Reuse-Based Test Traceability: Automatic Linking of Test Cases and Requirements

Size: px
Start display at page:

Download "Reuse-Based Test Traceability: Automatic Linking of Test Cases and Requirements"

Transcription

1 Inernionl Journl on Advnces in Sofwre, vol 7 no 3&4, yer 2014, hp:// Reuse-Bsed Tes Trcebiliy: Auomic Linking of Tes Cses nd Requiremens 469 Thoms Nock, Thoms Krbe Technische Universiä Berlin, Dimler Cener for Auomoive IT Innovions (DCAITI) Berlin, Germny Emil: {homs.nock,homs.krbe}@dcii.com Seffen Helke Brndenburg Universiy of Technology Cobus - Senfenberg (BTU) Cobus, Germny Emil: [email protected] Absrc Sfey sndrds demnd full requiremen rcebiliy, which includes complee rcing beween requiremens nd es cses o sipule how requiremen hs o be verified. However, implemening such concep rigorously is ime-consuming nd cosly. Furhermore, in he uomoive indusry his cos is repeedly incurred for ech vehicle series, becuse in conrs o oher developmen refcs, reuse sregies for rce links hve no ye been sufficienly reserched. This pper presens he novel pproch of Reuse-bsed Tes Trcebiliy, which llows for more cos-effecive implemenion of rce links in cerin cses. Firs, we idenify nd formlize scenrio, he so clled RT-Problem, for reusing rce links beween es cses nd reused requiremens, which hs been observed in indusry prcice. Nex, bsed on his formlizion we propose 3-lyered mehod, which uomiclly crees links beween es cses nd reused requiremens. For resons of prcicliy, we focus on he firs lyer, which represens rnsiive es-link reuse. Finlly, we presen he resuls of wo field sudies demonsring h our pproch is fesible in prcice. As he min conribuion of his work we show h he uomed reuse of es cses on he bsis of reused requiremens is boh possible nd useful. Keywords Reuse; Requiremens; Tes cses; Trcebiliy. I. MOTIVATION New sfey sndrds like ISO men demnd for rcebiliy is higher hn ever. Consequenly, uomoive compnies mus work hrd o esblish rcebiliy for every phse in he V-Model. For insnce, if sofwre error occurs, he specific pr of he source code h hs cused i should be idenified. This is chieved by rce linking developmen refcs. In hierrchicl developmen processes, links beween requiremens nd es cses re some of he firs o rise. These links re n inegrl pr of relionship nework. For exmple, n error is discovered by es cse. This es cse is rce linked wih sysem requiremen, which in urn is conneced o he source code. Ech kind of comprehensibiliy necessies links beween he requiremens involved. However, rigorously implemening such concep is imeconsuming nd cosly. Furhermore, in he uomoive indusry his cos mus be pid for ech vehicle series projec, repeedly, becuse in conrs o oher developmen refcs, reuse sregies h genere rce links uomiclly hve no been sufficienly reserched. Therefore, we propose novel mehod for reuse-bsed rcebiliy, which exends [1] nd llows for more coseffecive implemenion of rce links in cerin cses. Among oher hings, he ISO sndrd defines demnd for wo cegories of rce links. The firs is clled Tes Trcebiliy ISO P. 8 [2, p.25] nd reles o link convenion for es specificions. Ech specificion in es cse mus include reference o he version of he ssocied work produc. The second cegory reles o Reuse-bsed Trcebiliy ISO P. 6 [3, p.20] which demnds h every sfey-reled sofwre componen mus be clssified ccording o informion on reuse nd modificion. Thus, he sndrd defines four clsses: newly developed, reused wih modificion, reused wihou modificion, nd commercil off-he-shelf produc. Our pproch conribues o boh clims. Firs, we provide cos-effecive echnique for uomiclly genering rce links beween es cses nd requiremens, which ddresses he es rcebiliy of he ISO sndrd. Secondly, we provide he generion of rce links beween requiremens or es cses from previous projec nd he corresponding counerprs in new projec, o indice h previous refcs hve been reused. Furhermore, our frmework llows for hese links o be qulified, by using ypes reflecing wheher n refc ws modified or no. Srucure. The nex secion inroduces moiving exmple, illusring scenrio where rce links cn be reused. The secion lso gives imporn definiions of developmen refcs. The secion closes wih he presenion of he RT-Problem (Reuse-bsed Tes Trcebiliy Problem), which forms he bsis of his pper. Secion III gives poiners o reled work. We briefly survey exising rcebiliy models nd mehods. We lso idenify limiions of hese pproches o jusify he need for his work. Secion IV presens our 3- lyered mehod, where we focus on he firs lyer, he so-clled RT-linking echnique. Secion V describes heoreicl conceps behind our RT-linking sregy. Subsequenly, Secion VI presens he resuls of wo field sudies demonsring h our pproch is fesible in prcice. We lso compre our echnique wih he previous mnul procedure. To give he reder n impression of he complee mehod, Secions VII nd VIII skech he second nd he hird lyer. The pper closes wih conclusions nd fuure work in Secion IX. 2014, Copyrigh by uhors, Published under greemen wih IARIA -

2 Inernionl Journl on Advnces in Sofwre, vol 7 no 3&4, yer 2014, hp:// II. SYSTEM REQUIREMENTS AND TEST CASES A. Inroducory exmple Figure 1 shows n exmple bsed on rel specificion documens. The upper lef box conins refcs from previous vehicle series projec, e.g., vehicle funcion 1000: Inerrup of fron wiping during engine sr. Requiremens 1001 nd 1002 refine vehicle funcion The lower box conins es cses, e.g., es cse 5376: Wshing during engine sr. Requiremen 1002 nd es cse 5376 re conneced vi rce link. Requiremens reuse. Reuse hppens in ll phses of he V-Model; herefore, reuse lso pplies o requiremens. Requiremens re reused from previous vehicle series in order o specify new vehicle series. Techniclly, his reuse is chieved by copying nd dping he old requiremens o he new vehicle series projec. The upper righ box in Figure 1 shows he reuse requiremens. For exmple, he reuse requiremen 1002-new hs been chnged mos: he descripion of he wshing inerrupion hs been moved. Tes rce reuse. This dpion of requiremens exemplifies he min feure of Reuse-bsed Tes Trcebiliy: Is es cse 5376, which lredy verifies source requiremen 1002, lso suible for verifying rge requiremen 1002-new? More succincly: Cn es cse 5376 be linked wih rge requiremen 1002-new? Figure 1: Exmple requiremens nd es cses in DOORS B. Sysem Requiremens Specificion (SRS) A vehicle is described by mny SRS. Every sysem, like he Wiper Conrol or he Ouside Ligh Conrol is specified in one SRS. The min engineering refcs in SRS re vehicle funcions nd he sysem requiremens h refine hem. Individul vehicle funcions cn be very exensive. For insnce, he funcion wipe windscreen is chrcerized by severl civion possibiliies, wipe sges, pssenger nd pedesrin splsh proecion, ec., nd herefore is refined by more hn 300 requiremens. 470 Coun per vehicle series. If one funcion lone cn hve 300 requiremens, how mny requiremens does whole vehicle series hve? The following esime gives vgue ide: Modern vehicles hve up o 100 elecronic conrol unis (ECU). Usully, muliple uomoive sysems run on ech ECU. For simpliciy, we ssume h only one sofwre sysem runs on ech ECU. Furher, we ssume h midsize sysems hve les 1000 requiremens or more. Using hese ssumpions, modern vehicle cn ccumule hundreds of housnds or even millions of requiremens. Requiremens clssificion. In ddiion, requiremens hve clssifying properies such s Auomoive Sfey Inegriy Levels (ASIL), esbiliy, ownership, supplier sus or dependencies o oher SRS. Therefore, requiremen cegories exis, e.g., sfey criicl, esble or highly dependen requiremens. C. Sysem Tes Specificion (STS) Ech SRS hs les one ssocied STS, which conins es cses o verify he correc implemenion of he requiremens. The srucure of hese es cses corresponds o he common schem: Pre-condiion, pos-condiion, pss-condiion, es seps ec. [4, p.263]. Ech requiremen which is clssified s esble is rce linked o les one es cse. This fcilies comprehensibiliy o deermine he requiremensbsed es cse coverge. Coun per vehicle series. Agin, he quesion rises: How mny es cses does n enire vehicle series hve? Becuse he es cse coun corresponds o he requiremens coun, modern vehicle hs les s mny es cses s requiremens. Usully, more ess hn requiremens exis. Tes cse clssificion. Like requiremens, es cses hve clssifying properies such s es gols, es levels or es plforms. While es gols resul from quliy models s proposed in ISO 9126 [5], es levels describe he righ brnch of he V-Model. Auomoive-specific es plforms include Vehicle Nework or HiL (Hrdwre-in-he-Loop). D. Tes Concep (TC) The ISO dices he exisence of TC. I defines which es objecs mus be esed which es level on which es plform in order o fulfil which quliy gols (Wh? When? Where? Why?). The TC deermines he relionship beween he lef nd righ brnches of he V-Model. We focus on he sysem level of he V-Model becuse Reuse-bse Tes Trcebiliy uses he requiremen es objec ype. In our cse, he TC defines which es cses mus be rce linked wih which requiremens o sufficienly verify vehicle series. Usge of requiremens nd es cse clssificion. The TC does no conin specific sysem requiremens or es cses. I relies on he clssifying properies of he refcs involved. For insnce, requiremen s ASIL rnking influences esing expenses becuse i is srongly reled o he es gol nd es level properies of he es cse. The higher he ASIL rnking, he more es cses mus be rce linked wih requiremens. The TC llows us o ssess he rce link coverge beween SRS nd STS. 2014, Copyrigh by uhors, Published under greemen wih IARIA -

3 Inernionl Journl on Advnces in Sofwre, vol 7 no 3&4, yer 2014, hp:// E. RT-problem Reuse-bsed Tes Trcebiliy relies on specific siuion observed in indusril prcice: The RT-problem. Figure 2 depics how he RT-problem reflecs he Reuse relionship beween wo SRS nd he Tes relionship beween n STS nd hese wo SRS. In he exmple, requiremen of he funcion fron wiping (fw) from he SRS Src hs been reused by fw 0 in he SRS Tg. Figure 2: RT-problem wihin specificion documens R: Reuses. Among ohers, one reuse mehod is o copy n enire SRS ino he projec folder of he new vehicle series projec. Thus wo SRS resul: he SRS Src of he previous vehicle series nd he dped SRS Tg of he curren vehicle series. Boh SRS re in reuse relionship: The SRS Tg reuses he SRS Src. T: Tess. Ineresingly, he STS is no copied beween vehicle series. Insed, he es cses re reused by redirecing rce links from he SRS Src o he reusing SRS Tg. Overll, he RT-problem reflecs he siuion before he STS eners es relionship wih he SRS Tg. R- nd T-links. Techniclly, refcs re conneced by rce links. An R-link fw 0! R fw poins from rge requiremen fw 0 o source requiremen fw. We lso sy (fw 0, fw) is reuse pir. A T-link! T fw poins from es cse o (source) requiremen fw. Solving he RT-problem. The RT-problem is unsolved if he dshed T-link in Figure 2 does no exis. In his pper, we propose rnsiive RT-linking, new echnique o se he T-link! T fw 0 o he rge requiremen fw 0. Business cse. Erlier we esimed whole vehicle series migh hve hundreds of housnds of requiremens nd es cses. Therefore, he RT-problem mus be solved hundreds of housnds or even millions of imes for ech vehicle series projec. Usully, es cses re T-linked during heir creion. This T-linking requires lile effor in comprison o he creion of he es cse. STS re es cse collecions which re minined over muliple vehicle series generions. In ech new vehicle series projec hose STS mus be linked mnully. We observed h boh ime nd moivion ply n imporn role in why fewer nd fewer T-Links exis from projec o projec. The primry gol of Reuse-bsed Tes Trcebiliy is h es cses only need o be T-linked wih requiremens once, he ime hey re firs wrien down. III. RELATED WORK 471 A rce link connecs rce refcs nd defines he ype of relion beween hem [6, p.104]. In generl, rcebiliy is he possibiliy o esblish nd use rce links [7, p.9]. Thus, rcebiliy enbles comprehensibiliy. A rcebiliy (informion) model defines ll possible refcs nd heir ypes, s well s ll possible links nd heir ypes [7, p.13]. Our work conribues o he specil field of requiremens rcebiliy. Requiremens rces re rce links beween requiremens nd oher sofwre developmen refcs [8, p.91]. Requiremens rces lwys hve direcion: forwrds, bckwrds, iner or exr. Link direcion. A forwrd-rce connecs requiremen wih refcs which hve been creed ler in he developmen process. Exmples of forwrd rces re links o rchiecurl refcs, source code or es cses. A bckwrd-rce documens he origin of requiremen. Exmples re links from lws or sndrds. An iner-rce links requiremen wih noher requiremen. These links cn reflec dependencies, refinemen or even reuse. An exr-rce links requiremen wih non-requiremen. Exmples re rchiecurl refcs, source code or es cses. Link direcion in he RT-problem. An RT-problem consiss of wo links: n R-link nd T-link. The R-link connecs source nd rge requiremen. Therefore, i is n iner-rce link. Simulneously, i is bckwrd-rce link becuse i reflecs he origin of he rge requiremen. The T- link connecs es cse wih source requiremen. Thus, i is n exr- nd forwrd-rce link. We observe h even hough he RT-problem is very simple i conins iner, exr, forwrd nd bckwrd rce links. A. Trcebiliy models Trcebiliy models define he involved nd linkble refcs nd he possible link ypes [9, p.106]. The RT-problem is rcebiliy model. The concep of rcebiliy models ppered erly in he developmen of sofwre engineering: he firs models ppered in he 1980s. The following prgrphs inroduce relevn rcebiliy models from he ps 25 yers. Generl models wihou explici T-links. The SO- DOS model [10] represens linkble refcs vi relionl dbse scheme. The rce links re freely configurble. Thus, SODOS is cpble of connecing everyhing wih everyhing. In he erly 1990s, hyperex becme very populr. The ide ws o specify requiremens nd oher sofwre engineering refcs by mens of hyperex nd link hem using hyperlinks. Exmples of hyperex rcebiliy models include HYDRA [9], IBIS [11], REMAP [12], RETH [13], nd he TOORS [14] model. Hyperlinks re minly generic, so everyhing cn be conneced wih everyhing else. Around he urn of he cenury, rcebiliy models shifed heir focus from hyperex models o UML-bsed rcebiliy models [15] [16]. In ccordnce wih he SOTA (Se of he Ar), older rcebiliy models re more generl while newer models re more specific. Newer work focuses on links beween requiremens [17] or links beween requiremens nd design refcs [18]. Alhough i is possible o define T-links in generl rcebiliy models, he models discussed here do no explicily suppor T-links. 2014, Copyrigh by uhors, Published under greemen wih IARIA -

4 Inernionl Journl on Advnces in Sofwre, vol 7 no 3&4, yer 2014, hp:// Models wih T-links. In recen yers, sofwre esing hs become incresingly populr. Thus, T-links hve become n explici pr of rcebiliy models. Ibrhim e l. propose he Tol Trcebiliy Model [19]. They consider requiremens (R), es cses (T), design (D) nd code (C). The model is exhusive becuse i suppors pir-wise exr-rces beween he refcs R-T, R-D, R-C, T-D, T-C nd D-C. Furhermore, i suppors he iner-rces D-D nd C-C. Asuncion e l. hve developed n End-o-End rcebiliy model [20]. They consider mrkeing requiremens (M), use cses (U), funcionl requiremens (F) nd es cses (T), which cn be exr-linked in M-U, U-F nd F-T pipeline. Kirov e l. propose rcebiliy model, which uses performnce requiremens (PR), high level requiremens (HLR), rchiecurl requiremens (AR), sysem requiremens (SR), high level design (HLD), low level design (LLD), es cses (T) nd es plns (TP). Kirov s model llows links beween PR-AR, PR-SR, PR-T, HLR-SR, AR-SR, AR-T, AR-TP, AR-HLD, AR-LLD, SR-T, SR-TP, SR- HLD nd SR-LLD. Azri nd Ibrhim propose memodel [21] o llow rce links beween rbirry refcs, including code, roles nd even oupu files from developer ools. RT-problem. The reled work commonly drws holisic rcebiliy picures. Thus, sndrd gol is o define holisic rcebiliy models nd exhusively lis he engineering refcs nd possible rce link ypes. However, he RT-problem is specilized rcebiliy model which focuses on nrrow se of circumsnces. By using T-links explicily, i focuses on he relionship beween requiremens nd es cses. Addiionlly, he RT-problem inroduces new fcor, he represenion of requiremens reuse wih he help of R-links. B. Trcebiliy mehods nd echniques The Requiremens Trcebiliy Mrix (RTM) ws one of he firs echniques h could sysemiclly hndle rcebiliy [22]. The RTM is simply ble of requiremen rows nd linkble refc columns. Ech cell in he ble represens possible link. Requiremens engineering ools like DOORS [23] suppor he RTM. Newer work is bsed on he ide of uomiclly creing rce links beween refcs nd providing impc nlysis. Two surveys [24, p.2] [25, p.31] cegorize he SOTA of rcebiliy mehods s follows: evenbsed, rule-bsed, feure model-bsed, vlue-bsed, scenriobsed, gol-bsed nd informion rerievl-bsed. Even-bsed Trcebiliy (EBT). EBT [26] inroduces n even service where ny linkble refcs re regisered. The service kes over he rcebiliy nd refcs re no longer linked direcly. Thus, EBT suppors mininbiliy, s evens rigger when refcs chnge. Rule-bsed Trcebiliy (RBT). RBT [27] pplies grmmicl nd lexicl rules o find refcs in srucured specificion documens nd use cse digrms. A pirwise rule mching lgorihm looks for refcs, which mch rule. RBT links hose reled refcs. Feure Model-bsed Trcebiliy (FBT). FBT [28] uses he feure s connecing elemen beween requiremens nd rchiecure s well s requiremens nd design. FBT uses severl consisency crieri, e.g., wheher ech feure hs les one requiremen nd es cse. 472 Vlue-bsed Trcebiliy (VBT). VBT [29] ssumes h complee linkge beween ll involved refcs is no fesible. Thus, VBT suppors prioriized requiremens nd differenly precise rcebiliy schemes. The gol of VBT is o disinguish beween links h genere benefis nd links h only produce coss. Scenrio-bsed Trcebiliy (SBT). SBT [30] uses scenrios, such s se chr phs, which re linked wih requiremens nd code frgmens. The creion of new links is performed rnsiively vi code nlysis. SBT is cpble of compleing links beween requiremens nd code. Gol-bsed Trcebiliy (GBT). GBT [31] uses quliy model o define nonfuncionl quliy gols. Those nonfuncionl gols re hen conneced o funcionl requiremens. The gol of GBT is o rce he chnge impc from funcionl requiremens o nonfuncionl gols. Informion Rerievl-bsed Trcebiliy (IBT). In recen yers, IBT hs become incresingly populr. Severl pproches exis o finding nd linking reled refcs [32]. The generl ide behind IBT is o use informion rerievl lgorihms nd similriy mesures. C. Alignmen wih SOTA (Se-of-he-Ar) EBT propges requiremens chnge o linked refcs. Thus, EBT is echnicl even-bsed mehod o void mnul rcing of impc nd mnul buon clicks. Alhough i would be ineresing o uomiclly execue he RT-problem solving echnique fer requiremens reuse, we do no need EBT o solve he RT-problem mehodiclly. RBT uses grmmicl nd lexicl nlysis o find similr requiremens. Alhough i would be ineresing o find reuse pirs wih RBT, we ssume h ll R-links exis. Becuse of he impornce of vribiliy in he uomoive domin, oher reserch focuses on FBT [33]. VBT ries o reduce he number of links in order o reduce minennce coss. The RT-problem is specilized rcebiliy model o reflec simple circumsnce nd nlyze i holisiclly. Thus, we do no wn o remove ny links in his wy. SBT inroduces n ddiionl connecing refc o link requiremens nd code. Becuse we focus on requiremens nd es cses, we do no desire new refcs. Thus, SBT is lso no suible o solve he RT-problem. New echnique: RT-linking. Firsly, we propose new echnique o rnsiively link es cses by considering requiremens reuse: RT-linking. We presen 3-lyered mehod which inegres our RT-linking wih prs of he SOTA. RTlinking is he primry mehod lyer for creing new rce links beween es cses nd reusing requiremens compleely. To mke he linking more precise we need ddiionl filering echniques, which re execued during he complee RTlinking. These filering echniques define he oher wo lyers of he 3-lyered mehod. While he firs lyer esblishes ll links beween es cses nd reusing rge requiremens, he second nd hird lyers filer ou or highligh suspicious linking siuions. The second lyer uses he ide behind GBT o ssess he es coverge wih respec o es gols nd oher esing crieri. The hird lyer dps IBT o serch for similr RTproblems. 2014, Copyrigh by uhors, Published under greemen wih IARIA -

5 Inernionl Journl on Advnces in Sofwre, vol 7 no 3&4, yer 2014, hp:// IV. 3-LAYERED METHOD Figure 3 depics he mehod lyers s firs proposed in [1]. Ech lyer consiss of he sme hree phses. The specific sks in ech phse differ depending on he chrcerisics of he lyer. Ech subsequen lyer enhnces is predecessor s phses vi ddiionl sks. The generl sks performed in he hree phses re s follows: Exrc RT-problems from SRS Src, SRS Tg nd STS. Se/Filer T-links from STS o SRS Tg. Assess T-links nd highligh he link sus. Figure 4 depics he 3-lyered mehod in more deil. We will use he depiced exmple o briefly inroduce he lyers. A. Firs lyer: Trnsiive RT-Linking Exrc RT-problems. Figure 4 depics n RT-problem: The rge fron wiping fw Tg reuses he source fron wiping fw Src. Thus, (fw Tg, fw Src ) is reuse pir. The es cse fw Tes hs T-link o fw Src. Becuse fw Tes is no ye T-linked o fw Tg, one RT-problem is exrced. Se T-links. The T-links of ll exrced RT-problems re se rnsiively: If es cse is T-linked wih source requiremen nd his source requiremen is R-linked wih rge requiremen, hen he es cse is lso T-linked wih he rge requiremen. Assess T-links. Two scenrios cn occur for ech RTlinked rge requiremen: () I is exully idenicl o he source requiremen nd hence T-link needs no review or (b) i hs been chnged nd, herefore, he T-link mus be reviewed mnully. The hird phse of ech lyer highlighs he SRS Tg ccording o he ssessmen resuls. B. Second lyer: Tes Concep-driven filering Exrc RT-problems. Figure 4 indices h he es cse fw Tes mees he es gol correcness of inerfces. This informion is exrced from he STS nd ppended o he es cse of he RT-problem. We sy h he RT-problem is ugmened wih he clssifying propery es gol. 473 Filer T-links. The TC defines wheher es cse is needed o sufficienly verify vehicle series. In Figure 4, he TC defines h he es gol correcness of inerfces mus be me. Becuse he TC demnds for inerfce es cse such s fw Tes, he RT-linking connecs fw Tes nd fw Tg. Oherwise, fw Tes would hve been filered ou. Assess T-links. While he firs lyer cn only mke semens bou he exisence of T-links, he second lyer lso considers he TC. Therefore, for ech rge requiremen he following more deiled scenrios rise: () missing/superfluous es gols, (b) missing/superfluous es levels nd (b) missing/superfluous es plforms. The SRS Tg is highlighed ccording o he TC coverge. TC-driven filering hs been proposed in [34]. C. Third lyer: Cse-Bsed filering Exrc RT-problems. We ssume h he requiremens in Figure 4 hve clssifying propery, inerfces. While he source requiremen fw Src hs n inerfce o he column swich, he rge requiremen hs n ddiionl inerfce o he rin sensor. In oher words, he inerfces of he reuse pir (fw Tg, fw Src ) hve chnged. Agin, we use he clssifying properies o ugmen he exrced RT-problem. Filer T-links. A Cse Bse conins RT-cses. RT-cses re RT-problems which include n RT-decision nd review noe. The RT-decision defines wheher T-link cn be se o rge requiremen. Figure 4 depics simple RT-cse: if he inerfces chnge, inerfce ess mus be reviewed. This RT-cse is very similr o our curren RT-problem. Thus, he RT-decision Review needed is used o solve i. Assess T-links. While he second lyer only uses clssifying es cse properies, he hird lyer relies on fully ugmened RT-problems. Th mens RT-cses cn be defined freely by king ny clssifying propery ino ccoun. Thus, he ssessmen scenrios re s numerous s he RT-cse possibiliies. Finlly, he RT-cses review noes re copied ino he SRS Tg. Figure 3: 3-lyered mehod Figure 4: 3-lyered mehod in more deil 2014, Copyrigh by uhors, Published under greemen wih IARIA -

6 Inernionl Journl on Advnces in Sofwre, vol 7 no 3&4, yer 2014, hp:// 474 A. Fundmenl Exmple V. RT-LINKING: CONCEPTS Figure 1 showed n exmple wih rel requiremens nd es cses. However, rel requiremens nd es cses re very exensive nd lso confidenil. Therefore, he following secions will use he bsrc exmple in Figure 5 o simplify he problem nd concenre on is relevn feures. Phse 1: Exrc RT-Problems. Figure 5 shows he specificion documens SRS Src, STS nd SRS Tg. Ech exmple SRS conins one vehicle funcion, which is refined by requiremens. While SRS Src conins he source requiremens src i, SRS Tg conins he rge requiremens g i. The Reuse column indices for boh SRS which source or rge requiremens he R-links poin o. The Tes column in SRS Src indices wheher source requiremen is conneced vi T-link wih es cse. The T-links: Before column in STS displys which requiremens he es cses were linked wih before RT-linked hem. Figure 5 conins hree RT-problems wih he following R- (! R ) links nd T-links (! T ): g 1! R src 1 nd es 1! T src 1, g 2! R src 2 nd es 2! T src 2, g 3! R src 3 nd es 3/4! T src 3. Phse 2: Execue RT-linking. The rnsiive RT-linking uses he following ssumpion: IF AND IF THEN rge requiremen reuses source requiremen es cse verifies source requiremen he es cse lso verifies he rge requiremen. Afer performing he RT-linking, he T-Links: Afer column conins he nmes of he source nd rge requiremens which re linked wih he es cse by T-Link. The T? column in SRS Tg indices wheher here is T-link o es cse. The column is se o Check if he ex for he rge requiremen hs chnged or if RT-inconsisencies (see Phse 3) hve been uncovered. As Figure 5 shows, he second lyer of he rnsiive RT-linking resuls in hree solved RT-problems: g 1! R src 1 nd es 1! T src 1 ) es 1! T g 1, g 2! R src 2 nd es 2! T src 2 ) es 2! T g 2, g 3! R src 3 nd es 3/4! T src 3 ) es 3/4! T g 3. Phse 3: Assess T-links. The similriy column of SRS Tg represens he exul similriy of reuse pir in percen. I is clculed wih he help of well-known similriy mesures, e.g., Dice, Jro-Winkler or he Levenshein disnce [35]. As well s exul similriy, severl oher inconsisencies migh occur, e.g., he SRS Src describes fron nd rer wiper. A es cse verifies boh source requiremens: If he reverse ger is engged nd if he column swich is pushed hen he fron nd rer wipers will wipe. Now he rge vehicle series does no provide rer wiper. However, he SRS Tg reuses he fron wiper requiremen nd he T-link from he es cse. The inconsisency rises becuse he es cse verifies funcionliy (rer wiping) which does no exis in he rge vehicle series. B. RT-Linking Figure 5: Fundmenl Before-Afer exmple The following bsic ses describe he RT-problem: SRS Src ˆ= se of source sysem requiremens SRS Tg ˆ= se of rge sysem requiremens STS ˆ= se of sysem es cses The upper lef circle in Figure 6 represens SRS Src, i.e., he se of ll source sysem requiremens. The upper righ circle nlogously represens SRS Tg, i.e., he se of ll rge sysem requiremens. The lower circle shows he STS, i.e., he se of ll sysem es cses. All hree ses re disjoin, hus he overlpping res in Figure 6 do no symbolize inerseced ses, bu linked elemens beween he disjoin ses. Reuse pirs: R-links beween requiremens. An R- link r g! R r src lwys poins from rge o source. A reuse rge requiremen from SRS Tg herefore poins owrds reused source requiremen from SRS Src. Boh rge nd source requiremens cn hve muliple ougoing or incoming R-links. The following ses describe his informion: R := {(r g,r src ) 2 SRS Tg SRS Src r g! R r src } R R,Src := {r src 2 SRS Src 9r g : (r g,r src ) 2 R} R R,Tg := {r g 2 SRS Tg 9r src : (r g,r src ) 2 R} The se R conins reuse pirs (r g,r src ) which show h R-link is poining from r g o r src. Thus, (r g,r src ) 2 R is synonym for r g! R r src. The pir (r g,r src ) is lso reuse pir. The ses R R,Src nd R R,Tg conin ll requiremens h re pr of reuse pir. Thus, R R,Src conins ll reused source requiremens from SRS Src, nd R R,Tg conins ll reusing rge requiremens from SRS Tg. 2014, Copyrigh by uhors, Published under greemen wih IARIA -

7 Inernionl Journl on Advnces in Sofwre, vol 7 no 3&4, yer 2014, hp:// T-links from Tes Cses o Requiremens. A T-link! T r poins from es cse o requiremen. An cive es cse poins owrds les one requiremen. A verified requiremen hs les one incoming T-link from es cse. A es cse cn verify muliple source nd/or rge requiremens, depending on wheher i poins ino SRS Src, ino SRS Tg or boh. T : SRS Src [ SRS Tg!P(STS) T(r ) := { 2 STS! T r } R T,Src := {r src 2 SRS Src 9 2 STS :! T r src } R T,Tg := {r g 2 SRS Tg 9 2 STS :! T r g } For given requiremen r (source or rge), he funcion T derives ll es cses h re linked wih i. The se R T,Src conins ll source requiremens r src from SRS Src for which les one T-link! T r src poins from es cse from STS o r src. Anlogously, he se R T,Tg conins ll rge requiremens r g h re linked wih les one es cse. RT-linking. Wih hese forml conceps we cn reformule he ssumpion for he rnsiive RT-linking: IF AND IF THEN rge requiremen r g nd source requiremen r src re linked by n R-link es cse is linked wih r src by T-link cn lso be linked o r g by T-link. This is represened by he formul r g! R r src ^! T r src )! T r g An RT-link, i.e., soluion for one of he hree RT-problems from he bsrc exmple in Figure 5 is shown here: C. RT-digrm 475 The RT-digrm is mens o represen he number of linking siuions beween requiremens nd es cses. I cegorizes hese siuions ino differen ypes, e.g., reused bu no esed requiremens, reused nd esed requiremens. Figure 7 show he digrm schemiclly. The differen segmens of he digrm represen he differen ypes of linking siuions, which resul from he exisence or non-exisence of links beween he hree bsic ses SRS Src, STS, nd SRS Tg. Ech segmen is lbelled wih differen symbol (e.g.,, ) h represens he ype of he segmen. In he indusril use nd field sudies in Secion VI, he digrm segmens show he number of linking siuions. RT-insnces nd RT-ypes. From now on, we cll he differen linking siuions RT-insnces. Every RT-insnce is ssigned o n RT-ype (e.g., no esed bu reused requiremen). All RT-insnces from he sme segmen of he digrm re lso from he sme RT-ype. An RT-insnce is denoed by se, which conins eiher one refc (mening h his refc is no linked) Corresponding ypes:,,, one link (mening h he wo linked refcs re no linked o hird refc) Corresponding ypes:,,, wo links (mening h one R-link nd one T-link exiss, bu one T-link is missing o one of he prners of he reuse pir) Corresponding ypes: inconsisen, or hree links (fully linked, solved RT-problem wih reuse pir nd T-links o boh prners of he pir) Corresponding ypes: consisen. On he nex pge we will exmine he segmens of he RT-digrm. Ech segmen will lso be given shor nme for fuure reference. g 1! R src 1 nd es 1! T src 1 ) es 1! T g 1 Figure 6: Ech RT-problem is RT-insnce mong ohers Figure 7: Types of RT-insnces 2014, Copyrigh by uhors, Published under greemen wih IARIA -

8 Inernionl Journl on Advnces in Sofwre, vol 7 no 3&4, yer 2014, hp:// Requiremens wihou RT (, ). Figure 8 depics hose requiremens which hve no R-link nd no T-link. The segmen on he lef-hnd side represens ll discrded SRS Src requiremens which hve no been esed ( ). The segmen on he righ-hnd side conins ll new SRS Tg requiremens which hve no ssocied es cses ( ). : R Src T Src := {{r src } r src 2 SRS Src \ (R T,Src [ R R,Src )} : R Tg T Tg := {{r g } r g 2 SRS Tg \ (R T,Tg [ R R,Tg )} Reused requiremens wihou T ( ). Figure 8b depics ll reuse pirs (r g,r src ), which hve no T-link o eiher r g or r src. From he perspecive of he SRS Tg hese re ll reusble nd unesed rge requiremens. Alhough we use he word unesed, requiremens wih missing T-links do no remin unesed in indusril prcice. The mpping beween requiremens nd es cses is hen performed by engineers in n experience-bsed fshion. Of course, in his cse esing kes plce in SRS Tg ; i is simply less rceble. 476 Tes cses wihou T ( Src, Tg ). Figures 8e nd 8f depic he es cses which hve no T-links ino SRS Src or SRS Tg. In he conex of he corresponding SRS hose es cses re incive. [ Src : T(r src ) := {{} /2 T(r src )} r src 2SRS Src [ Tg : T(r g ) := {{} /2 T(r g )} r g 2SRS Tg Se of ll RT-insnces. An RT-insnce represens concree link beween one, wo, or hree refcs. The se of ll possible RT-insnces RT Ins is defined by: RT Ins := [ [ [ [ [ [ Src [ Tg :RT Src Tg := {{r g! R r src } (r g,r src ) 2 R ^ T(r g ) [ T(r src )=;} Tesed requiremens wihou R (, ). Figure 8c shows ll requiremens h re no in reuse relionship bu which hve ssocied es cses. The segmen on he lef-hnd side depics source requiremens which re no reused, hve no R- link bu do hve T-link from es cse ( ). The righ-hnd side shows ll new rge requiremens which hve no R-link bu new T-link ( ). : R Src T Src := {{r src } r src 2 R T,Src \ R R,Src } : R Tg T Tg := {{r g } r g 2 R T,Tg \ R R,Tg } The one-refc insnces {r src } 2, {r g } 2, {} 2 Src nd {} 2 Tg symbolize refcs which re no linked o ny oher refcs. The onelink insnces {r g! R r src } 2, {! T r src } 2, nd {! T r g }2 represen link beween excly wo refcs, which boh re no linked o ny oher refc. The wo-link insnces {r g! R r src,! T r src } 2 Src, nd {r g! R r src,! T r g } 2 Tg represen source nd rge requiremen linked by n R-link nd es cse which is linked o eiher he source requiremen or he rge requiremen. However, he second es link is missing. The hreelink insnces {r g! R r src,! T r src,! T r g }2 Src+Tg represen fully linked insnces. RT-problems ( ). Figure 8d shows he cener of he RTdigrm. I represens he RT-problems, i.e., ll RT-insnces, which hve reuse pir (r g,r src ) nd es cse which is T-linked o les one of he reuse prners. Therefore, he digrm cener bundles hree RT-ypes: RT-insnces which hve reuse pirs (r g,r src ) nd T-link o r src ( Src). RTinsnces wih reuse pirs which re only r g T-linked ( Tg). RT-insnces which hve reuse pirs nd T-link o boh prners of he pir ( Boh). () R Src T Src or R Tg T Tg (b) R T Src Tg :R T Src+Tg := 8 < {r g! R r src,! T r src } 9 = : (r g,r src ) 2 R ^ 2 T(r src ) ^ /2 T(r g ) ; 8 9 < {r g! R r src,! T r g } = [ : (r g,r src ) 2 R ^ 2 T(r g ) ^ /2 T(r src ) ; 8 9 < {r g! R r src,! T r src,! T r g } = [ : (r g,r src ) 2 R ^ 2 T(r src ) ^ 2 T(r g ) ; (c) R Src T Src or R Tg T Tg (d) R T Src+Tg (e) T(r src ) (f) T(r g ) Figure 8: Segmens in he RT-digrm 2014, Copyrigh by uhors, Published under greemen wih IARIA -

9 Inernionl Journl on Advnces in Sofwre, vol 7 no 3&4, yer 2014, hp:// D. RT-inconsisencies We will now exmine insnces of he ype :RT Src+Tg in more deil. In hese insnces, es cses re T-linked wih one or boh prners of n RT-problem s reuse pir (r g,r src ). Bu, in prcice es cses re no only linked wih one reuse pir. Usully, hey hve links o muliple reuse pirs or even requiremens which hve no reuse relionship o oher requiremens, which cuses inconsisencies. Therefore, RTinconsisencies re cused by missing T-links or unfvourble overlps of reuse pirs wih oher requiremens which re no pr of reuse pir, or by combining or spliing requiremens. An RT-inconsisency is no necessrily n error, bu n engineer should look ino he RT-insnce o check i. The following formuls describe he condiions for reuse pir o be clled consisen: Consisency rule I. The firs consisency rule sys h T-link mus poin o boh prners in reuse pir. If his rule is broken i indices eiher overlooked source T-links or new rge T-links. Two forms of rule I exis: I Src (r g,r src ) := T(r src ) T(r g ) I Tg (r g,r src ) := T(r g ) T(r src ) The firs form I Src sys h he se of ll es cses which re T-linked wih he source requiremen r src of reuse pir (r g,r src ) mus lso be T-linked wih he rge requiremen r g. The second inconsisency form I Tg is nlogously defined: ll es cses which re T-linked wih r g of reuse pir (r g,r src ) mus lso be T-linked wih r src. Consisency rule II. While he firs inconsisency rule ssesses reuse pir loclly, he second inconsisency rule kes oher requiremens ino ccoun. I sys h ech es cse h is T-linked o given reuse pir is no llowed o es oher requiremens which re no pr of noher reuse pir. Therefore, his second rule highlighs discrded source or newly dded rge funcionliy from he esing perspecive. Agin, wo forms of inconsisency rule II exis: II Src (r g,r src ) := 8 2 T(r g ) [ T(r src ): 8r 0 src 2 SRS Src :r 0 src 6= r src ) (! T r 0 src )9r 0 g 2 SRS Tg :! T r 0 g ^ (r 0 g,r 0 src ) 2 R) 477 exmple of fron nd rer wipers. The fron wiping requiremen hs been reused nd he reuse pir (fron g, fron src ) exiss. Becuse he es cse is T-linked wih fron src i hs been rnsiively RT-linked wih fron g. Thus, is T-linked wih boh prners of he fron wiping reuse pir. Now, is lso T- linked wih he source rer wiping requiremen rer src, which hs no been reused becuse he new vehicle series does no provide ny rer wiping. Since no reuse prner exiss for rer src, cuses (fron g, fron src ) o be inconsisen II Src : Tes cse verifies funcionliy which does no exis in he rge vehicle series. The second form II Tg is defined nlogously from he perspecive of he SRS Tg. Consisency rule III. The hird consisency rule indices wheher rge requiremen hs been mlgmed from muliple source requiremens or source requiremen hs been spli ino muliple rge requiremens. A T-link becomes problemic if source requiremen hs been spli. I is hen uncler which rge requiremen needs o be T-linked. Agin, wo forms of consisency rule III exis: III Src (r g,r src ) 0 g 2 SRS Tg : r g 6=r 0 g ^ (r 0 g,r src ) 2 R III Tg (r g,r src ) 0 src 2 SRS Src : r src 6=r 0 src ^ (r g,r 0 src ) 2 R The firs form III Src sys h he source requiremen r src of he reuse pir (r g,r src ) mus no be source prner of noher reuse pir. III Tg sys h he rge requiremen r g of he reuse pir (r g,r src ) mus no be rge prner of noher reuse pir. Exension of he cenre of he RT-digrm. The cenre of he RT-digrm couns consisencies nd inconsisencies. While consisenly solved RT-problems re couned in he upper region of he cenre, he inconsisen RT-insnces re couned in he lower region. As depiced in Figure 9, we furher differenie beween source nd rge inconsisencies in his lower cenre region. Source inconsisencies X Src indice missing T-links which poined o source requiremens bu no reusing rge requiremens or splis in source requiremens. Trge inconsisencies X Tg indice progress becuse of newly dded T-links. Source inconsisencies re bd inconsisencies nd rge inconsisencies re good inconsisencies. II Tg (r g,r src ) := 8 2 T(r g ) [ T(r src ): 8rg 0 2 SRS Tg :rg 0 6= r g ) (! T rg 0 )9rsrc 0 2 SRS Src :! T rsrc 0 ^ (rg 0,rsrc 0 ) 2 R The firs form II Src sys h reuse pir (r g,r src ) is consisen if ll es cses of r src re only T-linked wih oher source requiremens rsrc 0 which re pr of reuse pir (rg 0,r0 src ), for some rge requiremen rg 0. In ddiion, ll such es cses mus be T-linked wih rg 0. To improve he rede rs undersnding of inconsisency II Src we will repe he Figure 9: Inconsisencies in he digrm cenre 2014, Copyrigh by uhors, Published under greemen wih IARIA -

10 Inernionl Journl on Advnces in Sofwre, vol 7 no 3&4, yer 2014, hp:// 478 Inconsisency I Src. Figure 10 depics he reuse pir (r g,r src ) nd he dshed T-link from es cse o r src. The dshed T-link cuses he reuse pir o be inconsisen I Src becuse T(r src ) 6 T(r src ). This siuion represens ypicl RT-problem h needs do be solved. r src r g Inconsisency I Tg. In Figure 10, he reuse pir (r g,r src ) would be inconsisen I Tg if he dshed T-link poined from o r g insed of r src, i.e.,! T r g. In indusril prcice, his siuion usully occurs when new es cse hs been dded fer reusing requiremen. () Inconsisency I Src Inconsisency II Src. Figure 10b depics inconsisency II Src in reuse pir (r g,r src ). We clerly see h (r g,r src ) is consisen I Src nd I Tg becuse T(r src ) T(r g ) nd T(r g ) T(r src ). However, inconsisency II Src for (r g,r src ) is cused by he dshed T-link from o rsrc 0. From he perspecive of he reuse pir (r g,r src ), es cse is T-linked wih he requiremen rsrc 0, which hs no reuse pir prner nd hus no hs been reused. r src r src (b) Inconsisency II Src r g Inconsisency II Tg. The reuse pir (r g,r src ) in Figure 10b is inconsisen II Src. I would be inconsisen II Tg if he dshed T-link poined from o newly dded rg 0 insed of rsrc 0, which hs no been reused. r src r src r g r g Inconsisency II Src ^ II Tg. Figure 10c depics reuse pir (r g,r src ), which is inconsisen II Src nd II Tg. Agin, he reuse pir is consisen I Src nd I Tg. Tes cse is T-linked wih rsrc 0 nd rg 0, which re no reuse pir. The lef dshed T-link cuses inconsisency II Src, nd he righ dshed link cuses inconsisency II Tg. (c) Inconsisency II Src ^ II Tg Inconsisency III Src. Figure 10d depics wo reuse pirs, (r g,r src ) nd (rg 0,r src), which re boh consisen I Src nd I Tg. The source requiremen r src hs been spli ino wo rge requiremens r g nd rg 0. Tes cse hs been T-linked wih boh rge requiremens. Inconsisency III Src occurs becuse source requiremen r src is prner of boh reuse pirs. Inconsisency III Tg. Figure 10d depics III Tg if es cse ws T-linked wih ll requiremens of wo reuse pirs, (r g,r src ) nd (r g,rsrc). 0 r src r g (d) Inconsisency III Src r g Consisency. Figure 10e depics wo consisenly T-linked reuse pirs, (r g,r src ) nd (rg 0,r0 src). Ineresingly, inconsisency II Src^II Tg from Figure 10c hs been removed by dding he R-link rsrc 0! R rg 0. However, his is no generl soluion, since boh requiremens re no necessrily prner of reuse pir. However, his siuion cn sill be used s n indicor o find forgoen R-links. RT-Inconsisencies in he field. Afer lying he heoreicl foundion for n nlysis of RT-insnces nd RTinconsisencies, we cn now presen he resuls of wo field sudies, hus showing he prcicl relevnce of our RT-linking echnique vi rel specificion documens. r src r src r g r g (e) Consisency I ^ II ^ III Source requiremen Trge requiremen Tes cse (f) Legend Figure 10: (In)Consisency exmples 2014, Copyrigh by uhors, Published under greemen wih IARIA -

11 Inernionl Journl on Advnces in Sofwre, vol 7 no 3&4, yer 2014, hp:// VI. RT-LINKING: FIELD STUDIES From n indusry perspecive, he bigges dvnge of he RT-linking is linking speed. However, he field sudies will no focus on showing h uomic linking kes minues insed of dys (compred wih mnul linking). Insed, he primry gol is o show h RT-Linking is ccure. A. Primry gol nd preprion of he field sudy RT-Linking is effecive when i produces he sme links s he curren mnul linking. Furhermore, he RT-linking is even more effecive hn he mnul linking when i produces more T-links wih fewer RT-inconsisencies. Approch. In he ps, RT-problems hve been solved mnully. We unsolve hese hisoriclly solved RT-problems by removing ll T-links h poin o he rge requiremens. Nex, we solve he RT-problems by RT-linking hem gin. The mnully nd uomiclly solved RT-problems will hen be compred o ssess he success of his field sudy. Preprion. We were ble o conduc hese field sudies in n indusril environmen on rel specificion documens linked in n RT mnner in IBM DOORS. These documens describe hisoric linking siuion beween SRS Src,His, SRS Tg,His nd STS His of ps vehicle series requiremens nd es reuse: The SRS Src,His conins source requiremens. The SRS Tg,His reuses SRS Src,His. The STS His conins es cses which poin o SRS Src,His nd SRS Tg,His. The gol of he field sudies is o show h uomic linking produces he sme or even more T-links hn he curren mnul linking. To chieve his, he hisoric documens were copied, including ll links. Afer, ll T-links beween he copied STS RT nd he copied SRS Tg,RT were removed. Thus, ll documens only conined unsolved RT-problems: The SRS Src,RT is n unchnged copy of SRS Src,His. The SRS Tg,RT is copy of SRS Tg,His. The copied SRS s hve he sme reuse pirs s he hisoricl SRS s. The STS RT is copy of STS His wihou ny T-links ino SRS Tg,RT. The T-links ino SRS Src,RT remin. Preprion: Specil cse. Before nlysis of he overll linking siuion cn begin, we needed o rese ll T-links which cuse rge inconsisencies. In he hisoric linking siuion hose T-links refleced new es cses which were T-linked wih he SRS Tg,His bu no wih he SRS Src,His.We wned he hisoric siuion nd he siuion fer he RTlinking o be comprble in erms of rge inconsisencies. Therefore, we copied he T-links of ll es cses which exclusively verified SRS Tg,His ino SRS Tg,RT. Those new es cses would hve lso been T-linked fer RT-linking he refcs from he copied documens. Execuion. In order o compre he hisoric nd uomic overll linking siuions, ll unsolved RT-problems were solved by uomiclly RT-linking hem. B. Sysem A from vehicle series 1 o vehicle series Figure 11 shows RT-digrms o visulize he hisoric nd RT-linking siuion for smll-sized inerior sysem. Exminion of he peripherl regions. RT-linking solves RT-problems. Becuse only he cenre of he digrm represens RT-problems, uomic linking does no chnge mos of he peripherl regions. Boh digrms show 16 source ( ) nd 58 rge ( ) requiremens wihou R- nd T- links. Boh digrms conin 100 reuse pirs wihou T-links ( ). Becuse he RT-linking does no chnge he T-links ino he SRS Src, boh digrms show 39 source requiremens wihou R-links bu wih 77 T-links ( ). In he field sudies preprions we rese ll exclusive T-links ino he SRS Tg. Thus, boh digrms conin one rge requiremen wihou R-links bu wih 25 T-links ( ). Boh digrms show h 75 es cses hve no T-links ino he SRS Src ( Src ). Only one peripherl region disinguishes he hisoric from he RT-linking siuion: While 49 es cses hve no T-links ino SRS Tg,His, only 47 es cse hve no T-links ino SRS Tg,RT ( Tg ). This is firs clue h RT-linking is more efficien hn he hisoric procedure. Exminion of he digrm cenres. The digrm cenres revel h, hisoriclly, 70 RT-problems hve been solved consisenly while he RT-linking led o 74 consisenly solved RT-problems. The following more deiled exminion ddresses his observion :96:96 65:112 2:2:10 :107 39:77 1: () Hisoric RT-digrm :104 2:2:10 :105 39:77 1: :104: (b) RT-digrmm fer RT-linking Figure 11: Overll linking siuions 2014, Copyrigh by uhors, Published under greemen wih IARIA -

12 Inernionl Journl on Advnces in Sofwre, vol 7 no 3&4, yer 2014, hp:// Deiled look he inconsisencies. Tble I represens he (in)consisenly solved RT-problems wihin he digrm cenres. The His. siuion column represens he hisoric cenre regions, while he WvT linking column snds for he cenre regions of he RT-linking. The numbers R : T Src :T Tg represen he coun of reuse pirs (R), he coun of T-links o he source requiremens of he couned reuse pirs (T Src ) nd he coun of T-links o he rge requiremens (T Tg ). Becuse R-links re new concep hey hve been se uomiclly by mching documen inernl unique IDs of SRS Src nd SRS Tg. Thus, inconsisency III cn no pper wihin he scope of he field sudy. RT-digrms nd Tble I. To increse he relibiliy of he field sudies, wo independen DXL scrips (DXL: Doors exension Lnguge) were implemened. The firs scrip clcules he numbers for he RT-digrm, while he second scrip clcules he numbers in Tble I. The plusibiliy of he resuls is ssured vi he following rules: The numbers in he upper pr of he digrm cenres re he sme s in row 0 of he ble. The lower righ region of he RT-digrm cenres corresponds o he sum of he numbers in rows 2, 8 nd 10. The lower lef digrm cenre s numbers correspond o he sum of ll oher ble rows. Tble I: (In)consisencies in he digrm ceners (In)Consisency His. siuion RT-linking 0: consisen 70:96:96 74:104:104 1: I Src 1:5:4-2: I Tg 2:2:10 2:2:10 3: I Src ^ I Tg - - 4: II Src 56:92:92 57:94:94 5: I Src ^ II Src 4:5:0-6: I Tg ^ II Src 1:2:3 1:2:3 7: I Src ^ I Tg ^ II Src - - 8: II Tg - - 9: I Src ^ II Tg : I Tg ^ II Tg : I Src ^ I Tg ^ II Tg : II Src ^ II Tg 3:8:8 3:8:8 13: I Src ^ II Src ^ II Tg : I Tg ^ II Src ^ II Tg : I Src^I Tg^II Src^II Tg RT-linking is effecive. RT-linking is effecive if les he sme es cses re uomiclly T-linked wih SRS Tg,RT s hisoriclly were T-linked wih SRS Tg,His. Firs, he effeciveness is shown by he es cses no T-linked in he lower peripherl regions of boh RT-digrms. A simple for loop over ll hose es cses confirms h ech es cse which ws no T-linked uomiclly ws lso no T-linked hisoriclly. Becuse fewer es cses hve no T-links ino SRS Tg,RT fer he RT-linking, he following semen is rue: No es cses exis which hve hisoricl T-links ino SRS Tg,His bu no uomiclly se T-links ino SRS Tg,RT. Thus, he RT-linking is effecive. A second for loop over ll RT-insnces in Tble I confirms h ech solved RT-problem in he His. siuion column is lso conined in he RTlinking column wih he sme or more T-links. Becuse les he sme T-links exis, RT-linking is effecive. The exisence of more T-links lredy indices h RT-linking is even more effecive hn he curren linking procedure. RT-linking is even more effecive. RT-linking is more effecive hn he curren procedure if more es cses re T- linked nd fewer RT-inconsisencies pper. A look he digrm cenres revels h fer he uomic RT-linking, 47 es cses do no poin ino he SRS Tg,RT. Thus, wo fewer es cses re no T-linked in comprison o he hisoric linking siuion. Given h he linking is effecive, his leds o he conclusion h he RT-linking is even more effecive hn he curren procedure. A furher look Tble I confirms h more consisenly solved RT-problems exis fer he uomic linking. Row 0 of His. siuion couns 70 reuse pirs. The source nd rge requiremens of hose 70 reuse pirs ech coun 96 consisen T-links. Afer he uomic RT-linking, 74 reuse pirs were couned. The source nd rge requiremens re conneced consisenly wih es cses for every 104 T- links. In conclusion, RT-linking resuls in more T-links nd less RT-inconsisencies. Thus, RT-linking is more effecive hn he curren mnul procedure. Origin of new consisencies. Thus fr he field sudy hs reveled h he proposed mehod solves more RT-problems consisenly. The comprison of he cenres of he wo RTdigrms showed h he upper cenre region shows four ddiionl consisenly solved RT-problems, while he lower lef cenre region shows four fewer inconsisenly solved RTproblems. Row 0 of Tble I vlided he plusibiliy of he observions. Now quesion rises: From where did hese new consisencies origine? We nswer his quesion in he following secions by nlysing he inconsisency rnsiions shown in Tble II. Trnsiion rules (TR). Ech reuse pir ws nlysed wice: once hisoriclly nd once fer he RT-linking. Therefore, we know, which inconsisency reuse pir hd in boh cses. This enbles us o compre he inconsisency rnsiions of ech reuse pir. In he following, we will idenify which inconsisency rnsiions exis nd give exmples for ech rnsiion h occurred. Firs, summry of he four inconsisency rules: Consisency remins, inconsisency I Src is elimined, inconsisency II Src remins or is elimined, inconsisencies I Tg nd II Tg remin. These rules cn describe ll observed inconsisency rnsiions. 2014, Copyrigh by uhors, Published under greemen wih IARIA -

13 Inernionl Journl on Advnces in Sofwre, vol 7 no 3&4, yer 2014, hp:// TR 1 : Consisency remins. This firs rnsiion rule sys h ech hisoric RT-pir which is consisen, remins consisen fer RT-linking i uomiclly wih es cses. This ws he cse for ll 70 consisen RT-pirs. TR 2 : Inconsisency I Src is elimined. RT-linking elimines inconsisency I Src by definiion, becuse i rnsiively ses T-links beween source nd rge requiremens. Tbles I nd II confirm he eliminion of I Src, becuse hey never conin inconsisencies wih n odd number fer he RTlinking (becuse I Src denoes 2 0 ). TR 3 : Inconsisency II Src remins or is elimined. II Src cn become consisen if n inconsisency II Src occurs, becuse n inconsisency I Src occurred noher poin. Oherwise II Src remins. In Tble II, hisoric inconsisencies II Src remined (4 ) 4, 6 ) 6, 12 ) 12) or were elimined (4 ) 0, 5 ) 0) by he RT-linking. TR 4 : Inconsisencies I Tg nd II Tg remin. To enble comprison beween SRS Tg,His nd SRS Tg,RT in preprion of he field sudy, ll exclusive T-links ino SRS Tg,His were lso se exclusively o SRS Tg,RT. Exclusively mens h he T-link poins ino SRS Tg bu no ino SRS Src. Trge inconsisencies I Tg nd II Tg cused by his show h new es cses hve been T-linked wih he SRS Tg. Becuse he linking of new es cses does no impc RT-linking, ll rge inconsisencies remin. Tble II confirms his (2 ) 2, 6 ) 6, 12 ) 12). 481 Trnsiion: Consisency remins (0 ) 0). All source nd rge requiremens in Figure 12 build reuse pir: (A, ), (B, b). The es cse is T-linked wih ll prners of ll reuse pirs. Thus, TR 1 pplies nd consisency remins. b B A Figure 12: 0 ) 0 Trnsiion: I Src is elimined (1 ) 0). Figure 13 shows he reuse pir (A, ). On he lef hnd side he dshed T-link! T cuses he hisoric RT-problem o remin unsolved. This implies inconsisency I Src. The definiion of he RTlinking does no llow such siuions. Rule TR 2 pplies nd he T-link! T A exiss fer performing he RT-linking. A Figure 13: 1 ) 0 b A B A Tble II: Inconsisency rnsiions from His o RT His. ) RT-linking #Trnsiions 0 ) 0 (consisen ) consisen) 70 Trnsiion: I Tg remins (2 ) 2). Figure 14 depics he reuse pir (A, ). Becuse! T A origines from he new es cse,! T does no exis. This cuses inconsisency I Tg, which remins ccording o TR 4. 1 ) 0 (I Src ) consisen) 1 2 ) 2 (I Tg ) I Tg ) 2 A A 4 ) 0 (II Src ) consisen) 1 4 ) 4 (II Src ) II Src ) 55 5 ) 0 (I Src ^ II Src ) consisen) 2 5 ) 4 (I Src ^ II Src ) II Src ) 2 6 ) 6 (I Tg ^ II Src ) I Tg ^ II Src ) 1 12 ) 12 (II Src ^ II Tg ) II Src ^ II Tg ) 3 Figure 14: 2 ) 2 Trnsiion: II Src remins (4 ) 4). Figure 15 depics he reuse pir (B, b) nd source requiremen, which hs no been reused. Inconsisency II Src is cused by! T becuse verifies funcionliy h does no exis on he rge side. Rule TR 3 pplies: II Src cnno be elimined, becuse i is no cused by noher inconsisency I Src. Trnsiion exmples. To improve he reder s undersnding of inconsisency rnsiions, n exmple will be presened for ech row in Tble II. The following figures show rel bu nonymised rnsiions. Therefore, some inconsisency rnsiions pper isoled in single exmple while oher exmples conin muliple rnsiions. The figure on he lef hnd side lwys represens he hisoriclly solved RT-problem(s), while he righ hnd figure lwys shows he sme RT-problem(s), only uomiclly RT-linked. b B b Figure 15: 4 ) 4 B 2014, Copyrigh by uhors, Published under greemen wih IARIA -

14 Inernionl Journl on Advnces in Sofwre, vol 7 no 3&4, yer 2014, hp:// Trnsiion: II Src is elimined (4 ) 0). Figure 16 depics severl dependen RT-problems. The reuse pir (C, c) is consisen I Src becuse is T-linked o boh prners. Bu he T-links! T nd! T b cuse (C, c) o be inconsisen II Src. Rule TR 2 pplies. Thus, he inconsisencies I Src of (A, ) nd (B, b) re elimined by seing! T A nd! T B. Rule TR 3 pplies: The pir (C, c) is now consisen becuse I Src of (A, ) nd (B, b) ws he reson for is II Src. Trnsiion: I Src ^ II Src becomes consisen (5 ) 0). Figure 16 shows inconsisency II Src is elimined from he perspecive of (C, c). Becuse he rules TR 2 nd TR 3 lso pply o he pirs (A, ) nd (B, b) heir inconsisencies I Src ^ II Src re elimined. C. Sysem B from vehicle series 3 o vehicle series The gol of he firs field sudy ws o show h RTlinking is les s effecive s he curren mnul procedure. To suppor full nd deiled nlysis of he resuls, he field sudy ws performed on smll-sized sysem A. The second field sudy serves noher purpose: confirmion. Confirmion. The second field sudy ws performed on bigger sysem B, which hd five imes more requiremens nd es cses hn sysem A. The field sudy ws conduced using he sme preprions s he firs field sudy. All inconsisency rules were confirmed. No new rules ppered, bu more inconsisency rnsiions did. All new rnsiions cn be described by he four bsic inconsisency rules, TR 1, TR 2, TR 3 nd TR 4. b c C B A Figure 16: 4 ) 0 und 5 ) 0 b c C B A Trnsiion: I Src ^ II Src becomes II Src (5 ) 4). Figure 17 depics he reuse pir (B, b) nd source requiremen, which hs no been reused. Rule TR 2 pplies for (C, c): The missing T-link! T B is se vi he RT-linking. Inconsisency I Src for (B, b) is cused by! T. Therefore, I Src is no elimined by RT-linking nd TR 3 pplies: (C, c) remins II Src. b B Figure 17: 5 ) 4 Trnsiion: I Tg ^ II Src remins (6 ) 6). Figure 18 shows reuse pir (B, b) nd he source requiremen, which ws no reused. The T-link! T B cuses (B, b) o be inconsisen I Tg. Rule TR 4 forces I Tg o remin. Addiionlly, TR 3 pplies: (C, c) remins II Src becuse of! T. Trnsiion: II Src ^ II Tg sys (12 ) 12). Figure 18 lso shows he reuse pir (C, c). Agin, he T-link! T cuses (C, c) o be unresolvbly inconsisen II Src nd TR 3 pplies. Addiionlly, TR 4 pplies nd IITg remins. b c C B b b c Figure 18: 6 ) 6 und 12 ) 12 B C B D. RT-linking: Conclusion In Secion V, we proposed he bsic lyer of our 3- lyered mehod o uomiclly link es cses wih reusing requiremens. RT-linking uses he ssumpion: IF AND IF THEN rge requiremen reuses source requiremen es cse verifies source requiremen he es cse lso verifies he rge requiremen. Exension of he SOTA. We gve shor inroducion ino reserch ino requiremens rcebiliy in Secion III. There we summrized differen rcebiliy mehods (EBT, RBT, VBT,...), which uomiclly cree links beween requiremens nd oher refcs. The proposed RT-linking exends he reserch field vi new mehod: Reuse-bsed Tes Trcebiliy (RTT). Supporing indusril prcice. RT-linking did no jus rise from observing indusry prcice. We lso evlued he effeciveness of RT-linking under rel circumsnces wih DOORS exension plug-in. We conduced field sudy o compre he overll linking siuion of se of specificion documens fer mnul linking nd uomic RT-linking. Thnks o is promising resuls in erms of ccurcy, his plug-in hs been rnsferred o indusril prcice. In ddiion o is ccurcy, he complee linking nd link nlysis of SRS Tg now kes few minues insed of dys or even weeks of mnul link creion nd minennce. However, i is cler h some of he T-links hve o be reviewed mnully. Those T-links which cn be esblished wihou review define he business cse for RT-linking. Severl pilo projecs showed h hese vry beween 20% (sysems of new vehicle series wih mny new/chnged requiremens) nd 90% (sysems of fcelifs wih lile/no chnges). Overll we cn sy h specificion documens of fuure vehicle series projecs will likely be RT-linked. Oulook: Exension of he RT-linking. The min pr of his pper focused on he primry conribuion of his work: RT-linking. We will now provide n overview of exensions o RT-linking, s proposed in [1]. 2014, Copyrigh by uhors, Published under greemen wih IARIA -

15 Inernionl Journl on Advnces in Sofwre, vol 7 no 3&4, yer 2014, hp:// VII. OUTLOOK: TEST CONCEPT-DRIVEN FILTERING RT-linking is he firs mehod lyer. I solves he RTproblem. However, rel world esing necessies furher considerions. Sysemic es plnning sisfies boh ISO nd esing efficiency. Therefore, we inroduce n ugmenion o he RT-problem s es cse. Augmenion o he RT-problem. Tes gols (Wh purpose?), es levels (When?) nd es plforms (Where?) of he Tes Concep [Secion II-D] re used o deermine he esing expenses. These es plnning dimensions describe hree dimensionl esing expenses cube for ech vehicle funcion. The configurion of ech cube defines he esing expenses for vehicle funcion nd hus lso for heir refining requiremens. Figure 19 depics he RT-problem, which is ugmened wih clssifying es cse properies. Ech es cse ims o mee specific es gols, is execued during specific es levels nd is run on specific es plforms. These clssifying es cse properies re idenicl o he es plnning dimensions of he esing expenses cube. Figure 19 depics he concep behind he Tes Concep-driven Filering. Tes cse is linked wih rge requiremen r g if he clssifying properies of fi he configurion of he cube. In his conex, new RTinconsisencies rise, for exmple: (1) If es cse mees more es gols hn demnded by he cube for he vehicle funcion hen oo mny es gols re me. Thus, he esing is no minimlly efficien. (2) If he es cube demnds more es gols hen ll T-linked es cses pu ogeher, hen oo few es gols will be me. As resul, he esing is no complee. VIII. OUTLOOK: CASE-BASED FILTERING 483 In he second mehod lyer, we only ugmened he es cse of he RT-problem in order o connec i wih he Tes Concep. The hird lyer elimines his unused poenil by fully ugmening he RT-problem. In his wy, we fcilie similriy beween RT-problems. Full ugmenion of he RT-problem. Figure 19 depics he es cse ugmenion wih clssifying es cse properies. Figure 20 depics he ddiionl ugmenion wih clssifying requiremens properies. These requiremens nd es properies cn be defined freely, e.g., ASIL rnking, inerfces, requiremens muriy, OEM or supplier sus, es cse derivion mehod, ownership, ec. By virue of he R-link beween requiremens, propery chnges cn be deeced from source o rge in relion o he es properies. As he following exmple illusres, his presens counless possibiliies. We ssume h he owner of source requiremen nd T-linked es cse is Thoms. Furher, we ssume h he owner of he rge requiremen hs chnged o Jonhn. Cse-bsed Filering llows us o deec such siuions. The deecion mechnism dps he rerievl echniques of Cse-bsed resoning s follows: An RT-cse is srucurlly idenicl o n RT-problem, excep for n ddiionl RT-decision nd review noe. More precisely, Figure 20 does no depic n RT-problem bu n RT-cse. We use similriy funcion o ssess he similriy of he clssifying properies beween n RT-problem nd n RT-cse. Thus, we no only deec similr RT-problems for given RT-cse, bu lso dp he RT-decision nd review noe o solve he RT-problem. r src r g r src r g Figure 19: Tes plnning dimensions of he RT-problem Figure 20: Clssifying properies of he RT-problem Exension of RT-linking. exends RT-linking s follows: Tes Concep-driven Filering Exension of RT-linking. RT-linking s follows: Cse-bsed Filering exends IF AND IF THEN rge requiremen reuses source requiremen es cse verifies source requiremen he es cse lso verifies he rge requiremen ccording o he Tes Concep. This second mehod lyer hs been proposed in [34]. Furher, he filering echnique hs been implemened in DOORS DXL. I is currenly being evlued in n indusril environmen. IF AND IF THEN rge requiremen reuses source requiremen es cse verifies source requiremen he es cse lso verifies he rge requiremen ccording o he RT-Cse-bsis. A prooype of he hird lyer hs been implemened in DOORS DXL. An iniil presenion sprked he ineres of requiremens nd es engineers. 2014, Copyrigh by uhors, Published under greemen wih IARIA -

16 Inernionl Journl on Advnces in Sofwre, vol 7 no 3&4, yer 2014, hp:// IX. CONCLUSIONS AND FUTURE WORK In his pper, we proposed RT-linking, he min echnique of our 3-lyered mehod, o uomiclly solve he RTproblem. RT-problems occur fer requiremens reuse (R) bu before es reuse (T). The min gol is o reuse es cses on he bsis of requiremens reuse. Comprehensive requiremens reuse. We proposed new rce link ype: The Reuse- or R-link, which connecs reusing rge requiremens wih reused source requiremens. These R-links fcilie comprehensive reuse rcebiliy s demnded by ISO [3, p.20]. By virue of R-links we re ble o sysemiclly disinguish beween new or discrded requiremens nd requiremens which hve been reused wih or wihou modificion. Comprehensive es specificion. Tes cses re rce linked wih requiremens by Tes- or T-links o fcilie es rcebiliy ccording o ISO [2, p.25]. These T-links re influenced by he requiremens reuse; reuse of requiremens implies reuse of es cses. In his pper, we proposed rnsiive RT-linking o se T-links uomiclly from es cses o reusing rge requiremens on he bsis of previously T-linked source requiremens. Thnks o he promising resuls from he field sudies, RT-linking hs been rnsferred o indusril prcice. Comprehensive es plnning nd decisions. Alhough his pper focused on he firs mehod lyer, we gve shor overview of he second nd hird mehod lyers. Boh lyers provide ddiionl filer echniques o improve he RT-linking echnique. The second lyer rrnges RT-linking ccording o es plnning, while he hird lyer defines nd uses similriy beween RT-problems o reuse link decisions. Roe nd il he RT-problem. Ouside of indusril pplicion, n ineresing ide hs risen. We used requiremens, es cses nd specific link ypes o describe he RT-problem. However, i could be much more generl hn his if we used bsrc refcs nd bsrc link ypes insed. V-Models re usully chrcerized by mny differen rce linked refcs. As well s requiremens nd es cses, sysems, componens, sfey cses, rchiecure, feure models, funcionl models nd code lso exis, mong ohers. Even he SOTA ofen relies on holisic rcebiliy models [Secion III-A]. Fuure work could focus on he ineresing quesion of wheher generl RT-problem is ble o suppor rcebiliy model by successively roing or iling i hrough he V-Model, ech followed by generl RT-linking sep. X. ACKNOWLEDGEMENTS We hnk our DCAITI collegues Qung Minh Trn, Jons Winkler nd Mrin Beckmnn for discussions nd proof reding. Furhermore, we hnk our Dimler collegues for posiively impcing our conceps nd implemenions wih respec o relevnce, fesibiliy nd usbiliy. REFERENCES 484 [1] T. Nock, Auomic Linking of Tes Cses nd Requiremens, in Proceedings of he 5h Inernionl Conference in Sysem Tesing nd Vlidion Lifecycle (VALID), Venice, Ily, 2013, pp [2] Rod Vehicles - Funcionl Sfey, Pr 8: Supporing processes (ISO :2011), Inernionl Orgnizion for Sndrdizion, [3] Rod Vehicles - Funcionl Sfey, Pr 6: Produc Developmen: Sofwre Level (ISO :2011), Inernionl Orgnizion for Sndrdizion, [4] A. Spillner nd T. Linz, Bsiswissen Sofwrees, 4h ed. Heidelberg: dpunk.verlg, [5] Sofwre Engineering - Produc Quliy, Pr 1: Quliy Model (ISO :2001), Europen Commiee for Sndrdizion nd Inernionl Orgnizion for Sndrdizion, [6] R. Wkins nd M. Nel, Why nd How of Requiremens Trcing, IEEE Sofwre, vol. 11, no. 4, 1994, pp [7] J. Clelnd-Hung, O. Goel, nd A. Zismn, Sofwre nd Sysems Trcebiliy, 1s ed. Springer, [8] F. A. C. Pinheiro, Requiremens Trcebiliy, in Perspecives on Sofwre Requiremens, 1s ed., J. C. S. do Prdo Leie nd J. H. Doorn, Eds. Kluwer Acdemic Publishers, 2004, ch. 5, pp [9] K. Pohl nd P. Humer, HYDRA: A Hyperex Model for Srucuring Informl Requiremens Represenions, in Proceedings of he 2nd Inernionl Workshop on Requiremens Engineering (REFSQ), K. Pohl nd P. Peers, Eds. Jyväskylä, Finnlnd: Verlg der Augusinus- Buchhndlung, 1995, pp [10] E. Horowiz nd R. C. Willimson, SODOS : A Sofwre Documenion Suppor Environmen - Is Definiion, IEEE Trnscions on Sofwre Engineering, vol. 12, no. 8, 1986, pp [11] J. Conklin nd M. L. Begemn, glbis : A Hyperex Tool for Tem Design Deliberion, in Proceedings of he ACM Conference on Hyperex. Chpel Hill, NC, USA: ACM Press, 1987, pp [12] B. Rmesh nd V. Dhr, Supporing Sysems Developmen by Cpuring Deliberions During Requiremens Engineering, IEEE Trnscions on Sofwre Engineering, vol. 18, no. 6, 1992, pp [13] H. Kindl, The Missing Link in Requiremens Engineering, ACM SIGSOFT Sofwre Engineering Noes, vol. 18, no. 2, 1993, pp [14] F. A. C. Pinheiro nd J. A. Goguen, An Objec-Oriened Tool for Trcing Requiremens, in Proceedings of he 2nd Inernionl Conference on Requiremens Engineering. Colordo Springs, CO, USA: IEEE Compuer Sociey Press, 1996, pp [15] T. Tsumki nd Y. Morisw, A Frmework of Requiremens Trcing using UML, in Proceedings of 7h Asi-Pcific Sofwre Engineering Conference (APSEC). Singpur, Singpur: IEEE Compuer Sociey Press, 2000, pp [16] P. Leelier, A Frmework for Requiremens Trcebiliy in UML-Bsed Projecs, in Proceedings of 1s Inernionl Workshop on Trcebiliy in Emerging Forms of Sofwre Engineering, Edinburgh, Scholnd, 2002, pp [17] M. Nrmnli, A Business Rule Approch o Requiremens Trcebiliy, Mserrbei, Middle Es Technicl Universiy, [18] B. Turbn, M. Kucer, A. Tskpinis, nd C. Wolff, Bridging he Requiremens o Design Trcebiliy Gp, Inelligen Technicl Sysems, Lecure Noes in Elecricl Engineering, vol. 38, 2009, pp [19] S. Ibrhim, M. Munro, nd A. Dermn, Implemening Documen- Bsed Requiremens Trcebiliy: A Cse Sudy, in Proceedings of Inernionl Conference on Sofwre Engineering, P. Kokol, Ed. Innsbruck, Öserreich: ACTA Press, 2005, pp [20] H. U. Asuncion, F. Frncois, nd R. N. Tylor, An End-To-End Indusril Sofwre Trcebiliy Tool, in Proceedings of he 6h Join Meeing of he Europen Sofwre Engineering Conference nd he ACM SIGSOFT Symposium on The Foundions of Sofwre Engineering. Dubrovnik, Kroien: ACM, 2007, pp [21] A. Azmi nd S. Ibrhim, Implemening Tes Mngemen Trcebiliy Model o Suppor Tes Documens, Inernionl Journl of Digil Informion nd Wireless Communicions (IJDIWC), vol. 1, no. 1, 2011, pp , Copyrigh by uhors, Published under greemen wih IARIA -

17 Inernionl Journl on Advnces in Sofwre, vol 7 no 3&4, yer 2014, hp:// 485 [22] J. McMilln nd J. R. Vosburgh, Sofwre Quliy Indicors, Scienific Sysem Inc., Cmbridge MA., Tech. Rep., [23] DOORS (Dynmic Objec Oriened Requiremens Sysem), IBM, [24] S. Rochimh, W. M. N. Wn Kdir, nd A. H. Abdullh, An Evluion of Trcebiliy Approches o Suppor Sofwre Evoluion, in Inernionl Conference on Sofwre Engineering Advnces (ICSEA 2007). Cp Eserel, Frnkreich: IEEE Compuer Sociey, Aug. 2007, pp [25] R. Torkr, T. Gorschek, R. Feld, M. Svhnberg, U. A. Rj, nd K. Kmrn, Requiremens Trcebiliy: A Sysemic Review nd Indusry Cse Sudy, Inernionl Journl of Sofwre Engineering nd Knowledge Engineering, vol. 22, no. 3, 2012, pp [26] J. Clelnd-Hung, C. K. Chng, nd M. Chrisensen, Even-Bsed Trcebiliy for Mnging Evoluionry Chnge, IEEE Trnscions on Sofwre Engineering, vol. 29, no. 9, 2003, pp [27] G. Spnoudkis, A. Zismn, E. Pérez-Minn, nd P. Kruse, Rule- Bsed Generion of Requiremens Trcebiliy Relions, Journl of Sysems nd Sofwre, vol. 72, no. 2, Jul. 2004, pp [28] M. Riebisch, Supporing Evoluionry Developmen by Feure Models nd Trcebiliy Links, in 11h IEEE Inernionl Conference nd Workshop on he Engineering of Compuer-Bsed Sysems (ECBS). Brno, Tschechien: IEEE Compuer Sociey Press, 2004, pp [29] M. Heindl nd S. Biffl, A Cse Sudy on Vlue-Bsed Requiremens Trcing, in Proceedings of he 10h Europen Sofwre Engineering Conference held joinly wih 13h ACM SIGSOFT Inernionl Symposium on Foundions of Sofwre Engineering. Lissbon, Porugl: ACM Press, 2005, pp [30] A. Egyed nd P. Grünbcher, Supporing Sofwre Undersnding wih Auomed Requiremens Trcebiliy, Inernionl Journl of Sofwre Engineering nd Knowledge Engineering, vol. 15, no. 5, 2005, pp [31] J. Clelnd-Hung, R. Seimi, O. BenKhdr, E. Berezhnsky, nd S. Chrisin, Gol-Cenric Trcebiliy for Mnging Non-Funcionl Requiremens, in Proceedings of he 27h Inernionl Conference on Sofwre Engineering (ICSE). S. Louis, MO, USA: ACM Press, 2005, pp [32] R. Oliveo, M. Gehers, D. Poshyvnyk, nd A. De Luci, On he Equivlence of Informion Rerievl Mehods for Auomed Trcebiliy Link Recovery, in 18h IEEE Inernionl Conference on Progrm Comprehension (ICPC). Minho, Porugl: IEEE Compuer Sociey Press, Jun. 2010, pp [33] A. Cmyrev, R. Nörenberg, D. Hopp, nd R. Reissing, Consisency Checking of Feure Mpping beween Requiremens nd Tes Arefcs, Concurren Engineering Approches for Susinble Produc Developmen in Muli-Disciplinry Environmen, vol. 1, no. 1, 2013, pp [34] T. Nock, Auomische Verlinkung von Tesfällen und Anforderungen: Tesplngeseuere Filerung, Sofwreechnik-Trends, vol. 33, no. 4, 2013, pp [35] SimMerics (Open Source librry wih numerous lgorihms o clcule exul similriy beween wo exs), Source Forge, , Copyrigh by uhors, Published under greemen wih IARIA -

Improper Integrals. Dr. Philippe B. laval Kennesaw State University. September 19, 2005. f (x) dx over a finite interval [a, b].

Improper Integrals. Dr. Philippe B. laval Kennesaw State University. September 19, 2005. f (x) dx over a finite interval [a, b]. Improper Inegrls Dr. Philippe B. lvl Kennesw Se Universiy Sepember 9, 25 Absrc Noes on improper inegrls. Improper Inegrls. Inroducion In Clculus II, sudens defined he inegrl f (x) over finie inervl [,

More information

Term-based composition of security protocols

Term-based composition of security protocols Term-sed composiion of securiy proocols B Genge P Hller R Ovidiu I Ign Peru ior Universiy of Trgu ures Romni genge@upmro phller@upmro oroi@engineeringupmro Technicl Universiy of Cluj poc Romni IosifIgn@csuclujro

More information

Example What is the minimum bandwidth for transmitting data at a rate of 33.6 kbps without ISI?

Example What is the minimum bandwidth for transmitting data at a rate of 33.6 kbps without ISI? Emple Wh is he minimum ndwidh for rnsmiing d re of 33.6 kps wihou ISI? Answer: he minimum ndwidh is equl o he yquis ndwidh. herefore, BW min W R / 33.6/ 6.8 khz oe: If % roll-off chrcerisic is used, ndwidh

More information

Dynamic Magnification Factor of SDOF Oscillators under. Harmonic Loading

Dynamic Magnification Factor of SDOF Oscillators under. Harmonic Loading Dynmic Mgnificion Fcor of SDOF Oscillors under Hrmonic Loding Luis Mrí Gil-Mrín, Jun Frncisco Cronell-Márquez, Enrique Hernández-Mones 3, Mrk Aschheim 4 nd M. Psds-Fernández 5 Asrc The mgnificion fcor

More information

Phys222 W12 Quiz 2: Chapters 23, 24. Name: = 80 nc, and q = 30 nc in the figure, what is the magnitude of the total electric force on q?

Phys222 W12 Quiz 2: Chapters 23, 24. Name: = 80 nc, and q = 30 nc in the figure, what is the magnitude of the total electric force on q? Nme: 1. A pricle (m = 5 g, = 5. µc) is relesed from res when i is 5 cm from second pricle (Q = µc). Deermine he mgniude of he iniil ccelerion of he 5-g pricle.. 54 m/s b. 9 m/s c. 7 m/s d. 65 m/s e. 36

More information

Chapter 7. Response of First-Order RL and RC Circuits

Chapter 7. Response of First-Order RL and RC Circuits Chaper 7. esponse of Firs-Order L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural

More information

A Dynamic Model of Health Insurance Choices and Health Care Consumption 1. Jian Ni Johns Hopkins University Email: [email protected]

A Dynamic Model of Health Insurance Choices and Health Care Consumption 1. Jian Ni Johns Hopkins University Email: jni@jhu.edu A Dynmic Model of Helh Insurnce Choices nd Helh Cre Consumpion Jin Ni Johns Hopins Universiy Emil: [email protected] Niin Meh Universiy of Torono Emil: [email protected] Knnn Srinivsn Crnegie Mellon Universiy

More information

Detecting Network Intrusions via Sampling : A Game Theoretic Approach

Detecting Network Intrusions via Sampling : A Game Theoretic Approach Deecing Nework Inrusions vi Smpling : A Gme Theoreic Approch Murli Kodilm T. V. Lkshmn Bell Lborories Lucen Technologies 101 Crwfords Corner Rod Holmdel, NJ 07733, USA {murlik, lkshmn}@bell-lbs.com Absrc

More information

Appendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.

Appendix A: Area. 1 Find the radius of a circle that has circumference 12 inches. Appendi A: Area worked-ou s o Odd-Numbered Eercises Do no read hese worked-ou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa

More information

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees

More information

Influence of Network Load on the Performance of Opportunistic Scanning

Influence of Network Load on the Performance of Opportunistic Scanning Influence of Nework Lod on he Performnce of Opporunisic Scnning Mrc Emmelmnn, Sven Wiehöler, nd Hyung-Tek Lim Technicl Universiy Berlin Telecommunicion Neworks Group TKN Berlin, Germny Emil: [email protected],

More information

Optimal Contracts in a Continuous-Time Delegated Portfolio Management Problem

Optimal Contracts in a Continuous-Time Delegated Portfolio Management Problem Opiml Conrcs in Coninuous-ime Deleged Porfolio Mngemen Problem Hui Ou-Yng Duke Universiy nd Universiy of Norh Crolin his ricle sudies he conrcing problem beween n individul invesor nd professionl porfolio

More information

Cointegration: The Engle and Granger approach

Cointegration: The Engle and Granger approach Coinegraion: The Engle and Granger approach Inroducion Generally one would find mos of he economic variables o be non-saionary I(1) variables. Hence, any equilibrium heories ha involve hese variables require

More information

Capacitors and inductors

Capacitors and inductors Capaciors and inducors We coninue wih our analysis of linear circuis by inroducing wo new passive and linear elemens: he capacior and he inducor. All he mehods developed so far for he analysis of linear

More information

SOLID MECHANICS TUTORIAL GEAR SYSTEMS. This work covers elements of the syllabus for the Edexcel module 21722P HNC/D Mechanical Principles OUTCOME 3.

SOLID MECHANICS TUTORIAL GEAR SYSTEMS. This work covers elements of the syllabus for the Edexcel module 21722P HNC/D Mechanical Principles OUTCOME 3. SOLI MEHNIS TUTORIL GER SYSTEMS This work covers elemens of he syllabus for he Edexcel module 21722P HN/ Mechanical Principles OUTOME 3. On compleion of his shor uorial you should be able o do he following.

More information

Mr. Kepple. Motion at Constant Acceleration 1D Kinematics HW#5. Name: Date: Period: (b) Distance traveled. (a) Acceleration.

Mr. Kepple. Motion at Constant Acceleration 1D Kinematics HW#5. Name: Date: Period: (b) Distance traveled. (a) Acceleration. Moion Consn Accelerion 1D Kinemics HW#5 Mr. Kepple Nme: De: Period: 1. A cr cceleres from 1 m/s o 1 m/s in 6.0 s. () Wh ws is ccelerion? (b) How fr did i rel in his ime? Assume consn ccelerion. () Accelerion

More information

AP Calculus BC 2010 Scoring Guidelines

AP Calculus BC 2010 Scoring Guidelines AP Calculus BC Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board

More information

Age Biased Technical and Organisational Change, Training and Employment Prospects of Older Workers

Age Biased Technical and Organisational Change, Training and Employment Prospects of Older Workers DISCUSSION PAPER SERIES IZA DP No. 5544 Age Bised Technicl nd Orgnisionl Chnge, Trining nd Employmen Prospecs of Older Workers Luc Behghel Eve Croli Muriel Roger Mrch 2011 Forschungsinsiu zur Zukunf der

More information

Human Body Tracking with Auxiliary Measurements

Human Body Tracking with Auxiliary Measurements IEEE Inernionl Workshop on Anlysis nd Modeling of Fces nd Gesures, 003. Humn Body Trcking wih Auxiliry Mesuremens Mun Wi Lee, Isc Cohen Insiue for Roboics nd Inelligen Sysems Inegred Medi Sysems Cener

More information

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur Module 4 Single-phase A circuis ersion EE T, Kharagpur esson 5 Soluion of urren in A Series and Parallel ircuis ersion EE T, Kharagpur n he las lesson, wo poins were described:. How o solve for he impedance,

More information

Multiprocessor Systems-on-Chips

Multiprocessor Systems-on-Chips Par of: Muliprocessor Sysems-on-Chips Edied by: Ahmed Amine Jerraya and Wayne Wolf Morgan Kaufmann Publishers, 2005 2 Modeling Shared Resources Conex swiching implies overhead. On a processing elemen,

More information

2. The econometric model

2. The econometric model Age Bised Technicl nd Orgnisionl Chnge, Trining nd Employmen Prospecs of Older Workers * Luc BEHAGHEL (Pris School of Economics (INRA) nd CREST) Eve CAROLI (Universiy Pris Duphine, LED-LEGOS, Pris School

More information

One Practical Algorithm for Both Stochastic and Adversarial Bandits

One Practical Algorithm for Both Stochastic and Adversarial Bandits One Prcicl Algorihm for Boh Sochsic nd Adversril Bndis Yevgeny Seldin Queenslnd Universiy of Technology, Brisbne, Ausrli Aleksndrs Slivkins Microsof Reserch, New York NY, USA [email protected] [email protected]

More information

Statistical Analysis with Little s Law. Supplementary Material: More on the Call Center Data. by Song-Hee Kim and Ward Whitt

Statistical Analysis with Little s Law. Supplementary Material: More on the Call Center Data. by Song-Hee Kim and Ward Whitt Saisical Analysis wih Lile s Law Supplemenary Maerial: More on he Call Cener Daa by Song-Hee Kim and Ward Whi Deparmen of Indusrial Engineering and Operaions Research Columbia Universiy, New York, NY 17-99

More information

Identifying Merger Unilateral Effects: HHI or Simulation?

Identifying Merger Unilateral Effects: HHI or Simulation? Idenifying Merger Unilerl Effecs: HHI or Simulion? Jerome FONCEL Universiy of Lille, Frnce [email protected] Mrc IVALDI Toulouse School of Economics, nd CEPR, Frnce [email protected] Jrissy MOTIS

More information

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation

A Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion

More information

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements Inroducion Chaper 14: Dynamic D-S dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuing-edge

More information

The Grantor Retained Annuity Trust (GRAT)

The Grantor Retained Annuity Trust (GRAT) WEALTH ADVISORY Esae Planning Sraegies for closely-held, family businesses The Granor Reained Annuiy Trus (GRAT) An efficien wealh ransfer sraegy, paricularly in a low ineres rae environmen Family business

More information

Strategic Optimization of a Transportation Distribution Network

Strategic Optimization of a Transportation Distribution Network Sraegic Opimizaion of a Transporaion Disribuion Nework K. John Sophabmixay, Sco J. Mason, Manuel D. Rossei Deparmen of Indusrial Engineering Universiy of Arkansas 4207 Bell Engineering Cener Fayeeville,

More information

TSG-RAN Working Group 1 (Radio Layer 1) meeting #3 Nynashamn, Sweden 22 nd 26 th March 1999

TSG-RAN Working Group 1 (Radio Layer 1) meeting #3 Nynashamn, Sweden 22 nd 26 th March 1999 TSG-RAN Working Group 1 (Radio Layer 1) meeing #3 Nynashamn, Sweden 22 nd 26 h March 1999 RAN TSGW1#3(99)196 Agenda Iem: 9.1 Source: Tile: Documen for: Moorola Macro-diversiy for he PRACH Discussion/Decision

More information

STRATEGIC PLANNING COMMITTEE Wednesday, February 17, 2010

STRATEGIC PLANNING COMMITTEE Wednesday, February 17, 2010 em: STATEGC PLANNNG COMMTTEE Wednesdy, Februry 17, 2010 SUBJECT: EQUEST FO APPOVAL TO NAME THE WALKWAY FOM DADE AVENUE TO PAKNG GAAGE 2 DVESTY WAY ON THE BOCA ATON CAMPUS. POPOSED COMMTTEE ACTON Provide

More information

Chapter 8: Regression with Lagged Explanatory Variables

Chapter 8: Regression with Lagged Explanatory Variables Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One

More information

Example 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers.

Example 27.1 Draw a Venn diagram to show the relationship between counting numbers, whole numbers, integers, and rational numbers. 2 Rtionl Numbers Integers such s 5 were importnt when solving the eqution x+5 = 0. In similr wy, frctions re importnt for solving equtions like 2x = 1. Wht bout equtions like 2x + 1 = 0? Equtions of this

More information

4. International Parity Conditions

4. International Parity Conditions 4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency

More information

USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES

USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES Mehme Nuri GÖMLEKSİZ Absrac Using educaion echnology in classes helps eachers realize a beer and more effecive learning. In his sudy 150 English eachers were

More information

4 Convolution. Recommended Problems. x2[n] 1 2[n]

4 Convolution. Recommended Problems. x2[n] 1 2[n] 4 Convoluion Recommended Problems P4.1 This problem is a simple example of he use of superposiion. Suppose ha a discree-ime linear sysem has oupus y[n] for he given inpus x[n] as shown in Figure P4.1-1.

More information

Return Calculation of U.S. Treasury Constant Maturity Indices

Return Calculation of U.S. Treasury Constant Maturity Indices Reurn Calculaion of US Treasur Consan Mauri Indices Morningsar Mehodolog Paper Sepeber 30 008 008 Morningsar Inc All righs reserved The inforaion in his docuen is he proper of Morningsar Inc Reproducion

More information

This work is licensed under a Licença Creative Commons Attribution 3.0.

This work is licensed under a Licença Creative Commons Attribution 3.0. 3.0. Ese rblho esá licencido sob um Licenç Creive Commons Aribuion This work is licensed under Licenç Creive Commons Aribuion 3.0. Fone: hp:///rigos.sp?sesso=redy&cod_rigo=255. Acesso em: 11 nov. 2013.

More information

Department of Health & Human Services (DHHS) Centers for Medicare & Medicaid Services (CMS) Transmittal 1151 Date: November 16, 2012

Department of Health & Human Services (DHHS) Centers for Medicare & Medicaid Services (CMS) Transmittal 1151 Date: November 16, 2012 nul ysem ub 100-20 One-Time Noificion Depmen of elh & umn evices (D) enes fo edice & edicid evices () Tnsmil 1151 De: Novembe 16, 2012 hnge eques 8124 UBJT: Use of Q6 odifie fo Locum Tenens by oviding

More information

Chapter 1.6 Financial Management

Chapter 1.6 Financial Management Chaper 1.6 Financial Managemen Par I: Objecive ype quesions and answers 1. Simple pay back period is equal o: a) Raio of Firs cos/ne yearly savings b) Raio of Annual gross cash flow/capial cos n c) = (1

More information

9. Capacitor and Resistor Circuits

9. Capacitor and Resistor Circuits ElecronicsLab9.nb 1 9. Capacior and Resisor Circuis Inroducion hus far we have consider resisors in various combinaions wih a power supply or baery which provide a consan volage source or direc curren

More information

GUIDE GOVERNING SMI RISK CONTROL INDICES

GUIDE GOVERNING SMI RISK CONTROL INDICES GUIDE GOVERNING SMI RISK CONTROL IND ICES SIX Swiss Exchange Ld 04/2012 i C O N T E N T S 1. Index srucure... 1 1.1 Concep... 1 1.2 General principles... 1 1.3 Index Commission... 1 1.4 Review of index

More information

Performance Center Overview. Performance Center Overview 1

Performance Center Overview. Performance Center Overview 1 Performance Cener Overview Performance Cener Overview 1 ODJFS Performance Cener ce Cener New Performance Cener Model Performance Cener Projec Meeings Performance Cener Execuive Meeings Performance Cener

More information

CHARGE AND DISCHARGE OF A CAPACITOR

CHARGE AND DISCHARGE OF A CAPACITOR REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:

More information

INTERFEROMETRIC TECHNIQUES FOR TERRASAR-X DATA. Holger Nies, Otmar Loffeld, Baki Dönmez, Amina Ben Hammadi, Robert Wang, Ulrich Gebhardt

INTERFEROMETRIC TECHNIQUES FOR TERRASAR-X DATA. Holger Nies, Otmar Loffeld, Baki Dönmez, Amina Ben Hammadi, Robert Wang, Ulrich Gebhardt INTERFEROMETRIC TECHNIQUES FOR TERRASAR-X DATA Holger Nies, Omr Loffeld, Bki Dönmez, Amin Ben Hmmdi, Rober Wng, Ulrich Gebhrd Cener for Sensorsysems (ZESS), Universiy of Siegen Pul-Bonz-Sr. 9-, D-5768

More information

Signal Rectification

Signal Rectification 9/3/25 Signal Recificaion.doc / Signal Recificaion n imporan applicaion of juncion diodes is signal recificaion. here are wo ypes of signal recifiers, half-wae and fullwae. Le s firs consider he ideal

More information

Why Did the Demand for Cash Decrease Recently in Korea?

Why Did the Demand for Cash Decrease Recently in Korea? Why Did he Demand for Cash Decrease Recenly in Korea? Byoung Hark Yoo Bank of Korea 26. 5 Absrac We explores why cash demand have decreased recenly in Korea. The raio of cash o consumpion fell o 4.7% in

More information

Journeys Common Core Spelling Activities. First Grade. Units 1, 2, 3, 4, 5,6 A full year of activities!

Journeys Common Core Spelling Activities. First Grade. Units 1, 2, 3, 4, 5,6 A full year of activities! Firs Grde Unis 1, 2, 3, 4, 5,6 A full yer of civiies! Shor 1.m 2. 3.s 4.mn 5.dd Criss Cross Words c Wrie ech word five imes ech Lesson 1 Wh is Pl? Hve fmily memer prin ou word serch wih his week s spelling

More information

Steps for D.C Analysis of MOSFET Circuits

Steps for D.C Analysis of MOSFET Circuits 10/22/2004 Seps for DC Analysis of MOSFET Circuis.doc 1/7 Seps for D.C Analysis of MOSFET Circuis To analyze MOSFET circui wih D.C. sources, we mus follow hese five seps: 1. ASSUME an operaing mode 2.

More information

Task is a schedulable entity, i.e., a thread

Task is a schedulable entity, i.e., a thread Real-Time Scheduling Sysem Model Task is a schedulable eniy, i.e., a hread Time consrains of periodic ask T: - s: saring poin - e: processing ime of T - d: deadline of T - p: period of T Periodic ask T

More information

Individual Health Insurance April 30, 2008 Pages 167-170

Individual Health Insurance April 30, 2008 Pages 167-170 Individual Healh Insurance April 30, 2008 Pages 167-170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve

More information

Pulse-Width Modulation Inverters

Pulse-Width Modulation Inverters SECTION 3.6 INVERTERS 189 Pulse-Widh Modulaion Inverers Pulse-widh modulaion is he process of modifying he widh of he pulses in a pulse rain in direc proporion o a small conrol signal; he greaer he conrol

More information

ESIGN Rendering Service

ESIGN Rendering Service Markeing maerials on demand wihou phoo shoos or se-up Wih he ESIGN Rendering Service, we produce new, prinready markeing maerials for you in a cos-efficien and imely manner for he design of brochures,

More information

MTH6121 Introduction to Mathematical Finance Lesson 5

MTH6121 Introduction to Mathematical Finance Lesson 5 26 MTH6121 Inroducion o Mahemaical Finance Lesson 5 Conens 2.3 Brownian moion wih drif........................... 27 2.4 Geomeric Brownian moion........................... 28 2.5 Convergence of random

More information

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins) Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer

More information

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya. Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, [email protected] Why principal componens are needed Objecives undersand he evidence of more han one

More information

Acceleration Lab Teacher s Guide

Acceleration Lab Teacher s Guide Acceleraion Lab Teacher s Guide Objecives:. Use graphs of disance vs. ime and velociy vs. ime o find acceleraion of a oy car.. Observe he relaionship beween he angle of an inclined plane and he acceleraion

More information

Chapter 2 Kinematics in One Dimension

Chapter 2 Kinematics in One Dimension Chaper Kinemaics in One Dimension Chaper DESCRIBING MOTION:KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings moe how far (disance and displacemen), how fas (speed and elociy), and how

More information

1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z 1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z

1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z 1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z o ffix uden abel ere uden ame chool ame isric ame/ ender emale ale onh ay ear ae of irh an eb ar pr ay un ul ug ep c ov ec as ame irs ame lace he uden abel ere ae uden denifier chool se nly rined in he

More information

LNG Pricing Differences across the Atlantic - a Comparison between the United States and Europe

LNG Pricing Differences across the Atlantic - a Comparison between the United States and Europe LNG Pricing Differences cross he Alnic - Comprison beween he Unied Ses nd Europe Virginie Krone Micel Ponce Anne Neumnn Universiä Posdm 37h IAEE Inernionl Conference, New York June, 15-18, 214 Ouline 1.

More information

17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides

17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides 7 Laplace ransform. Solving linear ODE wih piecewise coninuous righ hand sides In his lecure I will show how o apply he Laplace ransform o he ODE Ly = f wih piecewise coninuous f. Definiion. A funcion

More information

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( )

Polynomial Functions. Polynomial functions in one variable can be written in expanded form as ( ) Polynomil Functions Polynomil functions in one vrible cn be written in expnded form s n n 1 n 2 2 f x = x + x + x + + x + x+ n n 1 n 2 2 1 0 Exmples of polynomils in expnded form re nd 3 8 7 4 = 5 4 +

More information

Regular Sets and Expressions

Regular Sets and Expressions Regulr Sets nd Expressions Finite utomt re importnt in science, mthemtics, nd engineering. Engineers like them ecuse they re super models for circuits (And, since the dvent of VLSI systems sometimes finite

More information

Information Technology Investment and Adoption: A Rational Expectations Perspective

Information Technology Investment and Adoption: A Rational Expectations Perspective Informion Technology Invesmen nd Adopion: A Rionl Expecions Perspecive Yoris A. Au Rober J. Kuffmn Docorl Progrm, Informion nd Decision Co-Direcor, MIS Reserch Cener nd Sciences, Crlson School of Mngemen,

More information

Reasoning to Solve Equations and Inequalities

Reasoning to Solve Equations and Inequalities Lesson4 Resoning to Solve Equtions nd Inequlities In erlier work in this unit, you modeled situtions with severl vriles nd equtions. For exmple, suppose you were given usiness plns for concert showing

More information

Permutations and Combinations

Permutations and Combinations Permuaions and Combinaions Combinaorics Copyrigh Sandards 006, Tes - ANSWERS Barry Mabillard. 0 www.mah0s.com 1. Deermine he middle erm in he expansion of ( a b) To ge he k-value for he middle erm, divide

More information

Distributing Human Resources among Software Development Projects 1

Distributing Human Resources among Software Development Projects 1 Disribuing Human Resources among Sofware Developmen Proecs Macario Polo, María Dolores Maeos, Mario Piaini and rancisco Ruiz Summary This paper presens a mehod for esimaing he disribuion of human resources

More information

Market Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand

Market Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand 36 Invesmen Managemen and Financial Innovaions, 4/4 Marke Liquidiy and he Impacs of he Compuerized Trading Sysem: Evidence from he Sock Exchange of Thailand Sorasar Sukcharoensin 1, Pariyada Srisopisawa,

More information

Signal Processing and Linear Systems I

Signal Processing and Linear Systems I Sanford Universiy Summer 214-215 Signal Processing and Linear Sysems I Lecure 5: Time Domain Analysis of Coninuous Time Sysems June 3, 215 EE12A:Signal Processing and Linear Sysems I; Summer 14-15, Gibbons

More information

3.1. Overview Serial Devices to Ethernet Gateway

3.1. Overview Serial Devices to Ethernet Gateway Overview Progrmmble Server (Seril-o-) Overview Overview.. Overview Seril o Gewy he CP DAS Progrmmble Server i deigned o bring nework conneciviy o your eril device. he progrmmble feure llow developer o

More information

Inductance and Transient Circuits

Inductance and Transient Circuits Chaper H Inducance and Transien Circuis Blinn College - Physics 2426 - Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual

More information

Automatic measurement and detection of GSM interferences

Automatic measurement and detection of GSM interferences Auomaic measuremen and deecion of GSM inerferences Poor speech qualiy and dropped calls in GSM neworks may be caused by inerferences as a resul of high raffic load. The radio nework analyzers from Rohde

More information

RESTORING FISCAL SUSTAINABILITY IN THE EURO AREA: RAISE TAXES OR CURB SPENDING? Boris Cournède and Frédéric Gonand *

RESTORING FISCAL SUSTAINABILITY IN THE EURO AREA: RAISE TAXES OR CURB SPENDING? Boris Cournède and Frédéric Gonand * RESTORING FISCAL SUSTAINABILITY IN THE EURO AREA: RAISE TAXES OR CURB SPENDING? Boris Cournède nd Frédéric Gonnd Wih populion geing fiscl consolidion hs become of prmoun impornce for euro re counries.

More information

Mortality Variance of the Present Value (PV) of Future Annuity Payments

Mortality Variance of the Present Value (PV) of Future Annuity Payments Morali Variance of he Presen Value (PV) of Fuure Annui Pamens Frank Y. Kang, Ph.D. Research Anals a Frank Russell Compan Absrac The variance of he presen value of fuure annui pamens plas an imporan role

More information

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,

More information

Markit Excess Return Credit Indices Guide for price based indices

Markit Excess Return Credit Indices Guide for price based indices Marki Excess Reurn Credi Indices Guide for price based indices Sepember 2011 Marki Excess Reurn Credi Indices Guide for price based indices Conens Inroducion...3 Index Calculaion Mehodology...4 Semi-annual

More information

AP Calculus AB 2007 Scoring Guidelines

AP Calculus AB 2007 Scoring Guidelines AP Calculus AB 7 Scoring Guidelines The College Board: Connecing Sudens o College Success The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and

More information

Term Structure of Prices of Asian Options

Term Structure of Prices of Asian Options Term Srucure of Prices of Asian Opions Jirô Akahori, Tsuomu Mikami, Kenji Yasuomi and Teruo Yokoa Dep. of Mahemaical Sciences, Risumeikan Universiy 1-1-1 Nojihigashi, Kusasu, Shiga 525-8577, Japan E-mail:

More information

The Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas

The Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas The Greek financial crisis: growing imbalances and sovereign spreads Heaher D. Gibson, Sephan G. Hall and George S. Tavlas The enry The enry of Greece ino he Eurozone in 2001 produced a dividend in he

More information

The Transport Equation

The Transport Equation The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be

More information

Keldysh Formalism: Non-equilibrium Green s Function

Keldysh Formalism: Non-equilibrium Green s Function Keldysh Formalism: Non-equilibrium Green s Funcion Jinshan Wu Deparmen of Physics & Asronomy, Universiy of Briish Columbia, Vancouver, B.C. Canada, V6T 1Z1 (Daed: November 28, 2005) A review of Non-equilibrium

More information

4.11 Inner Product Spaces

4.11 Inner Product Spaces 314 CHAPTER 4 Vector Spces 9. A mtrix of the form 0 0 b c 0 d 0 0 e 0 f g 0 h 0 cnnot be invertible. 10. A mtrix of the form bc d e f ghi such tht e bd = 0 cnnot be invertible. 4.11 Inner Product Spces

More information

Usefulness of the Forward Curve in Forecasting Oil Prices

Usefulness of the Forward Curve in Forecasting Oil Prices Usefulness of he Forward Curve in Forecasing Oil Prices Akira Yanagisawa Leader Energy Demand, Supply and Forecas Analysis Group The Energy Daa and Modelling Cener Summary When people analyse oil prices,

More information

Differential Equations. Solving for Impulse Response. Linear systems are often described using differential equations.

Differential Equations. Solving for Impulse Response. Linear systems are often described using differential equations. Differenial Equaions Linear sysems are ofen described using differenial equaions. For example: d 2 y d 2 + 5dy + 6y f() d where f() is he inpu o he sysem and y() is he oupu. We know how o solve for y given

More information

2 DIODE CLIPPING and CLAMPING CIRCUITS

2 DIODE CLIPPING and CLAMPING CIRCUITS 2 DIODE CLIPPING nd CLAMPING CIRCUITS 2.1 Ojectives Understnding the operting principle of diode clipping circuit Understnding the operting principle of clmping circuit Understnding the wveform chnge of

More information

A Re-examination of the Joint Mortality Functions

A Re-examination of the Joint Mortality Functions Norh merican cuarial Journal Volume 6, Number 1, p.166-170 (2002) Re-eaminaion of he Join Morali Funcions bsrac. Heekung Youn, rkad Shemakin, Edwin Herman Universi of S. Thomas, Sain Paul, MN, US Morali

More information

Single-machine Scheduling with Periodic Maintenance and both Preemptive and. Non-preemptive jobs in Remanufacturing System 1

Single-machine Scheduling with Periodic Maintenance and both Preemptive and. Non-preemptive jobs in Remanufacturing System 1 Absrac number: 05-0407 Single-machine Scheduling wih Periodic Mainenance and boh Preempive and Non-preempive jobs in Remanufacuring Sysem Liu Biyu hen Weida (School of Economics and Managemen Souheas Universiy

More information

A Curriculum Module for AP Calculus BC Curriculum Module

A Curriculum Module for AP Calculus BC Curriculum Module Vecors: A Curriculum Module for AP Calculus BC 00 Curriculum Module The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy.

More information

Random Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary

Random Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary Random Walk in -D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes

More information

TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS

TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS RICHARD J. POVINELLI AND XIN FENG Deparmen of Elecrical and Compuer Engineering Marquee Universiy, P.O.

More information

INTRODUCTION TO EMAIL MARKETING PERSONALIZATION. How to increase your sales with personalized triggered emails

INTRODUCTION TO EMAIL MARKETING PERSONALIZATION. How to increase your sales with personalized triggered emails INTRODUCTION TO EMAIL MARKETING PERSONALIZATION How o increase your sales wih personalized riggered emails ECOMMERCE TRIGGERED EMAILS BEST PRACTICES Triggered emails are generaed in real ime based on each

More information

The Torsion of Thin, Open Sections

The Torsion of Thin, Open Sections EM 424: Torsion of hin secions 26 The Torsion of Thin, Open Secions The resuls we obained for he orsion of a hin recangle can also be used be used, wih some qualificaions, for oher hin open secions such

More information