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Reliability Engineering

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Bath Tub curve

Time

Fai

lure

ra

te

Infant Mortality

Useful Life Wear Out

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Infant MortalityInfant Mortality Due to gross built in flaws caused by faulty Due to gross built in flaws caused by faulty

workmanshipworkmanship Transportation damage or installation errors, etc.Transportation damage or installation errors, etc.Examples: Examples: Poor seals or welds or solder jointsPoor seals or welds or solder jointsPoor connectionsPoor connectionsDirt or contamination on surfaces or in materialsDirt or contamination on surfaces or in materialsChemical impurities in metals or insulationChemical impurities in metals or insulationVoids, cracks, thin spots insulation or protective Voids, cracks, thin spots insulation or protective

coatingscoatingsIncorrect positioning of parts Incorrect positioning of parts

LIFE CHARACTERISTIC CURVE

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Useful Life PeriodUseful Life PeriodCharacterised mainly by occurrence of stress Characterised mainly by occurrence of stress

related failuresrelated failuresExponential distribution, constant failure rateExponential distribution, constant failure rate

Wear outWear out

Due to deterioration of the design strength of Due to deterioration of the design strength of the device as a consequence of operation the device as a consequence of operation and exposure to environmental fluctuations, and exposure to environmental fluctuations, corrosion / oxidation / ionic migration, etc. corrosion / oxidation / ionic migration, etc.

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Four Types of Part Failures

TypeType Dependent uponDependent upon Eliminated byEliminated by

QualityQuality Unrelated to Unrelated to stress or Timestress or Time

InspectionInspection

ReliabilityReliability StressStress ScreeningScreening

Wear-outWear-out TimeTime Qualification (life) Qualification (life) testing or periodic testing or periodic replacementreplacement

DesignDesign May be stress May be stress and/or time and/or time dependentdependent

Proper application Proper application and deratingand derating

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Reliability

Reliability is the probability that an Reliability is the probability that an item will perform its intended function item will perform its intended function for a specified time interval under for a specified time interval under stated conditionsstated conditions

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R(t) = e-t

R(t) is the probability that the item will R(t) is the probability that the item will operate without failure for the time period t, operate without failure for the time period t, under specified operating conditionsunder specified operating conditions

e - base of natural logarithm = 2.71828e - base of natural logarithm = 2.71828

λ - failure rate in Fits λ - failure rate in Fits

1 Fit = 1 Failure / 101 Fit = 1 Failure / 10-9-9 hours hours

Fit - Fit - FFailure Unailure Unitit , , FFailure ailure iin n ttimeime

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MTBF and MTTR

Up

Down

Time

Ut

Dt

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Availability

The probability that the system is operating The probability that the system is operating at time t.at time t.

MTBF.MTBF.

AvailabilityAvailability = ---------------------. = ---------------------.

MTBF + MTTR.MTBF + MTTR.MTBF … Mean time between failures.MTBF … Mean time between failures.

MTBF = 1/ λ hours.MTBF = 1/ λ hours.MTTR … Mean time to repair (expressed in MTTR … Mean time to repair (expressed in

hours).hours).

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Maintainability

The measure of the ability of an item to be The measure of the ability of an item to be retained in or restored to a specified retained in or restored to a specified condition when maintenance is performed condition when maintenance is performed by personnel having specified skill levels, by personnel having specified skill levels, who use prescribed procedures and who use prescribed procedures and resources at each level of maintenance and resources at each level of maintenance and repair.repair.

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Failure Distribution Versus

Environment VIBRATIONVIBRATION 27%27% TEMPERATURE TEMPERATURE 40%40% MOISTUREMOISTURE 19%19% SAND & DUSTSAND & DUST 6%6% SALTSALT 4% 4% ALTITUDEALTITUDE 2% 2% SHOCKSHOCK 2% 2%

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