A New Estimation Model for Small Organic Software Project

Transcription

1 8 03 ACADEMY PUBLISHER A New Estmaton Model o Small Oganc Sotwae Poject Wan-Jang Han, Tan-Bo Lu, and Xao-Yan Zhang School O Sotwae Engneeng, Bejng Unvesty o Posts and Telecommuncaton, Bejng, Chna Emal: {hanwanjang, lut, xaoyan}@upt.edu.cn L-Xn Jang Depatment o Emegency Response, Chna Eathquake Netwoks Cente, Bejng, Chna Emal: jlx@ses.ac.cn Astact It s vey had to estmate sotwae development eot accuately. So a, no model has poved to e successul at eectvely and consstently estmatng sotwae development eot o cost. So t s useul to eseach a patcula model o a patcula type o poject. A new model o small oganc poject s poposed o sotwae eot estmaton. Ths model s ased on actual poject data and well-estalshed theoes, usng Gauss-Newton model to calate the paametes o the COCOMO model, usng Fuzzy logc models to mantanng the mets o the COCOMO model. In patcula, ths model has een successully used n some small poject, and has demonstated geat potental to pedct sotwae cost moe accuately. Index Tems sotwae cost estmaton, sotwae eot estmaton, small poject, oganc poject, Fuzzy, Constuctve Cost Mode I. INTRODUCTION As thee ae a geat vaety o sotwae development poject n many aeas, sotwae estmaton s ecomng moe and moe mpotant n eectve sotwae poject management, especally n cost estmaton. Accuate sotwae estmaton can povde poweul assstance when sotwae management decsons ae eng made; o nstance, accuate cost estmaton can help an oganzaton to ette analyze the easlty o a poject and to eectvely manage the sotwae development pocess, theeoe, geatly educng the sk. Lots o attempts [], [], [3], [4], [], [6] have een made to solve the polem n the last ew decades, no appoach has poven to e successul n eectvely and consstently pedctng sotwae eot. So t s useul to eseach a model o patcula type o poject. Ths pape oes a new model to estmate the sotwae eot o small oganc poject ased on the data o actual pojects and t s the mpovement o COCOMO. Manuscpt eceved Octoe, 0; evsed Mach 7, 03. We have taken nto consdeaton the eatues o the eot estmaton polem and some technques and have poposed a new model. We mply Gauss-Newton model and Fuzzy model to the COCOMO, and have valdated ou appoach wth late poject data. Gauss-Newton model ae used n ou model to automatcally calate the paametes o the COCOMO model. II. BACKGROUND Ou new model s ased on the standad COCOMO model, the gauss newton algothm and the uzzy logc model, we ely evew these technques. A. COCOMO Model The COCOMO model ognally pulshed y Boehm s one o most popula paametc cost estmaton models o the980s[], []. At pesent, the model s stll the most mpotant n the sotwae eld. In the mddle o 990 s, Boehm poposed COCOMO II[], [] ased on COCOMO8. Nowadays, t s consdeed as one o the most extensvely used and appoved sotwae estmatng model n academa and ndustal aea. The asc pncple o COCOMO model s to expess eot wth sotwae sze and a sees o cost acto, as the ollowng equaton: B PM = A ( Sze) ( EM ) B. Gauss Newton Algothm Gauss Newton algothm s a method used to solve non-lnea least squaes polems. The method s named ate the mathematcans Cal Fedch Gauss and Isaac Newton [7], [8]. Non-lnea least squaes polems ase o nstance n non-lnea egesson, whee paametes n a model ae sought such that the model s n good ageement wth avalale osevatons. Gven m unctons = (,, m ) o n vaales β= (β,,β n ), wth m n, the Gauss Newton algothm nds the mnmum o the sum o squaes, as n (). m = S( β ) = ( β ) () 03 ACADEMY PUBLISHER do:0.4304/jsw

2 03 ACADEMY PUBLISHER 9 Statng wth an ntal guess β (0) o the mnmum, the method poceeds y the teatons, as n (). whee S ( S) ( S) ( β ) S( β ) ( + ) ( s) β s = β + Δ, () S S( β ) +Δ = + Δ+ Δ Δ β β β Δ s a small step. We then have. j I we dene the Jacoan matx as n (3). J() β =, (3) β β we can eplace S wth β j J and the Hessan matx can e appoxmated y (4). S( β +Δ) S( β ) + J Δ+ Δ J J Δ (4) ( S) ( S) (assumng small esdual), gvng: J J.We then take the devatve wth espect to Δ and set t equal to zeo to nd a soluton as n (). S +Δ J + J J Δ= () ( S ) ( β ) 0 Ths can e eaanged to gve the nomal equatons whch can e solved o Δ as n (6). ( J J ) Δ= -J J (6) In data ttng, whee the goal s to nd the paametes β such that a gven model uncton y=(x, β) ts est some data ponts (x, y ), the unctons ae the esduals. ( β) = y - ( x, β) Then, the ncement Δ can e expessed n tems o the Jacoan o the uncton, as n (7). ( J J ) Δ = J (7) C. Fuzzy Logc Models A uzzy system [9] s a mappng etween lngustc tems, such as hgh complexty and low cost that ae attached to vaales. Thus an nput nto a uzzy system can e ethe numecal o lngustc wth the same applyng to the output. A typcal uzzy system s made up o thee majo components: uzze, uzzy neence engne (uzzy ules) and deuzze. The uzze tansoms the nput nto lngustc tems usng memeshp unctons that epesent how much a gven numecal value o a patcula vaale ts the lngustc tem eng consdeed. The uzzy neence engne peoms the mappng etween the nput memeshp unctons and the output memeshp unctons usng uzzy ules that can e otaned om expet knowledge. The geate the nput memeshp degee, the stonge the ule es, thus the stonge the pull towads the output memeshp uncton. Tangula uzzy numes ae a suset o uzzy sets wth popetes that make them well suted o modelng and desgn-type actvtes. Speccally, t has a tangula shape epesented y the tple <a,, c>,lke Fg.. Fgue. Tangula uzzy numes III. THE ESTIMATION MODEL FOR SMALL ORGANIC PROJECT The estmaton model o small oganc poject s a pocess that takes Lne o Codes (LOC) as nputs n ode to estmate the wokloads. So ou goal s to t a cuve to data om actual sotwae pojects. A. The Model Functon Fom The esults o eseach and pactce show that the elatonshp etween Code Lne and eot s nonlnea [0][]. And om the tend o the data ttng cuve, we also got that non-lnea egesson analyss s t o ou model. Hence, we appled nonlnea egesson ttng method to om ou model n ths pape. We ted to gan an equaton as a elaton uncton etween LOC and eot, shown as n (8). y = ( x) (8) On the othe hand, asng on COCOMO 8 model, we adjusted the om o the model, shown as n (9). y = a x (9) In the Equaton (9), y s epesented o the human esouce needed (peson hou), x s epesented o Code Lnes, a and ae oth paametes. B. The Fttng Pocedue o the Model Now let s look at the poject data, as n Tale Ⅰ, whch ae o the type o small oganc poject. TABLE I. PROJECT DATA No LOC Peson- Hou It s desed to nd a model uncton o the om o (9), that s to say, the model uncton s PH = a LOC,whch ts est the data n the least squaes sense, wth the paametes a and to e detemned. 03 ACADEMY PUBLISHER

3 0 03 ACADEMY PUBLISHER Denote y x and y the value o LOC and the Peson-Hou om the TaleⅠ, =,,9. We wll nd a and such that the sum o squaes o the esduals, = y a x, (=,,9) s mnmzed. ate seven teatons o the Gauss Newton algothm the optmal values a= and =0.747 ae otaned. The plot n Fg. shows the cuve detemned y the model o the optmal paametes vesus the oseved data. sequence om hgh to low to ensue the weghts o each cost dve[]. : Fo these cost dves, consdeng the mpotance o them, thee should e PERS (CD ) > PREX (CD )> RCPX (CD 3 )> PDIF (CD 4 )> SCED (CD ). Hee comes to the Tangula uzzy judgment matx, lke TaleⅡ. TABLE II. TRIANGULAR FUZZY JUDGMENT MATRIX OF THESE COST DRIVER PROJECT DATA CD CD CD CD3 CD4 CD CD (,,) (/3,/, (,3,4) (3,4,) (4,,6) ) CD (,,3) (,,) (3,4,) (4,,6) (,6,7) CD3 (/4,/3, (/,/4. (,,) (,3,4) (3,4,) /) /3) CD4 (/,/4, (/6,/, (/4,/3, (,,) (,3,4) /3) /4) /) CD (/6,/, /4) (/7,/6, /) (/,/4, /3) (/4,/3, /) (,,) Fgue. LOC-Peson Hou So, we have acheved the expesson o ou estmaton model as ollows: PH = LOC (0) C. The Adaptaton o the Model In ode to mpove estmatng accuacy o ou model, we also consde the actos that mpact the eot. Theeoe, the equaton o ou model can e adjusted nto () PH = LOC F () In Equaton (), F s a multple whch s a coecton acto to ou model. And F s expessed as n (). () = = F = (w CD) CD In Equaton (), CD means Cost Dve, w s the Weght o Cost Dve. Accodng the chaacte o small oganc poject, we choose ve cost dves, whch ae PREX (expeence), PERS (skll o capalty), RCPX (elalty and complexty), PDIF (platom dculty), SCED (Requed development schedule), eeed to cost dves o CocoMo II. Each cost dve epesents one acto that contutes to the development eot. We use CD, CD, CD 3, CD 4, CD to epesent PREX, PERS, RCPX, PDIF, SCED, espectvely. Snce the mpotance o evey cost dve s deent, we mantan the mets o coecton acto o COCOMO model. Ratng o evey cost dve s lngustc tems such as vey low, low, nomnal, hgh, vey hgh, exta hgh, and the value o evey atng can get y eeng COCOMO II model. w s the ato o these cost dve, also a key o uzzy evaluaton. When we compae wth each o the two cost dve, t s dcult to desce the mpotance y nume, so we use the Tangula Fuzzy Nume, y the : Computng the weghts o cost dve. () Fom TaleⅡ,we can get the tangula uzzy weght vecto: w= (0.9, 0.9, 0.30), w= (0.43, 0.44, 0.4), w3= (0., 0., 0.), w4= (0.08, 0.08, 0.080), w= (0.049, 0.04, 0.04), () Fo evey ow, Addng each element, we can get : s= (.6, 3.78,.08), s= (.84,.9,.78), s3= (6.4,8.8,0.83), s4= (0., 3.33, 6.), s= (, 9, 3) (3) Calculatng the maxmum Egen value vectoλm ax, we can get the Max Egen value E(λm ax )=.7. (4) Consstency checkng CI=0.067, CR=0.04< 0., And E (λm ax ) < ode ctcal maxmum egenvalue. Hence, ths Tangula uzzy matx satsy the consstency check. 3: Calculatng the Tangula uzzy weght vectos expectatons value E(w ) =0.30, E(w ) = 0.43, E(w 3) = 0., E(w 4) = 0.08, E(w ) = 0.04, 03 ACADEMY PUBLISHER

4 03 ACADEMY PUBLISHER Fom these expectatons value, weghts o each cost dve can e shown as n Tale Ⅲ. TABLE III. EACH WEIGHTS OF COST DIVER. Cost PREX PERS RCPX PDIF SCED dve w Aove all, ou estmaton model o small oganc sotwae poject s shown as the ollowng equaton: PH = LOC We can get Ⅱ model = w om Tale Ⅲ, ( w CD ) = CD CD om COCOMO D. The Evaluaton o the Model We can use MRE (Magntude o Relatve Eo) to evaluate the accuacy o estmaton esults. MRE can compae actual value and estmated value, whch can e desced as ollows : MRE= (ActualValue-EstmaedValue)/ActualValue. In act, MMRE s a moe useul evaluaton tool, = n MMRE= n MRE.To evaluate ou model, we = calculated out that MMRE s equal to 8.8% om the ollow-up 8 pojects. IV. IN THE CASE OF THE APPLICATION The small poject estmaton model has een adapted to seveal pojects and t has eceved eally good eects. Fo nstance, a case o small oganc poject, the nput s 00 LOC, we estmate the eot wll e PH eoe adaptaton, shows n Fg. 3. Then we take coecton to the value wth cost dves. The values o each acto ae shown elow: PREX = (nomnal), PERS =0.86 (hgh), RCPX = (nomnal), PDIF = (nomnal), SCED = (nomnal), that s to say, F= So, the nal esult o estmaton s Eot=3.64 Peson-Hous. In ths case, the poject actually took 36 Peson-Hous, MRE=9.3%, ths value ascally ts the evaluaton value om the model. Fgue 3. A case o sotwae estmaton On the othe hand, we also appled othe methods to estmate the eot o ths case, ut the MRE > 0%. So ou model s moe sutale to ths type o poject. V. CONCLUSIONS Sotwae development s a complex pocess, so s t vey dcult to pedct sotwae development eot accuately. Ths pape put owad a sotwae eot estmaton model o small oganc poject. The model s ased on actual poject data and well-estalshed theoes whch povdes a pomsng tool to deal wth many dcultes o small sotwae estmaton; thus, t s useul o poject management. In patcula, ths model has een successully used n some small poject, and has demonstated geat potental to pedct sotwae cost moe accuately. At the same tme, othe type o sotwae estmatng model can also e omed n tems o methods o ths model. It can povde assstance n poject plannng. The advantage o ths model s smplcty, pactcalty and automated admnstaton. Next mpovement thought o the model s ) model mpovement n connecton wth lage scale poject. ) gadual optmzaton o coecton acto computaton. ACKNOWLEDGMENT Ths wok was suppoted n pat y the Natonal Natual Scence Foundaton o Chna (Gant No ). REFERENCES [] B. W. Boehm, Sotwae Engneeng Economcs, Pentce Hall PTR, 98. [] B. W. Boehm, et al. Sotwae Cost Estmaton wth COCOMOII, Pentce Hall, 000. [3] S. Chulan, Bayesan analyss o sotwae cost and qualty models, Ph.D. Dssetaton, Unvesty o Southen Calona, LosAngeles, 999. [4] M. Shepped and G. Kadoda, Compang sotwae pedcton technques usng smulaton, IEEE Tans. Sotwae Eng, vol. 7, no., pp. 04 0, Noveme 999. [] A. B. Nass, L. F. Capetz, and D. Ho, Sotwae estmaton n the ealy stages o the sotwae le cycle, n Intenatonal Coneence on Emegng Tends n Compute Scence, Communcaton and Inomaton Technology, 00, pp. -3. [6] R. J. Madachy, Heustc sk assessment usng cost actos, IEEE Sotwae, vol. 4, no. 3, pp. 9, May/June 997. [7] P. K. Suamanan, Gauss-Newton methods o the complementaty polem, Jounal o Optmzaton Theoy and Applcatons, vol. 77. no. 3, pp , June 993. [8] M. Y. Yena and A. F. Izmalov, The Gauss-Newton method o ndng sngula solutons to systems o nonlnea equatons, Computatonal Mathematcs and Mathematcal Physcs, vol. 47, no., pp , May 007. [9] R. Fulle, Intoducton to Neuo-Fuzzy Systems, Physca- Velag, ACADEMY PUBLISHER

5 03 ACADEMY PUBLISHER [0] E. Castllo, A. S. Had, and R. Mnguez, Dagnostcs o non-lnea egesson, Depatment o Appled Mathematcs and Computatonal Scences, Unvesty o Cantaa, Santande; Span, Unvesty o Castlla-La Mancha, Cudad Real, Had; Mnguez, Jounal o Statstcal Computaton and Smulaton, Septeme 009. [] L-Xn Jang and Wan-Jang Han, Reseach on Sze Estmaton Model o Sotwae system Test ased on testng steps and Its Applcaton, Compute Scence and Inomaton Pocessng (CSIP), 0 Intenatonal Coneence, pp [] Han Wan-jang and Lu Tan-o, Study On Qualty Evaluaton Model O Communcaton System, System Scence, Engneeng Desgn and Manuactung Inomatzaton (ICSEM), 0 3d Intenatonal Coneence, pp. -4. Wan-Jang Han was on n HeLongJang povnce, Chna, 967. She eceved he Bachelo Degee n Compute Scence om He Long Jang Unvesty n 989 and he Maste Degee n Automaton om Han Insttute o Technology n 99. She s an assstant poesso n School O Sotwae Engneeng, Bejng Unvesty o Posts and Telecommuncaton, Chna. He techncal nteests nclude sotwae poject management and sotwae pocess mpovement. Tan-Bo Lu was on n Guzhou Povnce, Chna, 977. He eceved hs Maste Degee n compute scence om Wuhan Unvesty n 003 and hs PH.D Degee n compute scence om the Insttute o Computng Technology o the Chnese Academy o Scences n 006. He s an Assocate poesso n School o Sotwae Engneeng, Bejng Unvesty o Posts and Telecommuncatons, Chna. Hs techncal nteests nclude nomaton and netwok secuty, tusted sotwae and PP computng. Xao-Yan Zhang was on n Shandong Povnce, Chna, 973. She eceved he Maste Degee n Compute Applcaton n 997 and he PH.D Degee n Communcaton and nomaton system om Bejng Unvesty o Posts and Telecommuncaton, Chna, n 0. She s an Assocate poesso n School o Sotwae Engneeng, Bejng Unvesty o Posts and Telecommuncatons, Bejng, Chna. He techncal nteests nclude sotwae cost estmaton and sotwae pocess mpovement. L-Xn Jang was on n HeLongJang povnce, Chna, 966. He eceved hs Bachelo Degee and Maste Degee n physcal geogaphy om Bejng Unvesty n 989 and 99. He s a poesso n the depatment o Emegency Response o Chna Eathquake Netwoks Cente. Hs techncal nteests nclude sotwae cost estmaton and Emegency Response sotwae development. 03 ACADEMY PUBLISHER