Theoretical Count of Function Points for Non-Measurable Items

Theoretical Coun t of F unction P oin ts for Non-Measurable Items Nilo Serpa Instituto de Ciˆ encias Exatas e T ecnologia , UNIP - Universidade Paulista, SGAS Qua dra 913 , s/n o - Conjunto B - Asa Sul - B ras ´ ılia - DF, Br asil CEP 70 390-13 0 e-mail: nilo @techsolarium.com POLITEC Glo bal IT Services, SIG Q uadra 4 - lote 173, Setor Gr ´ afico - Bras ´ ılia - DF, Bra sil CEP 70 610-44 0 Abstract: This pap er studies and prop oses an extended technique of function p oin t counting for items classified as non-measurable. The main ob jectiv e is to expand the conv entional technique of counting to ensure that it comprises consistentl y the tasks inv olved in bu ilding p ortals and sites in general. I n addition, it also applies to measure the cost of contin ued activities related to these w eb applications. The e xt ended technique is p otentia lly u seful to measure several pro ducts associated with information systems, including p eriodicals p ublishable in in tranets. Keywords: function p oints; intellectual effort; inertia of developmen t; econophysics; Lagrangian dynamics; metrics Biographical notes: Nilo Serpa is Magiste r in Scientia , in Astronomy , from the Universidade do Br asil , and Master of Business Administration from the F unda¸ c˜ ao Getulio V ar gas , Brazil. His M agi ster Thesis wa s a b out applications of the inhomogeneous Lema ˆ ıtre-T olman cosmology with an original app roac h of weak gravitatio nal lensing in that cosmology . He sp ecializes in Managemen t Pro cess and Information T echnology from the F unda¸ c˜ ao Oswaldo Cruz , Brazil. H is training in Physics at th e Centr o Br asileir o de Pesquisas F ´ ı sic as - C B PF - ranges from Quantum Mechanics to Sup ergravit y , including Gauge Field Theories, T opological Effects and Sup ersymmetry . He received his degree of Architect in th e year 1981, now having thirty years exp erience in IT as a Pro ject Manager and Dev elopment Manager, and fifteen years exp erience in Physics as researc her and professor. In the early Eighties, it w as p upil of the semiologist U m b erto Eco, exp erience that contributed for h is interest on the semantic s of the mathematical formalizations. He is A ssociate Professor of Physics, Softw are Engineering and Professional Ethics at the Universidade Paulista , Brazil, and Senior Developmen t Manager at POLITEC Glob al IT Servic es , Brazil. He is Analyst of T raining with great exp erience in e-learning, having w orked in collab oration with some of th e greatest names in the area of qualification of human resources, such as the Canadian Soft ware Engineer John F ranklin Arce. He is also Sp ecial Pro ject Manager at th e General Coordination of In formation and Informatics of the Ministry of W ork and Employmen t, Brazil. Having received a Senior training in F unction Poin t Analysis, he has created a metho dology named ”Priorit y Poi nt Analysis” to measure an IT Coordination by the problems it faces. He is author of the bo ok R evers˜ oes Ge op ol ´ ıtic as: Ge o gr afia, F ´ ı sic a e Filosofia na So cie dade Glob alizada (2002). His main w orks in Physics are ”Thermod ynamics of Diab etes Mellitus: the Physica l Reasons of Ob esit y and Sedentarism us as Decisive V ariables in Predictive Mo dels”, ”New L ectu res on Sup ergra v ity”, ” El-Ni ˜ no: Influ ˆ encia Exterior, Mat ´ eria Ne gr a e Caudas Gr avitacionais ”, ”The Counting of Galaxies from T yp e Ia Sup ern ov ae Rate” and ”Mo delling the Dynamics of the W ork-Emplo yment System with Predator-Prey Intera ctions”. He is invited reviewer of the journal Ec onomic Mo del li ng . His areas of in terest include Cosmolog y , Field T heory , G eop olitics, Econophysics and Information T echnology . Y ou c an not imagine how everything is vague until try to do it ac cur ately. Bertr and Russel l 1 In tro duction The function p oint analysis (FP A) is a standardized techn ique for mea s uring so ftw ar e developmen t, aiming to es ta blish a gauge of the softw are size based o n nilo@tec hsolarium.com 2 Nilo Serp a the functionalities to b e implement ed, considering the viewp oint of the user (IFPUG, 200 0 ). Some usage thoughts hav e b e e n made to the extent that softw are systems are b ecoming more complex (Micro F ocus, 2008), s uch as: 1. ” F unction points are not a very go o d measure when sizing maintenance efforts (fixing problems) or when try ing to understa nd the pe rformance is sues. Much of the effort a sso ciated with fix ing problems (pro duction fixes) is due to trying to resolve and understand the pr oblem (detective work)”. 2. ” FP a nalysis (FP A) is not useful to size W eb Design. FP A is useful to s iz e w eb development, but not web design.[...] FP A is no t useful in estimating the time necessa r y to create gra phics, imag es, page lay outs, so on and so forth”. During the eighties and un til the beginning of the 21st century , a n umber o f authors hav e discussed the metric pro c e dures in vogue (Albre cht & Gaffney, 198 3), (Dreger, 198 9), analyzing its applicability to ob ject- oriented softw are (Whitmire, 19 93), its adv an tag es and disa dv an tages (Jo nes, 199 4). Also, Kemerer (1 9 93) studied the reliability o f the FP A technique. Impor tant contributions to understanding the complexity inherent to s oft ware engineering w ere brought by Indian schoo l (Jalote, 1998),(Ram et al , 2000 ). More en thusiastic w or ks ab out FP A app eared s inc e 200 0 (Gar m us & Her ron, 2001). The function po ints mea surement technique has generated m uch controv ersy since its dissemination as an I SO recognized to ol to size infor mation s ystems, bo th as re gards its ge neral purpo s es (do es it measure pro ductivity , size, complexity or functionality?) and in relation to mathematical r igor under the concept of metric. In particular, with res pect to the la tter, being the num b er of function p oints a dimensionless quantit y , so me a uthors claim that there was no wa y to a nalyze and seek information from num b ers not asso ciated with a r eference sy stem (Abran & Ro billa rd, 1994). T his is not entirely true. In science there a re many dimensionless num b ers widely applied in s e veral fields as h ydro dyna mics, ge o physics, optics and others. A dimensionless metric, b eing indep endent of the re a lit y bene a th ev alua tion, is useful to compare t wo or mo r e ob jects abstracting a lot of deta ils of these ob jects, placing them in the same plane of obser v a tion a nd providing a pe r sp ective that would b e inconceiv able without a standardize d a pproach. Perhaps the difficulty is to prec is e the mathematical structure and the semantics o f the metric, that is , what the metric forma lly measures. One o f the ma jor contractual problems faced b o th in the gov ernmental sphere and in the context of priv ate ent er prise is the rem unera tion of the a ctivities not measurable by the technique of function p oint analysis. Some devices hav e b een adopted, but with high degree of a rbitrariness , making the calculation uncertain and often unfair, and vulnerable to cr itical assessments of the orga ns of co ntrol. In addition, an ar bitr ary co n tro l of the estimates may b e evidence of unprofessional management. Also, so mething more is miss ed out as observed by Lok an (2008): F unction p oints ar e oriente d towar ds data-str ong systems, typifie d by business softwar e. Pr o c essing in these systems is simple. Most effort go es into defining data structur es. Not al l systems fit this p attern. Scientific and engine ering softwar e is often fun ct ion- str ong: dominate d by the intern al pr o c essing r e quir e d t o tr ansform inputs to outputs . The pr esent mo del, a lthough it stemmed from the need to mea sure the de velopment effor t of s ites and p ortals, a ims to incor p or ate no t just the t ypical non-measura ble items but all function-stro ng softw are pro cesses, including ope rational sys tem migratio ns. It is susceptible to br o ad questioning the measurement of all the tasks required in the design and developmen t of web applica tions (esp ecially p ortals), now applied to the Ministry of W ork and Employmen t in Brazil (hereafter MTE), no t only by the a esthetic and functional asp ects but a ls o b y the technology of the softw are resources in use. It sho uld also co nsider that ther e is here , as in other IT activities, a s ig nificant amount o f intellectual effor t that, while difficult to measure in an y ar ea, mu st be prop erly computed and paid even so by an indirect and approximate manner. There are cre ative works published on the techniques of scor ing for web systems (Abrah˜ ao & Pastor , 200 3 ), (Drach, 200 5), a nd fo r situa tions in which a priori non-measura bilit y is comp ensated by a technique to per form FP A based on the sour c e co de (Mustafa et al , 200 5). Also , recent a nalytical studies call a ttention to imp orta n t issues that r emain unr esolved and that should a ttract g reater interest fro m the international communit y of IT (Hern´ andez-L´ opez et al , 2011). It draws attention, howev er, the fact that none o f them is the prop osition of a c o mplete for malism that includes the repr esentation of the intellectual effort, the hours work ed a nd pro ductivity of the to o l applied, the mo s t relev ant of the few b enchmarks for web sy stems. Indeed, the size in function p oints is not intended to mea sure pro ductivity a nd development effor t, but to measure softw are in terms o f its functiona lit y . Nevertheless, from the moment that we fo cus on the trinomial qua lit y-c ost- time it is impera tive to co mpute the assets embedded in the engineering itself. It is noteworth y , as well po in ted Aramo-Immonen et al (2011 ), the influence that cultural differences have o n the pro ductivity in globalized softw are engineer ing, which makes even more complex the challenge of managing pro ductivity and costs, mainly in larg e corp or ations. It is the r eality of this fact, coupled with the need to co un t function po in ts in the manag ement of IT s e rvices, whic h forces us to broaden the horizons of the tec hnolo gy , so that we can standardize our practices, r egardless of culture The or etic al Count of F un ction Points for Non-Me asur able Items 3 or activity , preventing the pro lifer ation of comp etitor pro cedures, a nd, consequently , the misconceptions w hich they can pr o duce. The name ”function p oint” not even seem to fit the web developmen t by the a bsence ther e of the classic al counting e lemen ts. How ever, a web lay out contains int rins ic functionalities b eside men us, h yp erlinks , v alidit y chec ks of fill, etc.; the communicational function of the web layouts overlaps unequivoca lly to other asp ects; whence the difficulty to sco re so abstrac t assignment; whence the request for the a pplication of more forma l techniques. In sum, the classica l FP A inv olves co un ting of type data functions and t yp e transaction functions, suc h as inputs, outputs, inquiries , files and mov ements. F o cusing only the functiona lities asso cia ted with data-strong structures, the measurement ba sed on function po ints at MTE do es not recog nize as worthy of metric criteria all the neces s ary interface architecture a nd pr esentation features, which ensure accessibility , friendly op e r ability , as well as effective dissemination of sub jects. 2 Metho dology The basic premise of finding a criter ion for counting the cases in q ue s tion are the disadv antages o f its own current, namely • W o r thlessness of pr ofessional sp ecialization in the absence of a prop er technique of counting and measuring, a fact which causes the depreciatio n of professiona l pr ofile in the work market; • E xp osure of the Co ordination of IT to the questions of the org ans of control bec ause of the degree of arbitra riness in the c alculation curr en tly practiced; • Under estimation of int ellectual effort, low ering the int ang ible v alue of ho ur s worked; • Abso rption of the fragility of the standard coun t done in other instances, ins ofar as mos t of these error s w ould b e co mpens a ted by the low and alwa ys lo wering cos t o f construction and developmen t of prese n tation layers in the E x tranet, Int ra net or Internet; • Ina ccurate billing fro m contractors. Since the obvious disadv antages a re shown for all, we deal with the necessary too ls to seek the establis hmen t of the tec hnique des crib ed above. The first task undertaken was a survey , to gether with exp erts, comprising a consistent a nd clea r ro ll o f jobs r e lated to the demands for the w eb area . The list, for matted in T a ble 1, w as constructed keeping in mind the subsequent use of P ER T - P rogra m Ev aluation and Review T echnique - (Boiteux, 1985), th us containing the time int er v a ls needed to per form jobs o f low, medium a nd high c o mplexity in optimistic, pessimistic and mo s t likely p ersp ectives. All conv oked professionals , invited to construct the T able, ar e g raphic designers (or industrial designers , with sp ecialization in visual pr ogramming) with practice as query develop ers and hav e more than ten years exp erience in web developmen t. They are pro fessionals able to develop visual desig ns in v arious areas since the cr eation of corp or ate ident ity to several graphic pieces for b oth prin t and digital media. As we know, the are a of web design r equires the domain of imp ortant concepts of usability , navigation and web standards. Each pr o fessional (fiv e in all) built his own T able, so that the final T a ble adopted computed the av erage of individual T ables. The co mplexit y of the task is a linguistic v ar iable assuming the fuzzy v alues ”low”, ”av era ge” and ” high” 1 . In fact, fuzzy mo dels are very useful in infor mation techn o lo gy such a s those based on the crea tion of causal a nd cognitive maps of risks provided by expe r ts exp erience (Bo dea & Dascalu, 2010). W e note that in present mo del the complexity is classified by the duration of the ta sk. The criter ia for classificatio n o f complexit y hav e b een established by the res pective groups of exp ert professiona ls s elected to determine the times of PE R T. F or example, a high co mplexity query in SQL acces ses more than three tables, while for a low co mplexit y query only o ne table is accessed. Also the ta s k list has not exha usted the rang e of all non-measura ble items; insomuc h, T able 1 may b e expa nded as necessa r y . Parallel to the construc tio n of the T able, I have imagined that the theoretica l num b er of function p oints for the ca ses no t dir ectly meas ur able would b e, a priori , a function of time consumed and some feature of the developmen t to ol used, so that, N = f ( t, i ) , (1) where N is the n umber of function p oints, t is the time taken for completion of the task and i is called ”inertia of developmen t” or ”constra in t capacity”, i. e., an index that repres ent s the constra in ts imp osed by the to ol (T able 3). If desired, from the para meter i we may define the pr o ductivit y p o f the to ol as, p = 1 i . The v alues of i were esta blished with the aid of professiona l exp erience accumulated ov er the y ear s of work a nd by r ep o rts on pro ductivity from suppliers . Time is defined as in PE R T, i. e., T = O + 4 M P + P 6 , (2) where O is the optimistic estimate, P is the p essimistic estimate and M P is the mo r e likely estimate. 4 Nilo Serp a T able 1 T asks, complexities and du rations T ask Complexi t y Optimist P ess imist Most likely HTML conv ersion Lo w 0:30:00 3:00:00 1:45:00 Average 1:00:00 4:00:00 2:30:00 High 1:30:00 6:00:00 3:45:00 PDF conv ersion Standard 0:30:00 0:30:00 0:30:00 Multimedia i nserting Lo w 0:30:00 2:00:00 1:15:00 Average 1:00:00 3:30:00 2:15:00 High 1:30:00 6:00:00 3:45:00 Image creation and treatment Lo w 0:30:00 2:30:00 1:30:00 Average 2:00:00 5:30:00 3:45:00 High 4:00:00 12:00:0 0 9:00:00 F orm creation Lo w 0:30:00 4:00:00 2:30:00 Average 2:00:00 8:00:00 6:00:00 High 4:00:00 12:00:0 0 9:00:00 Lay out creation and development Lo w 8:00:00 8:00:00 8:00:00 Average 19:00:0 0 24:00:0 0 21:30:0 0 High 38:00:00 40:00:00 39:00:0 0 Lay out adequation Standard 3:00:00 8:00:00 5:30:00 Lay out montage Lo w 8:00:00 9:00:00 8:30:00 Average 22:00:0 0 24:00:0 0 23:00:0 0 High 36:00:00 40:00:00 38:00:0 0 Creation of T ables Lo w 0:30:00 2:00:00 1:40:00 Average 2:00:00 4:00:00 3:00:00 High 4:00:00 8:00:00 6:00:00 Creation of CSS Lo w 4:00:00 6:00:00 5:00:00 Average 12:00:0 0 12:00:0 0 12:00:0 0 High 24:00:00 24:00:00 24:00:0 0 Creation of JS/ASP functions Lo w 3:00:00 3:00:00 3:00:00 Average 5:00:00 5:00:00 5:00:00 High 7:00:00 7:00:00 7:00:00 Adequation SQL, JS/ASP functions Lo w 2:30:00 2:30:00 2:30:00 Average 3:30:00 3:30:00 3:30:00 High 4:30:00 4:30:00 4:30:00 Creating SP/SQL and components Lo w 4:30:00 4:30:00 4:30:00 Average 6:30:00 6:30:00 6:30:00 High 9:00:00 9:00:00 9:00:00 Adequation of pro cedure Lo w 0:20:00 0:25:00 0:23:00 Average 0:50:00 1:00:00 0:55:00 High 1:50:00 2:20:00 2:00:00 Creating maintenance page Standard 0:05:00 0:10:00 0:08:00 Surv ey with the cli ent Standard 24:00:00 36:00 :00 32:00 :00 Site conv ersion to CMS High 240:00: 00 472:00: 00 3 20:00:00 The or etic al Count of F un ction Points for Non-Me asur able Items 5 3 The systemic view of the soft w are dev elopmen t As once told Mario Bunge (1961), ”One of the mos t difficult and interesting problems of rational decis ion is the choice among p ossible diverging paths in theory construction a nd amo ng compe ting scientific theories, i.e., systems of accura te testable hypotheses. This tas k inv olves many b eliefs-some warrant ed a nd others not as warranted and marks decisive cro s sroads.[...] The s et o f metascientific c riteria dealing with the v a rious traits of acceptable scientific theories is w ha t g uides the choice among c o mpeting courses in theory constructio n a nd among the pro ducts of this activity”. I usua lly say that it is ea s y to prop o se co mplicate things; difficult is to prop ose simple things. The set of metascientific criteria I adopted includes simplicity among the requirements tha t pr esent mo del is supp os e d to satisfy . Here, the s implicit y refers to semantical and pragmatica l s implicities, that is, to an econo m y of additional meaning pr e-supp ositions and to a n economy of work by who counts the sy s tem or pro ject. I star ted from an eco nophysical vision, acco rding to which a pro ject is a system endow ed with its own dynamics o f evolution of h uman and mater ial inv estment s. As a physical system, and circumscrib ed by the developmen t p ers pective, w e have a Lag rangian function that describ es this dynamic (Goldstein et al , 2001), taking in to account the rele v ant para meters for the mea surement of softw are pro jects. The simplest and t ypica l Lagr angian form is given by , L = 1 2 N ˙ N 2 − V , (3) where the overdot indicates time deriv ative a nd V is the po ten tial o f the pro ject to g enerate function p oints. W e note that Lagra ngian L is not an explicit function o f time. The function L is such that, d L dt = ∂ L ∂ N dN dt + ∂ L ∂ ˙ N d ˙ N dt and ob eys the Euler- Lagrang e equation, d L dt − " dN dt d dt  ∂ L ∂ ˙ N  + ∂ L ∂ ˙ N d ˙ N dt # = 0 , (4) ∂ L ∂ N dN dt − dN dt d dt  ∂ L ∂ ˙ N  = 0 , d dt  ∂ L ∂ ˙ N  dN dt − ∂ L ∂ N dN dt = 0 , d dt  ∂ L ∂ ˙ N  − ∂ L ∂ N = 0 . Equation (4) may b e rear ranged and must determine a ”conserved cur r ent” J according to, d dt  L − ˙ N ∂ L ∂ ˙ N  = 0 , from which, ∂ L ∂ ˙ N ˙ N − L = J = C te . (5) The qua n tity dt is the time differential, ˙ N a nd N a re the generalized coo rdinates of the sy stem. The deriv atives of the Lagrangia n ar e a lwa ys taken with r esp ect to the explicit gener alized co or dinates. As in physics the Lagra ng ian refers to ene r gy units (such as k g .m 2 /s 2 ), the analogica l ”co nserved current” J in present theo ry refer s to the intellectual effor t p er squa red hour . Applying equation (5 ) to function (3) we obtain, 1 2 N ˙ N 2 + V = J. (6) Having conjecture d and tested a few options of empirical formulas to match equation (6 ), I pro po sed the fo llowing more a dv anced express ion as the b est appr oach, N = C i K ( P − O + 1)  O + 4 M P + P 6  , (7) where K is the contractual adjustment parameter, and C is the intellectual effort co n version factor for function po in ts according to T able 2. It is not the ca se of arbitra r y statement but ta cit ass umption. A tacit a ssumption is p erformed from s ome rational premises of a logical argument and, by co rrob ora tion with exp erience, attains the status of a p ostulate. So, to be acceptable as po stulate, ta c it equatio n (7) has to b e tested. Fixing O and P as time-extre mes , we ca n do M P = t (the time v ariable estimate). Adopting K = 1 and inser ting expression (7 ) into equation (6) we deduce, 1 2 C i ( P − O + 1 ) ( O + 4 t + P ) 6 C 2 i ( P − O + 1) 2 × 16 36 + V = J. (8) The ”conserved current” J is fixed aro und 4 C i / ( P − O + 1 ) 2 , s o that, V = 4 C i ( P − O + 1 ) 2 −       1 2 N z }| { C i ( P − O + 1 ) ( O + 4 M P + P ) 6 C 2 i ( P − O + 1) 2 16 36 | {z } ˙ N 2       . (9) Figure 1 shows the shape of theoretical curves of the po ten tial V a ccording to the inertia of developmen t i for three v alues of K . A negative or e ven null p otential may 6 Nilo Serp a signify that the combination tool- effort-time is no t b eing pro ductive. Thereby , the potential can b e an essential instrument to supp ort pro ject manager s , providing a guide to b etter match the av aila ble resourc e s . W e see that function (7) clearly satisfies the equation (4) and ensur es cur rent’s units and time co n tro l of the nu mber of function p oints, k eeping the P ER T time in the whole description (this is desira ble, since the num b er of function po in ts is very time-sensitive to the PER T estimate). The Lagrangia n (3) represents the dynamics of the pro ject along the time. The ”conser ved current” gives the effective intellectual effort p er sq ua red ho ur 2 . T o well understand my p oint in fav or of exp onential representation, it is necessar y a brief lo ok at the r e lation betw een exp onential g rowth a nd geometr ic progr ession. If the r atio of a growth rate to the incre a sing quantit y itself is a constant, we are dealing with a pro cess that may b e explained by an obser v ational series of type a, ak, ak 2 , ak 3 , ..., ak n , says, a ge ometric progr ession of ratio k . Such increasing quan tity , Q , being considere d as a contin uous function o f time, t , may b e dyna mically describ ed b y means of a differen tial equation of type dQ/dt = r Q for a = Q (0), to what the unique solution is Q = a.exp ( r t ). Thus, any set o f meas urements of the quantit y Q for t = 0 , 1 , 2 , 3 , is a geometric pr ogress ion where k = e r . As w e see , expo nen tial growth refer s to a contin uous natural change in which m ultiplication is fractally-r epea ted; geo metric progre ssion is a discr ete subset of that contin uous (Serpa, 2005). In science, the use of e xpo nent iatio n is p erv asive in several fields, ma inly in econo mics and physics. 0.0 0.2 0.4 0.6 0.8 1.0 −0.1 0.0 0.1 0.2 Curves of potential V (P=8, MP=5.5, O=3, C=5.4) i V K=1 K=1.2 K=3 Figure 1: The or etic al curves of the p otential V r anging fr om i = 0 to i = 1 for di ffer ent values of K . Now, the coun ting of function po in ts m ust b e a contin uous pr o cess, s ince precision is a pivotal claim to pay for a task . As exp onentiation gr ows fas ter than m ultiplication, the first is useful to describ e a quantit y that must evolv e more quickly b eneath the weigh t o f another quantit y that repres en ts the ev er increasing T able 2 Conv erting factors for function p oints Step F actor Survey 3.2 Elab oratio n 5.8 Construction (**) T ests 2.6 Alteration 1.5 Implantation 1.2 (**) La nguages In ternet/In tranet F actor PHP , J av a Script and ASP 3.5 HTML 1.8 Jav a, CMS to ols , ETL 5.4 per formance of the mo dern to o ls. Y et, the intellectual effort is obviously very influenced by the to ol in use, so that it is rea sonable to accept the factor C i . Since function points are now being applied far beyond the basic purp os e of a s izing mechanism for softw are pro jects, including litigation inv o lv ing softw are contracts a nd so ftw ar e taxation, the par ameter K enters to preven t pro blems alr eady in the ear ly sta g es o f negotiation, adjusting the rang e of the counting to the provisos of a given contract. There are numerous conv ersion T ables in the market. T ables (2) and (3) purpo sely prese nt fracta l weigh ts to conv erting time in function po int s, since at the end we wan t to find monetary v alues. The application of weigh ts is very known from fuzzy logic (Aguiar, 1 999) to quantify int uitive concepts as ”intellectual effort” and ”inertia o f developmen t”; here they were defined also in co mpa rison with similar T ables used for the reverse path, i. e., for the tra nsformation of function p oints in hours w or ked (CTIS, 2004), taking int o account the le vel of intellectual inv estment in each pha se. J us t as exp erts opine on the hierarch y of the pro ject phases, they also opine on the degree of intellectual relev ance, fro m 1 to 6, ado pted for each comp onent pha se of the pro ject, as present ed in T able 2, including the elemen ts with higher weigh ts at higher e ffort. The ra nge of the weight s was delimited to confine the num b er of function po int s within acceptable int er v als. Also , informations provided by suppliers w ere used in some cases (T a ble 3). F or instance, a certain supplier of CMS to ols rep or ted that Lumis 3 gives a gain of thirty p ercent in pr o ductivit y co mpared to older similar a nd less friendly applications. This means that i is equa l to 1 − 0 . 3 = 0 . 7, be ing 1 the weigh t of the hardest to ol ado pted a s refer e nce to compare the p ow er of Lumis. In other words, Lumis adjusts intellectual effort from C to C 0 . 7 . The contractual adjustment parameter K regulates the growth of the num be r of function p oints a ccording to the budget levels for each institution, keeping s cores on appro pr iate scales. The or etic al Count of F un ction Points for Non-Me asur able Items 7 T able 3 Inertia of developmen t i for some to ols T ool i HTML 1.00 ASP 0.90 CMS to ols (Lumis, Vignette, etc.), PHP 0.70 Statistics to ols 0.65 Management to ols 0.60 DBA to ols (Quer y Analyzer , V. Studio, etc.) 0.52 T ext pro ces sors 0.60 T ext editor s 0.50 Developmen t to ols (Photosho p, Co rel, etc.) 0.68 Human ware 0.00 ETL 0.36 0.0 0.2 0.4 0.6 0.8 1.0 1 2 3 4 5 Curves of FP (P=8, MP=5.5, O=3, C=5.4) i FP K=1 K=2 K=3 Figure 2: The or etic al curves of function p oint c ounts r anging fr om i = 0 to i = 1 for di ffer ent values of K . Note that f or K > 1 the amount of function p oints de cr e ases. 4 Results Let us understa nd in details the for m ula (7 ). Mathematics changes to num b er, by o wn s y n tax, a clause written in plain la nguage. Unfortunately , the teaching of the sub ject do es not alwa ys makes this clear, so that the mathematical expr essions ass o c iated with empirical pro cesses often s eem obscur e. So , by the requirement of sema n tical s implicit y , the simple claus e, ”The num ber of function p oints is directly prop ortio nal to the intellectual effort ( C ) p ow ered by the constra in t capacity o f the to ol ( i ) and to the e stimated av era g e time to complete the tas k, and inv er sely prop or tio nal to the difference be t ween the optimistic and the p essimistic ending outlo o ks”, means in symbolic languag e nothing mor e than equation (7), says, N = C i K ( P − O + 1)  O + 4 M P + P 6  . 5 10 15 20 2 4 6 8 10 12 14 Curves of function points (P=8, MP:=[1,20], O=3, C=5.4) MP FP K=1 K=2 K=3 Figure 3: The or etic al curves of function p oint c ounts r anging fr om M P = 1 to M P = 20 and i = 0 to i = 1 for di ffer ent values of K . In other words, the total score increases with the time consumed and the intellectual effort, but decre a ses as the tool is more pro ductive. Of cours e, the more the to ol o ptimizes the work, the mo re the cost in intellectual effort is par ed ( C i ), and we may lo ok at par ameter K a s a constant of prop or tionality . The time v ariance is g iven by , σ 2 =  P − O 6  2 , (10) where σ is the standard de v iation. In terms of the deviation σ w e may wr ite, N = C i K (6 σ + 1)  O + 4 M P + P 6  . (11) Note that when tw o or more quantities are indep endent degrees of freedom that interact with o ne a nother, we m ultiply them (in present case, time, inertia and effort). Given that the PE R T factor has temp ora l dimension and tends to increase a s the complexity of the work, to slow the correlative incr ease of the score p oints and to obtain a dimensionless nu mber that can b e int er pr eted as the num ber o f function p oints it is needed a deno minator with relev an t time conten t. The difference betw een p essimistic and optimistic estimates plus one, P − O + 1, provides the maxim um time s pan within which the work will b e consummated; it enters the formula with w eight K = 1 based o n the given IT current contract at MTE to b etter fit the economic reality of this Ministry , with the addition of 1 ensuring that the denominator sha ll never b e zero if the tw o estimates are iden tical. This means that the tota l sco re decreases a s the optimistic time g ets aw ay from the pes simistic outlo ok, a ma nner to provide a kind of ”discount” in function p oints fro m the delay of task completion (uncertaint y in the ending time of the tas k ). 8 Nilo Serp a Indeed, the idea o f a discount in function p o int s by the ”uncertaint y” in the delivery time w as accepted as a fair criterion in face of the ev er- present urgency of the user. It is co n venien t to recall here that the conv ersion factor C accounts for the intellectual weight of each task and the inertia i tells to us whether the effort will b e greater or smaller a ccording to the chosen to ol. When no softw are to ol is used, i. e., the activity is per formed only with hum anware, the v alue o f the inertia of developmen t is zer o. This applies to r aising activities in whic h employ ees are not in use of soft wares for management a nd monitoring of pro jects, spreadsheets and others, b eing the work o rganized in notes a nd handmade s ch edules. This exp onent cov ers the r ange [0 , 1], b eing highest in the HTML mark up languag e, taken as a mor e co nstraining technological alternative for web. The inertia was fixed within the class o f each to ol. Figure 2 shows the shap e o f theoretical curves of counting acco rding to the inertia of developmen t i fo r three v alues of K . Figure 3 shows the shap e of theoretical curves of counting in a different per sp ective, accor ding to the simultaneous v ariation of time M P and ine r tia of developmen t i for the same three v alues of K . An interesting question app ear s when no too l is used, such that, for i = 0, there is alwa ys C p ow ered by 0, i. e., C 0 = 1 . Thus, the intellectual effort w ould b e, by definition, equal to 1 in any situa tio n in which no too l was r equired. In this ca se, the conclusion is simply that without the use of a n y to ol it would b e large ly ar bitrary to differentiate intellectual efforts, since the idea is precisely to ev aluate changes in effort in the presence o f a to ol in a cer tain pro ject phase. Ther e fore, if no to ol is applied, we no r malize the effort fo r all individuals and pro ject pha s es, so that it do es not dep end on particular task or individual its e lf. In this case, the difference in function p oints is in charge of the PER T time and v ariance P − O (indeed, it is logic a lly co nsistent with the fact that without to ol ther e is no ” measurement apparatus” that allows to ev aluating the intellectual effort by the in tera ction ma n-to ol). F or instance, let us take the hypothetic counting o f a survey with the client not supp orted b y any soft ware. F rom T a ble 1 w e hav e the following v alues: • O = 24 : 00 h , • P = 36 : 00 h , • M P = 32 : 00 h . F rom T able 2 w e extract for C the v a lue 3 . 2 corres p onding to the sur vey step. Since ther e is no to o l, i = 0. Then, formula (7) computes, N = 1 13  24 + 4 × 3 2 + 36 6  ≃ 2 . 41 . T aking the v alue of the function p oint for new implemen tations , V p =R$480 . 00, the total v alue to pay by the ta sk would be V t =R$1 , 156 . 92. Now, supp osing the us e of manag ement to ols ( i = 0 . 6 0 ), we get, N = 3 . 2 0 . 60 13  24 + 4 × 32 + 3 6 6  ≃ 4 . 84 , amount of p oints tha t mult iplied by the p oint v a lue furnishes V t =R$2 , 324 . 84. T he difference in v alues means that b etw een using and not using a to ol there is a logical difference of in tellectual effort; as well as the knowledge r e quired for the survey , it is necessa ry to know the s pecific s oft ware. Now w e will se e some examples of calculation, fr o m the exp erience in MTE, to v alidate equatio n (7) as a po stulate. Be the task of dra fting a new form of medium complexity . F r om T able 1 we hav e the following v alues: • O = 2 : 0 0 h , • P = 8 : 00 h , • M P = 6 : 00 h . F rom T able 2 we extract for C the v alue 5 . 8 corres p onding to the elab oration step. Since the to ol is the HTML ma rkup langua ge, i = 1. Then, formula (7) computes, N = 5 . 8 7  2 + 4 × 6 + 8 6  = 4 . 69 52 . (12) T aking the v alue of the function point for new implemen tations , V p =R$480 . 00, the total v alue to pay by the task would b e V t =R$2 , 253 . 70. F or a form of high complexity , have done at the same conditions, • O = 4 : 0 0 h , • P = 12 : 00 h , • M P = 9 : 00 h , N = 5 . 8 9  4 + 4 × 9 + 1 2 6  = 5 . 5852 , (13) amount of p oints tha t mult iplied by the p oint v a lue furnishes V t =R$2 , 680 . 89. Note that the difference in amount to b e paid is controlled b y the denominator with weigh t 1 times the expanded time-range P − O + 1. Finally , the example o f the creatio n/developmen t of a layout. F or high complexity we get from T a ble 1, • O = 38 : 00 h , • P = 40 : 00 h , • M P = 3 9 : 00 h , v alues which introduced in form ula (7) dur ing the construction phase in HTML provide, N = 1 . 8 3  38 + 4 × 3 9 + 40 6  = 2 3 . 40 , (14) amount of points that multiplied b y the p oint v alue gives V t =R$11 , 232 . 00 . The or etic al Count of F un ction Points for Non-Me asur able Items 9 A caution to be taken, howev er, refers to whether the for m is, even b eing new, a new implemen tatio n or can b e co nsidered within the co n text of an evolving maintenance in the b o dy of a bro a der set of ob jects belo nging to the same application. If it is new, but belo nging to a previo usly developed application in another ar ea, it will b e considered new implementation; if it is new, but b elonging to a previous ly develop ed application in the same area , it will b e considered evolving maintenance. 4.1 The coun ting of the Pro jectiv e Statistical Bulletin The Pro jectiv e Statistical Bulletin is a r eal quarterly publication of the MTE , ma de av a ilable on the Intranet in ”pdf” format with online abstract. Thus, it is not an web applica tion, so it is necessa ry to q uantif y the parametric v aria ble i in terms o f inertia o f development of s tatistical mo delling to ols in use. T e c hnically , the editors of the bulletin as sume that i = 0 . 65, being the in tellectual effort punctuated by T able 2, item ”Elab ora tion”, i. e., C = 5 . 8 . Regarded as a highly complex pr o duct, it provides the fo llowing s teps: 1. Sur vey o f v ariables • O = 20 : 00 h , • P = 30 : 0 0 h , • M P = 25 : 00 h , • i = 0 , 7 (search in s tatistical data bases), • C = 3 , 2 (survey). Thu s, expres s ion (7) computes N = 3 , 2 0 , 7 11 ×  20 + 1 00 + 3 0 6  = (15) = 0 , 205 × 25 = 5 , 13 . 2. E TL pro ces s • O = 50 : 00 h , • P = 80 : 0 0 h , • M P = 65 : 00 h , • i = 0 , 36 (ETL to ol), • C = 5 , 4 (ETL la ng uage). Thu s, expres s ion (7) computes N = 5 , 4 0 , 36 31  50 + 260 + 80 6  = (16) = 0 , 059 × 65 = 3 , 85 . 3. Sta tis tica l analysis • O = 50 : 00 h , • P = 80 : 00 h , • M P = 65 : 00 h , • i = 0 , 65 (statistical to ols), • C = 5 , 8 (elab oration). Thu s, ex pression (7) co mputes N = 5 , 8 0 , 65 31 ×  50 + 260 + 80 6  = (17) = 0 , 1 01 × 65 = 6 , 57 . 4. T e x t ela bo ration • O = 40 : 00 h , • P = 60 : 00 h , • M P = 50 : 00 h , • i = 0 , 40 (W ord to ol), • C = 5 , 8 (elab oration). Thu s, ex pression (7) co mputes N = 5 , 8 0 , 4 21 ×  40 + 200 + 60 6  = (18) = 0 , 0 96 × 50 = 4 , 81 . The total function p oints is, N T otal = 5 , 1 3 + 3 , 9 + 6 , 57 + 4 , 8 1 = 2 0 , 41 , amount that mult iplied by the po in t v alue for developmen t ( V p =R$480 . 00) pro duces V t =R$9 , 796 . 80. This ex ample is sufficient to give an idea of how to apply the T a bles in sco ring a v ariety of tasks. 4.2 Impr op er c ounting In so me cases, whe n the estimate e q uals the optimistic and p ess imis tic, we hav e the ” a be r ration count”, that is, an amount o f function p oints higher tha n the initial av erag e score exp e cted. In these situa tio ns, I recommend to assign a maximum similarity of 80% b etw een the t wo estimates ; in other w or ds, the p essimistic es timate should exceed the optimistic at leas t 20 % of the latter to maintain the ob jectivity o f the equation (7 ). Le t us take the ex ample of creation/development of low complexity lay out. By T able 1, • O = 8 : 0 0 h , • P = 8 : 00 h , • M P = 8 : 00 h . 10 Nilo Serp a These v alues en tered in the formula (7) during the construction phas e in HTML provide, N = 1 . 8 2 , 6  8 + 4 × 8 . 8 + 9 . 6 6  = 6 . 092 , (19) amount of points that multiplied b y the p oint v alue gives V t =R$2 , 924 . 30. If this were no t done, N = 1 . 8 1  8 + 4 × 8 + 8 6  = 1 4 . 4 , (20) amount of p oints that multiplied by the po int v alue furnishes V t =R$6 . 91 2 , 00, a result that, by go o d sense, would be muc h more suitable for a lay out of medium complexity . Here, w e see ho w the num ber of function po in ts is strongly sensitive to the dur ation of the task . Therefore, considerable degr ee o f caution is part of the counting of function p oints, even in the classical approach of the technique. The rea de r must note that the pr escrib ed minimum difference p erce ntage of 20 % betw een optimistic and pessimistic per sp e ctiv es of task completion was established to addr ess the particular situations (not to all non-measura ble task s ) in which pr ofessionals can not discern ob jectiv e estimates of duration, whether by level of control ov er the work, whether b y features of the to ol, or even by total dedication to the demand (it is common among progra mmers to devote e xclusively to a certain problem un til it is so lved). Thus, the co rresp onding 20 % v a riance, enough to ens ure sig nificant re s ults in the present metr ic , is primarily applicable to str ong-function items such as the rea der c an infer from a quick lo ok a t T able 1 (this T able highlights in g rey background the typical tasks where occ ur s ab erration coun ts). T able 4 shows a r eal counting a t MTE with co lumns having p oint v alues for the ta s ks and deflation factor s acco rding to the current contract (the function point for adequa tio n is mo re exp ensive). This co un ting applied the 20 % v ariance betw een optimistic and p essimistic estimates. There is also the is s ue o f high nu mber o f pag e s, images and other s in the dev elopment of sites and po rtals, which can distort co nsiderably the final v alue to be paid by extr ap olating at very fa ir the paymen t for the required w or k. Unless the so -called ” maintenance page s ”, for the manag ement of co n tent for a ll other development items (images, pa ges, videos, etc.) I suggest the following rule: 1. num b er of pages, ima ges, etc. b etw een 1 and 9 ⇒ Qua ntity = 1; 2. num b er of pages, ima ges, etc. ≥ 1 0 and < 6 0 ⇒ Q uantity = 2; 3. num b er of pages, ima ges, etc. ≥ 6 0 and < 1 00 ⇒ Quanti ty = 3; 4. num b er of pages, ima ges, etc. ≥ 1 0 0 and < 5 00 ⇒ Quanti ty = 4; 5. num b er of pages, ima ges, etc. ≥ 5 0 0 and < 1 000 ⇒ Qu a ntity = 8; 6. num b er of pages, images , etc. ≥ 1 000 ⇒ Qu a ntity = 16. 4.3 The c ounting as c ontinuous function of the time Strictly sp eaking , a pro ject constitutes a t ypica l nonlinear s ystem. How ever, for all practical pur po ses, it is r easonable to do a simple linear appro ach for the time evolution of the num b er co unts, applying a p osteriori cor rections in or der to minimize the effects of unpredictable fluctua tio ns. The theo retical coun t of function points is a contin uous function of the most likely time M P . This is a simple conclusio n, if we think that b oth O and P are fixed, being M P widely v ariable. While i and C are usually regarded as parameters, i can b e taken by a flux b etw een 0 and 1 (figures 2 and 3) if we think tha t the pro ductivity of a to ol v aries c o nt inuously with practice stemming from the freq uen t use. Althoug h a go o d way to visualize the shap e functions, it is a difficult and p o orly pragmatic approach (to quantify the increased pro ductivity of the too l accor ding to usa ge is a pro cess that e nds, fo r all purp oses, in the r eduction of observ ational v ariable M P ). In the case of time, the deriv ative of N with resp ect to M P will g ive us the incre a se or decrease in the num b er of function p oints p er hour difference in M P . Thus, the equation dN dM P = 2 C i 3 K ( P − O + 1) (21) provides the num b er o f po in ts per hour to b e added or subtracted fr om the total initial targe t after completion of the task, when w e regis ter the per formed rang e of M P . Thu s, the final num b er o f function p oints is given by the gauge function, N ± dN dM P = C i K ( P − O + 1)  O + 4 M P + P 6  ± (22) ± 2 C i H 3 K ( P − O + 1) , ⌣ N = C i K ( P − O + 1)  O + 4 M P + P ± 4 H 6  , (23) where ⌣ N is the gauged num b er of function p oints and H is the num b er of hour s to sum o r subtract from M P . Equation (23 ) is very useful to adjusting function p oints for simple jobs with no need of new additional counts. In these cases, it is enough to calibr a te the num b er of hours ( M P ) to fit the r equired paymen t. 5 Conclusion a nd final remarks This study pres e n ted a n extended technique of measurement by function p oints for the so-called non- measurable items. It s how ed how to apply this technique The or etic al Count of F un ction Points for Non-Me asur able Items 11 T able 4 T asks, complexities and durations for one real counting at MTE Counting C Compl O(h) MP(h) P(h) i Poin ts/unity Poin t v alue Amoun t Defl T ot v a lue Defl v alue T ot p oints 1- System CPMR 1.1- Pr ocedure adequation 3.5 high 1.83 1.88 2.33 0.52 2.4895 537.00 100 2 133,68 7.25 66,84 3.63 248.95 1.2- SQL adequation 3.5 high 3.6 4 4.5 0. 52 4.0553 537.00 150 2 326,65 7.86 163,328. 93 608.30 1.3- JS creation 3.5 av erage 4 4.2 5 0.52 4.1243 480.00 30 1 59,3 90.41 59, 3 90.41 123.7 3 1.4- Comp onent creation 3.5 high 4 4.2 5 0.52 4.1243 480.00 30 1 59, 390.41 59 ,390.41 123. 73 1.5- A SP adequation 3.5 high 3.6 3.8 4.5 0.52 3.9207 537.00 180 2 378, 977.34 189,4 8 8.67 705.73 1.6- A SP cr eation 3.5 high 5.6 5.8 7 0. 52 4.7691 480.00 160 1 366,26 6.45 366,266. 45 763.06 TOT AL 1,324, 369.73 904,708. 5 0 2,57 3.50 to different examples of the everyday tasks in a r e al IT area, the General Co or dination o f Information and Informatics o f the Ministry o f W ork and Employment at Br azil. The use o f this tec hnique, now included in our Systems Developmen t Metho dology , has proven to b e compatible with lo cal market prac tice s and budgeting constraints normally present in the public administration. Clearly , no counting technique is per fect. With practice, we see that some counts will pro duce higher v alues, some lower v alues, in a dialec tic that so metimes seems unfair, but that at the final will s how equilibrium of the ov erall balance billed by a simple tradeoff betw een the individual amo un ts. As Anita Cassidy a nd Keith Gug g enberger say , ”Metrics should be viewed as navigationa l data r ather than as co nclusions o r destinations” (Cassidy & Guggenberger , 2001 ). It should be noted tha t the T ables may increase at a ny time due to po ssible needs for a daptation to unfor eseen situations. I a m firmly co nvinced that the technique w or ks, bo th by the relative success it has a ch ieved as the logic up on which it was built. An yway , qualit y is an is sue that p ermeates all activities and their outcomes , including methodolo gies and techniques o f calculation. As can be seen, the int ro ductio n of the theor e tical expression (7) for calculating function p oints relating to the so-called non-measura ble items do es not wan t to maximize o r minimize the a mo un ts inv olved. This e quation merely establish a fair and logical cr iter ion of v aluation, based on k nowledge em b o died in the market, in such a wa y as to provide mana gers with to ols technically well made and safe, a nd to include in metric contractual features, with the same imp or tance and seriousness , so essential IT tasks such as creation and developmen t of the shap e of our sites a nd p ortals. 6 Ac kno wledgements The author a ckno wledges the IT Manager of the Ministry of W ork and E mploymen t at B razil, Mr. Sergio Alves Cotia, for the comments on the manuscript and for his int eg ral supp ort to this work. 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Softw are Eng ineering Pr o ductivity Handbo o k, McGraw-Hill. The or etic al Count of F un ction Points for Non-Me asur able Items 13 Note 1 The fuzzy logic tries to fulfill the gap of infinite degrees of uncertaint y b etw een ”to b e” or ”not to b e”. The intrinsic imp erfections of the information represented in natural language have b een treated more ap p ropriately by fuzzy logic than by t h e t heory of probabilities. 2 The energy consumed by the intellectual effort during time t has its equ iv alen t in function p oin ts. The effort reduces, after all, to an amount of function p oints, so that the u n its of L and J are the same. 3 The Lu mis is a Brazilian softw are company pioneering in developmen t of pro ducts and solutions for enterprise p ortals.