Probably /4/6 CS 5 elably Aaly Yahwa K. Malaya Colorado Sae very Ocober 4, 6 elably Aaly: Oule elably eaure: elably, avalably, Tra. elably, T M MTTF ad (, MTBF Bac Cae Sgle u wh perae falure, falure rae Sgle u wh eporary falure Cobaoral elably: Block Dagra Seral, parallel. K-ou-of- ye Iperfec coverage edudacy TM, pare Geeralzed Ocober 4, 6 YKM
Probably /4/6 Perae faul elably decay Teporary faul elably Aaly Ofe Seady ae characerzao Deg faul elably growh durg eg & debuggg A pace hule Challeger Lauch, 986 Ocober 4, 6 Bac elably Meaure elably: duraoal (defaul (correc operao durao (,} Avalably: aaeou A( correc operao a a } If eady-ae value, o a fuco of e. Traaco elably: gle raaco a raaco perfored correcly} For eporary faul, Avalably or Traaco elably ay be uable eaure. Ocober 4, 6 4 YKM
Probably /4/6 Mea Te o Falure (MTTF T: r.v. e o falure MTTF E( T d( d d [ ( ] ( d f ( d + ( d Noe : ( falure (, } T } F( df( d( d d Noe : xe x a x Ocober 4, 6 5 Falure wh epar MTT for reparable ye larly defed. falure operaoal operaoal good repar bad repar TBF TTF repar MTBF MTTF + MTT MTBF, MTTF ae whe falure perae or MTT Seady ae avalably MTTF / (MTTF+MTT Ocober 4, 6 6 YKM
Probably /4/6 Mo Te (Hgh-elably Sye elably hroughou he o u rea above h. Mo e T M : durao whch ( h. h ay be choe o be perhap.95. h.75 (.5.5 TM 4 6 e Ocober 4, 6 7 Bac Cae: Sgle wh Perae Falure Falure rae: probably of falure/u e Aupo: coa falure-rae Z( Good Bad dp( p d p ( ( Falurerae Faou bah-ub e Bur- Operag lfe wearou Bur-: urvvg u roger Wearou: affec of agg Ocober 4, 6 8 YKM 4
Probably /4/6 Sgle wh Perae Falure ( dp( p d p ( Soluo : p ( e ( ( e " Expoeal relably" A, ( e (.68.75 e -.5. 7.5 5 5 / e Ocober 4, 6 9 Sgle : Perae Falure ( ( e A( ae a ( h cae. MTTF ( d e [ ] e d Ex : a u ha MTTF, hr. Fd falure rae. /,.x -5 /hr Ex : Copue o e T M f h.95. e -T M.95 T M - l(.95/.5/ Ex : Aue.x -5, fd T M. A: T M 58.8 hr (copare wh MTTF, Ocober 4, 6 YKM 5
Probably /4/6 Sgle : Teporary Falure( Teporary: ere, rae, perae wh repar bad good Good µ Bad Y. K. Malaya, S. Y. H. Su: elably Meaure of Hardware edudacy Faul-Tolera Dgal Sye wh Iere Faul. IEEE Tra. Copuer (8: 6-64 (98 dp( p( + µ p( d dp( + p( µ p( d ca be olved by laplace rafor ec. p ( p ( e Slarly p ( µ + ( e + µ ( + µ ( + µ Our work Ocober 4, 6 Sgle : Teporary Falure( p ( p, p ( e ( + µ µ ( + µ µ ( + µ + ( e + µ ( eady ae probable ex Avalably A( p p( + µ µ Seady - ae avalably + µ Ocober 4, 6 YKM 6
Probably /4/6 Sgle : Teporary Falure( elably (duraoal ( o falure (, } Good a } - e ae a perae falure Thu MTTF Mo e : alo ae Good µ Good Fr falure Bad Ocober 4, 6 Cobaoral elably Cocepual odelg, applcable o (, A(, (. Sere cofgurao: all u are eeal. Aupo: acally depede falure S good good I geeral g} S g} g} good} If ( e [ + + + ] + + + S he ( e.e. falure rae add : Ocober 4, 6 4 YKM 7
Probably /4/6 A cha a rog a ' weake lk Do you agree? Aue.95, 4.75 S.64 A -u ye v a gle ye. Each of he u are decal. elably.75 Sgle u.5 u.5 M 4 6 8 Te Cobaoral: Sere Ocober 4, 6 5 Cobaoral: Parallel Parallel cofgurao: a lea oe u u be good. epree a deal reduda ye. all u bad}. e. ( ( ( I geeral bad b.} bad b.} ( b.} bad} Ocober 4, 6 6 Cobaoral: Parallel YKM 8
Probably /4/6 Parallel Cofgurao: Exaple Proble: Need ye relably f Soluo : How ay parallel u are eeded ( ( l x l( x x, <? Aue.9999 (.,.9 gve x 4. eeber, we re coder a deal ye Ocober 4, 6 7 Cobaoral: Parallel Coverage good} + ha ake over + C( faled} faled} where C falure deeced ad ucceful wchover} Falure deeco: requre cocurre deeco. Need redudacy. Swchover: good ae loaded. Proce reared Ocober 4, 6 8 YKM 9
Probably /4/6 Iperfec Coverage + C(- Aug I geeral.7 C (.9 elably.8.7.6 Two parallel odule.5.5.5.75 Coverage Ocober 4, 6 9 k-ou-of- Sye decal odule wh a. Idepede falure. operaoal f k of he odule are good. k / p ( p k Sye elably.75.5.5 gle odule.5.5.75 Module elably k-ou-of- Ocober 4, 6 Plo: / YKM
Probably /4/6 Trple Modular edudacy Popular hgh-relably chee: -ou-of- Majory voer Varou pleeao TM ( ( + V Ipleeao ue. Iperfec voer? Ocober 4, 6 TM: Perae Falure Le e TM ( e MTTF - - (e TM - e ( d - e - d 5 (gle odule MTTF : 6 TM Sgle croover po Solvg we ge cro.5. TM wore afer <.5! Ocober 4, 6 YKM
Probably /4/6 TM Mo e Th Ex : /year, gle TM e uercal oluo MTTF yr.8 e Th.95.5.45 Teporary faul: eady ae Ex :. µ A A TM TM A A.9997 A.99 A. A, A TM µ + µ. Ocober 4, 6 TM+Spare TM core, - pare (aue ae falure rae A: Sye falure whe all bu oe odule have faled. + + + + falure w [-(- - -(- ] Le w ( a, a: relave coplexy << a [-(- - -(- ] Ex:.9, a - We ca ee ha ax 4 Ca we do beer? Ocober 4, 6 4 YKM
Probably /4/6 TM+Spare ( B: Oe of he la wo fal, reove oe arbrarly. + + + + + falure a [-.5(- - -(- ] Dagreee deecor.995.99.985 TM core Swchg v.98 Schee A crcu.975 Schee B pare.97.965 4 5 6 7 Mod ule Ocober 4, 6 5 edudacy: Geeralzed elably Copuao correc oupu} B G B G B G} + B G} falure ode correcable}] + P C If ad a gle falure ode doae + P C [falure ode } f f B: Noredudaudacy B: ed- B: deec/correc Ocober 4, 6 6 YKM
Probably /4/6 Geeralzed elably: Ex: Meory Approxao Ex : Meory ye, oal b/word, : relably of a gle word.oe b b error error word Ex : Oe word 8 b daa plu 4 check b (- error - correco capably. Aug perfec deeco/correco -5 b + [(- correcg /u e, wh redudacy : whou redudacy : S + P C S b Hag code. Aue word 6.6 7.9 Noe : acual of error rae hee day very all. S word f b ] 9 5 b Ocober 4, 6 c/ 7 z( Geeralzao: Falure ae lead o Webull Drbuo f T ( β ( η η β η η β : hape paraeer, for coa rae η : cale paraeer Ofe ued o ge a ( β whereβ, η β β ( η beer f, f for rg or fallg falure rae. e ( e eeded, β ( η Ocober 4, 6 8 YKM 4
Probably /4/6 Webull Drbuo Ocober 4, 6 9 YKM 5