elably /6/ elably Aaly Perae faul Πelably decay Teporary faul ΠOfe Seady ae characerzao Deg faul Πelably growh durg eg & debuggg A pace hule Challeger Lauch, 986 Ocober 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 6, YKM
elably /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 6, Falure wh epar MTT for reparable ye larly defed. falure operaoal operaoal good repar bad repar TBF TTF repar MTBF MTTF + MTT MTBF, MTT ae whe falure perae or MTT Seady ae avalably MTTF / (MTTF+MTT) Ocober 6, 4 YKM
elably /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 6, 5 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 6, 6 YKM
elably /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 6, 7 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 5.5 hr (copare wh MTTF,) Ocober 6, 8 YKM 4
elably /6/ Geeralzao: Falure ae z( α ( lead o Webull Drbuo f T ( α ( : hape α paraeer, for :cale paraeer α ( Ofe ued o ge a beer f, f coa rae for rg or fallg falure rae. See lk a: hp://d.ze.co/~dape/dr.h e α eeded, Ocober 6, 9 Sgle : Teporary Falure() Teporary: ere, rae, perae wh repar bad good Good µ Bad 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 6, YKM 5
elably /6/ Sgle : Teporary Falure() µ µ ) ( + µ ) ( + p( p() e + ( e + µ Avalably A( p( eady ae probable ex µ, p( p( + µ + µ µ Seady - ae avalably + µ ) Ocober 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 6, YKM 6
elably /6/ Cobaoral elably ΠCocepual odelg, applcable o (, A(, (. Sere cofgurao: all u are eeal. ΠAupo: acally depede falure good I good I good} S g} I geeral S g} g} If ( e + + S he ( e [ + +.e. falure rae add : L + L + ] Ocober 6, A cha a rog a ' weake lk Do you agree? Aue.95, 4.75 ΠS.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 6, 4 YKM 7
elably /6/ Cobaoral: Parallel Parallel cofgurao: a lea oe u u be good. epree a deal reduda ye. all u bad} bad I bad I. e. ( )( )( ) I geeral b.} b.} ( ) b.} bad} Ocober 6, Cobaoral: Parallel 5 Parallel Cofgurao: Exaple Proble : Need ye relably Soluo : How ay parallel u are eeded f ( ( ) l x l( x L ), ) x <? Aue.9999 (.),.9 gve x 4. eeber, we re coder a deal ye Ocober 6, 6 Cobaoral: Parallel YKM 8
elably /6/ Coverage good} + ha ake over + C( ) faled} faled} where C falure deeced ad ucceful wchover} Falure deeco: requre cocurre deeco. Need redudacy. Swchover: Πgood ae loaded. ΠProce reared Ocober 6, 7 Iperfec Coverage + C(- ) Aug I geeral.7 C ( ).9 elably.8.7.6 Two parallel odule.5.5.5.75 Coverage Ocober 6, 8 YKM 9
elably /6/ 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 k-ou-of- gle.5.5.75 Module elably Ocober 6, Plo: / 9 Trple Modular edudacy Popular hgh-relably chee: -ou-of- Majory voer Varou pleeao TM ( ) ( ) + V Ipleeao ue. Iperfec voer? Ocober 6, YKM
elably /6/ TM: Perae Falure Le e TM MTTF ( e - (e 5 6 - TM - e ( d - e - ) d (gle odule MTTF : ) TM Sgle croover po Solvg we ge cro.5. TM wore afer <.5! Ocober 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 :. A.99 µ A A TM TM µ A A, A + µ.9997 A A. TM. Ocober 6, YKM
elably /6/ TM+Spare TM core, - pare (aue ae falure rae) A: Sye falure whe all bu oe odule have faled. Ca we do + + + + falure beer? w [-(-) - -(-) ] Le w ( a ), a: relave coplexy << a [-(-) - -(-) ] Ex:.9, a - We ca ee ha ax 4 Ocober 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 Module Ocober 6, 4 YKM
elably /6/ edudacy: Geeralzed elably Copuao correc oupu} B G I B G I B + B G} falure ode correcable}] + P C If ad a gle falure ode doae + P C G} [falure ode } f f B: Noredudaudacy B: ed- B: deec/correc Ocober 6, 5 Geeralzed elably: Ex: Meory Approxao Ex : Meory ye, oal b/word, b error error deeco/correco Ex : Oe word 8 b daa plu 4 check b (-error correcg Hag code). Aue : relably of a gle word. Oe b word -5 correco capably. Aug perfec b /u e, + [(- wh redudacy : whou redudacy : S + P C S b word 6.6 7.9 Noe : acual of error rae hee day very all. S ) word f b ] 9 5 b Ocober 6, 6 YKM