容错计算英文版课件：lec02-measures

1、Fault-Tolerant ComputingMotivation, Background, and ToolsOct. 20061Terminology, Models, and MeasuresAbout This PresentationEditionReleasedRevisedRevisedFirstOct. 2006This presentation has been prepared for the graduate course ECE 257A (Fault-Tolerant Computing) by Behrooz Parhami, Professor of Elect

2、rical and Computer Engineering at University of California, Santa Barbara. The material contained herein can be used freely in classroom teaching or any other educational setting. Unauthorized uses are prohibited. Behrooz ParhamiOct. 20062Terminology, Models, and MeasuresTerminology, Models, and Mea

3、sures for DependabilityOct. 20063Terminology, Models, and MeasuresOct. 20064Terminology, Models, and MeasuresImpairments to DependabilityErrorMalfunctionDegradationFailureFaultIntrusionHazardDefectFlawBugCrashOct. 20065Terminology, Models, and MeasuresThe Fault-Error-Failure CycleSchematic diagram o

4、f the Newcastle hierarchical model and the impairments within one level.Includes both components and design000FaultCorrectsignalReplaced with NAND?Oct. 20066Terminology, Models, and MeasuresThe Four-Universe ModelCause-effect diagram for Aviienis four-universe model of impairments to dependability.O

5、ct. 20067Terminology, Models, and MeasuresUnrolling the Fault-Error-Failure CycleCause-effect diagram for an extended six-level view of impairments to dependability.Oct. 20068Terminology, Models, and MeasuresMultilevel ModelComponentLogicServiceResultInformationSystemLegend:ToleranceEntryOct. 20069T

6、erminology, Models, and MeasuresAnalogy for the Multilevel ModelAn analogy for our multi-level model of dependable computing. Defects, faults, errors, malfunctions, degradations, and failures are represented by pouring water from above. Valves represent avoidance and tolerance techniques. The goal i

7、s to avoid overflow.Oct. 200610Terminology, Models, and MeasuresWhy Our Concern with Dependability?Reliability of n-transistor system, each having failure rate l R(t) = enlt There are only 3 ways of making systems more reliableReduce lReduce nReduce tAlternative:Change the reliability formula by int

8、roducing redundancy in systemOct. 200611Terminology, Models, and MeasuresHighly Dependable Computer SystemsLong-life systems: Fail-slow, Rugged, High-reliabilitySpacecraft with multiyear missions, systems in inaccessible locationsMethods: Replication (spares), error coding, monitoring, shieldingSafe

9、ty-critical systems: Fail-safe, Sound, High-integrityFlight control computers, nuclear-plant shutdown, medical monitoringMethods: Replication with voting, time redundancy, design diversityHigh-availability: Fail-soft, Robust, High-availabilityTelephone switching centers, transaction processing, e-co

10、mmerceMethods: HW/info redundancy, backup schemes, hot-swap, recoveryJust as performance enhancement techniques gradually migrate from supercomputers to desktops, so too dependability enhancement methods find their way from exotic systems into personal computersOct. 200612Terminology, Models, and Me

11、asuresAspects of DependabilityReliabilityMaintainabilityAvailabilityPerformabilitySecurityIntegrityServiceabilityTestabilitySafetyRobustnessResilienceReliability, MTTF = MTFFRisk, consequenceControllability,observabilityPerformability, MCBFPointwise av., Interval av., MTBF, MTTROct. 200613Terminolog

12、y, Models, and MeasuresConcepts from Probability TheoryCumulative distribution function: CDFF(t) = probx t = 0 f(x) dx tProbability density function: pdff(t) = probt x t + dt / dt = dF(t) / dt Expected value of xEx = - x f(x) dx = k xk f(xk) +Liftimes of 20 identical systemsCovariance of x and yyx,y

13、 = E (x Ex)(y Ey) = E x y Ex Ey Variance of xsx = - (x Ex)2 f(x) dx = k (xk Ex)2 f(xk) +2Oct. 200614Terminology, Models, and MeasuresSome Simple Probability DistributionsOct. 200615Terminology, Models, and MeasuresReliability and MTTFReliability: R(t)Probability that system remains in the “Good” sta

14、te through the interval 0, t Two-state nonrepairable systemR(t + dt) = R(t) 1 z(t) dtHazard functionConstant hazard function z(t) = l R(t) = elt (system failure rate is independent of its age) R(t) = 1 F(t) CDF of the system lifetime, or its unreliabilityExponential reliability lawMean time to failu

15、re: MTTFMTTF = 0 t f(t) dt = 0 R(t) dt +Expected value of lifetimeArea under the reliability curve(easily provable)Oct. 200616Terminology, Models, and MeasuresFailure Distributions of InterestExponential: z(t) = l R(t) = elt MTTF = 1/lWeibull: z(t) = al(lt) a1 R(t) = e(-lt)a MTTF = (1/l) G(1 + 1/a)E

16、rlang: MTTF = k/lGamma:Erlang and exponential are special casesNormal:Reliability and MTTF formulas are complicatedRayleigh: z(t) = 2l(lt)R(t) = e(-lt)2 MTTF = (1/l) p / 2Discrete versionsGeometricBinomialDiscrete Weibull R(k) = q k Oct. 200617Terminology, Models, and MeasuresComparing Reliabilities

17、Reliability gain: R2 / R1 Reliability difference: R2 R1 Reliability functionsfor Systems 1/2Reliability improv. indexRII = log R1(tM) / log R2(tM) System Reliability (R)Mission time extensionMTE2/1(rG) = T2(rG) T1(rG)Mission time improv. factor:MTIF2/1(rG) = T2(rG) / T1(rG)Reliability improvement fa

18、ctorRIF2/1 = 1R1(tM) / 1R2(tM)Example:1 0.9 / 1 0.99 = 10 Oct. 200618Terminology, Models, and MeasuresAvailability, MTTR, and MTBF(Interval) Availability: A(t)Fraction of time that system is in the “Up” state during the interval 0, t Two-state repairable systemAvailability = Reliability, when there

19、is no repairAvailability is a function not only of how rarely a system fails (reliability) but also of how quickly it can be repaired (time to repair)Pointwise availability: a(t)Probability that system available at time tA(t) = (1/t) 0 a(x) dx tSteady-state availability: A = limt A(t) MTTF MTTF mMTT

20、F + MTTR MTBF l + mA = = =Repair rate1/m = MTTR(Will justify thisequation later)In general, m l, leading to A 1Oct. 200619Terminology, Models, and MeasuresSystem Up and Down TimesShort repair time implies good Maintainability (serviceability)Oct. 200620Terminology, Models, and MeasuresPerformability

21、 and MCBFPerformability: PComposite measure, incorporating both performance and reliability Three-state degradable systemP = 2pUp2 + pUp1 Simple exampleWorth of “Up2” twice that of “Up1”pUpi = probability system is in state Upi tpUp2 = 0.92, pUp1 = 0.06, pDown = 0.02, P = 1.90 (system performance eq

22、uiv. To that of 1.9 processors on average)Performability improvement factor of this system (akin to RIF) relative to a fail-hard system that goes down when either processor fails:PIF = (2 2 0.92) / (2 1.90) = 1.6 Question: What is system availability here?Oct. 200621Terminology, Models, and MeasuresSystem Up, Partially Up, and Down TimesImportant to prevent direct transitions to the “Down” sta