The Economic Impact of Public Beta Testing: The Power of Word-of-Mouth

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1 Supply Chain and Information Managmnt Confrnc Paprs, Postrs and Procdings Supply Chain and Information Systms Th Economic Impact of Public Bta Tsting: Th Powr of Word-of-Mouth Zhngrui Jiang Iowa Stat Univrsity, Kvin P. Schib Iowa Stat Univrsity, Sr Nilakanta Iowa Stat Univrsity, Follow this and additional works at: Part of th Managmnt Information Systms Commons Rcommndd Citation Jiang, Zhngrui; Schib, Kvin P.; and Nilakanta, Sr, "Th Economic Impact of Public Bta Tsting: Th Powr of Word-of-Mouth" (2011). Supply Chain and Information Managmnt Confrnc Paprs, Postrs and Procdings This Confrnc Procding is brought to you for fr and opn accss by th Supply Chain and Information Systms at Iowa Stat Univrsity Digital Rpository. It has bn accptd for inclusion in Supply Chain and Information Managmnt Confrnc Paprs, Postrs and Procdings by an authorizd administrator of Iowa Stat Univrsity Digital Rpository. For mor information, plas contact

2 Th Economic Impact of Public Bta Tsting: Th Powr of Word-of- Mouth Abstract Th advnt of th Intrnt has brought many fundamntal changs to th way businss is conductd. Among othrs, a growing numbr of softwar firms ar rlying on public bta tsting to improv th quality of thir products bfor rlas. Whil th bnfits rsulting from improvd softwar rliability hav bn widly rcognizd, th influncs of public bta tstrs on th diffusion of a nw softwar product hav not bn documntd. Through thir word-of-mouth ffct, public bta tstrs can spd up th diffusion of a softwar product aftr rlas, and hnc incras th tim-discountd rvnu pr adoptr. In this rsarch, w tak into considration both th rliability-sid and th diffusion-sid of th bnfits, and dvlop mthodologis to hlp firms dcid th optimal numbr of public bta tstrs and th optimal duration of public bta tsting. Numrical rsults show th firm s profit can incras substantially by taking advantag of th world-of-mouth of public bta tstrs. This bnfit is mor significant if firms rcruit bta tstrs from thos who can bnfit from a softwar product but cannot afford it. Kywords Bta tsting, softwar rliability, word-of-mouth, softwar diffusion, Bass modl Disciplins Managmnt Information Systms Commnts This articl is from th ICIS 2011 Procdings (Dcmbr 5, 2011). Postd with prmission. This confrnc procding is availabl at Iowa Stat Univrsity Digital Rpository:

3 THE ECONOMIC IMPACT OF PUBLIC BETA TESTING: THE POWER OF WORD-OF- MOUTH Zhngrui Jiang Collg of Businss Iowa Stat Univrsity 2340 Grdin Businss Building Ams, IA Compltd Rsarch Papr Sr Nilakanta Collg of Businss Iowa Stat Univrsity 2340 Grdin Businss Building Ams, IA Abstract Kvin P. Schib Collg of Businss Iowa Stat Univrsity 2340 Grdin Businss Building Ams, IA Th advnt of th Intrnt has brought many fundamntal changs to th way businss is conductd. Among othrs, a growing numbr of softwar firms ar rlying on public bta tsting to improv th quality of thir products bfor rlas. Whil th bnfits rsulting from improvd softwar rliability hav bn widly rcognizd, th influncs of public bta tstrs on th diffusion of a nw softwar product hav not bn documntd. Through thir word-of-mouth ffct, public bta tstrs can spd up th diffusion of a softwar product aftr rlas, and hnc incras th tim-discountd rvnu pr adoptr. In this rsarch, w tak into considration both th rliabilitysid and th diffusion-sid of th bnfits, and dvlop mthodologis to hlp firms dcid th optimal numbr of public bta tstrs and th optimal duration of public bta tsting. Numrical rsults show th firm s profit can incras substantially by taking advantag of th world-of-mouth of public bta tstrs. This bnfit is mor significant if firms rcruit bta tstrs from thos who can bnfit from a softwar product but cannot afford it. Kywords: Bta tsting, softwar rliability, word-of-mouth, softwar diffusion, Bass modl Thirty Scond Intrnational Confrnc on Information Systms, Shanghai

4 Track 5: Economics and Valu of Information Systms 1. Introduction Bta tsting is th last phas of a softwar dvlopmnt lifcycl bfor commrcial rlas. This stag typically bgins aftr alpha tsting is compltd and all known major issus ar rsolvd. During bta tsting, a pr-rlas vrsion of softwar is givn to a group of usrs to tst in ral world nvironmnts; onc dtctd, bugs ar rportd back to th dvlopmnt tam. Bta tsting contributs to quality assuranc in svral ways. First, bta tstrs systms nvironmnts can vary in both hardwar and softwar much mor so than th tsting nvironmnt in a lab. Sinc th actual usrs nvironmnts ar oftn difficult or impossibl to duplicat in a lab nvironmnt, bta tstrs can hlp idntify dfcts or compatibilitis issus that cannot b dtctd in tsting labs. Scond, bta tstrs ar not part of th dvlopmnt tam, and thus ar likly to b lss biasd. Third, bta tsting hlps dtrmin whthr th softwar mts th rquirmnts in trms of functionality and usr xpctation. Th fdback from bta tstrs can b usd to tst fatur dsign and hlp improv markting and customr support aftr rlas. In traditional bta tsting, th intrnally tstd softwar is distributd only to a small numbr of slctd and traind bta tstrs. Th dvlopmnt tam and th bta tstrs maintain clos communication throughout th bta tsting procss. Mor rcntly, with th xplosiv growth of th Intrnt, an incrasing numbr of softwar firms ar rlying on th Intrnt to rcruit bta tstrs. To diffrntiat it from th traditional bta tsting practics, this nw Intrnt-nabl bta tsting practic is somtims rfrrd to as public bta tsting. 1.1 Public bta tsting Public bta tsting, somtims also rfrrd to as opn bta, is a form of nontraditional bta tsting whr th bta softwar is rlasd to a public sit and may b downloadd by anyon intrstd. As mor usrs gain high spd Intrnt connctivity, thy ar abl to download and tst vry larg bta softwar rlass. Th trm bta has bcom a wll known and wll usd phras among computr usrs. Som xampls of wll known public btas ar Microsoft s Windows Vista community tchnology prviws, whr Microsoft would modify faturs and functionality of th oprating systm basd upon fdback from th bta tsting community. Othr vry popular btas ar Googl s Gmail, Googl Calndar, and Googl Nws (Fstr, 2005). Mobil applications for smart phons and tablts hav also influncd th public bta tsting phnomnon. For xampl, srvics such as Jott ( offrd an iphon app that intrfacd with a srvic to transcrib voic to txt. Jott wnt liv in Dcmbr 2006 as a bta. In August 2008, aftr attracting 420,000 usrs, Jott lft bta and rlasd a prmium srvic (Arrington, 2008). Thr ar vn wbsits spcializing in bringing togthr dvloprs and bta tstrs for iphon apps. For xampl, ibtatst.com allows iphon app dvloprs to publish apps, and tstrs from around th world may to download th apps and rport issus and commnts back to th dvloprs. As of May, 2011, ibtatst.com listd ovr 10,000 bta tstrs in 36 countris. Bcaus of th shr numbr of public bta tstrs for a projct, th quality of bta tstrs is mor difficult to control in public bta tsting than in traditional bta tsting. This disadvantag, though, is ovrshadowd by th availability of a larg numbr of bta tstrs in a short priod of tim at substantially lowr cost, thus lading to th popularity of th public bta tsting practic. Public bta tst has bcom a cost fficint mchanism in softwar product dvlopmnt bcaus it involvs a larg numbr of ndusrs in th product dvlopmnt lif cycl. Also, fatur idntification and altrnations ar nabld soonr. Furthrmor, in addition to quality assuranc, public bta tsting also brings othr bnfits ovr its traditional bta tsting countrpart. On such additional bnfit is th improvd awarnss of th nw product, ralizd through th word-of-mouth of th public bta tstrs. Basd on thir own xprinc, bta tstrs can sprad th quality/availability and othr information about th nw product to potntial adoptrs, thus spding up th diffusion of th product throughout its lifcycl. Bcaus of th timdiscount factor, a fastr diffusion lads to incrasd prsnt valu pr sal. Public bta tst has bn provn usful not only for brandd firms to incras markt pntration but also for Wb 2.0 firms (firms that ar unknown in th marktplac) to gain rcognition and markt shar (Mhr and Shrimali 2008). Although th softwar nginring aspct of bta tsting is important, th markting aspct of th problm should also b considrd. Howvr, w hav not sn any xisting rsarch that xamins th 2 Thirty Scond Intrnational Confrnc on Information Systms, Shanghai 2011

5 Jiang t al. / Th Economic Impact of Public Bta Tsting markt rlatd costs and bnfits of public bta tsting. Takn into considration both th rliability-sid and th diffusion-sid of th bnfits, th study attmpts to addrss th following qustions: How many public bta tstrs should b rcruitd and how long should th public bta tsting last? How is th solution affctd whn th markting rlatd costs and bnfits ar ignord? Dos th composition of th bta tstrs affct th optimal bta tsting stratgy and a firm s profitability? How is th bta tsting stratgy affctd in cas th bta vrsion has an xpiration dat? 1.2 Litratur rviw Compard to othr phass of th softwar dvlopmnt procss, bta tsting has rcivd lss attntion. On rfrnc w hav sn is a practitionr s guid on bta tsting (Fin, 2002). In his discussion of th costs and bnfits associatd with bta tsting, Fin has focusd primarily on th softwar nginring aspct and proposs various guidlins to improv th fficincy of bta tsting. Anothr study (Wipr and Wilson, 2006) uss Baysian statistical mthods to stimat th failur rat and th numbr of faults during th bta tsting phas of a softwar projct. Th authors also apply th proposd modl to hlp dtrmin how long th softwar should b tstd and by how many bta tstrs. Bsids bnfiting quality assuranc, bta tsting can also srv as an ffctiv tool for product promotion (Dolan and Mathws, 1993). Howvr, no mthodology is proposd to masur th markting sid of th bnfit of bta tsting. This study is also rlatd to th litratur on fr softwar, sinc bta softwar vrsions could b intrprtd as a form of fr softwar. Som of th xisting studis hav analyzd ntwork xtrnality rlatd bnfits of offring fr softwar (.g., Haruvy and Prasad 1998, Gallaughr and Wang 1999). Two rcnt articls hav also xamind th word-of-mouth of fr softwar adoptrs, and proposd fr offr policis basd on th bnfit rsulting from th word-of-mouth ffct (Jiang and Sarkar 2010, Jiang 2010). Thr is a critical diffrnc btwn fr softwar offr and public bta tsting. Th purpos of a fr offr is not quality assuranc, hnc softwar rliability and th rliability-rlatd costs and bnfits ar not considrd in ths prior studis. Bta tsting focuss on bug dtction and product validation, thrfor this study xplicitly modls rliability growth as wll as th rlatd bnfits such as th rduction in th cost of failurs in th fild. Furthrmor, th two studis that xamin th bnfits of fr adoptrs word-of-mouth ffct do not trat th duration of fr offr as a dcision variabl, sinc fr offr is assumd to tak a ngligibl amount of tim. In this study, th duration of public bta tsting is on of th two critical dcision variabls. To undrstand both th softwar rliability-sid and th diffusion-sid of th costs and bnfits, this study draws on thoris and modls from two distinct strams of litratur: th softwar rliability litratur in softwar nginring and th product diffusion litratur in markting. Th softwar rliability litratur includs softwar rliability growth modls that captur bug dtction pattrns ovr tim. Such modls can b broadly dividd into two catgoris; rror-sding modls and failur rat modls (Pham 2000, 2006). Th widly usd Non-Homognous Poisson Procss modl blongs to th scond catgory. Th modl by Gol and Okumoto (1979), also known as th G-O modl, is th most parsimonious NHPP modl and is frquntly usd in various applications of rliability modls (McDaid and Wilson, 2001; Xi and Yang 2003). Th G-O modl shows that th numbr of undtctd bugs dcrass at a dcrasing rat ovr tim and th bug dtction rat at any givn tim is always proportional to th xpctd numbr of undtctd bugs. Th product diffusion litratur in markting cntrs on th sminal work by Bass (1969); th modl is wll known as th Bass modl. Th Bass modl capturs th word-of-mouth ffct from arlir adoptrs on futur adoptrs: th largr th numbr of xisting adoptrs, th mor likly that th rmaining potntial adoptrs will also adopt. Th modl has bn shown to b applicabl to durabl goods, non-durabl goods, and information goods (Bass 2004). Following th Bass modl, numrous xtnsions and applications hav bn dvlopd and tstd. Among othrs, th Bass modl has bn usd to study nw product growth, dynamic pricing, product ntry stratgy, and softwar piracy (Mahajan t al. 2000). Th rst of th papr is organizd as follows. In Sction 2, w rviw th Bass modl and discuss th rliability assumptions basd on th G-O modl. In Sctions 3 and 4, w xamin th various tradoffs involvd in a public bta tsting dcision, propos modls, and analyz solutions for two diffrnt cass, on with all public bta tstrs abl to afford th softwar and th othr with a portion of th bta tstrs not abl to afford th product. Th third cas, whr a bta vrsion has an xpiration dat, is analyzd in Thirty Scond Intrnational Confrnc on Information Systms, Shanghai

6 Track 5: Economics and Valu of Information Systms Sction 5. W conclud th papr in Sction 6 with discussions on managrial implications and futur rsarch dirctions. 2. Th Modls W adopt two wll-known modls to form th thortical basis for our solution. Th word-of-mouth ffct of bta tstrs on futur adoptrs is modld basd on th Bass diffusion modl (Bass 1969). Th bug dtction pattrn is modld basd on th Gol and Okumoto Non-Homognous Poisson Procss modl (Gol and Okumoto 1979). 2.1 Th Bass Modl Th Bass diffusion modl (Bass 1969) is on of most citd and most influntial modls in markting. Th modl assums that th probability that a potntial adoptr will adopt at a givn tim t is proportional to th numbr of xisting adoptrs by tim t. In othr words, th largr is th numbr of xisting adoptrs, th mor likly that thos who hav not adoptd will also adopt at a givn tim. Th dirct and indirct influncs of th xisting adoptrs on futur adoptrs ar also rfrrd to as th word-of-mouth ffct. Th Bass modl can b rprsntd by dy( q [ p Y( ][ m Y( ], (1) dt m whr p is th cofficint of innovation, q is th cofficint of imitation, m dnots th total numbr of potntial adoptrs or markt siz, and Y( rprsnts th cumulativ numbr of adoptions by tim t. According to Bass (1969), th cumulativ numbr of adoptions at a givn tim t is ( pq) t m(1 ) Y (, (2) ( pq) t ( q / p) 1 and th non-cumulativ rat of adoption at tim t quals 2 ( pq) t dy( m( p q) S (. (3) ( pq) t 2 dt p [( q / p) 1] Onc th thr paramtrs (p, q, and m) ar known, th ntir diffusion path is dtrmind. In th product diffusion litratur, ths thr paramtrs ar oftn stimatd using historical sals data for xisting products. Othr things bing qual, a largr p lads to a highr initial adoption rat, a highr q suggsts a largr influnc of xisting adoptrs on futur adoptrs. S( and Y( ar proportional to m at any point in tim. Bsids xplaining th diffusion pattrn for xisting products, th Bass modl can also b usd to projct th futur diffusion pattrn of a nw product basd on sals data for similar products (Bass t al. 2001; Bayus 1993). 2.2 Th Rliability Growth Modl W modl th bug dtction procss basd on th classic Gol and Okumoto Non-Homognous Poisson Procss modl (Gol and Okumoto 1979), also known as th G-O modl. Th G-O modl adopts th following important assumption rgarding th rat of bug dtction: Assumption 1. Th liftim of ach bug is dpndnt of othrs, and instantanous bug dtction rat at a givn tim is always proportional to th numbr of uncovrd bugs at that tim. Basd on Assumption 1, th tim it taks to dtct ach givn bug follows an indpndnt and idntical xponntial distribution. Dnoting th failur rat of a bug by b, th lif tim of ach bug following th following distribution: f bt ( b, and th probability that a givn bug will b found bfor tim t is 4 Thirty Scond Intrnational Confrnc on Information Systms, Shanghai 2011

7 Jiang t al. / Th Economic Impact of Public Bta Tsting bt F( 1. W dnot th xpctd numbr of undtctd bugs at th start of tsting by N, and that at th tim of rlas (t ) by u(t ). Basd on th G-O modl, w hav u(t ) = N -bt. Assumption 2. Public bta tstrs valuat th softwar indpndntly and thir collctiv bug dtction fficincy is proportional to th total numbr of tstrs. This assumption is not includd in th G-O modl sinc th amount of tsting rsourcs is considrd xognous in that modl. W adopt it in this study bcaus th numbr of public bta tstrs is a dcision variabl to b dtrmind. Basd on this assumption, onc th numbr of public bta tstrs is givn, thir collctiv bug dtction fficincy is known and subsquntly th G-O can b applid. Basd on Assumptions 1 and 2, if w dnot th bug failur rat du to ach public bta tstr s tsting by λ, and th numbr of bta tstrs by X, th bug failur rat as a rsult of th bta tstrs collctiv ffort is b = λx. Th numbr of rmaining bugs rmaining aftr tim τ thus quals u X ( ) N. 3. Cas I (High-Valuation Bta Tstrs Only) Basd on whthr a potntial adoptr s rsrvation pric, i.., th highst pric a buyr is willing to pay, is highr than th sal pric of a softwar product or not, w classify all potntial adoptrs of a softwar product into two classs. A potntial adoptr blongs to th high-valuation class if his rsrvation pric is qual to or highr than th sal pric; a potntial adoptr blongs to th low-valuation class if his rsrvation pric is blow th sal pric. For instanc, a collg studnt who is intrstd in photo diting may bnfit from Adob Photoshop Lightroom. If th studnt is willing to pay th rgular pric of th softwar, sh blongs to th group of high-valuation potntial adoptrs; othrwis, sh should b classifid as a low-valuation potntial adoptr. Whn a softwar firm maks its nw product publicly availabl for bta tsting, th conomic implications ar diffrnt dpnding on th class ach public bta tstr blongs to. In this sction, w analyz Cas I, whr all public bta tstrs ar from th class of high-valuation potntial adoptrs. Th mor gnral Cas II, whr a portion of th bta tstrs ar from th class of low-valuation potntial adoptrs, will b xamind in th nxt sction. For both Cas I and Cas II, w assum that th word-of-mouth ffct from ach bta tstr is th sam as that from a paid adoptr. 1 Whil firms provid diffrnt incntivs to ncourag participation in bta tsting, most public bta tstrs ar drawn by th promis of a fr product or th opportunity to try a product that intrsts thm. For both Cas I and Cas II, w assum that vry public bta tstr will rciv a complt product fr of charg at th nd of public bta tsting. Aftr softwar rlas, th bta tstrs automatically turn into adoptrs of th nw softwar product thy hav tstd. As xplaind in th Introduction, public bta tsting can affct both th quality and th diffusion of a nw softwar product. In what follows, w first xamin th impact of bta tsting on th diffusion of a nw softwar product, which dtrmins th total rvnu gnratd during th dmand window, and thn assss th impact of bta tsting on th softwar s quality, which affcts th cost of softwar failurs during opration/usag. 1 In cas thir word-of-mouth influncs ar diffrnt, th modl can b xtndd by introducing a paramtr to dnot th ratio btwn th word-of-mouth influncs for a public bta tstrs and a paid adoptr. W xpct th qualitativ rsults to rmain valid aftr this rvision. Thirty Scond Intrnational Confrnc on Information Systms, Shanghai

8 Track 5: Economics and Valu of Information Systms 3.1 Impact of Public Bta Tsting on Softwar Diffusion W dnot th numbr of bta tstrs by X and th duration of bta tsting by t. For softwar products, thr typically xists a finit dmand window (Cohn t al. 1996), dnotd by D. Th duration of such dmand window is oftn du to various xtrnal factors such as advancmnts in hardwar tchnology, oprating systms, or othr compting softwar applications; thrfor, w assum that D is xognous in this rsarch. Undr Cas I, all bta tstrs blong to th high-valuation class, implying that thy would purchas th softwar vn if thy wr chargd th rgular sal pric. By contributing to bta tsting, howvr, ths bta tstrs rciv th final product fr of charg. Thrfor, undr Cas I, th firm loss th potntial rvnu from all bta tstrs. Clarly, this loss incrass with th numbr of public bta tstrs mployd during bta tsting. On th othr hand, onc th product is rlasd, th word-of-mouth ffct from ths bta tstrs can hlp spd up th diffusion of th nw softwar. Bcaus of th discount factor, th incrasd spd of diffusion can lad to highr tim-discountd rvnu pr adoptr. Thrfor, in dciding th optimal numbr of bta tstrs, a softwar firm nds to considr th tradoffs btwn th loss of potntial rvnu and th bnfits rsulting from th word-of-mouth of th bta tstrs. This tradoff can b graphically illustratd using th two diffusion curvs shown in Figur 1. Th curv on th lft shows how th diffusion would procd if th softwar wr rlasd immdiatly aftr lab tsting. As shown in this curv, th diffusion of th nw softwar would start from a rlativly low rat without th word-of-mouth ffct of th public bta tstrs, and hnc it would tak som tim for th diffusion to rach a prfrrd rat. In contrast, with bta tsting, although th commrcial launch of th product is dlayd, th diffusion can start from a highr rat onc th product is rlasd aftr bta tsting. This ffct is shown in th curv on th right. For xpositional convninc, w trm th scnario with bta tsting as scnario BT and th hypothtical on without bta tsting as scnario NBT. Basd on th basic prmis of th Bass modl, w arriv at th following conclusion: Thorm 1. Undr Cas I, th diffusion curv aftr bta tsting prfctly matchs th portion of th hypothtical diffusion curv, obtaind by assuming that th product is rlasd without bta tsting, aftr tim θ, whr θ is dtrmind by th numbr of public bta tstrs X: pm qx pm px Y 1 ln[( ) /( )] ( X ). p q S( Without th word-ofmouth of bta tstrs, th diffusion starts slowly S B(t ) Duration of bta tsting Th word-of-mouth of bta tstrs spds up th diffusion rat 0 θ=y -1 (X) D t 0 τ D t Scnario NBT: Rlas without Bta Tsting Scnario BT: Rlas aftr Bta Tsting Figur 1. Rlas with and without Bta Tsting Basd on Thorm 1, th diffusion curv for scnario BT matchs th solid sgmnt of th curv for scnario NBT. Thrfor, w conclud that th word-of-mouth ffct of th public bta tstrs undr Cas I is quivalnt to lft-shifting th hypothtical diffusion curv by tim θ. By forgoing th potntial rvnu from tim 0 to θ undr th hypothtical curv, th firm is abl to jump-start th diffusion of th nw 6 Thirty Scond Intrnational Confrnc on Information Systms, Shanghai 2011

9 Jiang t al. / Th Economic Impact of Public Bta Tsting softwar product immdiatly aftr bta tsting. Furthrmor, by comparing th distanc btwn θ and D undr scnario NBT with th distanc btwn τ and D undr scnario BT, it is vidnt that whn th duration of bta tsting τ is lss than th lft-shifting θ, som of th potntial adoptrs, who othrwis would not hav th chanc to adopt undr scnario NBT, will b abl to adopt undr scnario BT. Thrfor, with a rlativly shortr bta tsting duration, at last a portion of th loss of potntial rvnu du to th fr adoption by public bta tstrs can b compnsatd by th purchass mad by thos who othrwis would not hav adoptd during th dmand window. On th othr hand, if τ > θ, som of th adoptrs undr scnario NBT will not b abl to adopt undr scnario BT. This is quivalnt to shortning th dmand window. As a rsult, th firm loss rvnu not only bcaus of th public bta tstrs, but also bcaus of th shortnd sals window. For this scnario to b bnficial, th improvmnt in softwar quality as a rsult of prolongd bta tsting must b significant nough to justify th largr loss of potntial rvnu. W now driv th prsnt valu of th rvnu gnratd aftr bta tsting. Sinc th two solid curv sgmnts in Figurs 2 prfctly matchs ach othr, w can us th hypothtical diffusion rat S H( (aftr tim θ) to obtain th diffusion rat aftr bta tsting. For instanc, th diffusion rat at tim (τ + φ) for scnario BT quals th diffusion rat at tim (θ + φ) scnario NBT. Th discount factor, howvr, is diffrnt undr th two scnarios unlss th duration of bta tsting τ quals th amount of lft-shifting θ. With a discount rat of r, th discount factor for sals occurring at tim (τ + φ) undr scnario BT is r( ) r( ), whil th discount factor for th sals occurring at tim (θ + φ) undr scnario NBT is. Hnc, if w us th diffusion rat S ( for scnario NBT to rprsnt S B( for scnario BT, th discount factor nds to b appropriatly adjustd. Furthrmor, th ffctiv sals duration aftr bta tsting is (D τ), which also nds to b considrd in th modl formulation. Assuming a constant pric Pr throughout th dmand window, th tim-discountd rvnu aftr bta tsting is rprsntd by R ( X, ) Pr D S( r( t ) 3.2 Impact of Public Bta Tsting on Softwar Rliability dt. W nxt xamin th contributions of th bta tstrs to th quality of th nw softwar and th rsulting bnfit. Th improvmnt in quality is a function of both th numbr of bta tstrs X and th duration of tsting τ. With mor public bta tstrs or a longr tsting duration, mor bugs ar xpctd to b discovrd, lading to a mor rliabl product. On th othr hand, as xplaind arlir, mor highvaluation bta tstrs rsult in a largr loss of potntial rvnu, and a longr tsting tim dlays th firm from raping th bnfit of thir invstmnt and may possibly lad to loss of markt opportunity. Thrfor, ths tradoffs nd to b considrd in dtrmining th optimal bta tsting stratgy. To quantify th bnfit of improvd quality, consistnt with th litratur (.g., Dalal and Mallows 1988; Ehrlich t al. 1993), w assum that th total cost of softwar failurs in th fild (including th dirct cost of fixing th bugs and th indirct costs such as liability cost or loss of goodwill) is a linar function of th numbr of undtctd bugs at th tim of rlas. Suppos th xpctd numbr of bugs just bfor th start of bta tsting by N, and th bug failur rat du to ach public bta tstrs tsting by λ. Th avrag cost pr softwar failur is dnotd by c. Basd on th rliability assumptions discussd in Sction 2.2, th xpctd numbr of undtctd bugs at th nd of X bta tsting is u( X, ) N for X bta tstrs and a tsting duration of τ. Th total cost of softwar failurs, thrfor, quals X L ( X, ) cn. 3.3 Problm Formulation and Solution Th profit of th nw softwar product quals th total rvnu minus th cost of softwar failurs, i.., V( X, ) R( X, ) L( X, ). Th optimal public bta tsting problm for Cas I can thus b formulatd as Thirty Scond Intrnational Confrnc on Information Systms, Shanghai

10 Track 5: Economics and Valu of Information Systms Max V ( X, ) Pr X, D S( r( t ) ln[( mp Xq) /( mp Xp)] s.t.. p q dt cn X, (4) In ordr to obtain th bst public bta tsting solution for a nw softwar product, dcision-makrs nd to projct (i) th diffusion curv aftr rlas, dtrmind by th thr Bass modl paramtrs m, p, and q, (ii) th numbr of undtctd bug at th start of bta tsting (N) and th bug failur rat du to a bta tstr s tsting (λ), and (iii) th xpctd cost of on softwar failur duration opration/usag (c). Among ths paramtrs, th diffusion path can b projctd basd on prvious sals data for analogous products (Bayus, 1993; Bass t al., 2001). Th paramtrs N and λ can b stimatd by fitting th G-O modl to bug dtction data for similar products or initial bug dtction data for th nw product. Th xpctd cost of a softwar failur can b stimatd by domain xprts who ar familiar with th softwar s oprational nvironmnt. This cost should includ both th dirct cost of idntifying and fixing th rror and th indirct cost such as liability cost and th loss of goodwill as a rsult of a softwar failur. Analogous to most dcision problms of this typ, th quality of th solution obtaind basd on th proposd modl dpnds on how rliabl th stimatd modl paramtrs ar. Th formulation of th modl, howvr, dos not chang with th valus of th modl paramtrs. Sinc no prior study has takn into considration both softwar rliability and softwar diffusion, w ar unabl to find any diffusion data and bug dtction data for th sam softwar projct. Instad of using randomly gnratd valus, howvr, w stimat th paramtr valus basd on data for two diffrnt softwar systms. Th Bass modl paramtrs ar basd on spradsht sal data for UK (Givon t al. 1995): p = 0.002, q = 0.648, and m = 1,025K. Th xpctd numbr of undtctd bug at th start of bta tsting is stimatd to b N = 500 and th bug dtction rat pr bta tstr is assumd to b λ = 0.3. Ths two paramtrs ar stimatd and adjustd basd on tsting data for a ral-tim control softwar (Pham 2006, pp ). Th xpctd cost of a softwar failur c, is assumd to b $50,000. Th pric of th softwar (Pr) is st to $100 and th duration of th dmand window (D) is 10 yars. Basd on ths paramtr valus, w obtaind th following optimal solution: X * = 104K, τ * = 0.38 yar, and th corrsponding optimal profit is $70.98 million. 3.4 What if Bta Tstrs Word-of-mouth Effct is Ignord? In ordr to undrstand th impact of th word-of-mouth ffct on th solution of public bta tsting and a firm s profitability, in this subsction w considr a hypothtical scnario whr th bta tstrs xrt no word-of-mouth influnc on futur adoptrs. Without th word-of-mouth ffct from th bta tstrs, th lft-shifting illustratd in Figur 1 is not applicabl. Furthr, aftr bta tsting, th numbr of rmaining potntial adoptrs dcrass from m to (m X). Basd on th Bass modl, th diffusion rat at any givn point in tim is always proportional to th total numbr of potntial adoptrs. Hnc, th problm formulation for this hypothtical scnario is D m X Max V ( X, ) Pr S( X, 0 m ln[( mp Xq) /( mp Xp)] s.t.. p q r( t ) dt cn Using th sam paramtr valus, w obtain th following optimal solution: X * = 98K, τ * = 0.38 yar, and th corrsponding optimal profit is $35.9 million. Thrfor, vn without th word-of-mouth ffct of th bta tstrs, a firm would still rcruit public bta tstrs to hlp improv th quality of th softwar. Compard with th scnario whr th word-of-mouth from th bta tstrs is considrd, th firm should rcruit slightly fwr tstrs, and th duration of tsting should rmain about th sam; th total profit, howvr, will drop significantly without th bta tstrs word-of-mouth. Th drop in profit is du to th fact that th firm cannot incras th spd of diffusion by taking advantag of th word-of-mouth from th public bta tstrs. This diffrnc can b illustratd by comparing th two diffusion curvs with and without th word-of-mouth from th bta tstrs. From Figur 2, it is vidnt that without th bta tstrs word-of-mouth ffct, diffusion will start slowly, and th total sal within th dmand window is X, (5) 8 Thirty Scond Intrnational Confrnc on Information Systms, Shanghai 2011

11 Jiang t al. / Th Economic Impact of Public Bta Tsting significantly lowr. Thrfor, th word-of-mouth ffct should b considrd whn making public bta tsting dcisions. S( S( 0 D τ a. With Word-of-mouth 0 D τ b. Without Word-of-mouth Figur 2. Diffusion Curvs with and without th Word-of-mouth of Bta Tstrs 4. Cas II (including low-valuation public bta tstrs) Undr Cas I, w considr th scnario whr all bta tstrs ar high-valuation potntial adoptrs. Undr a mor gnral Cas II, th public bta tstrs includ both high-valuation and low-valuation potntial adoptrs. 2 As dfind in th prvious sction, low-valuation potntial adoptrs hav a rsrvation pric lowr than th sal pric, hnc thos low-valuation bta tstrs would not purchas th softwar if thy ar chargd th rgular sal pric. Thrfor, by rcruiting low-valuation potntial adoptrs as bta tstrs, th firm still bnfits from thir word-of-mouth; unlik undr Cas I, howvr, th firm dos not los any potntial rvnu from ths low-valuation public bta tstrs. Hnc, all ls bing qual, a largr portion of low-valuation bta tstrs is mor bnficial to a softwar firm. As th bst possibl scnario, th firm should rcruit bta tstrs only from th low-valuation potntial adoptrs. Howvr, this idal scnario is practically impossibl bcaus it is difficult to judg whthr ach potntial adoptr blongs to th high-valuation class or low-valuation class. 4.1 Problm Formulation and Solution Suppos th firm rcruits (1+δ)X public bta tstrs, among which X ar from th high-valuation class, and δx ar from th low-valuation class. W nxt xamin th impact of th public bta tstrs on th diffusion of a softwar product aftr rlas. Sinc th Bass modl considrs only thos potntial adoptrs who can buy th product at th st pric, low-valuation potntial adoptrs ar not countd in th markt siz paramtr m. To captur th word-of-mouth of ths xtra δx low-valuation adoptrs, w modify quation (1) for th Bass modl as follows: dy( / dt p ( q / m)[ Y( X ] p ( q / m) Y(, whr p p ( q / m) X. From (6), w conclud that taking into considration th word-of-mouth ffct of th low-valuation bta tstrs is quivalnt to incrasing th cofficint of innovation (p) by (q/m)δx. With th highr cofficint of innovation, w dnot th rvisd diffusion rat function by 2 ( pq) t m( p q) S ( (. (7) p q) t 2 p [( q / p) 1] (6) 2 Hr w assum that a low-valuation bta bstr and a high-valuation bta tstr hav th bug dtction fficincy and th sam amount of word-of-mouth influnc. Thirty Scond Intrnational Confrnc on Information Systms, Shanghai

12 Track 5: Economics and Valu of Information Systms Th discountd rvnu gnratd throughout th dmand window, bcoms R ( X, ) Pr D S( r( t ) dt, ln[( pm qx ) /( pm px )] whr. p q W nxt xamin th xpctd cost of softwar failurs. With th assumption that low-valuation and highvaluation bta tstrs hav th sam bug dtction fficincy, th xpctd numbr of undtctd bugs (1 ) X bcoms u ( X, ) N at th nd of bta tsting. Th total cost of softwar failurs thus bcoms (1 ) X. L ( X, ) cn Taking into considration th rvisd rvnu and cost of softwar failurs, th optimal public bta tsting solution for Cas II can b obtaind basd on: Max V ( X, ) Pr X, D S( r( t ) 2 ( pq) t m( p q) s.t. S( ( pq p [( q / p) ln[( mp Xq) /( mp Xp)], p q p p ( q / m) X. dt cn ) t 1] 2, (1 ) X, (8) Using th sam paramtr valus for Cas I, and lt δ=1.0, implying that thr ar an qual numbr of low-valuation and high-valuation bta tstrs, w numrically obtain th optimal solution for Cas II: X * = 87K and τ * =0.24 yar. Th optimal profit is $76.9 million. From this xampl, w can s that with lowvaluation bta tstrs, th optimal bta tsting duration shortns, th optimal numbr of high-valuation bta tstrs dcrass, whil th total numbr of fr adoptrs (174K) significantly incrass. As a rsult, th optimal profit incrass. Th incrasd profit is a rsult of two factors: first, mor bta tstrs lad to a high spd of diffusion; scond, fwr high-valuation bta tstrs cost th firm lss in loss of potntial rvnu. 4.2 Bnfits of Low-valuation Bta Tstrs Th ratio btwn th low-valuation and high-valuation public bta tstrs, δ, may b controlld if th firm is abl to idntify crtain low-valuation potntial adoptrs or if th firm targts a crtain sgmnt of th population (.g., collg studnts) that includs a highr prcntag of low-valuation potntial adoptrs. In ordr to undrstand th impact of δ, w rpat th numrical analysis for diffrnt valus of δ. Th rsults 3 ar summarizd in Figur 3. From this figur, w can s that as th prcntag of lowvaluation bta tstrs incrass, th optimal tsting duration dcrass, th optimal numbr of highvaluation dcrass, whil th total numbr of public bta tstrs incrass; and th ovrall profit incrass along th way. From th rsult, w conclud that a highr δ lads to a numbr of advantags: (i) th loss of potntial rvnu from th high-valuation bta tstrs is lowr; (ii) th total numbr of public bta tstrs is highr, lading to mor bug dtction and mor word-of-mouth influnc on potntial adoptrs aftr rlas; and (iii) a shortr bta tsting duration incrass th prsnt valu of ach sal. Thrfor, a firm should rcruit as many as low-valuation bta tstrs as possibl. 3 For clarity, th optimal duration of public bta tsting (τ * ) is convrtd to days (assuming 250 working days pr yar) in all figurs. 10 Thirty Scond Intrnational Confrnc on Information Systms, Shanghai 2011

13 Jiang t al. / Th Economic Impact of Public Bta Tsting Figur 3. Impact of th Ratio btwn Lowvaluation and High-valuation Bta Tstrs (δ) 4.3 Snsitivity Analysis Dpnding how mission-critical th softwar product is, th cost of softwar failurs during opration/usag can vary gratly. In ordr to undrstand how snsitiv th solution is to th cost of softwar failurs, w vary th valu of c and rcord th rsults as shown in Figur 4. As w can s from th figur, as th xpctd cost of a softwar failur incrass, it is optimal to rcruit slightly mor bta tstrs, and th tsting should last longr. Th duration of tsting incrass at a highr pac than th numbr of bta tstrs. Th nt profit dcrass bcaus th cost of failur is highr, and th longr tsting duration dlays th rvnu gnration. Figur 4. Impact of Cost of A Softwar Failur (c) To undr th impact of th bug dtction rat on th public bta tsting solution, w rpat th numrical analysis basd on varying valus of λ; th rsults ar as shown in Figur 5. W conclud from this figur that if bugs ar asir to dtct or if th bta tstrs ar mor fficint at bug dtction, rprsntd by a highr λ, it is optimal to rcruit fwr public bta tstrs and rduc th duration of public bta tsting, with th optimal duration of bta tsting dcrasing at a highr pac than th optimal numbr of bta tstrs. Ovrall, th rsulting nt profit incrass as th bug dtction fficincy incrass. Thirty Scond Intrnational Confrnc on Information Systms, Shanghai

14 Track 5: Economics and Valu of Information Systms Figur 5. Impact of Bug Dtction Efficincy (λ) In th Bass modl, th cofficint of innovation (p) dtrmins th initial diffusion rat aftr a nw product is rlasd, with a high p valu implying a highr initial diffusion rat. To undrstand its impact on th optimal public bta tsting solution, w obtain th optimal solutions corrsponding to diffrnt valus of p. Th rsults ar shown in Figur 6. From this figur, w can s that as th valu of p incrass, th optimal numbr of bta tstrs dcrass, th optimal duration of public bta tsting incrass, and th rsulting nt profit incrass. W conclud from this rsult that if th diffusion of a nw product can tak off rlativly quickly by itslf, thn a firm can rcruit fwr tstrs to rduc of th loss of potntial rvnu, and th loss in bug dtction can b compnsatd by a slightly longr tsting duration. Figur 6. Impact of Cofficint of Innovation (p) W also xamin th impact of th cofficint of imitation (q), anothr important paramtr in th Bass modl. This paramtr masurs th amount of influnc that xisting adoptrs hav on thos who hav not adoptd. A highr q valu lads to a fastr spd of product diffusion, manifstd by a highr adoption rat at th pak and a quickr tim to pak. Similar to th othr snsitivity analyss, w obtain diffrnt optimal solutions corrsponding to diffrnt valus of q. Th rsults ar shown in Figur 7. From this figur, w can s that th gnral impact of q on th optimal solution is similar to that of p. Howvr, th diffrnc is that as th valu of q incrass, th optimal numbr of bta tstrs drops at a much fastr rat. This is bcaus q rflcts th as th amount of influncs from xisting adoptrs on futur adoptrs; as such influncs incrass, a smallr numbr of bta tstrs will b sufficint to sprad th word about th product. Onc again, th loss of potntial rvnu can b savd, and th softwar quality can b assurd with longr bta tsting duration. Th ovrall profit tnds to incras as a rsult. 12 Thirty Scond Intrnational Confrnc on Information Systms, Shanghai 2011

15 Jiang t al. / Th Economic Impact of Public Bta Tsting Figur 7. Impact of Cofficint of Imitations (q) 5. Cas III (Bta Vrsion with Tim Limitation) Undr both Cas I and Cas II, w assum that all bta tstrs rciv th product for fr, and th bta vrsion has no contnt or tim limitation, i.., th bta vrsion has all th functionality and can b usd for a long as th usrs want. In practic, howvr, w frquntly obsrv bta softwar vrsions coming with a tim-limitation. Windows 7 from Microsoft is a good xampl of such practic. Th bta vrsion of th oprating systm xpird on Jun 1, Aftr that, public bta tstrs had to ithr purchas th commrcial vrsion or stop using th oprating systm. In this sction, w xamin Cas III, undr which th bta vrsion availabl for public bta tsting will continu to function for a fixd tim priod aftr rlas. W again assum that th public bta tstrs includ both high-valuation and low-valuation adoptrs. Th low-valuation bta tstrs will not purchas th commrcial softwar vrsion bcaus thir rsrvation pric is lowr than th sal pric. Thy will simply stopping using it aftr th bta vrsion xpirs. On th othr hand, th high-valuation bta tstrs bhav diffrntly. Som may hav compltd most of th tasks thy can prform with th softwar, and hnc dcid not to purchas th commrcial vrsion. Othrs may plan to continu to us th softwar, hnc will purchas th commrcial vrsion. For thos who dcid to mak th purchas, sinc thy hav known th softwar wll nough, w assum that thy will purchas th commrcial vrsion shortly aftr th xpiration of th bta vrsion. Thrfor, th ky diffrnc btwn Cas III and Cas II is that th firm dos not los th potntial rvnu from a portion of th high-valuation public bta tstrs. W dnot th proportion of public bta tstrs who will also buy th commrcial vrsion by, and th grac priod btwn th rlas of th commrcial vrsion and th xpiration of th bta vrsion by G. Th discountd rvnu gnratd by th purchas mad by th high-valuation public bta tstrs thus r( G) quals Pr X. Thrfor, th dcision problm for Cas III can b formulatd as: Max V ( X, ) Pr X X, r( G) Pr 2 ( pq) t m( p q) s.t. S( ( pq p [( q / p) ln[( mp Xq) /( mp Xp)], p q p p ( q / m) X. D ) t S( 2 1], r( t ) dt cn (1 ) X, (9) Thirty Scond Intrnational Confrnc on Information Systms, Shanghai

16 Track 5: Economics and Valu of Information Systms Adopting th sam paramtr valus from th numrical analysis for Cas II, and st = 0.5 and G = 1.0, w obtain th optimal solution for Cas III: X * = 151K, τ * =0.14 yar, and V * = $82.2million. In ordr to furthr undrstand how th optimal solution is affctd by th prcntag of high-valuation public bta tstrs who will also mak th purchas, w vary th valu of from 0 to 1.0 and summariz th solutions in Figur 8. At = 0, Cas III is ssntially Cas II. From this figur, w can s that as th valu of incrass, th firm should rcruit mor public bta tstrs and rduc th tsting duration. As xpctd, th nt profit incrass monotonically as a largr prcntag of high-valuation bta tstrs ar willing to mak th purchas aftr th xpiration of th bta vrsion. Figur 8. Impact of th Proportion of Bta Tstrs Who Will Buy () Aftr comparing problms (8) and (9) and th numrical rsults, on may b tmptd to draw th conclusion that Cas III is strictly bttr than Cas II sinc a firm is abl to rcovr a portion of th loss of rvnu from th high-valuation fr adoptrs. In practic, howvr, th ability for a firm to impos an xpiration dat for a nw product may vary dpnding on th charactristics and popularity of th product, th firm s rputation, and th undrlying markt condition. Sinc public bta tstrs invst thir tim in hlping improv th product, most of thm would xpct somthing in rturn. Thrfor, stting an xpiration dat on th bta vrsion may affct potntial adoptrs willingnss to participat in bta tsting and sprad th word about th product. Thrfor, for a littl-known and low-valu product in a comptitiv nvironmnt, offring a bta vrsion without any limitation may b th only ralistic way to lur a sufficint numbr of public bta tstrs in a rasonabl amount of tim. Thrfor, w should not rush to th conclusion that Cas III is always bttr than Cas II. Instad, th public bta tsting stratgis should b slctd basd on th markt nvironmnt and product charactristics; subsquntly, on of th proposd modls can b usd to dcid th optimal numbr of bta tstrs and th optimal duration of public bta tsting. 6. Discussion and Futur Rsarch With th asy accssibility of th Intrnt, public bta tsting has gaind trmndous popularity in th softwar industry. Th bnfits of public bta tsting, howvr, hav not bn formally analyzd. In this rsarch, w fill th void by showing that public bta tsting not only improvs th rliability of a nw softwar product, but also spds up th diffusion of th product aftr rlas. In addition, w show that th bnfit of public bta tsting can b furthr nhancd with low-valuation bta tstrs. Th incras in low-valuation bta tstrs has a significant impact on th profitability of a nw softwar product with a two-fold advantag. First, th tsting duration is shortnd. Scond, high-valuation tstrs, thos who would hav paid th full pric for th softwar, ar fwr. Th combind ffct rsults in potntially highr profit ovr th lif of th product. 14 Thirty Scond Intrnational Confrnc on Information Systms, Shanghai 2011

17 Jiang t al. / Th Economic Impact of Public Bta Tsting Bsids improving softwar rliability and spding up th diffusion, public bta tsting has othr practical implications. In a comptitiv markt, th ability to quickly rach a critical mass in customr bas can dictat markt succss or failur. By turning a larg numbr of public bta tstrs into arly adoptrs, a firm can quickly stablish a comptitiv advantag ovr its comptitors. Furthrmor, with a largr bas, a firm can latr rap othr bnfits including th sal of nwr improvd softwar vrsions and/or othr complimntary products or srvics. Thr ar a numbr of problms that may warrant furthr study. Th cost of adquat mchanisms for handling th incrasd numbr of tstrs is an issu that nds to b factord in futur studis. Anothr issu that is not addrssd hr is th impact of public bta tsting on th quality and marktability of products with succssiv gnrations. A third possibl dirction is to xamin th fficacy of public bta tsting in spding up th diffusion of a nw product in a comptitiv markt. Rfrncs Bass, F.M A Nw Product Growth for Modl Consumr Durabls, Managmnt Scinc (15:5), pp Bass, F. M Th Bass modl: a commntary, Managmnt Scinc (50:12 Supplmn, pp Bass, F.M., Gordon, K., Frguson, T.L. and Githns, M. L DIRECTV: Forcasting Diffusion of A Nw Tchnology Prior To Product Launch, Intrfacs (31:3), pp. S83-S93. Bayus, B.L High-dfinition Tlvision: Assssing Dmand Forcasts for a Nxt Gnration Consumr Durabl, Managmnt Scinc (39:11), pp Cohn, M.A., Eliashbrg, J., and Ho, T Nw Product Dvlopmnt: Th Prformanc and Timto-Markt Tradoff, Managmnt Scinc (42:2), pp Dalal, S.R., and Mallows, C. L Whn should on stop tsting softwar? Journal of th Amrican Statistical Association (83:403), pp Ehrlich, W., Prasanna, B., Statmpfl, J., and Wu, J Dtrmining th Cost of a Stop-Tst Dcision, IEEE Softwar (10:2), pp Fin, M. R. Bta tsting for bttr softwar, John Wily & Sons, Nw York, Fstr, P A long winding road out of bta, ZDNt, availabl from Gallaughr, J. Wang, M., Y Ntwork Effcts and th Impact of Fr Goods: An Analysis of th Wb Srvr Markt, Intrnational Journal of Elctronic Commrc (3:4), pp Givon, M., Mahajan, V., and Mullr, E Softwar Piracy: Estimation of Lost Sals and th Impact on Softwar Diffusion, Journal of Markting (59:1), pp Gol, A.L. and Okumoto, K Tim-Dpndnt Error-Dtction Rat Modl for Softwar and Othr Prformanc Masurs, IEEE Transactions on Rliability (R-28:3), Haruvy, E., Prasad, A Optimal Product Stratgis in th Prsnc Of Ntwork Extrnalitis, Information Economics and Policy (10:4), pp Hu, Q., Saundrs, C., and Gblt, M Rsarch Rport: Diffusion of Information Systms Outsourcing: A Rvaluation of Influnc Sourcs, Information Systms Rsarch (8:3), pp Jiang Z How to giv away softwar with succssiv vrsions, Dcision Support Systms (49:4), pp Jiang Z., Sarkar, S Spd Mattrs: Th Rol of Fr Softwar Offr in Softwar Diffusion, Journal of Managmnt Information Systms (26:3), pp Mahajan, V., E. Mullr, Y.Wind Nw-product diffusion modls. Kluwr, Boston. McDaid, K. and S. P. Wilson Dciding how long to tst softwar, Th Statistician (50:2), pp Mhra, Amit and Shrimali, G Introduction of Softwar Products and Srvics Through Public 'Bta' Launchs (Octobr 1, 2008), NET Institut Working Papr No Availabl at SSRN: Pham, H Softwar Rliability, Springr, Singapor. Pham, H Systm Softwar Rliability, Springr, London. Dolan, R. J., J. M. Matthws "Maximizing th utility of customr product tsting: Bta tst dsign and managmnt," Journal of Product Innovation Managmnt (10:4), pp Thirty Scond Intrnational Confrnc on Information Systms, Shanghai

18 Track 5: Economics and Valu of Information Systms Tng, J.T., Grovr, V., and Guttlr, W Information Tchnology Innovations: Gnral Diffusion Pattrns and its Rlationships to Innovation Charactristics, IEEE Transactions on Enginring Managmnt (49:1), pp Wipr, M. P., Wilson, S. P "A Baysian analysis of bta tsting," Tst (15:1), pp Xi, M., B. Yang A Study of th ffct of imprfct dbugging on softwar dvlopmnt cost, IEEE Trans on Softwar Enginring (29:5), pp Thirty Scond Intrnational Confrnc on Information Systms, Shanghai 2011