OPTIMAL REDUNDANCY ALLOCATION FOR INFORMATION MANAGEMENT SYSTEMS
|
|
- Drusilla James
- 8 years ago
- Views:
Transcription
1 Relablty ad Qualty Cotol Pactce ad Expeece OPTIMAL REDUNDANCY ALLOCATION FOR INFORMATION MANAGEMENT SYSTEMS Ceza VASILESCU PhD, Assocate Pofesso Natoal Defese Uvesty, Buchaest, Roaa E-al: Abstact: Relablty allocato eques defg elablty objectves fo dvdual subsystes ode to eet the ultate goal of elablty. Idvdual elablty objectves set fo softwae developet ust lead to a adequate ato of te-legth, level of dffculty ad sks, as well as decease developet pocess total cost. Thus, edudacy esues eetg the elablty equest by toducg a suffcet quatty of spae equpet. But the sae te, ths soluto leads to a cease weght, sze ad cost. The a of ths pape s the vestgato of elablty allocato to specfc sets of softwae applcatos () ude the ccustaces of zg developet ad pleetato costs by usg the Roe Reseach Laboatoy ethodology ad by coplyg wth the codtos of costs zato tggeed by the toducto of edudaces [GHITA 00]. The pape aalyses the ways whch the softwae elablty allocato gadual ethodology ca be exteded. It also aalyses the ssue of optal syste desg tes of elablty allocato by usg stuets of atheatcal pogag ad appoaches the vaato of elablty ad syste cost by takg to accout the edudacy toduced the syste. Ths pape s also gog to povde a exaple of calculus whch uses a epesetatve softwae syste ad llustates the ethodology of optal allocato of specfc sets of softwae applcatos elablty. Key wods: Relablty allocato; Optal edudacy; Icease of softwae applcatos elablty; Applcato softwae tools Itoducto Relablty allocato eques defg elablty objectves fo dvdual subsystes ode to eet the ultate goal of elablty. Idvdual elablty objectves set fo softwae developet ust lead to a adequate ato of te-legth, level of dffculty ad sks, as well as decease developet pocess total cost. Thus, edudacy esues eetg the elablty equest by toducg a suffcet quatty of spae equpet. But the sae te, ths soluto leads to a cease
2 Relablty ad Qualty Cotol Pactce ad Expeece weght, sze ad cost. I ths espect, softwae elablty allocato gadual ethodology [ROME 97] ca be exteded to clude the appoach used [GHITA 96]. The latte aalyses the ssue of optal syste desg tes of elablty allocato by usg stuets of atheatcal pogag ad appoaches the vaato of elablty ad syste cost by takg to accout the edudacy toduced the syste. Cosequetly, the a of ths pape s the vestgato of elablty allocato to specfc sets of softwae applcatos () ude the ccustaces of zg developet ad pleetato costs by usg the Roe Reseach Laboatoy ethodology ad by coplyg wth the codtos of costs zato tggeed by the toducto of edudaces [GHITA 00]. Befoe poceedg ay futhe soe theoetcal clafcatos ae eeded. Fstly, elablty allocato as vewed by [ROME 97] efes to allottg elablty specfcatos at syste level to softwae odule level (be thee a o-edudat cofguato). Relablty allocato as vewed by [GHITA 00] efes to the optal allocato of edudacy ode to each the elablty level set though elablty specfcatos. I coclusos, the copleetaty of the two appoaches s woth etog. Secodly, wth the cotext of foato aageet systes, the te edudacy efes both to the exstece of seveal specfc sets of softwae applcatos () developed ad desged depedetly ad whch have the sae fuctos, ad to testg ad upgadg these sets. All ths cosdeed, ths pape s also gog to povde a exaple of calculus whch uses a epesetatve softwae syste ad whch llustates the dea of the possblty of egg the two ethodologes. Moeove, the cocluso that s to be daw s that the odelg of the elablty cease by techologcal eas (.e. by testg ad upgadg the softwae) ad by edudacy s a ecessty. The Icease of Softwae Applcatos Relablty though Redudacy The hypothess udelyg the aalyss of the softwae elablty cease of the foato aageet systes s that these systes ae pat of those systes that ae fault-toleat. I ths espect, edudacy (vewed as the use wth a syste of oe eleets tha ecessay fo ts fuctog ode to have the syste u flawlessly eve the pesece of beakdows/falues [SERB 96]) s the basc eleet that assues the elablty of these systes. Othe eleets ay coce hadwae o softwae subsystes ad ca be taced at ay level, statg fo dvdual copoets up to the whole syste (hadwae ad/ softwae). Wth egad to elablty, the foato aageet systes softwae has a heachcal fuctoal patto, begg wth the Msso Specfc Tools Set (MSTS), Softwae Applcatos sets () ad the softwae odules wth the, all of whch cludg edudat copoets ad echass to eestablsh the fuctog. The basc ethods fo the fault toleace theoy fo the hadwae feld ca be adapted ad appled to the softwae of the foato aageet systes. Thus, ode to assue ts toleace to falues, ecodg logcal fuctos by usg edudat codes, eo ecogto ad eo eoval by sceeg faults wth the help of ultple (edudat) softwae odules stalled dffeet syste equpets o fuctoal ecofguato of
3 Relablty ad Qualty Cotol Pactce ad Expeece the syste by actvatg a spae softwae eleet that s to eplace the faled eleet ca be used. These ethods udele the suggestos ade by the foato aageet systes desges to use the followg basc fos of edudat softwae achtectues (fos that assue a cease elablty egadless of the heachcal fuctoal level - MSTS,, softwae odule): - The tple odula edudacy. It cludes thee detcal fuctoal odules that cay out sla tasks. The esults ae subject to the pocess kow as votg that scees a possble eoeous fuctog of oe of the odules. - Duplcato wth copaso. It s based o two fuctoal odules that assue cayg out sla tasks. If due to the paallel fuctog esults (outputs) dffe, dagoss pocedues ae caed out to detfy the faulty odule. - Dyac edudacy. It cotas seveal odules wth sla fuctos. Howeve, oly a pat of the fuctos ae opeatoal, wheeas the othe s o stad-by. Whe a falue s detfed the oes o stad-by becoe opeatoal ad take ove the tasks of the faulty oes. All these thee basc fos of edudat softwae achtectues ae to be foud the pleetato of the specfc sets of softwae applcatos (). I ode to evaluate the latte s elablty pefoace ths pape stats fo the hypothess that sceeg faults s stataeous ad that the faults of the dvdual copes of s ae depedet. Moeove, I a to eploy elablty logcal odels covetoally epeseted a way sla to those specfc to the evaluato of the elablty fuctos fo edudat hadwae stuctues. The followg exaples dsplay the evaluato of elablty pefoace usg as bblogaphy the evaluato of elablty fuctos of edudat stuctues [SERB 96]. Exaple The tple odula edudacy ade up of detcal s The tple odula edudacy s ade up of thee detcal s whee R ( t) s the elablty fucto ad a vote whee R V ( t) s ts elablty fucto. The elablty fucto of the tple odula edudacy ca be odeled by statg fo the logcal elablty odel (fg. ) R (t) R (t) R V (t) V R (t) Fgue. The elablty logcal odel fo the tple odula edudacy
4 Relablty ad Qualty Cotol Pactce ad Expeece Fo a good fuctog of the softwae syste, at least s ad the V vote ust fucto coectly. The fuctog pobablty of the edudat syste ude dscusso s gve by the geeal foula [SERB 96] fo k-out-of- systes: whch s () t C R() t ( R() t ) R RV k R R V ( ) () t R () t R ( t) Exaple The tple odula edudacy ade up of o- detcal s The thee s pefo the sae fuctos but they ae dffeet tes of desg ad pleetato. The elablty logcal odel s sla to the oe fg., wth the obsevato that the s have dffeet elabltes whch ae gve the otato R () t. I ode to calculate the elablty fucto the ethod of exhaustve eueato of syste states s used. I table the pobabltes of coect fuctog of the syste ad the pobabltes assocated to these evets ae peseted. Table. The pobabltes of good fuctog of the syste wth o-detcal s Seq. The evets assug the good fuctog The pobablty of the evet. R ( t) R ( t) R ( t). R ( t) R ( t) ( R ( t) ). 4. R ( t) R ( t) ( ) ( ) R () t ( R t ) R ( t) R ( t) The good fuctog of the syste s assued by jog all fou evets. They ae copatble wth oe aothe ad thus the pobablty of the good fuctog of the tple odula edudacy s: R() t RV () t [ R () t R ( t) R ( t) + R ( t) R ( t) ( R ( t) ) + + R () t ( R () t ) R () t + ( R () t ) R () t R ()] t RV () t [ R () t R () t + R () t R () t + R () t R () t - R () t R () t R ()] t I the two exaples, the odelg of the elablty fucto of the edudaces does ot take to accout the staces of eo-copesato. Cosequetly, 4
5 Relablty ad Qualty Cotol Pactce ad Expeece the pobablty of the evet to have falues, < falues, < falues ad the thee s to fucto: P R λt λt λt () t ( ) R () ( ) () ( ) t R t!!! whee ( λ ) s the falue ate of a. Thee s a ube of P peutatos fo the tple (,, ) wth a vew to detfyg the eos of the thee s:, P, sau 6, > > Each tple s assocated wth a P,, codtoed pobablty defed as: The syste fuctos coectly f t cotas, o eos, whee ca be set to ay value, < ad <. Cosequetly, the elablty fucto of the s calculated accodg to the elato: R () () ( ) P () ( ) λt λt () ( λt t P R t R t R t ) R R () t 0 0 0,, P P,, () t P P R () t + R () t ,0,0 0 P P,, ( λt)! ( λt) + +!!! + +!!! P 00 P!,0,0 ( λt) By ackowledgg that fo softwae systes thee s a expoetal epatto fo λt u te, fo whch R () t e, t esults: o R () t λt +! ( λt) 0! ( λt) R () t! R () t By eplacg, t esults: () R () t + R () t ( R () t ) + R ( t) R t! + 0 P! P,, ( λt) + +!!! 5
6 Relablty ad Qualty Cotol Pactce ad Expeece Exaple Dyac edudacy Be thee a dyac edudacy ade up of two s, a basc (fuctoal) oe - ad a spae oe -. The spae ca be fuctog o o stad-by ad ca be detcal (o ot) wth the fuctoal oe. The followg otatos ae to be used: R () t R () t R ( t) - the elablty fucto of the basc ; - the elablty fucto of the spae fuctog ; - the elablty fucto of the spae stadby. The logcal odel of the dyac edudacy s peseted fg.. R (t) R C R (t) Fgue. The logcal elablty odel of the dyac edudacy The dyac edudacy ca successfully fucto o log-te f the followg evets take place:. (basc ) fuctos well fo the (0, t) te duato; fo the pobablty of ths evet we gve the otato P R ( t) ;. fals at te oetτ, wheeτ < t ; (spae ) s pope fuctog codto ad t woks well fo the te teval ( τ, t). The pobablty of falue wth the fte sall te teval ( τ, τ + dτ ) s f ( τ ) dτ, ad the pobablty of at the τ oet ad of the fuctog fo the τ oet utl the t oet, wth fuctog codto at the τ oet s: f ( τ ) R R ( τ ) R ( t τ ) dτ If 0 < τ < t, the pobablty of the P coposed evet s: t P f ( τ ) R ( τ ) R ( t τ ) dτ R 0 The two evets ae copatble. Thus, the pobablty of a good fuctog of the dyac edudacy s: t R() t R () t + f ( τ ) R ( τ ) R ( t τ ) dτ R 0 6
7 Relablty ad Qualty Cotol Pactce ad Expeece The Optal Allocato of Applcato Softwae Redudaces The poble of elablty allocato ssues dug the stage of povsoal elablty evaluato. The pape [GHITA 00] offes solutos fo the optal allocato of elablty fo geeal stuatos by tacklg the topc of objects ade up copoet equpets ad puts fowad a way of choosg the type of edudacy that best eets the elablty equeet. I what follows I would lke to deal wth the ssue of adaptg the ethodology of elablty allocato to the elablty of specfc sets of softwae applcatos ad to peset a ethodology- adequate calculato poga that would eable solvg case studes. The fst thg ude cosdeato s the poble of avalablty allocato (adapted afte [SERB 96]) f the IT syste s desged as a seal coecto of (paallel) edudaces of subsystes. Usually, syste desg stats by toducg a u ube of fuctoally ecessay equpets ts stuctue. The esultg stuctue s, fo the elablty pot of vew, a seal oe. Sce seal stuctues have the lowest elablty, they ay ot eet elablty equeets ad, cosequetly, the desge s to cease syste elablty statg fo edudacy the ube of eleets. By gvg the otato of D ( ) to the avalablty of equpet ube, equpet whch has " " edudat (sae type of) equpets ad the otato of ( l,,..., ) to edudacy at poduct level, whee s the ube of equpets, t esults that D() s expessed as: D D Avalablty calculato D ( ) depeds o the type of edudacy pactced (edudacy though the desg of paallel systes, out of, o by usg spae equpet). I the fst two alteatves, edudat equpets wok ude the sae codtos as basc equpet does. O the oe had, that assues a techcally ease soluto. Howeve, the ssug elablty s less good copaed to the last alteatve. Fo ths alteatve of paallel edudacy D + ( ) d fo 0, t esults D d d λ λ + μ whee D s the avalablty of a equpet of type. Though edudacy, the elablty equeets ca be et by toducg eough spae equpet. Noetheless, weght, sze ad cost cease. If we gve the otato of C () to the cost of edudat equpets wth the syste, the latte s calculated as follows: C ( ) ( ) c whee c s the cost of a equpet of type. 7
8 Relablty ad Qualty Cotol Pactce ad Expeece Fo the cost elato t esults that the fucto ceases ootoously as agast ay copoet. Of all solutos, the oe that eets the elablty codto at the lowest cost ust be chose. I cocluso, the poble of the optal desg of the syste s foulated as follows: of all edudat solutos, oe ust fd the soluto that zes the cost C(), be thee a estcto, whch D D() s calculated accodace wth the elatos above. The elablty equests fo ca be expessed as follows: P P o whee K D K D P s the pobablty of good fuctog; K D s the avalablty coeffcet; P ad K D ae the u values of elablty dcatos. The elablty equeet ca be thus et by [GHITA 96] [GHITA 00]: a) ceasg syste s copoets elablty; b) ceasg (povg) syste s epaablty; c) usg soe elablty edudaces. The thd alteatve s gog to be dscussed oe detals the followg paagaphs. Usually softwae desg stats fo the basc pcple of a u ad fuctoally ecessay ube of odules wth the syste. Relablty aalyss pots out that the latte s a seal stuctue of low elablty. Relablty cease dug the desg stage s doe by havg a edudacy toduced as fa as the ube of odules s coceed. If P ( ) s the otato fo the pobablty of good fuctog of a that has edudat odules of the sae type ad the edudacy at the level of the, whee epesets the whole set of s s gve the otato (,,..., ) ube of s, t esults that P ( ) s expessed though the elato: P ( ) P ( ). Calculatg pobabltes P ( ) depeds o the type of edudacy eployed: edudacy by desgg systes of paallel softwae odules; edudacy by desgg systes of out of softwae odules; the use of spae softwae. The last alteatve has the advatage of assug a elablty cease supeo to the othe two fo whch the systes of edudat softwae odules wok the sae ae as the basc oes. 8
9 Relablty ad Qualty Cotol Pactce ad Expeece edudacy s: whee P The pobablty of a k k ( ) C P ( P ) k + good fuctog fo the fst two alteatves of + k P - pobablty of good fuctog of a odel of type ; P λt e (a expoetal epatto law follows); wth λ - falue testy of the odule type ad t - sso duato. If the syste s of a paallel type ad f > the syste s of a -out- of- type. As fo the edudacy though spae softwae odules, each odule togethe wth the edudat odules fos a kt that fals whe the + odules fal. follows: whee P I ths case, the pobablty to have a exact ube of k falues s calculated as k λ t ( k) P( ν k) ( λ t) e, λ - falue testy of odules; ν - ube of type faled odules. But P ( ) P( ) P ν, thus esultg the elato: k λ ( ) ( t) ( e t λ )/ k! k 0 The pevous foula s vald f we ae to accept the hypothess accodg to whch falue ad odule eplaceet s stataeously doe though a spae odule ad that pobablty equals. By havg the calculus foulas the good fuctog of aalyzed t esults that they ae ootoously ceasg fuctos. I cocluso, egadless of the P level, thee s the possblty of eachg the desed elablty level by cludg eough edudat softwae odules. l P ( ) s l P ( ) Howeve, oe obsevato ust be ade ths espect: by toducg ay ube of edudat softwae odules wth the stuctue of a, ts coplexty ad cost autoatcally cease. I all softwae systes, total cost educto s a effcecy cteo uaously accepted. Cosequetly, a optal equlbu betwee the desed elablty fo a, the ube of edudat softwae odules ad the cost of ths actvty eeds to be eached. I the geeal cocept of cost we clude the desg/ developet costs, softwae ateace/ explotato costs ad dowte costs. By gvg the cost of toducg wth the edudat odules the otato C ( ), ts value ca be estated as follows: 9
10 Relablty ad Qualty Cotol Pactce ad Expeece whee C ( ) c, c s the cost of a odule of type. Fo the cost elato t esults that the fucto ceases ootoously as copaed wth ay copoet. Fgue pesets a qualtatve gaph of elablty ad cost vaato as copaed wth the edudacy eployed. Each dot o the gaph coespods to a vecto, ad by ceasg the ube of copoets the dots ove up ad to the ght. The optal desg of the s doe by selectg the dots that go ove P (edudat dots that eet the elablty equeet) of the ost cost-effectve alteatve. Thus, t esults that the poble of fdg a optal desg soluto petas to atheatcal pogag (optu wth estctos) ad that t dsplays ceta patculates [GHITA 00]: t s a poble of o-lea pogag - P ( ) s ot a lea fucto as copaed wth aguet ; t s a poble of whole ubes pogag- aguets ae whole ubes. Cosequetly, the poble of elablty allocato s a poble of whole ubes o- lea pogag that s to be woked out by usg specfc ethods. Fgue. Vaato of elablty ad cost accodace wth the edudacy I the gaph dsplayed fgue thee s a le of dots o the uppe sde called doat vectos ad they ae optal solutos as copaed wth the othe dots. Thus the optal soluto s the fst vecto fo the le of doat vectos that go ove level P. It esults that detfyg the optal soluto s a atte of usg the appopate ethods by whch soe doat vectos ae obtaed. A vecto s called doat f the followg codtos ae et: ' ' P > P C > C. ( ) ( ) ( ) ( ). P( ) P( ' ) C( ) C( ' ) The detfcato of the doat vectos s doe by usg the fuctos: P ( k + ) ( k) l c P( k ) ϕ 0
11 Relablty ad Qualty Cotol Pactce ad Expeece whch evaluate the pobablty cease pe ut of cost fo a copoet wth k edudaces. All pocedues ae wokable f the fuctos ϕ ( k) ae covex ad fo the pevously etoed stuctues (- out- of- systes o spae oes) ϕ ( k) ae covex. The pocedue below supples a le of doat vectos ( k) ( ( k), ( k),..., ( k) ), k,,, N whch. () (0, 0,, 0). (k+) s ecuetly deduced as follows ( k + ) ( k) + daca I ( k + ) ( k) daca I whee I s the dex ube that axzes fucto ϕ ( k) ; (f thee ae oe dces I, ode to obta axu possble oe of the s selected as dex I);. Algoth stall esults fo: N k : P k P { ( ( )) } I cocluso, the pocedue leads to a le of doat vectos deduced oe fo the othe by addg oe ut fo each aguet that eaches the geatest cease pobablty pe ut of cost. The cha begs wth the detcal ull vecto ad eds wth the fst vecto that eets the elablty codto (C). Ths pocedue supples a cha of doat vectos that does ot ecessaly clude all possble doat vectos betwee the detcal vald vecto ad vecto ( k ). Cosequetly, t does ot always supply a optal soluto, but a quas-optal oe. The pocedue has the advatage of copletely takg algoth fo ad of beg easy to pleet o a copute. Its a dsadvatage esdes the fact that t stats fo vecto (0, 0,..., 0) ad thus a ube of steps ust be take towads fdg the fst doat vecto that eets the elablty ad cost equests. A oe dect ethod (wth fewe steps) towads obtag a cha of doat vectos s the oe ecoeded [BARLOW 9] ad whch volves usg oe of the followg pocedues. Pocedue It s sla to the pocedue pevously descbed ad t helps detee the whole cha of doat vectos by statg fo vecto (0, 0,..., 0) ad successvely toducg edudaces accodace wth the cease cteo. Pocedue It s a opeatoal alteatve that helps detee oe doat vecto that coespods to the posed level of pobablty P. It s based o the ( ),..., patculaty that lets pobablty P be, thee s a costat value so that all the copoets of the doat vecto eet the codto: k k P. { : ϕ ( ) < δ ( )} ϕ k ae postve ad ootoously deceasg ad ( P ) > 0 Sce fuctos ( ) δ, the pevous elato always assues fdg copoets. The advatage of ths pocedue cossts dectly supplyg vecto that coespods to the posed
12 Relablty ad Qualty Cotol Pactce ad Expeece pobablty level P. The dsadvatage les ot offeg ay clue as to the ae of choosg the costat value δ ( P ), whch s doe though successve tals. Pocedue It cossts jog pevous pocedues by usg the advatages. If a level of pobablty doat vecto ( ) δ usg pocedue. P s posed, a estate value fo the costat ( P ) δ ad ts coespodg ae establshed though successve tals, so that P ( t, ( )) < P δ by Oce ( δ ) s establshed, by usg pocedue the cha of doat vectos s establshed ts tu utl the doat vecto obtaed. P, P s that eets codto ( t ) Case Study: The Methodology of Optal Allocato of Relablty I ths sub-chapte we gve a exaple that llustates the ethodology of optal allocato of elablty [VASILESCU 05] by usg the optzed ethod of doat vectos calculato that was explaed detal the pevous paagaphs (pocedues -). () () () (k) (k) (k).... () () ().. Modulul () Modulul () Modulul () Fgue 4. Specfc set of softwae applcatos () wth edudaces at the softwae odules level I ode to set the bass of ths calculus, hee ae the tal data of the poble. We aalyze a IT syste, whch a coad ad cotol actvty s suppoted though a specfc set of softwae applcatos () cosstg of thee softwae odules (fgue 4). Table depcts the falue testes ad the specfc costs. Table. Specfc set of softwae applcatos - tal data I λ (hou - ) c (u.c.) 0, , ,000 50
13 Relablty ad Qualty Cotol Pactce ad Expeece Fo axu geealty we pefeed expessg the c values ut costs (u.c.). Fo a effectve aalyss of ths case study ad ode to obta elevat esults we aalyzed the fuctog of the thee s fo the te legth of t000 hous. The elablty of the softwae applcatos set s ceased by toducg a edudacy wth ts odules. The type of edudacy chose s the oe based o toducg soe spae softwae odules. The elablty equeet s P 0,95. Poble: The optal desg of the by choosg the edudacy alteatve that eets the elablty equeet ad that volves the lowest cost fo the edudat odules. The soluto to ths poble s gve by pocedue, fo P 0,95. I ode to establsh a oetatve value fo the costat ( P ) δ we take P 0,75 < P 0,95 as a pobablty ad assue that all ts copoets, P, P P ae equal. Cosequetly, P P 0,75 0, 9. The teeday esults ae povded table 4. As we otce fo the table, P ( 7) 0, 8867 s the closest value to P 0,9 ad cosequetly/ t esults that, ax k : P( k) < P 7. Table 4. Establshg the oetatve value of the costat ( ) k P (k) R (k) 0 0,008 0,008 0,095 0,0477 0,0948 0,45 0,57 0,94 4 0,80 0, ,747 0, ,98 0, ,0959 0, ,0575 0,944 If { k : ϕ ( k) < δ ( P )} δ ϕ, the oetatve value s: ϕ ( 7) P l c P ( 8) ( 7) δ - teeday esults P 0,004 By usg pocedue we obta the copoets of the doat vecto that have to eet the codto: { k : ϕ ( k) < δ ( P )},
14 Relablty ad Qualty Cotol Pactce ad Expeece As a esult, the fstϕ that eets the pevous codto s ϕ () 8 0, 00060, aely the fst doat vecto ( 7,8,6) ϕ that eets the pevous codto s ϕ ( 6) 0, wth ts coespodg pobablty P 0,6 < 0, 95.. It esults the Moeove, by eployg the ule of cease fo pocedue the esult s the cha of doat vectos peseted table 5 ad the coespodg values P ( ) ad C ( ). Table 5. Cha of doat vectos P ( ) C ( ) , , , , , We otce that the fst doat vecto that eets the codto P ( ) 0, 95 at the lowest cost s ( 8,,6), wheeas ts coespodg pobablty s ( ) 0, 975 C u.c. the cost of ( ) 6400 P at We also obseve that by usg pocedue we eeded 5 steps to obta the esult, wheeas fo the pocedue we would have eeded exta steps. I ode to pleet foulas ad do the calculatos we used Mcosoft Excel due to the possblty t offes to toduce tal data a apd ae, ad also because of the elegat ad explct layout fo the esults povded by ts speadsheets. Excel speadsheet cells explaato: D4:D6 - testy of falues the odules that wee gve the otatos, ad ; E4:E6 - odules specfc cost; H - sso duato hous; B9:B - ube of edudat odules toduced; D9:D (H9:H, L9:L) - values of odules elablty; fo exaple, cell D0 cotas the foula D9+POWER($F$4$D$4$H$;B0)/FACT(B0)EXP(-($F$4$D$4$H$)); E9:E (I9:I, M9:M) - values of the elablty cease fo odules pe ut cost; fo exaple, cell E0 cotas the foula (/$E$4)LN((D/D0)); C5:E5 (C9:E9) - chas of doat vectos; fo exaple, cell C6 cotas the foula IF(MAX(E7;I7;M7)E7;C5+;C5); F5:F9 - values of oveall elablty; fo exaple, cell F5 cotas the foula D6H6L6; G5:G9 - values of oveall costs; fo exaple, cell G5 cotas the foula C5$E$4+D5$E$5+E5$E$6. 4
15 Relablty ad Qualty Cotol Pactce ad Expeece Fgue 6. Optal allocato of the elablty by usg the ethod of calculatg the doat vectos- esults 5
16 Relablty ad Qualty Cotol Pactce ad Expeece I cocluso, ode to eet the posed elablty equeet a specfc set of softwae applcatos tools s eeded. The latte cludes: eght odules type oe, eleve odules type two ad sx odules type thee. The cost of the s 6400 ut cost. Refeeces. BARLOW, R., PROSCHAN, F. Matheatcal Theoy of Relablty, Joh Wley, New Yok, 998. GHITA, A., IONESCU, V. Metode de calcul î fabltate, Edtua Acadee Tehce Mltae, Buchaest, 996. GHITA, A., IONESCU, V., BICA, M. Metode de calcul î eteabltate, Edtua Acadee Tehce Mltae, Buchaest, SERB, A. Sstee de calcul toleate la defecta Edtua Acadee Tehce Mltae, Buchaest, VASILESCU, C. Alocaea opta a fabltat setulo specfce de aplcat softwae d ssteele C4ISR, The 0 th Iteatoal Scetfc Cofeece, Acadea Fotelo Teeste, Sbu, Novebe 4-6, Syste ad Softwae Relablty Assuace Notebook, poduced fo Roe Laboatoy, New Yok, TR Softwae Relablty Measueet ad Test Itegato Techques, poduced fo Roe Laboatoy, New Yok, 99 Ceza Vaslescu has gaduated the Faculty of Electocs ad Ifoato Scece wth the Mltay Techcal Acadey - Buchaest 997. He holds a PhD dploa Copute Scece fo 006. He has gaduated 00 the Advaced Maageet Poga ogazed by Natoal Defese Uvesty of Washgto D.C., USA. Also, he has eceved the US Depatet of Defese Chef Ifoato Offce (CIO) cetfcato fo the Ifoato Resouces Maageet College of Washgto D.C. Cuetly he s the head of the IT&C Offce wth the Regoal Depatet of Defese Resouces Maageet Studes - Basov ad assocate pofesso at the Natoal Defese Uvesty - Buchaest. He s the autho of oe tha 0 joual atcles ad scetfc pesetatos at cofeeces the felds of hadwae/softwae elablty, coad ad cotol systes ad foato esouces aageet. He has coodated as poga aage the actvty of establshg Roaa of a teatoal educatoal poga the feld of foato esouces aageet, collaboato wth uvestes fo USA. Besde hs eseach actvty, he has coodated Ta the Taes ad Educate the Educatos actvtes wth teatoal patcpato. Ma publshed books: - Ifoato Maageet, Mltay Techcal Acadey Publshg House, Buchaest, Ifoato Techology fo Maageet, Regoal Cete of Defese Resouces Maageet Publshg House, Basov, 00. Codfcatos of efeeces: [BARLOW 98] BARLOW, R., PROSCHAN, F. Matheatcal Theoy of Relablty, Joh Wley, New Yok, 998 [GHITA 96] GHITA, A., IONESCU, V. Metode de calcul î fabltate, Edtua Acadee Tehce Mltae, Buchaest, 996 [GHITA 00] GHITA, A., IONESCU, V., BICA, M. Metode de calcul î eteabltate, Edtua Acadee Tehce Mltae, Buchaest, 000 [ROME 9] TR Softwae Relablty Measueet ad Test Itegato Techques, poduced fo Roe Laboatoy, New Yok, 99 [ROME 97] Syste ad Softwae Relablty Assuace Notebook, poduced fo Roe Laboatoy, New Yok, 997 [SERB 96] SERB, A. Sstee de calcul toleate la defecta Edtua Acadee Tehce Mltae, Buchaest, 996 [VASILESCU 05] VASILESCU, C. Alocaea opta a fabltat setulo specfce de aplcat softwae d ssteele C4ISR, The 0 th Iteatoal Scetfc Cofeece, Acadea Fotelo Teeste, Sbu, Novebe 4-6, 005 6
Optimizing Multiproduct Multiconstraint Inventory Control Systems with Stochastic Period Length and Emergency Order
585858585814 Joual of Uceta Systes Vol.7, No.1, pp.58-71, 013 Ole at: www.us.og.uk Optzg Multpoduct Multcostat Ivetoy Cotol Systes wth Stochastc Peod Legth ad egecy Ode Ata Allah Talezadeh 1, Seyed Tagh
More informationOpinion Makers Section
Goupe de Taal Euopée Ade Multctèe à la Décso Euopea Wog Goup Multple Ctea Decso Adg Sée 3, º8, autome 008. Sees 3, º 8, Fall 008. Opo Maes Secto Hamozg poty weghts ad dffeece judgmets alue fucto mplemetato
More information16. Mean Square Estimation
6 Me Sque stmto Gve some fomto tht s elted to uow qutty of teest the poblem s to obt good estmte fo the uow tems of the obseved dt Suppose epeset sequece of dom vbles bout whom oe set of obsevtos e vlble
More informationA Markov Chain Grey Forecasting Model: A Case Study of Energy Demand of Industry Sector in Iran
0 3d Iteatoal Cofeece o Ifomato ad Facal Egeeg IED vol. (0) (0) IACSIT ess, Sgapoe A Makov Cha Gey Foecastg Model: A Case Study of Eegy Demad of Idusty Secto Ia A. Kazem +, M. Modaes, M.. Mehega, N. Neshat
More informationEFFICIENT GENERATION OF CFD-BASED LOADS FOR THE FEM-ANALYSIS OF SHIP STRUCTURES
EFFICIENT GENERATION OF CFD-BASED LOADS FOR THE FEM-ANALYSIS OF SHIP STRUCTURES H Ese ad C Cabos, Gemasche Lloyd AG, Gemay SUMMARY Stegth aalyss of shp stuctues by meas of FEM eques ealstc loads. The most
More informationFinite-Difference-Frequency-Domain Simulation of Electrically Large Microwave Structures using PML and Internal Ports
Fte-ffeece-Fequecy-oa Sulato of Electcally Lage Mcowave Stuctues usg PML ad teal Pots vogelegt vo MSc Eg Podyut Kua Talukde aus Netakoa Bagladesh vo de Fakultät V - Elektotechk ud foatk - de Techsche Uvestät
More informationA Study of Unrelated Parallel-Machine Scheduling with Deteriorating Maintenance Activities to Minimize the Total Completion Time
Joural of Na Ka, Vol. 0, No., pp.5-9 (20) 5 A Study of Urelated Parallel-Mache Schedulg wth Deteroratg Mateace Actvtes to Mze the Total Copleto Te Suh-Jeq Yag, Ja-Yuar Guo, Hs-Tao Lee Departet of Idustral
More informationRandomized Load Balancing by Joining and Splitting Bins
Radomzed Load Baacg by Jog ad Spttg Bs James Aspes Ytog Y 1 Itoducto Cosde the foowg oad baacg sceao: a ceta amout of wo oad s dstbuted amog a set of maches that may chage ove tme as maches o ad eave the
More informationFuzzy Task Assignment Model of Web Services Supplier in Collaborative Development Environment
, pp.199-210 http://dx.do.org/10.14257/uesst.2015.8.6.19 Fuzzy Task Assget Model of Web Servces Suppler Collaboratve Developet Evroet Su Ja 1,2, Peg Xu-ya 1, *, Xu Yg 1,3, Wag Pe-e 2 ad Ma Na- 4,2 1. College
More informationRevenue Management for Online Advertising: Impatient Advertisers
Reveue Maagemet fo Ole Advetsg: Impatet Advetses Kst Fdgesdott Maagemet Scece ad Opeatos, Lodo Busess School, Reget s Pak, Lodo, NW 4SA, Uted Kgdom, kst@lodo.edu Sam Naaf Asadolah Maagemet Scece ad Opeatos,
More informationA CPN-based Trust Negotiation Model on Service Level Agreement in Cloud Environment
, pp.247-258 http://dx.do.og/10.14257/jgdc.2015.8.2.22 A CPN-based Tust Negotato Model o Sevce Level Ageemet Cloud Evomet Hogwe Che, Quxa Che ad Chuzh Wag School of Compute Scece, Hube Uvesty of Techology,
More informationBank loans pricing and Basel II: a multi-period risk-adjusted methodology under the new regulatory constraints
Baks ad Bak Systems, Volume 4, Issue 4, 2009 Domeco Cuco (Italy, Igo Gafacesco (Italy Bak loas pcg ad Basel II: a mult-peod sk-usted methodology ude the ew egulatoy costats Abstact Ude the ew Basel II
More informationNumerical Methods with MS Excel
TMME, vol4, o.1, p.84 Numercal Methods wth MS Excel M. El-Gebely & B. Yushau 1 Departmet of Mathematcal Sceces Kg Fahd Uversty of Petroleum & Merals. Dhahra, Saud Araba. Abstract: I ths ote we show how
More informationAverage Price Ratios
Average Prce Ratos Morgstar Methodology Paper August 3, 2005 2005 Morgstar, Ic. All rghts reserved. The formato ths documet s the property of Morgstar, Ic. Reproducto or trascrpto by ay meas, whole or
More informationIntegrated Workforce Planning Considering Regular and Overtime Decisions
Poceedgs of the 2011 Idusta Egeeg Reseach Cofeece T. Dooe ad E. Va Ae, eds. Itegated Wofoce Pag Cosdeg Regua ad Ovetme Decsos Shat Jaugum Depatmet of Egeeg Maagemet & Systems Egeeg Mssou Uvesty of Scece
More informationNumerical Comparisons of Quality Control Charts for Variables
Global Vrtual Coferece Aprl, 8. - 2. 203 Nuercal Coparsos of Qualty Cotrol Charts for Varables J.F. Muñoz-Rosas, M.N. Pérez-Aróstegu Uversty of Graada Facultad de Cecas Ecoócas y Epresarales Graada, pa
More information6.7 Network analysis. 6.7.1 Introduction. References - Network analysis. Topological analysis
6.7 Network aalyss Le data that explctly store topologcal formato are called etwork data. Besdes spatal operatos, several methods of spatal aalyss are applcable to etwork data. Fgure: Network data Refereces
More informationA Comparative Study for Email Classification
A Coparatve Study for Eal Classfcato Seogwook You ad Des McLeod Uversty of Souther Calfora, Los Ageles, CA 90089 USA Abstract - Eal has becoe oe of the fastest ad ost ecoocal fors of coucato. However,
More informationA Single-Producer Multi-Retailer Integrated Inventory System with Scrap in Production
Research Joural of Appled Sceces, Egeerg ad Techology 5(4): 54-59, 03 ISSN: 040-7459; e-issn: 040-7467 Maxwell Scetfc Orgazato, 03 Subtted: July 09, 0 Accepted: August 08, 0 Publshed: February 0, 03 A
More informationAnalysis of marketing data to extract key factors of telecom churn management
fca Joual of usess Maagemet Vol. 5(0) pp. 84-84716 eptembe 011 valable ole at http://www.academcjouals.og/jm DOI: 10.5897/JM11.944 IN 1993-833 011 cademc Jouals Full Legth Reseach Pape alyss of maketg
More informationSIMULATION OF THE FLOW AND ACOUSTIC FIELD OF A FAN
Cofeece o Modellg Flud Flow (CMFF 9) The 14 th Iteatoal Cofeece o Flud Flow Techologes Budapest, Hugay, Septembe 9-1, 9 SIMULATION OF THE FLOW AND ACOUSTIC FIELD OF A FAN Q Wag 1, Mchael Hess, Bethold
More informationChapter Eight. f : R R
Chapter Eght f : R R 8. Itroducto We shall ow tur our atteto to the very mportat specal case of fuctos that are real, or scalar, valued. These are sometmes called scalar felds. I the very, but mportat,
More informationA Fast Clustering Algorithm to Cluster Very Large Categorical Data Sets in Data Mining
A Fast Clusterg Algorth to Cluster Very Large Categorcal Data Sets Data Mg Zhexue Huag * Cooperatve Research Cetre for Advaced Coputatoal Systes CSIRO Matheatcal ad Iforato Sceces GPO Box 664, Caberra
More informationANOVA Notes Page 1. Analysis of Variance for a One-Way Classification of Data
ANOVA Notes Page Aalss of Varace for a Oe-Wa Classfcato of Data Cosder a sgle factor or treatmet doe at levels (e, there are,, 3, dfferet varatos o the prescrbed treatmet) Wth a gve treatmet level there
More information9.5 Amortization. Objectives
9.5 Aotization Objectives 1. Calculate the payent to pay off an aotized loan. 2. Constuct an aotization schedule. 3. Find the pesent value of an annuity. 4. Calculate the unpaid balance on a loan. Congatulations!
More informationChapter 3. AMORTIZATION OF LOAN. SINKING FUNDS R =
Chapter 3. AMORTIZATION OF LOAN. SINKING FUNDS Objectves of the Topc: Beg able to formalse ad solve practcal ad mathematcal problems, whch the subjects of loa amortsato ad maagemet of cumulatve fuds are
More informationUnderstanding Financial Management: A Practical Guide Guideline Answers to the Concept Check Questions
Udestadig Fiacial Maagemet: A Pactical Guide Guidelie Aswes to the Cocept Check Questios Chapte 4 The Time Value of Moey Cocept Check 4.. What is the meaig of the tems isk-etu tadeoff ad time value of
More informationPolyphase Filters. Section 12.4 Porat 1/39
Polyphase Flters Secto.4 Porat /39 .4 Polyphase Flters Polyphase s a way of dog saplg-rate coverso that leads to very effcet pleetatos. But ore tha that, t leads to very geeral vewpots that are useful
More informationSTATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS. x, where. = y - ˆ " 1
STATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS Recall Assumpto E(Y x) η 0 + η x (lear codtoal mea fucto) Data (x, y ), (x 2, y 2 ),, (x, y ) Least squares estmator ˆ E (Y x) ˆ " 0 + ˆ " x, where ˆ
More informationA multivariate Denton method for benchmarking large data sets
09 A multaate Deto metho fo bechmakg lage ata sets ee Bkke, Jacco Daalmas a No Mushkua The ews epesse ths pape ae those of the autho(s) a o ot ecessaly eflect the polces of tatstcs Nethelas Dscusso pape
More informationMeasuring the Quality of Credit Scoring Models
Measur the Qualty of Credt cor Models Mart Řezáč Dept. of Matheatcs ad tatstcs, Faculty of cece, Masaryk Uversty CCC XI, Edurh Auust 009 Cotet. Itroducto 3. Good/ad clet defto 4 3. Measur the qualty 6
More informationThe Analysis of Development of Insurance Contract Premiums of General Liability Insurance in the Business Insurance Risk
The Aalyss of Developmet of Isurace Cotract Premums of Geeral Lablty Isurace the Busess Isurace Rsk the Frame of the Czech Isurace Market 1998 011 Scetfc Coferece Jue, 10. - 14. 013 Pavla Kubová Departmet
More informationProject 3 Weight analysis
The Faculty of Power ad Aeroautcal Egeerg Arcraft Desg Departet Project 3 Weght aalyss Ths project cossts of two parts. Frst part cludes fuselage teror (cockpt) coceptual desg. Secod part cludes etoed
More informationKeywords: valuation, warrants, executive stock options, capital structure, dilution. JEL Classification: G12, G13.
Abstact he textbook teatmet fo the aluato of waats takes as a state aable the alue of the fm ad shows that the alue of a waat s equal to the alue of a call opto o the equty of the fm multpled by a dluto
More informationT = 1/freq, T = 2/freq, T = i/freq, T = n (number of cash flows = freq n) are :
Bullets bods Let s descrbe frst a fxed rate bod wthout amortzg a more geeral way : Let s ote : C the aual fxed rate t s a percetage N the otoal freq ( 2 4 ) the umber of coupo per year R the redempto of
More informationMaintenance Scheduling of Distribution System with Optimal Economy and Reliability
Egeerg, 203, 5, 4-8 http://dx.do.org/0.4236/eg.203.59b003 Publshed Ole September 203 (http://www.scrp.org/joural/eg) Mateace Schedulg of Dstrbuto System wth Optmal Ecoomy ad Relablty Syua Hog, Hafeg L,
More informationADAPTATION OF SHAPIRO-WILK TEST TO THE CASE OF KNOWN MEAN
Colloquum Bometrcum 4 ADAPTATION OF SHAPIRO-WILK TEST TO THE CASE OF KNOWN MEAN Zofa Hausz, Joaa Tarasńska Departmet of Appled Mathematcs ad Computer Scece Uversty of Lfe Sceces Lubl Akademcka 3, -95 Lubl
More informationResearch on Cloud Computing Load Balancing Based on Virtual Machine Migration
Send Odes fo Repnts to epnts@benthascence.ae 334 The Open Cybenetcs & Systecs Jounal, 205, 9, 334-340 Open Access Reseach on Cloud Coputng Load Balancng Based on Vtual Machne Mgaton Lu Kun,*, Xu Gaochao
More informationA Time Delay System Case Study: Computer Integrated Manufacturing and Management System Robustness
A Te Delay Syste Case Study: Copute Itegated Maufactug ad Maageet Syste Robustess Jozef B. Lewoc*, Ato Izwosk** Slawo Skowosk*** * BPBT Leade (Leadg Desge), ul Powst. Sl. 93/28, 53-38 Woclaw, Polad **
More informationFault Tree Analysis of Software Reliability Allocation
Fault Tree Aalyss of Software Relablty Allocato Jawe XIANG, Kokch FUTATSUGI School of Iformato Scece, Japa Advaced Isttute of Scece ad Techology - Asahda, Tatsuokuch, Ishkawa, 92-292 Japa ad Yaxag HE Computer
More informationI = Prt. = P(1+i) n. A = Pe rt
11 Chapte 6 Matheatcs of Fnance We wll look at the atheatcs of fnance. 6.1 Sple and Copound Inteest We wll look at two ways nteest calculated on oney. If pncpal pesent value) aount P nvested at nteest
More informationCredibility Premium Calculation in Motor Third-Party Liability Insurance
Advaces Mathematcal ad Computatoal Methods Credblty remum Calculato Motor Thrd-arty Lablty Isurace BOHA LIA, JAA KUBAOVÁ epartmet of Mathematcs ad Quattatve Methods Uversty of ardubce Studetská 95, 53
More informationProjection model for Computer Network Security Evaluation with interval-valued intuitionistic fuzzy information. Qingxiang Li
Iteratoal Joural of Scece Vol No7 05 ISSN: 83-4890 Proecto model for Computer Network Securty Evaluato wth terval-valued tutostc fuzzy formato Qgxag L School of Software Egeerg Chogqg Uversty of rts ad
More informationMulti-Channel Pricing for Financial Services
0-7695-435-9/0 $7.00 (c) 00 IEEE Proceedgs of the 35th Aual Hawa Iteratoal Coferece o yste ceces (HIC-35 0) 0-7695-435-9/0 $7.00 00 IEEE Proceedgs of the 35th Hawa Iteratoal Coferece o yste ceces - 00
More informationMunicipal Creditworthiness Modelling by Clustering Methods
Mucal Cedtwotess Modellg by Clusteg Metods Pet Háek, Vladmí Ole Isttute of System Egeeg ad Ifomatcs Faculty of Ecoomcs ad Admstato Uvesty of Padubce Studetská 84, 53 0 Padubce Czec eublc Pet.Haek@uce.cz,
More informationSTOCK INVESTMENT MANAGEMENT UNDER UNCERTAINTY. Madalina Ecaterina ANDREICA 1 Marin ANDREICA 2
"AROACHES IN ORGANISATIONA MANAGEMENT" 15-16 Noveber 01, BCHAREST, ROMANIA STOCK INVESTMENT MANAGEMENT NDER NCERTAINTY Madaa Ecatera ANDREICA 1 Mar ANDREICA ABSTRACT Ths paper presets a stock vestet aageet
More informationSecurity Analysis of RAPP: An RFID Authentication Protocol based on Permutation
Securty Aalyss of RAPP: A RFID Authetcato Protocol based o Permutato Wag Shao-hu,,, Ha Zhje,, Lu Sujua,, Che Da-we, {College of Computer, Najg Uversty of Posts ad Telecommucatos, Najg 004, Cha Jagsu Hgh
More informationThe analysis of annuities relies on the formula for geometric sums: r k = rn+1 1 r 1. (2.1) k=0
Chapter 2 Autes ad loas A auty s a sequece of paymets wth fxed frequecy. The term auty orgally referred to aual paymets (hece the ame), but t s ow also used for paymets wth ay frequecy. Autes appear may
More informationInvestment Science Chapter 3
Ivestmet Scece Chapte 3 D. James. Tztzous 3. se P wth 7/.58%, P $5,, a 7 84, to obta $377.3. 3. Obseve that sce the et peset value of X s P, the cash flow steam ave at by cyclg X s equvalet
More informationAbraham Zaks. Technion I.I.T. Haifa ISRAEL. and. University of Haifa, Haifa ISRAEL. Abstract
Preset Value of Autes Uder Radom Rates of Iterest By Abraham Zas Techo I.I.T. Hafa ISRAEL ad Uversty of Hafa, Hafa ISRAEL Abstract Some attempts were made to evaluate the future value (FV) of the expected
More informationThe Gompertz-Makeham distribution. Fredrik Norström. Supervisor: Yuri Belyaev
The Gompertz-Makeham dstrbuto by Fredrk Norström Master s thess Mathematcal Statstcs, Umeå Uversty, 997 Supervsor: Yur Belyaev Abstract Ths work s about the Gompertz-Makeham dstrbuto. The dstrbuto has
More informationHow do bookmakers (or FdJ 1 ) ALWAYS manage to win?
How do bookakers (or FdJ ALWAYS aage to w? Itroducto otatos & varables Bookaker's beeft eected value 4 4 Bookaker's strateges5 4 The hoest bookaker 6 4 "real lfe" bookaker 6 4 La FdJ 8 5 How ca we estate
More informationFinite Production Rate Model With Quality Assurance, Multi-customer and Discontinuous Deliveries
Fte Producto Rate Model Wth ualty Assurace, Mult-custoer ad Dscotuous Delveres Yua-Shy Peter Chu, L-We L, Fa-Yu Pa 3, Sga Wag Chu * Departet of Idustral Egeerg Chaoyag Uversty of Techology, Tachug 43,
More informationStatistical Pattern Recognition (CE-725) Department of Computer Engineering Sharif University of Technology
I The Name of God, The Compassoate, The ercful Name: Problems' eys Studet ID#:. Statstcal Patter Recogto (CE-725) Departmet of Computer Egeerg Sharf Uversty of Techology Fal Exam Soluto - Sprg 202 (50
More informationCHAPTER 2. Time Value of Money 6-1
CHAPTER 2 Tme Value of Moey 6- Tme Value of Moey (TVM) Tme Les Future value & Preset value Rates of retur Autes & Perpetutes Ueve cash Flow Streams Amortzato 6-2 Tme les 0 2 3 % CF 0 CF CF 2 CF 3 Show
More informationOnline Appendix: Measured Aggregate Gains from International Trade
Ole Appedx: Measured Aggregate Gas from Iteratoal Trade Arel Burste UCLA ad NBER Javer Cravo Uversty of Mchga March 3, 2014 I ths ole appedx we derve addtoal results dscussed the paper. I the frst secto,
More informationBanking (Early Repayment of Housing Loans) Order, 5762 2002 1
akg (Early Repaymet of Housg Loas) Order, 5762 2002 y vrtue of the power vested me uder Secto 3 of the akg Ordace 94 (hereafter, the Ordace ), followg cosultato wth the Commttee, ad wth the approval of
More informationDerivation of Annuity and Perpetuity Formulae. A. Present Value of an Annuity (Deferred Payment or Ordinary Annuity)
Aity Deivatios 4/4/ Deivatio of Aity ad Pepetity Fomlae A. Peset Vale of a Aity (Defeed Paymet o Odiay Aity 3 4 We have i the show i the lecte otes ad i ompodi ad Discoti that the peset vale of a set of
More informationCH. V ME256 STATICS Center of Gravity, Centroid, and Moment of Inertia CENTER OF GRAVITY AND CENTROID
CH. ME56 STTICS Ceter of Gravt, Cetrod, ad Momet of Ierta CENTE OF GITY ND CENTOID 5. CENTE OF GITY ND CENTE OF MSS FO SYSTEM OF PTICES Ceter of Gravt. The ceter of gravt G s a pot whch locates the resultat
More informationAnnuities and loan. repayments. Syllabus reference Financial mathematics 5 Annuities and loan. repayments
8 8A Futue value of a auity 8B Peset value of a auity 8C Futue ad peset value tables 8D Loa epaymets Auities ad loa epaymets Syllabus efeece Fiacial mathematics 5 Auities ad loa epaymets Supeauatio (othewise
More informationAPPENDIX III THE ENVELOPE PROPERTY
Apped III APPENDIX III THE ENVELOPE PROPERTY Optmzato mposes a very strog structure o the problem cosdered Ths s the reaso why eoclasscal ecoomcs whch assumes optmzg behavour has bee the most successful
More informationRUSSIAN ROULETTE AND PARTICLE SPLITTING
RUSSAN ROULETTE AND PARTCLE SPLTTNG M. Ragheb 3/7/203 NTRODUCTON To stuatos are ecoutered partcle trasport smulatos:. a multplyg medum, a partcle such as a eutro a cosmc ray partcle or a photo may geerate
More informationIDENTIFICATION OF THE DYNAMICS OF THE GOOGLE S RANKING ALGORITHM. A. Khaki Sedigh, Mehdi Roudaki
IDENIFICAION OF HE DYNAMICS OF HE GOOGLE S RANKING ALGORIHM A. Khak Sedgh, Mehd Roudak Cotrol Dvso, Departmet of Electrcal Egeerg, K.N.oos Uversty of echology P. O. Box: 16315-1355, ehra, Ira sedgh@eetd.ktu.ac.r,
More informationA New Bayesian Network Method for Computing Bottom Event's Structural Importance Degree using Jointree
, pp.277-288 http://dx.do.org/10.14257/juesst.2015.8.1.25 A New Bayesa Network Method for Computg Bottom Evet's Structural Importace Degree usg Jotree Wag Yao ad Su Q School of Aeroautcs, Northwester Polytechcal
More information10.5 Future Value and Present Value of a General Annuity Due
Chapter 10 Autes 371 5. Thomas leases a car worth $4,000 at.99% compouded mothly. He agrees to make 36 lease paymets of $330 each at the begg of every moth. What s the buyout prce (resdual value of the
More informationEstimating Surface Normals in Noisy Point Cloud Data
Estiatig Suface Noals i Noisy Poit Cloud Data Niloy J. Mita Stafod Gaphics Laboatoy Stafod Uivesity CA, 94305 iloy@stafod.edu A Nguye Stafod Gaphics Laboatoy Stafod Uivesity CA, 94305 aguye@cs.stafod.edu
More informationOptimal multi-degree reduction of Bézier curves with constraints of endpoints continuity
Computer Aded Geometrc Desg 19 (2002 365 377 wwwelsevercom/locate/comad Optmal mult-degree reducto of Bézer curves wth costrats of edpots cotuty Guo-Dog Che, Guo-J Wag State Key Laboratory of CAD&CG, Isttute
More informationAn Effectiveness of Integrated Portfolio in Bancassurance
A Effectveess of Itegrated Portfolo Bacassurace Taea Karya Research Ceter for Facal Egeerg Isttute of Ecoomc Research Kyoto versty Sayouu Kyoto 606-850 Japa arya@eryoto-uacp Itroducto As s well ow the
More information1. The Time Value of Money
Corporate Face [00-0345]. The Tme Value of Moey. Compoudg ad Dscoutg Captalzato (compoudg, fdg future values) s a process of movg a value forward tme. It yelds the future value gve the relevat compoudg
More informationRESOURCE SCHEDULING STRATEGIES FOR A NETWORK-BASED AUTONOMOUS MOBILE ROBOT. Hongryeol Kim, Joomin Kim, and Daewon Kim
RESOURCE SCHEDULING SRAEGIES FOR A NEWORK-BASED AUONOMOUS MOBILE ROBO Hongyeol K, Joon K, and Daewon K Depatent of Infoaton Contol Engneeng, Myong Unvesty Abstact: In ths pape, effcent esouce schedulng
More informationStudy on prediction of network security situation based on fuzzy neutral network
Avalable ole www.ocpr.com Joural of Chemcal ad Pharmaceutcal Research, 04, 6(6):00-06 Research Artcle ISS : 0975-7384 CODE(USA) : JCPRC5 Study o predcto of etwork securty stuato based o fuzzy eutral etwork
More informationof the relationship between time and the value of money.
TIME AND THE VALUE OF MONEY Most agrbusess maagers are famlar wth the terms compoudg, dscoutg, auty, ad captalzato. That s, most agrbusess maagers have a tutve uderstadg that each term mples some relatoshp
More informationPreprocess a planar map S. Given a query point p, report the face of S containing p. Goal: O(n)-size data structure that enables O(log n) query time.
Computatoal Geometry Chapter 6 Pot Locato 1 Problem Defto Preprocess a plaar map S. Gve a query pot p, report the face of S cotag p. S Goal: O()-sze data structure that eables O(log ) query tme. C p E
More informationThe simple linear Regression Model
The smple lear Regresso Model Correlato coeffcet s o-parametrc ad just dcates that two varables are assocated wth oe aother, but t does ot gve a deas of the kd of relatoshp. Regresso models help vestgatg
More informationLocation Analysis Regarding Disaster Management Bases via GIS Case study: Tehran Municipality (No.6)
Urba - Regoal Studes ad Research Joural 3 rd Year No.10 - Autum 2011 Locato Aalyss Regardg Dsaster Maagemet Bases va GIS Case study: Tehra Mucpalty (No.6) M. Shoja Aragh. S. Tavallae. P. Zaea Receved:
More informationTHE PRINCIPLE OF THE ACTIVE JMC SCATTERER. Seppo Uosukainen
THE PRINCIPLE OF THE ACTIVE JC SCATTERER Seppo Uoukaie VTT Buildig ad Tapot Ai Hadlig Techology ad Acoutic P. O. Bo 1803, FIN 02044 VTT, Filad Seppo.Uoukaie@vtt.fi ABSTRACT The piciple of fomulatig the
More informationA Bayesian Combination Forecasting Model for Retail Supply Chain Coordination
A Bayesa Cobato Forecastg Model or Retal Supply Cha Coordato W.J. Wag* ad Q. Xu Glorous Su School o Busess ad Maageet, Doghua Uversty Shagha, P.R.Cha *wejew@dhu.edu.c ABSTRACT Retalg plays a portat part
More informationA Parallel Transmission Remote Backup System
2012 2d Iteratoal Coferece o Idustral Techology ad Maagemet (ICITM 2012) IPCSIT vol 49 (2012) (2012) IACSIT Press, Sgapore DOI: 107763/IPCSIT2012V495 2 A Parallel Trasmsso Remote Backup System Che Yu College
More informationMoney Math for Teens. Introduction to Earning Interest: 11th and 12th Grades Version
Moey Math fo Tees Itoductio to Eaig Iteest: 11th ad 12th Gades Vesio This Moey Math fo Tees lesso is pat of a seies ceated by Geeatio Moey, a multimedia fiacial liteacy iitiative of the FINRA Ivesto Educatio
More informationThe impact of service-oriented architecture on the scheduling algorithm in cloud computing
Iteratoal Research Joural of Appled ad Basc Sceces 2015 Avalable ole at www.rjabs.com ISSN 2251-838X / Vol, 9 (3): 387-392 Scece Explorer Publcatos The mpact of servce-oreted archtecture o the schedulg
More informationFractal-Structured Karatsuba`s Algorithm for Binary Field Multiplication: FK
Fractal-Structured Karatsuba`s Algorthm for Bary Feld Multplcato: FK *The authors are worg at the Isttute of Mathematcs The Academy of Sceces of DPR Korea. **Address : U Jog dstrct Kwahadog Number Pyogyag
More informationVendor Evaluation Using Multi Criteria Decision Making Technique
Iteatoal Joual o ompute pplcatos (975 8887) Volume 5 No.9, ugust Vedo Ealuato Usg Mult tea ecso Makg Techque. Elachezha Reseach Schola, ept. o Poducto Techology, M.I.T.ampus, a Uesty, hompet, hea-6 44.
More informationPOSTRACK: A Low Cost Real-Time Motion Tracking System for VR Application
POSTRACK: A Low Cost Real-Te Moto Trackg Syste for VR Applcato Jaeyog Chug, Nagyu K, Gerard Joughyu K, ad Cha-Mo Park VR Laboratory, Departet of Coputer Scece ad Egeerg, Pohag Uversty of Scece ad Techology
More informationROULETTE-TOURNAMENT SELECTION FOR SHRIMP DIET FORMULATION PROBLEM
28-30 August, 2013 Sarawak, Malaysa. Uverst Utara Malaysa (http://www.uum.edu.my ) ROULETTE-TOURNAMENT SELECTION FOR SHRIMP DIET FORMULATION PROBLEM Rosshary Abd. Rahma 1 ad Razam Raml 2 1,2 Uverst Utara
More informationSHAPIRO-WILK TEST FOR NORMALITY WITH KNOWN MEAN
SHAPIRO-WILK TEST FOR NORMALITY WITH KNOWN MEAN Wojcech Zelńsk Departmet of Ecoometrcs ad Statstcs Warsaw Uversty of Lfe Sceces Nowoursyowska 66, -787 Warszawa e-mal: wojtekzelsk@statystykafo Zofa Hausz,
More informationThe Digital Signature Scheme MQQ-SIG
The Dgtal Sgature Scheme MQQ-SIG Itellectual Property Statemet ad Techcal Descrpto Frst publshed: 10 October 2010, Last update: 20 December 2010 Dalo Glgorosk 1 ad Rue Stesmo Ødegård 2 ad Rue Erled Jese
More informationOptimal replacement and overhaul decisions with imperfect maintenance and warranty contracts
Optmal replacemet ad overhaul decsos wth mperfect mateace ad warraty cotracts R. Pascual Departmet of Mechacal Egeerg, Uversdad de Chle, Caslla 2777, Satago, Chle Phoe: +56-2-6784591 Fax:+56-2-689657 rpascual@g.uchle.cl
More informationPeriodic Review Probabilistic Multi-Item Inventory System with Zero Lead Time under Constraints and Varying Order Cost
Ameica Joual of Applied Scieces (8: 3-7, 005 ISS 546-939 005 Sciece Publicatios Peiodic Review Pobabilistic Multi-Item Ivetoy System with Zeo Lead Time ude Costaits ad Vayig Ode Cost Hala A. Fegay Lectue
More information9.4 Annuities. Objectives. 1. Calculate the future value of an ordinary annuity. 2. Perform calculations regarding sinking funds.
9.4 Annuities Objectives 1. Calculate the futue value of an odinay annuity. 2. Pefo calculations egading sinking funds. Soewhee ove the ainbow... skies ae blue,... and the deas that you dae to dea...eally
More informationAn Analysis of the Impact of Transaction Cost on the Borrower s Refinancing Decisions
Joual of Ecoocs, Busess ad Maagee, Vol., No. 3, Augus 14 A Aalyss of he Ipac of Tasaco Cos o he Boowe s Refacg Decsos D J, J Zheg, Na Zhag, ad Swe Ga Absac Assug ha he ae ees ae follows he Vasce odel,
More informationThe Popularity Parameter in Unstructured P2P File Sharing Networks
The Popularty Parameter Ustructured P2P Fle Sharg Networks JAIME LLORET, JUAN R. DIAZ, JOSE M. JIMÉNEZ, MANUEL ESTEVE Departmet of Commucatos Polytechc Uversty of Valeca Camo de Vera s/, 4622 Valeca SPAIN
More informationOptimization Model in Human Resource Management for Job Allocation in ICT Project
Optmzato Model Huma Resource Maagemet for Job Allocato ICT Project Optmzato Model Huma Resource Maagemet for Job Allocato ICT Project Saghamtra Mohaty Malaya Kumar Nayak 2 2 Professor ad Head Research
More informationSequences and Series
Secto 9. Sequeces d Seres You c thk of sequece s fucto whose dom s the set of postve tegers. f ( ), f (), f (),... f ( ),... Defto of Sequece A fte sequece s fucto whose dom s the set of postve tegers.
More informationGreen Master based on MapReduce Cluster
Gree Master based o MapReduce Cluster Mg-Zh Wu, Yu-Chag L, We-Tsog Lee, Yu-Su L, Fog-Hao Lu Dept of Electrcal Egeerg Tamkag Uversty, Tawa, ROC Dept of Electrcal Egeerg Tamkag Uversty, Tawa, ROC Dept of
More informationAutomated Event Registration System in Corporation
teratoal Joural of Advaces Computer Scece ad Techology JACST), Vol., No., Pages : 0-0 0) Specal ssue of CACST 0 - Held durg 09-0 May, 0 Malaysa Automated Evet Regstrato System Corporato Zafer Al-Makhadmee
More informationLearning Objectives. Chapter 2 Pricing of Bonds. Future Value (FV)
Leaig Objectives Chapte 2 Picig of Bods time value of moey Calculate the pice of a bod estimate the expected cash flows detemie the yield to discout Bod pice chages evesely with the yield 2-1 2-2 Leaig
More informationModels for Selecting an ERP System with Intuitionistic Trapezoidal Fuzzy Information
JOURNAL OF SOFWARE, VOL 5, NO 3, MARCH 00 75 Models for Selectg a ERP System wth Itutostc rapezodal Fuzzy Iformato Guwu We, Ru L Departmet of Ecoomcs ad Maagemet, Chogqg Uversty of Arts ad Sceces, Yogchua,
More informationhttp://www.elsevier.com/copyright
Ths atce was pubshed a Eseve oua. The attached copy s fushed to the autho fo o-commeca eseach ad educato use, cudg fo stucto at the autho s sttuto, shag wth coeagues ad povdg to sttuto admstato. Othe uses,
More informationDECISION MAKING WITH THE OWA OPERATOR IN SPORT MANAGEMENT
ESTYLF08, Cuecas Meras (Meres - Lagreo), 7-9 de Septembre de 2008 DECISION MAKING WITH THE OWA OPERATOR IN SPORT MANAGEMENT José M. Mergó Aa M. Gl-Lafuete Departmet of Busess Admstrato, Uversty of Barceloa
More informationAn Approach of Degree Constraint MST Algorithm
I.J. Ifomato Techology a Compute Scece, 203, 09, 80-86 Publhe Ole Augut 203 MECS (http://www.mec-pe.og/) DOI: 0.585/jtc.203.09.08 A Appoach Degee Cotat MST Algothm Sajay Kuma Pal Depatmet Compute Sc. a
More information