to clculte sze of ll cremets usg m ccordg to equto 3.8 sze sze sze k szel m m = m = m k m l (3.8) Cse 2: Ths occurs where more th two hstorcl loges est Whe oly oe hstorcl logy ests t becomes esy to compute the respectve szes of ll cremets. A complcto therefore rses whe more th oe hstorcl referece ests becuse y referece pcked wll yeld dfferet estmte for gve cremet.ths work therefore proposes the use of Bet dstrbuto to solve ths problem I order to use Bet dstrbuto we wll eed to hve the followg vlues. Optmum estmte (OE) 2. Lest lkely estmte (LLE) 3. Epected estmte (ES) Optmum estmte (OE)=the lrgest estmte for gve cremet geerted by gve hstorcl logy (referece) ths essetlly mes tht the ctul sze of ths cremet s epected ot to eceed ths estmte. Lest lkely estmte=the smllest estmte for gve cremet geerted by gve hstorcl logy (referece) ths mples tht the ctul sze of ths estmte s ot epected to go below ths estmte. Epected estmte=verge of the estmtes for gve cremets lyg betwee lest lkely estmte d most lkely estmte t essetlly mes tht the ctul sze of the cremet hs the hghest probblty of fllg here. I our erler emple lets ow ssume tht refereces est for ll the cremets t s therefore requred tht we clculte multpler geerted by ech referece s show equto (3.9-3.22). For cremet I the multpler geerted by ts referece s sze ref m = (3.9) For cremet J the multpler geerted by ts referece s sze ref m = (3.20) For cremets K the multpler geerted by ts referece s szek ref mk = (3.2) k For cremets L the multpler geerted by ts referece s szel ref ml = (3.22) l Ech multpler wll yeld dfferet estmte for gve cremet d so the chllege wll be to kow whch estmte s the closest to the ctul sze of the cremet. It s for ths reso tht ths thess proposes the use of Bet dstrbuto to solve ths problem. How to compute the estmtes re show Tble 6. For ech cremet ts sze estmte re ts colum. For stce m m cremet I ts sze estmtes re optmum estmte s pcked m k m l s the hghest estmte geerted from the colum d the lowest estmte s pcked s lest lkely estmte, the epected estmte s tke s the verge of the estmtes lyg betwee optmum estmte d lest lkely estmte becuse most weght ted to le here. I the tble bove let s tke Icremet I s our emple d pckg m s the optmum estmte, m s the lest lkely estmte the the epected Multpler used Icremet I estmtes Icremet J estmtes Icremet K estmtes Icremet L estmtes Estmte m m mk ml Estmte 2 m m mk ml Estmte 3 m m k k mk k ml k Estmte 4 m m l l mk l mk l Tble 6: Estmtes of ech cremet. ISSN: 0974-7230 JCSB, ope ccess ourl Volume 7(3)079-088 (204) - 084
Ctto: Ocheg P, Mwg W (204) Softwre Sze Estmto Icremetl Softwre Developmet Bsed O Improved Prwse Comprso Mtrces. 7: 079-088. do:0.472/csb.0004 estmte wll be sumof remg estmtes lyg betweeoe dlle Epected estmte= (3.23) umber of estmteslyg betwee LLE d OE I ths cse epected estmte s estmted s follows m ES = + m k (3.24) 2 Where LLE= m d OE= m Icremet I sze s therefore estmted s OE + 4ES + LLE sze = (3.25) 6 The sze estmtes of other cremets re computed the sme wy. It s worth otg tht the emple used here hs oly four dfferet estmtes for gve cremet ths could be more or less depedg o umber of cremets to be developed to delver system d the umber of Hstorcl loges (refereces vlble). A specl cse est whe oly two refereces est d hece results two estmtes for gve Icremet. If ths scero comes up the verge of the two estmtes s tke the estmte of the cremet. Step 6: Clculte the totl softwre sze At ths pot we hve sze estmtes for ll the cremets d the chllege therefore s to compute the sze of the whole softwre.e. totl sze deoted here s T s. Becuse the totl softwre s beg developed cremetlly there s substtl code tht s wrtte to glue the ew cremet to the lredy developed cremet. The term used for ths the COCOMO models s brekge, becuse some of the estg code d desg hs to be meded to ft ew cremet. Ths reserch wll refer to glug code s cremetl brekge therefore the proected sze of gve cremet fctorg the cremetl brekge s estmted ccordg to equto (3.26) S = sze + csze (3.26) Where S s the cremet sze wth brekge code fctored, sze s the tl cremet sze estmte computed from referece logy ccordg to equto (3.8) or bet dstrbuto depedg o the cse tht rses from step 5. The prmeter c reflects the cremetl brekge (or overhed) ssocted wth the prevous cremet whch s epressed percetge. K sserted tht 20% of the dded code stged d cremetl releses of product goes to chgg the prevous code. Cusumo d Selby reported tht fetures my chge by over 30% s drect result of lerg durg sgle terto. I recet pper the uthors rgued tht the cremetl tegrto brekge c be epected to le rge from 5% to 30%. If c hs vlue of 0.5, t correspods to 5% brekge. I order to smplfy the dscusso, t s ssumed tht ll the code of sze s developed from scrtch.e. code reuse s ot tke to cosderto the cse of code reuse s beyod the scope of ths reserch. Therefore the totl system sze T s s computed ccordg to equto (3.27) T = sze + C sze for =, 2... d =,2... (3.27) s = = Cosderg equto (3.26) equto (3.27) smplfes to T = S (3.28) s = Where T s s the totl softwre sze, S s the et cremet sze s defed equto (3.26) Compred to the LOC d Fucto pot methodology, the prwse frmework hs the dvtge of combg user udgmet, eperece d hstorcl logy to geerte sze estmtes whch re superor. The two methods oly use user eperece eglectg the mportce of hstorcl logy whch s useful predctg sze of future or curret proects. Methodology Dt d dt collecto form The m focus of the reserch ws to fd out f the prwse comprso mtr frmework produces superor sze estmtes of softwre compred to the curretly populr estg Putm s Loc estmto [] d to prove f there s y drect reltoshp betwee ccurcy of the sze estmtes produced by the model used the estmto procedure d the fct tht softwre s delvered o tme or ot.e. f softwre proect meets dedle. I order to ccomplsh these obectves the followg formto ws mog the dt gthered. Lguge used to develop softwre 2. Strt d ed dte of the developmet of the softwre 3. Number of developers llocted for the softwre proect 4. The estmto model used to estmte sze 5. Sze estmte geerted by the model 6. The ctul sze of the softwre upo completo I order to cpture ll these d more formto two questores were desged (The choce of the questore ws pproprte becuse t llowed for the forms to be set to the proect mgers erler whch ebled them to fmlrze themselves wth the cotet before perso meetg ws coducted to gude them s they flled out the forms. Secod questore ws form of tble to represet uflled mtr. Eperts flled the form ccordg to ther udgmet cpturg reltve szes of dfferet cremets tht were developed to delver the whole softwre. The use of more th oe epert ws vtl checkg cosstecy d hve pltform for comprso. Dt source The source for the proect dt for ths reserch ws from JJpeople frm whch s Softwre frm tht develops wde rge of softwres usg JAVA d lso serves trg groud for youg softwre developers who re terested the sme lguge. JJpeople hs ts offces Vcouver, Lodo d ts Afrc brch Nrob. Use of ths frm s dt coveyed severl dvtges to ths reserch. Frst sce oe of the m ms of ths proect s to estblsh the sze of the softwre the frm eclusve use of obect oreted lguge (JAVA) mde the coutg of les of codes (LOC) reltvely esy. Secodly the frm develops wde rge of pplcto mkg the dt dverse ths brodeed the level of terest the results, s opposed to, sy, dtbse composed of oly oe type of pplcto. The frm lso dcted tht they hve used cremetl developmet some of ther pplcto therefore fttg well wth ths reserch. The wllgess of the mgemet to provde dt d dvce o the frmework ws lso good for ths reserch. Dt-Collecto Procedure d proect ttrbutes For ech of the proects, there ws -perso meetg wth the proect mger who flled out the forms. There were two m purposes to ths lbor tesve pproch. The frst gol ws to dscuss ech of the questos to esure tht t s well uderstood d tht ech ISSN: 0974-7230 JCSB, ope ccess ourl Volume 7(3)079-088 (204) - 085
Ctto: Ocheg P, Mwg W (204) Softwre Sze Estmto Icremetl Softwre Developmet Bsed O Improved Prwse Comprso Mtrces. 7: 079-088. do:0.472/csb.0004 of the mgers would swer cosstetly. The secod purpose ws to mpress upo the mgers the mportce of ther prtcpto ths work. Proects selected possessed two ttrbutes: Frst, they were smll to medum sze. The verge proect sze ths study s ust uder 60 KSLOC. The proect selected from the dtbse were lso frly recet wth the oldest developed 2003. All proects ecept proect umber eght hd ot used y prevous code.e. there ws o code reuse. Proect umber eght ws ust selected becuse t ws eclusvely developed cremetlly therefore ftted well wth ths reserch Dt Alyss The focus of ths reserch ws to check how close the sze estmtes geerted by the prwse sze estmto frmework were close to the ctul sze. Therefore error lyss ws doe to check how the sze estmtes from the prwse estmto frmework devtes from the ctul sze. The focus therefore ws o the degree to whch the prwse frmework model s estmted sze (MM EST mtches the ctul sze (MM ACT ). If the models were perfect, the for every proect MM EST = MM ACT clerly, ths ws rrely, f ever, the cse. A smple lyss pproch ws to look t the dfferece betwee MM EST dmm ACT. The problem wth ths bsolute error pproch ws tht the mportce of the sze of the error vred wth proect sze. For emple, o 80KLOC, bsolute error of 0KLOC seemed lkely to cuse serous proect dsrupto terms of stffg, wheres the sme error o 000KLOC proect seemed much less of problem. I lght of ths, Boehm d others hve recommeded percetge error test, s follows: MM EST MM ACT Percetge Error = (4.) MM ACT Ths test elmted the problem cused by proect sze d better reflected the mpct of y error. However, the lyss ths reserch cocetrted o the prwse comprso frmework estmtes verge performce over the etre set of proects. Errors were of two types: uderestmtes, where MM EST <MM ACT ; d overestmtes, where MM EST >MM ACT. Both of these errors c hve serous mpcts o proects. Lrge uderestmtes wll cuse the proect to be uderstffed, d s the dedle pproches, proect mgemet wll be tempted to dd ew stff members. These results Pheomeo kow s Brooks lw: Addg mpower to lte softwre proect mkes t lter [0]. Otherwse productve stffs re ssged to techg the ew tem members, d wth ths, cost d schedule gols slp eve further. Overestmtes c lso be costly tht stff members, otg the proect slck, become less productve (Prkso s Lw: Work epds to fll the tme vlble for ts completo ) or dd so-clled gold pltg, defed s ddtol systems fetures tht re ot requred by the user. I lght of the serousess of both types of errors, overestmtes d uderestmtes, Cote et l. hve suggested mgtude of reltve error, or MRE test, s follows: MRE MM MM EST ACT = (4.2) MM ACT N Where N s the umber of proects used ths reserch By mes of ths test, the two types of errors do ot ccel ech other out whe verge of multple errors s tke, d therefore ws used s the test ths reserch. Grphs were drw to gve good pctorl comprso betwee the ctul sze d the estmtes from prwse frmework usg EXCEL Results d dscusso Proect ttrbutes Proects selected possessed two ttrbutes: Frst, they were smll to medum sze. The verge proect sze ths study s ust uder 600 SLOC. The proect selected from the dtbse were lso frly recet wth the oldest developed 200.All proects ecept proect umber eght hd ot used y prevous code.e. there ws o code reuse. Proect umber eght ws ust selected becuse t ws eclusvely developed cremetlly therefore ftted well wth ths reserch. Tble 7 below compres the ctul sze of the softwres d the estmtes geerted by prwse methodologes. The focus of ths reserch s o the degree to whch the prwse comprso methodology estmtes compre to the ctul sze. If the estmtes mtch the ctul sze perfectly the error mrg ws zero clerly ths ws ot the cse y of the proects Tble 7. The error mrg ws computed to check the devto of the prwse sze estmte methodology from the ctul vlue. Errors were of two types: uderestmtes, Where prwse estmtes<ctul sze d overestmtes, where prwse estmtes>ctul sze. Both of these errors c hve serous mpcts o proects. Lrge uderestmtes hs serous mpcts o proects. Lrge uderestmtes wll cuse the proect to be uderstffed, d s the dedle pproches, proect mgemet wll be tempted to dd ew stff members. These results pheomeo kow s Brook s lw: Addg mpower to lte softwre proect mkes t lter []. Otherwse productve stff s ssged to techg the ew tem members, d wth ths, cost d schedule gols slp eve further. Overestmtes c lso be costly tht stff members, otg the proect slck, become less productve (Prkso s Lw: Work epds to fll the tme vlble for ts completo ) or dd so-clled gold pltg, defed s ddtol systems fetures tht re ot requred by the user [6]. I lght of the serousess of both types of errors, overestmtes d uderestmtes, Cote et l. hve suggested mgtude of reltve error, or MRE Proect No Actul sze (KLOC) Estmte of Prwse Absolute % error MRE methodology (KLOC) error mrg (KLOC) 42. 39.64 2.46 4.75 0.0475 2 72.2 69.49 2.63 3.65 0.0365 3 29.52 28.23.29 3.0 0.030 4 42.82 43. 0.29 0.68 0.0068 5 6.73 7.22 0.49 2.93 0.0293 6 96.22 96.4 0.9 0.097 0.00097 7 67.3 70.0 2.79 4.5 0.045 8 52.76 49.44 3.32 6.29 0.0629 9 46.92 47.0 0.09 0.9 0.009 0 37.54 38.09 0.55.47 0.047 4.723 3.967 0.756 5.3 0.053 2 24.666 24.06 0.605 2.453 0.02453 3 30.464 29.000.464 4.806 0.04806 4 09.659 09.40 0.249 0.227 0.00227 55.968 Me ( X ) 55.36986 Tble 7: Showg error mrg betwee ctul sze d estmtes from prwse methodology. ISSN: 0974-7230 JCSB, ope ccess ourl Volume 7(3)079-088 (204) - 086
Ctto: Ocheg P, Mwg W (204) Softwre Sze Estmto Icremetl Softwre Developmet Bsed O Improved Prwse Comprso Mtrces. 7: 079-088. do:0.472/csb.0004 Actul Estmte Prwse Estmte MRE = Actul Estmte By mes of ths test, the two types of errors do ot ccel ech other out whe verge of multple errors s tke, d therefore ws tke s the test used ths lyss. Ths test elmtes the problem cused by proect sze d better reflects the mpct of y error. From the error mrg t ws oted tht percetge error rged 6.29 to 0.097 whch correspods to MRE of 0.063 d 0.00097 respectvely. It c lso be oted tht s the proect get bgger the methodology ted to geerte more ccurte results. From the results show the tble t s clerly depcted tht wth rel eperece from the developer the estmtes developed by prwse methodology c result more ccurte estmtes especlly lrge proects whch re ssocted more wth mssve rsk s compred to reltvely smller rsks. The respectve mes of ctul sze d estmtes computed from prwse comprso methodology were computed s show Tble 7 d the dfferece ther me s 0.5984 represetg.07% error the estmtes geerted by prwse methodology. Ths clerly shows tht the method geertes close estmtes tht c be reled upo by softwre mgers mkg mor decsos pror to embrkg o the process of softwre developmet. The vlues of the ctul sze of the proects, the sze estmtes geerted by the prwse comprso methodology d the error mrg s show the br chrt below order to gve cler mpresso of how the estmtes re close. As clerly depcted the br chrt below the estmtes geerted by prwse methodology d the ctul sze re so close. The error mrg s lso show the br chrt to gve cler mpresso of how close the estmtes re to the ctul vlue (Fgure 2). Putm s methodology of Loc estmto ws lso used to estmte the sze of the fourtee proects d the results re show Tble 8. The error mrg ws computed to check the devto of the estmtes geerted by the Putm s methodology from the ctul sze. From the error mrg t ws oted tht percetge error rged.64 to.20 wth.64 beg the hghest error percetge devto of the estmte from the ctul sze. Proect No Actul sze (KLOC) SIZE IN KLOC Estmte of Prwse Absolute % error MRE methodology (KLOC) error mrg (KLOC) 42. 45.89 3.79 9.00 2 72.2 76.87 4.75 6.59 3 29.52 32.66 3.4 0.64 4 42.82 45.45 2.63 6.4 5 6.73 6.00 0.73 4.36 6 96.22 200.43 4.2 2.5 7 67.3 69.04.73 2.57 8 52.76 50.99.77 3.35 9 46.92 50.0 3.09 6.59 0 37.54 38.99.45 3.86 4.723 4.900 0.77.20 2 24.666 27.000 2.334 9.46 3 30.464 34.00 3.546.64 4 09.659 5.879 6.22 5.67 55.968 Me ( X ) 58.43707 Tble 8: Comprg ctul sze versus estmtes from Putm s methodology. ACTUAL SIZE COMPARED TO PUTMAN,S METHODOLOGY ESTIMATES AND ERROR MARGIN PROJECT NO ACTUAL SIZE PUTMAN,S ESTIMATES ERROR MARGIN Fgure 3: Br chrt showg comprso of ctul sze, estmtes by prwse methodology d error mrg. PUTMAN ERROR MARGIN COMPAIRED TO PAIRWISE METHODOLOGY I order to show clerly how the estmtes devte from the ctul sze clculto of me s computed Tble 8 d the dfferece the me s 2.46907 whch represet 4.4%. Error the devto s show SIZE IN KLOC PUTMAN ERROR MARGIN PAIRWISE ERROR MARGIN ACTUAL ESTIMATES COMPARED TO ESTIMATES BY PAIRWISE METHODOLOGY AND ERROR MARGIN PROJECT NO Fgure 4: Br chrt comprg error mrgs geerted by the two methods. sze kloc Actul sze prwse methodology Error mrg The vlues of the ctul sze of the proects, the sze estmtes geerted by the Putm s methodology d the error mrg s show the Fgure 3 order to gve cler mpresso of how the estmtes compre to the ctul sze. Cocluso PROJECT NO Fgure 2: Br chrt showg comprso of ctul sze, estmtes by prwse methodology d error mrg. Compred to Putm s methodology the prwse methodology ws superor geertg estmtes of sze cremetl developmet of softwre. As oted Tble 2 devto of the me of estmtes geerted by prwse comprso methodology devted from the ctul sze by.07% whle those of Putm s methodology devted by 4.4% ths therefore cofrms the superorty of the prwse ISSN: 0974-7230 JCSB, ope ccess ourl Volume 7(3)079-088 (204) - 087
Ctto: Ocheg P, Mwg W (204) Softwre Sze Estmto Icremetl Softwre Developmet Bsed O Improved Prwse Comprso Mtrces. 7: 079-088. do:0.472/csb.0004 Proect No methodology. The Tble 9 d br chrt Fgure 4 shows the prwse error mrg s compred to those of Putm s methodology Ackowledgmet Error mrg (Putm s method) 3.79 2.46 2 4.75 2.63 3 3.4.29 4 2.63 0.29 5 0.73 0.49 6 4.2 0.9 7.73 2.79 8.77 3.32 9 3.09 0.09 0.45 0.55 0.77 0.756 2 2.334 0.605 3 3.546.464 4 6.22 0.249 Tble 9: Comprso of error mrgs. Error mrg (prwse method) The uthors would lke to thk Dr Stephe Km d Clvs Oteo for ther cotrbuto to the des d proofredg of ths pper. Refereces. Dlcher D (994) Fllg dow s prt of growg up; the study of flure d the softwre egeerg commuty. Softwre Egeerg Educto 750: 489-496. 2. Lmbert J (986) A Softwre Szg Model. Jourl of Prmetrcs 6: 75-87. 3. Stdsh Group (2000) Chos 2000 (Stdsh, Des, Mss, 2000) 4. Albrecht AJ, Gffey (983) Softwre fucto, source les of code, d developmet effort predcto: A softwre scece vldto. IEEE Trsctos o Softwre Egeerg 9: 639-648. 5. Beedktsso O, Dlcher D (2003) Effort estmto cremetl softwre developmet. IEE Proceedgs Softwre 50: 35 357. 6. Bozok G (986) Softwre Sze Estmtor (SSE). Cetre Ntol d Etudes Sptles (CNES), Toulouse, Frce, Jue 986. 7. Sty T (977) A Sclg method for Prortes Herrchcl Structure. J Mth Psychology 5: 234-28. 8. Sty T (980) The Alytc Herrchy Process, McGrw-Hll, New York, NY: 980. 9. Zhed F (986)The Alytc Herrchy Process-A Survey of the Method d ts Applcto. Iterfces, 6: 96-08. 0. Mrd E (200) Improvg Subectve Estmtes Usg Pred Comprsos. Proceedgs of the 0 th Itertol Symposum o Softwre Metrcs (METRICS 04) 8: 87-9.. Dy Ho, Luzferdocpretz, Just wog (2008) Clbrtg fucto pot bckfrg coverso rtos usg euro-fuzzy techque. Itertol Jourl of Ucertty, Fuzzess d Kowledge-Bsed Systems 6. Submt your et muscrpt d get dvtges of OMICS Group submssos Uque fetures: User fredly/fesble webste-trslto of your pper to 50 world s ledg lguges Audo Verso of publshed pper Dgtl rtcles to shre d eplore Specl fetures: Ctto: Ocheg P, Mwg W (204) Softwre Sze Estmto Icremetl Softwre Developmet Bsed O Improved Prwse Comprso Mtrces. J Comput Sc Syst Bol 7: 079-088. do:0.472/csb.0004 350 Ope Access Jourls 30,000 edtorl tem 2 dys rpd revew process Qulty d quck edtorl, revew d publcto processg Ideg t PubMed (prtl), Scopus, EBSCO, Ide Copercus d Google Scholr etc Shrg Opto: Socl Networkg Ebled Authors, Revewers d Edtors rewrded wth ole Scetfc Credts Better dscout for your subsequet rtcles Submt your muscrpt t: http://www.edtorlmger.com/systemsbology ISSN: 0974-7230 JCSB, ope ccess ourl Volume 7(3)079-088 (204) - 088