Safety Critical Computer Systems: Failure Independence and Software Diversity Effects on Reliability of Dual Channel Structures 1

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1 Prin ISSN: 3-6; Onlin ISSN: DOI: 55/ic-5- Say Criical Compur Sysms: Failur Indpndnc and Sowar Dirsiy Ecs on Rliabiliy o Dual Channl Srucurs H Hriso, W Bo y Words: Say Criical Sysms; rliabiliy; ailur indpndnc; dirsiy; dual channl srucurs Absrac Th papr xamins Say Criical ral-im Sysms (SCS), in paricular hir dual-channl srucurs Th analyical sudy on compur-basd SCS rcogzing ailurs comparing h rsuls o boh channls is basd on h hory o rliabiliy Th aim is o sablish rliabl modls ha includ indpndnc ra bwn ailurs o boh channls and hir dirsiy Th crad ormulas ar usd o calcula h uncion o rliabiliy, probabiliy o say ailurs and hazard ailurs Th innsiy o ailurs o h sysm and h innsiy o is rcory, h raio bwn Common Mod Failurs (CMF) and ailurs o indiidual channls ar xplicily prsnd in h modls or h indpndnc o hardwar and sowar Fauls ar inroducd Th analyical modls obaind allow aluaing h cs o indpndnc o channls and h dph o hir dirsiy A ormula or calculaing h impromn o say hanks o h dual-channl archicur in comparison o a singl-channl srucur o h sam oupu rliabiliy paramrs has bn workd ou Analyical modls can b usd o calcula indicaors o sysms in ordr o sablish hir complianc wih say sandards Analyical modls can b usd o calcula indicaors o spciic sysms o drmin hir complianc wih say sandards Th rsuls mak possibl o ind ou chcal soluions wih br rliabiliy and say aurs Inroducion Say Criical Sysms Say Criical ral-im Sysms (SCS) conrol spcial criical chnology procss or opraion (SCTP) whos ailurs could lad o loss o lis, gra human and marial alus and/or inadmissibl damag o h ronmn Thr ar a lo o xampls o SCTP and sysms ha gorn hm in ranspor [], aiaion [], mdicin, nrgy scor, miliary sphr, c Th hardwar, sowar and ransmission rac o sysms ha procss and ransmi inormaion ar subjcd o incrasd rliabiliy and say rquirmns According o h SCTP naur, chcal soluions ar diidd ino wo main groups Th irs group includs SCTP suiabl o din h cririon o sa bhaior ar h ailur o hir conrol sysms, a cririon o limi uncionaliy or sop h conrolld procss [3] Ths ar undsirabl bu no hazardous Th auhors graully acknowldg h suppor o Ningbo Ursiy o Tchnology C Wong Educaion Fund ouags o SCTP ha cra corcion o rmo h ailur and allow h procss o conu Such sysms ar said o ha ail-sa bhaior and hir ailurs ar say ailur [] Th scond group includs such sysms whr h ail-sa bhaiour is inappropria Du o h naur o h procss in aiaion, spac ranspor, air raic conrol, in li-supporing sysms, c, in mos cass i is no possibl o din h cririon o say pos- ailur condiion or bhaiour Each sopping o h procss is inadmissibl Similar SCTP ha o m h rquirmns or aailabiliy or conuiy o SCTP Ths cass also rr o SCS bu hy ar no longr ail-sa Thr is a gnral cririon, according o which sysms all ino his class I is h admissibiliy o risk arising rom a possibl ailur Th risk is sandardizd wih say sandards ha ar ursal, irrlan o h chcal soluion and concrn boh xamind groups Say Sandards Say is absnc o inadmissibl risk Say canno b absoluly guarand, whar i any masurs ar akn Thr is always hazard Th problm is whhr rsidual risk Qd is accpabl, admissibl Admissibiliy is drmind by rgulaions [4] Th admissibl alu o hazard (Tolrabl Hazard Ra) can b dirn and dpnds on h applicaion o SCS Thror, i is spokn abou lls o admissibl hazard Say Ingriy Ll (SIL) [6,7] Sandard EN 56 has lgally sablishd Railway Signaling & Inrlocking say Th quaai sandards ar dind according o applicaion o SCS: SIL Q d 6, SIL Q d 7, SIL3 Q d 8, SIL4 Q d 9 Sandards can b idid also or aiaion (FAA), auomoi (ISO 66), mdical (IEC 634), nuclar (IEC 653) indusris, c 3 Tchcal Soluions Onc h quaai sandards o say ha bn sablishd, i is no rlan or h usr how hy ha bn achid Alhough i is no mandaory, in conrol o RTP o h irs group i may urn appropria o apply ailsa approach Th modrn compur-basd sysms us modiicaion o his principl (quazi ail-sa) as in igur : a compur dic F is assignd o opra as uncional inormaion chnologis and conrol 4 9 Unauhcad Download Da /3/8 :37 AM

2 and anohr spciic dic conrols i i prorm is uncions corrcly and wihou ailurs [8] I i dcs a ailur, i swichs o h conrolld objc CO, which is h drmind sa condiion Wih conrol on procsss o h scond group, say is achid hrough high rliabiliy For his purpos Rdundancy in dirn orms is usd: dual channl srucurs, N-rsion programming, homognously or dirsiy rsraion, TMR or mor M N complx ons, ring nwork srucurs, c Spcial rquirmns ar pu also o h lcommucaion sysms, which mus conain all ncssary Say rlad mchasms [5] Figur Gnralizd archicur o compur-basd ail-sa sysms 4 Why No This will b dmonsrad wih a simpl xampl ha or h nds o SCS i is inadmissibl o apply usual srucur «o» [8] Wih inpu cor X i (x x, x w ) a h oupus o microprocssor μp (igur ), a combinaion o logic signals Y(y y, y ) appars and hs signals orm a cor o lngh bis Whn h dic is sricabl, h oupu cor is drmind by h algorihm, inrnal mmory and inpu daa Th xpcd uncional cor is X i,i, a rsul o ransormaion X i Y i Wih ailurs o h microprocssor, incorrc cors can b obaind, which ar disinguishd rom h ral (uncional) cor Y i by on, wo or mor digis (d,,3) Inormaion in lcommucaions is ransrrd wih indpndn bis o h lgram and h cod disanc bwn cors is a powrul ool o dc disorion and corrc rrors in h commucaion channl Microprocssor procssing is qui dirn Hming disanc d is no procion mans Th probabiliy o apparanc o incorrc cors dos no dpnd on hir Hming disancs o h corrc cor F СО Quazi ail-sa Х µp Figur Summarizd schm o microprocssor Y I is no possibl o drmin probabiliy disribuion p i (i) o incorrc cors wih any possibl Faul and Error, which, moror, can no b orsn and gin in adanc Wihou gra drimn o accuracy or h modl, qual probabiliy disribuion can b assumd, whrin probabiliy o obain h i -h cor rom h incorrc cors wih lngh is q i I is h sam or anyon ls This also applis o uncional cor Y i, which is on o all cors and ariss ar a ailur wih h sam probabiliy All ohr incorrc cors ar wih summd probabiliy ar ailur o appar any incorrc cor () p Σ L probabiliy o any ailur in h microprocssor is Q Thn probabiliy Q i or pos-ailur apparanc o h i -h cor (i, ) will b () Qi q Q Q i, and probabiliy Q hazard or apparanc o any incorrc cor is (3) Q Q hazard Th probabiliy or incorrc oupu signal wih cor lngh 8 will b (4) Q hazard,996q I can b sn ha hazard Q hazard is approximaly qual o h probabiliy o ailur, i commnsurabl wih unrliabiliy In a complx sysm conaing housands o componns, n whn hy ar o marginal low innsiy o ailurs o ordr o λ 9 /h, h bs arag im ha can b achid bwn ailurs MTBF is o h [] or probabiliy o ailur Q 5 6 Ths ar alus ha ar o magud sral ordrs grar han h admissibl on Th conclusion is ha concp «o» is inapplicabl in SCS 5 Dual-channl Soluions Wih all ariy o concpual and spciic chcal soluions mond abo, hr is a class o sysms ha ha obaind h wids disribuion: dul-channl srucurs [,7,8] Boh srucural us ar consanly swichd on " " schm or h rsr on is swichd on as sandby "+" Ths sysms ar usd in all aras o SCS applicaion by world-amous compas such as Simns, Bombardir, Thals, c Th dual-channl principl is a possibl soluion o h problms crad by compur-basd Say Criical F- srucur in igur Th mos sigican o hm is rcogion o ailurs ha conrol dic mus possss o idy h ailur and promply swich o h dind pos ailur ra Wih absolu ss, h ailur is idid slowly and chcally inicinly On o h mos widly usd ss is a rlai s, whrin cor X applid o h inpu is procssd in wo 4 inormaion chnologis and conrol Unauhcad Download Da /3/8 :37 AM

3 X CANNEL Y CO COMPARATOR O X CANNEL Y Figur 3 Dual-channl srucur channls, and, and oupu cors Y and Y o h sam lngh ar compard using principl is is Thir complianc is a masur o prormanc, whr comparaor gis O o implmn conrol on h objc (igur 3) Th conrol dic includs condiionally a comparaor and h scond channl 6 Subjc and Purpos o h Sudy Dual-channl compur-basd srucurs ar wll known and widly usd bu hr ar rliabiliy propris and aurs ha ar no complly sudid Thy ar h subjc o sudy in his papr Th xaminaions ar ocusd in paricular o dual-channl compur-basd sysms or comparison o h yp gin in igur 3 Th aim o h sudy is o sablish analyical modls or quaai drminaion o rliabiliy and say o dual-channl SCS considring h c o wo acors: indpndnc o ailurs in h channls and dirsiy o hir sowar Similar horical rsuls can b ound in [,,3] bu hy ha bn mad wih anohr ormulaion o h problm, rla only o som rliabiliy indicaors and do no ak ino accoun h c o boh acors Thr is no quaai assssmn o c " " on say and srucural paramrs inluncing i Indpndnc o Channls Two Groups o Rasons or Undcd Failurs I is known ha i wo ns A and B ar indpndn, hn h condiional probabiliy o ach, proidd ha h ohr on has occurrd, is qual o is uncondiional probabiliy h probabiliy o happn n A dos no dpnd on whhr n B has or has no occurrd, i qualiy P(AB) P (A)P(B) is ulilld Th low o ailurs and rcoris in h sysms o lcrocs, compurs and lcommucaions is rcogzd o b a Poisson low [3,5] I has h propry lack o ar-c, which mans h indpndnc o succssily occurring ailurs Any ailur dos no caus a nx on and is no corrlad wih i This indpndnc is alid or h ailurs o indiidual channl bu i sprads in boh channls Th hazard in Say Criical dual-channl sysms, consising o rmoal o h non-uncional and possibly hazardous signal, can b crad by wo groups o auls and rrors: Common o boh channls causs or ailurs Common-Mod Failur (CMF) [] ha: ar du o rrors in h gnral spciicaion, in manuacuring and opraion, o ronmn cs such as lcromagc inrrnc, wahr condiions, c; ar conaind in componns common or boh channls: powr supply, inpu-oupu orgazaion, common sowar, comparison, c Simulanous indpndn ailurs in boh channls caus rronous, bu accidnally on h sam cors, du o which ailurs rmain udid (accidnally non idicabl ANI Th irs group CMF-causs ar common or h wo channls and ac boh nd rsuls in h sam way L ak η -Faul, and h innsiy o ailurs causd by hm is λ η Thy lad o unrcogsabl by comparison ailurs Th scond group includs gnrally rcogsabl Faul L ak α-faul, and h innsiy o ailurs causd by hm is λ α Th say o a dual channl sysm is basd on h assumpion ha h channls ar indpndn, CMF-causs ar mimizd and probabiliy o unrcogzd α-faul is small nough O cours, h rlaionship bwn h main low o ailurs λ o boh kinds and h rasons causing hm ar mdiad by h inpu daa and opraion algorihms o channls Probabiliy o Accidnally Undcd Failurs In ordr o appar rronous bu quialn oupu cors, hy mus b warpd in h sam mannr in boh channls and bcom on and h sam pos-ailur cor Y j Th probabiliy o his o happn wih qually probabl disribuion o incorrc cors is (5) q q i i q q Exampl L 3, and cors b labld in an ascnding ordr o dcimal numbrs 8 cor ar obaind: inormaion chnologis and conrol 4 Unauhcad Download Da /3/8 :37 AM

4 Ar a ailur in dual-channl sysm, ss o combinaions o cors in boh channls can b ormd according o marix (6) A ach momn only on cor is corrc: uncional cor Y i L i b No 3 In h marix shown abo combinaion 33 is markd, which mans ha boh channls ha gnrad his cor Th conrolling c wih rliabl opraion is alidad (O) wih his combinaion Howr, O a h oupu o comparaor will b obaind no only in h 3 rd posiion Th comparaor will b misld also in h j-h, k-h posiions, c, rly in all ohr posiions - wih h sam numbrs o cors Th probabiliy o obain any o hm is (6) Channl Channl q q In his paricular cas hy ar 7 Th probabiliy o als O will b ( q)q, and probabiliy o accidnal non-idicaion Q a will b (7) Qa ( q) q Q Q ( ), hr Q α and Q α ar probabiliis o apparanc o ailurs in channl and channl Equaion (7) can b usd o quaaily alua h probabiliy o accidnal non-idicaion Q a o simulanous indpndn ailurs in boh channls 3 Inlunc o Indpndnc o Failurs on Rliabiliy-Say Faurs o a Dual-Channl Sysm 3 Equialn Rliabiliy Schm Sysm is srial in rliabiliy I any o is lmns ails, h sysm also ails I channl gnras a low wih innsiy λ α, and channl gnras a low wih innsiy λ α, hn h orall innsiy is α-faul (igur 4a, 4b) (8) λ α λ α + λ α Wih channls wih qual rliabiliy, h innsiy o ailurs in ach on is (9) λ α λ α,5 λ α Th innsiy o all ailurs is h sum o innsiis o all h componns o h parn (igur 4b, 4c) () λ λ α +λ α +λ η λ α +λ η λ α +λ α +λ η +λ η 3 Funcion o Rliabiliy R() Th dual channl compur-basd sysm is rliabl in wo cass: Whn hr is no CMF and in boh channls hr ar no rcogsabl ailurs by α-faul; Whn ailurs rcogsabl by comparison ha accidnally causd uncional insad o incorrc cors In h irs cas h sysm is sricabl: no CMF (R η ) and ach o h wo channls wih rliabiliis R α and R α is sricabl: R' R η R α R α In h abo-quod xampl (6), his mans ha h uncional combinaion 33 can also b obaind whn ailurs ar in on, and n in boh channls Sinc ns ar incompaibl, h rliabiliy o hs componns mus b addd oghr o gi a oal rliabiliy or h scond cas In h scond cas in on o h wo channls or in boh channls hr is α-faul bu by chanc hy ha gnrad a uncional cor, Y i In h xampl mond abo (6) i mans ha uncional combinaion 33 can b obaind also wih ailurs in on o h channls and n in boh channls Sinc h ns ar incompaibl, hs componns o rliabiliy ha o b summd o obain h oal rliabiliy or h scond cas () R' ' R R + R + η α α a b с α α α η α η α α α η η Figur 4 Equialn circui o a dual channl srucur η η 4 inormaion chnologis and conrol Unauhcad Download Da /3/8 :37 AM

5 Furhrmor, h irs cas and h scond on ar incompaibl, and hror h sough probabiliy R or h dual channl sysm " " o b sricabl is modlld wih hir sum, which ar procssing is rducd o () R R' + R" Rη Rα + R + α Wih qual rliabiliy in h wo channls and homognous Poisson procss wih consan n ra (λ cons), h dual channl srucur rliabiliy is obaind in h orm (3) λη λ cons R,5λα +,5λα 33 Probabiliy o Hazard Failur Q h () Th logic, conncd wih h wo rasons or an udid and possibly hazard ailur (p ), is shown graphically in igur 5 CMF-ailur ns and accidnally unrcogsd α -ailur, unlik h ns in p 3 ar compaibl and hir oal innsiy is no h sum o hir parial innsiis Th Boolan uncion o non-idicaion F, whn a ailur is no logically dcd, is (4) F z η, z a η α α / whr logical ariabl z η ( whn hr is a ailur, whn hr is no ailur) is h logical ariabl o ailurs wih CMF origin (p ) and z / a CMF a Figur 5 Logical circui o non-idicaion o ailurs corrsponds o accidnally unrcogsd simulanous ailurs in boh channls To modl h probabiliy o non-idicaion o ailurs, logical-probabilisic ransiion rom (4) has o b implmnd Haing applid h horm o D Morgan, an unrpaabl Boolan uncion in basis conjuncion-nga- ion F za z η, which is appropria or compl subsiuion, is obaind Applying h ruls o logical-probabilisic ransiions, or h probabiliy o no dc ailurs, i can b obaind (5) Q ( Q η )( Q a ), whr Q is h probabiliy sough or an udid ailur, Q η probabiliy or unrcogsabl CMF ailur, and Q a probabiliy an accidnally udid rcogsabl ailur Subsiuing rom (7) o (5), or h probabiliy o no rcogz a ailur is (6) Q R ( ) η Wih xponal disribuion and channls qually rliabl, h probabiliy o an udid ailur is (7) Q ( ),5λα λη Q Q α α 34 Probabiliy o a Say Failur Say ailurs ar crad only by α-faul, CMF ailurs do no ac Say saus Th ailur is rcogzd, and O signal is hung in wo cass In h irs cas, on o h channls opras and h ohr has aild, or ic rsa, bu h oupu cor o h aild on is dirn rom h corrc cor o h channl opraing Taking ino accoun ha h ns ar incompaibl and h aild channl can gnra any o i incorrc cors, h probabiliy o his is a sum o probabiliis, i (8) Q' s Rα + R α In h scond cas boh channls ha aild and gnra dirn oupu signals (wih dirn numbrs, s (6)) Th probabiliy o his is h sum o probabiliis or all such cass (9) Q ' ' s q jq α q k Q α Q α Q α j k q k q j q Q s () Sinc h wo cass ar muually xclusi, hn h probabiliy o say ailur o h dual-channl srucur is h sum o hir probabiliis () Qs ' '' ( ) Q s + Q s Rα + Rα + Q α Wih xponal disribuion and qualiy o rliabiliis in boh channls, h probabiliy o say ailur ailurs is,5λ α,5λα 5λα () Qs ( ) + ( ) Q Q α α 4 Channl Dirsiy Ec on Dual-Channl Sysm Rliabiliy and Say Faurs 4 Dirsiy Dual-channl srucur channls can b homognous and dirsiy Dirsiy is a mhod o soling h problm (logical, chcal, c) in wo dirn ways (A and B) basd on h sam inpu daa As i is known, dirnc may consis in dirgnc o approach and mhod o problm soling, in implmnaion o arious principls or arious company chnologis inormaion chnologis and conrol 4 3 Unauhcad Download Da /3/8 :37 AM

6 Sowar dirsiy is mos widly sprad Th dirnc may occur in algorihms, programming languags, daa prsnaion (inrs, rrs), c I is usually achid hrough dirsiy and indpndnc o programming ams soling boh A and B rsions o h problm I h dirnc is in mhods and algorihms, i is said o b ariicial (orcd) dirsiy, which wih coding can b achid by on and h sam am Dirsiy is h mos ci ool or dcing rrors Is cinss is du o h propris o rrors unlik h propris o auls Whn h causs or ailurs ar hardwar auls, ailurs ar indpndn o whhr h channls ar homognous or dirsiy Thy ha hir own, spciic o ach α-faul No such dpndnc xiss wih rrors Errors (wih dsign, consrucion, programming, documnaion, chnology, c) ar sysmaic, «by birh», on and h sam or all producd sris I boh channls according o copis o on and h sam program, A B rrors o h only sowar lad o on and h sam incorrc rsuls and ailurs rmain unrcogsabl Whn h channls opra on arious programs, A B rrors ar dcd bcaus hy ar no on and h sam, ar o accidnal naur and on random locaions in sowar, du o which lad o inappropria rsuls In dp dirsiy channls hr is no dpndnc o rrors missing (λ η ) and hy can b xamind as α Faul as hardwar auls 4 Schms o Dirsiy Implmnaions Th schm, which is usd o implmnd dirsiy, can b dirn, g: H+S: wo channls and opra in paralll or in squnc or im undr arious programs A and B can b spara and indpndn procssing, ransrs, rcords, c bu ar supplid wih h sam inpu inormaion Hardwar auls, puls inrrnc and sowar rrors ar rcogsabl This schm is h mos icin bu ry inicin in rms o rsourcs H+S: wo hardwar channls opra in paralll on on and h sam program, A C Hardwar ailurs ar rcogsabl bu sowar rrors ar CMF-Faul and canno b idid Whn hy opra synchronously and in phas, no puls inrrnc ar rcogsabl as wll 3 H+S: wo dirn programs ar prormd by on compur in squnc Alhough crad by indpndn ams, i h programs pro o b ry clos by h way o using hardwar, h sam c o ailur on procssing and h rsuling oupu cors can b obaind As a rsul, rlan bu incorrc rsuls can b obaind and ailurs will rmain unrcogsabl by comparison 43 Equialn Schm o Dirsiy Sysm Rliabiliy Failurs can b du o boh hardwar auls and sowar rrors -Error Hnc rliabiliy o any H+S sysm dpnds on boh α-faul and η-faul In h prsn conx hr is a sysm consisn in rliabiliy (igur 4c) Each o α, η,, ailurs is indpndn rom h ohrs No mar whr ailurs occur, in channls or, hy rsul in non-sricabiliy o h r sysm Th oal innsiy o ailurs is h sum o innsiis o dirn kinds o ailurs: () λ λ α + λ η λ α + λ α + λ η + λ η λ α + λ η + λ α + λ η λ α λ η λ λ whr λ α innsiy o α ailurs rcogsabl by comparison o oupu rsuls; λ α innsiy o α ailurs du o auls; λ α innsiy o α ailurs du o rrors; λ η innsiy o η ailurs unrcogsabl by comparison; λ η innsiy o η ailurs du o gnral auls; λ η innsiy o η ailurs du o gnral rrors Two spara, parial mrics or indpndnc o ailurs will b inroducd du o wo rasons: For hardwar auls (3) ϕ λα λ + λ α η λ λ α, λ α ϕλ, λ η ( ϕ)λ For sowar rrors (4) λα Δ λ + λ α η λ λ α λ α Δλ, λ η ( Δ)λ In his subsiuion h probabiliy o an udid ailur (7) aks h orm,5( λ + α λα ) (5) ( λ + ) η λη Q ( ) Q α, and wih includd parial mrics ϕ and Δ ( ϕλ + Δ ) λ (6) Q,5 [( ϕ ) λ + ( Δ ) ] λ ( ) From gnral ormula (6) i ollows ha: Whn all ailurs ar du o CMF-causs ϕ and Δ, probabiliy o non-idicaion is maximal ( λ + λ ) λ (7) Q Q, max ϕ Δ i all sysm ailurs rmain udid bu only on o hm, h on ha lads o a uncional cor, is no poally hazard Whn all ailurs ar indpndn ϕ and Δ, probabiliy o non-idicaion is mimal (8) Q,5( λ ) + λ ( ) min 5 Impromn o SCS Say o as a Funcion o Indpndnc and Dirsiy 5 Formal Modl Q max Raio ξ bwn probabiliy o non-idicaion (7) whn h sysm is irually rducd o a 4 4 inormaion chnologis and conrol Unauhcad Download Da /3/8 :37 AM

7 singl-channl on and is currn alu or h gnral cas (6) is inroducd ξ ( ) ( λ + λ ) (9), 5 ( ϕλ + Δ λ ) [( ϕ ) λ + ( Δ ) λ ] Equaion (9) can b usd o calcula impromn (in ims) o say du o grar indpndnc o ailurs in h channls Th maximum impromn o say is masurd by raio ξ max o h maximum (7) and mimum (8) alus o probabiliy or non-idicaion o ailurs (3) ξ max ( ) ( λ + λ ),5( λ + λ ) [ims] Wih oo ralisic λ λ + λ -4 /h, 4 h and 8 bis probabiliy o hazard ailur in h dualchannl sysm will b rducd ξ max 45 ims 5 Cas Sudis Sysm H+S In indiidual hardwar channls ϕ, and in h wo paralll channls dirn, indpndn programs ar usd I is why sowar dirsiy is dp and rror rcogion is ry gra Δ : ( ) λ + λ (3) Q ( ) Th impromn o say is gras and may b calculad by (3) Sysm H+S I is mos on ha on and h sam sowar is usd in boh synchronously working channls and rrors lad o unrcogsabl incorrc oupu rsuls Thr is no sowar dirsiy, ailurs du o hardwar auls ar η and α and rcogion in rgard o rrors is pracically zro Δ,5ϕλ (3) [( ϕ ) λ + ] λ Q ( ) Sysm H+S A dual-channl sysm o on hardwar channl wih wo dirn programs has mrics or hardwar indpndnc in inral ϕ, a ha bing closr o h dsird as much as mor dirnly h wo spara programs us hardwar Th idicaion o ailurs is also in h sam inral and h caus o ailurs is rrors Th ormula or calculaing is (6), h sam as in H+S, bu wih h corrsponding daa o channls 53 Modls or Rcorabl Sysms Th rliabiliy uncion R() o non-rcorabl sysms (or rcorabl bu ul o h irs ailur) whr opraion im ul ailur is includd and coicin o μ aailabiliy a o rcorabl sysms, which is μ + λ dpndn on sric rsoraion ra μ, ar similar probabilisic quais Ths quais ar usd o masur h probabiliy o objc aailabiliy Using his analogy and summing up h rsuls, ormal modls o rliabiliy and say indicaors ar gin in h abl Formulas or drming rliabiliy and say indicaors Unrcorabl sysms Rcorabl sysms Rliabiliy and aailabiliy Probabiliy o uiad ailurs Probabiliy o say ailur wih channls o qual rliabiliy andλ cons : Q R R R Q kα η kα + Rη ( Qk ) α a kα + η kα η ( ) kα Qs QkaRka + Q ka s + ( ) ka ka ka [ ( ϕ ) λ + [( Δ) λ ]] R μ η, η, μ + ( ϕ) λ + ( Δ) λ R ka 5( ϕλ + Δλ ) ka μ + μ,5( ϕλ + Δλ ) inormaion chnologis and conrol 4 5 Unauhcad Download Da /3/8 :37 AM

8 Figur 6 Non-idicaion o ailurs (λ, ϕ) Figur 7 Impromn o say ξ as a uncion o indpndnc ϕ 6 Examinaion on Indpndnc and Dirsiy Ecs To sablish h c o ailur indpndnc and dirsiy o channls, calculaions or h schms xamind in p 5 ha bn carrid ou wih dirn alus o paramrs inold Hr, bcaus o h limid plac, h rsuls ar gin only or on o h mos common schms: H + S Considring ha prcion o h sowar can b achid and dmonsrad or rlaily simpl problms using h mhods o rror-r programming [], i is assumd ha sowar CMF causs ha bn rducd o zro (λ ) I is only ailurs du o innsiy auls λ ha rmain Undr hs consrains according o (3) h probabiliy o non-idicaions o ailurs in dual-h channl 4 6 inormaion chnologis and conrol Unauhcad Download Da /3/8 :37 AM

9 Figur 8 Dpndnc o unrcogsd ailurs on h cor lnghs sysm wih qual rliabiliy o channls is ( ϕ ) λ,5ϕλ (33) Q ( ), and rcorabl sysms wih oal innsiy o rcory μ μ (34),5ϕλ μ +,5( ϕ ) λ μ +,5ϕλ Th rsuls o uncion (λ, ϕ) ar shown in igur 6 I can b sn ha h probabiliy o non-idicaion o ailurs grows wih hir innsiy raching h highs alus wih ϕ, whn h srucur is rducd o a singl channl on Th probabiliy sharply dcrass wih incrasing h indpndnc o channls This procss is paricularly snsii wih ϕ This snsiiiy is n br illusrad in igur 7 In paricular, aon should b paid o comparison o a dual-channl sysm wih a singl-channl on wih arious alus o inluncing acors Using quaion (33) and applying i o h cas, h c on say is ound ξ (35) ( ϕ) λ,5 ϕλ ( ) λ λ ξmax Th graphs by his ormula ar shown in igur 7 I whn ϕ :,5λ ( ) is sn ha indpndnc o ailurs has paricularly srong c on highly-rliabl sysms (λ ) Th grar h innsiy o ailurs and/or h oldr sysm bcoms, h smollr is h c o indpndnc o channls Thus wih 8 bis, ϕ and λ i is rachd o 54 ims smallr probabiliy o poally hazard ailur and ar aging impromn sharply dclins Bu n wih alus o inrs in pracic λ,[/h] and ϕ,9, raio ξ 494 ims rmains imprssi Figur 8 shows dpndncy (, ϕ) wih μ [/h] From h graphs i is sn ha wih incrasing h lngh o cors, probabiliy o non-idicaion sharply dcrass Th srongr his c is, h biggr is indpndnc o channls From h rsuls shown abo i can b concludd ha all dsign and chnological masurs ha o b akn o rduc CMF-componn o zro As or h hardwar soluions, his is largly achiabl ask Th siuaion rlad o h problm o sowar is dirn Errors in complx sowar sysms ar a sourc o CMF ha can b orcom wih small rsourcs on o which is dirsiy Δ Conclusion This sudy is an amp o modl rliabiliy and say prormanc o a class o wid-sprad Say Criical Compur Sysms I has bcom clar wha and how rliabiliy and probabiliy o rcogsd and unrcogsd ailurs dpnd on I has bn conirmd ha indpndnc o h wo channls in dual-channl srucurs is crucial or idn- inormaion chnologis and conrol 4 7 Unauhcad Download Da /3/8 :37 AM

10 iicaion o ailurs and hnc or say opraion o sysms Th conribuion o his papr is h quaai modls usd o alua hs aurs Thy show ha h posii c on say o dual-channl naur is xrmly srong, nar h absolu indpndnc o channls Whn rliabiliy paramrs o spciic sysms ha bn sudid by sablishd ormulas, hir indicaors can b calculad o drmin complianc wih say sandards (i 3) Using hs modls and rsuls o xaminaions carrid ou, i is possibl o impro chcal soluions or propos nw ons wih highr rliabiliy and say Rrncs Tg, G, S Vlasnko, c Railway Signaling and Inrlocking Eurailprss 9 Rirson, L Dloping Say-Criical Sowar CRC Prss, 3 3 Hriso, H, V Triono Rliabiliy and Scuriy o Commucaions Noi znaa, 7 (in Bulgarian) 4 Bown, J, Y Saridon Say-criical Sysms, Formal Mhods and Sandards Sowar Enginring Journal, Frankoa, M, P Luly Modlling o Failur Ecs wihin Say-Rlad Commucaions wih Say Cod or Railway Applicaions Mchac, Transpor, Commucaion, Soia, 5 6 Elsir, B V Say Insrumnd Funcions Say Ingriy Manuscrip rcid on 585 Hriso Hriso, DSc, is Prossor a h Tchcal Ursiy o Soia H graduad rom h Mchacal and Elcrical Insiu o Soia, MSc programm in Tlcommucaions in 96 H dndd a PhD hsis in Moscow (97) and a hsis or h dgr o Docor o Scincs a h Tchcal Ursiy o Soia (988) H has dlopd and is a primary achr o arious courss rlad mainly o criical say sysms, which is also h subjc o his xbooks Eln dissraions ha bn dndd undr his sciic suprision Pro Hriso is h auhor o or 33 sciic paprs including 3 books (xbooks, manuals, and monographs), 3 inons and mor han 5 sciic projcs H was awardd Honorary Gold Mdal o h Tchcal Ursiy o Soia and was lcd a mmbr o h Transpor Acadmy o Russia, Docor Honoris Causa o h S Prsburg Sa Ursiy o Railways H has bn in coopraion wih h Ursiy o Tchnology o Ningbo, China, which has ordrd h dlopmn o his papr Conacs: Ningbo Ursiy o Tchnology Fnghua Road, Ningbo 35 l: China and Tchcal Ursiy Soia 8 S limn Ohridski Boulard 756 Soia Bulgaria l: mail: cac@u-soiabg Ll (SIL) Ealuaion Tchqus, 7 EN 56 EN56 Th Spciicaion and Dmonsraion o Rliabiliy, Aailabiliy, Mainainabiliy and Say RAMS 8 Chriso, Chr, N Soycha, M Chrisoa Dirsiy as a Man or Rliabiliy and Say Springr-Vrlag, Brlin Hidlbrg (), Transpor Sysms Tlmaics, Commucaions in Compur and Inormaion Scinc, 4,, anz, H Th ELETRA Railway Signalling Sysm: Fild Exprinc wih an Acily Rplicad Sysm wih Dirsiy Alcal Ausria AG, Win, Ausria, 995 Thomson, Jim Common-Mod Failur Considraions in High- Ingriy C&I Sysms Say in Enginring Rrid Nombr, Lilwood, B, V Sankoic, L Srigi Inroducion o Ñommon-mod Failur Probabiliy and Dirsiy Ciy Ursiy London, wwwcsrciyacuk 9 Marin, Sh Rliabiliy Compur Sysms and Nworks Wily-Inrscinc, 8 3 Epsin, B, I Wissman Mahmaical Modls or Sysms Rliabiliy CRS HRESS, 8 4 Marcos Mainar Lalmolda Tsing Say-criical Sowar Sysms Th Ursiy Noingham 9 5 Gind, E Inroducion o h Thory and Pracic o Rliabiliy (in Bulgarian) Acadmic Publishing Hous Marin Drino, Soia, 6 Hrisoa, M Modls and Algorihms or Us Rdundancy in h Faul-Tolranc Sysms (in Bulgarian) Mchacs, Transpor, Commucaions, 8, No Wang Bo, born in 98, go a docor s dgr in in Economics and now is an associa prossor o Ningbo Ursiy o Tchnology China, docoral uor o Soia Transporaion Ursiy o Bulgariaÿand also is an honorary associa prossor o Moscow Naional Aiaion Ursiy o Tchnology In Acadmic rsarch: Prsidd or i high-nd projcs launchd by Chins Burau o Forign Exprs; Prsidd or and accomplishd a longiudinal projc launchd by h proincial ducaion dparmn; Prsidd or a 8-housand Yuan horizonal projc launchd by Ningbo Traic Dachmn; Took a major par in wo projcs on inrnaional coopraion launchd by Misry o Scinc and Tchnology o China (China-Russia(3/6), China-Ukrain(/6)); Took par in many mucipal projcs; Publishd narly paprs as h irs auhor on cor journals; Sciic rsarch unds narly on million a yar Conacs: School o Xiangshan Rsarch Insiu Ningbo Ursiy o Tchnology Fnghua Road, Ningbo 35 China l: mail: bo35@homailcom 4 8 inormaion chnologis and conrol Unauhcad Download Da /3/8 :37 AM