Chapter 6:Reliability

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Chapter 6Reliability

• Coverage
• Reliability, Maintainability, and Availability
• Reliability of Systems
• Design for Reliability
• Reference
• C.E. Ebeling. An Introduction to Reliability and
  Maintainability Engineering. McGraw-Hill, 1997

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Reliability, Maintainability and Availability

• Definitions
• Reliability is the probability of a component or
  system performing a required function for a
  specific period of time under the specified
  operating conditions
• Maintainability is the probability that a failed
  component or system will be restored to a
  specified condition within a period of time when
  maintenance is performed in accordance with
  prescribed procedures
• Availability is the probability that a component
  or system is performing its required function at
  a given point in time or over a stated period of
  time when operated and maintained in a prescribed
  manner

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Reliability, Maintainability and Availability

• Reliability Pr(a system function over period t)
  R(t) PrT?t T time to failure
  1 F(t) F(t)is the probability that a
  failure occurs before time t
• Reliability ? better design
  better usage better
  preventive maintenance
• Maintainability ? better maintenance planning
• Availability A

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Reliability, Maintainability and Availability

• Lifetime T X f(t) f(u)
  How to estimate f, F? graphical R(t) 1
  F(t) R(T) Prt ? T0 ? t ? T, Y(t) 1
  Y(t) 0,1 How to estimate
  R(t)?Collect lifetime data from field tests or
  from lab - Censored data/sampling -
  Accelerated testing

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Reliability, Maintainability and Availability

• MTTF Mean Time to Failure MTTR Mean
  Time to Repair MTBF Mean Time
  between Failures
• MTTFE(T)
• MTTR where h(t) is a p.d.f. of
  the repair-time distribution f(t) is a p.d.f.
  of the failure distribution, F(t), R(t) and H(t)
  are CDFs

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Reliability, Maintainability and Availability

• Hazard rate(failure rate) function
• Probability that it will fail or rate of failure
  at t given that it has survived till t
• ?(t)

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Bathtub Curve
Burn-in
?(t)
Wear out
Useful age
Early failures
Wear-out failures
Random failures
t

• ?(t) could be increasing (IFR), decreasing (DFR)
  or constant (CFR)?Bathtub curve
• Burn-in (DFR) manufacturing defects, defective
  parts, poor quality control cracks, etc. ?
  screening, QC, etc.
• Useful age (CFR) environment, random load,
  huamn error, chance events ? redundancy, excess
  strength
• Wear-out (IFR) fatigue, corrosion, aging,
  friction, etc. ? PM, part replacement,
  technology, etc.

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Reliability, Maintainability and Availability

• Some lifetime distributions
• Normal
• Exponential X f(t) ?e-?t, ?gt0 F(t) 1 -
  e-?t R(t) e-?t h(t) ?
• Weibull distribution

t
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Reliability, Maintainability and Availability

• Weibull distribution (cont.) f(t)
  F(t) 1 - R(t) ?(t)
  ? time dependent failure rates ?
  scale parameter ? shape parameter, ? 1
  exponential
• Gamma distribution f(t) k
  int. erlang

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Reliability of Systems

• System a collection of components working
  towards a common goal
• Reliability for time dependent situation
• Series networks Rs R1.R2
  Example R1 0.9 R2 0.9 Rs 0.81 for 45
  items 0.6561. Adding a series component reduces
  Rs
• Parallel networks (active redundancy) (1-Rs)
  (1-R1)(1-R2) Rs 1- (1-R1)(1-R2)
• Example R1 0.9 R2 0.9 Rs 0.99 Adding
  a parallel component increases Rs
• Mixed Networks

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Reliability of Systems

• How to increase reliability
• Increase component reliability(better design,
  better preventive maintenance, better usage)
• Redundancy (better system design) Active
  Standby
• Partial Active Redundancy r out of m
  network At least r units must function
  successfully for the success of the system.
  Consider m identical independent units.

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Reliability of Systems

• R(i,m) Pr( i out of m working)
  
• Reliability of system

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Reliability of Systems

• Series
• Parallel (active redundancy) R(t)
  1-(1-e-?t)m if all ?i are the same

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Reliability of Systems

• Stand-by system (Passive Redundancy-no repairs)
• As soon as one fails, the other is switched on
• Arrangement for finding out the failure
• Switching should be 100 reliable
• The stand-by units should be maintained properly
• The failed units should be repaired
• X1 X2 Xn For all X independent
  units, each exponential with ?, no
  repairs R(t)
• MTTF (k/ ?) (compare with active) ?
  use convolution models, renewal theory

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Reliability of Systems

• Reliability Apportionment Models (8.3 and 8.4
  Jardine)

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Design for Reliability

• Many models available ( Reliability Centered
  Maintenance)
• FMEA Failure Mode and Effect Analysis
• FMECA Failure Mode, Effect and Criticality
  Analysis
• Failure Mode Observable Manner in which a
  component fails

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Design for Reliability

• Approach
• Define the system, its scope and its boundaries
  and its interactions with the environment
• Identify modes e.g. Shorts, opens, power
  losses, ruptures, fractures
• For each mode, identify causes e.g. abnormal
  voltage surge external or internal
  mechanical stress vibration
  contamination dirt fatigue
  vibration, load friction wear-out,
  lack of lubrication corrosion presence
  of chemicals, salty, humid
  atmosphere

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Design for Reliability

• Assessment of effect effect on system
  Mode cause effect failure in
  tank wall supply atmosphere tank rupture,
  production stoppage
• Estimation of frequency of occurrences
• Classification of severity Category I
  Catastrophic II Critical III
  Marginal IV Negligible

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Design for Reliability

• Computation of criticality index Ck
  ?kp?k?pt Where Ck criticality index
  ?kp fraction of component p with failure
  mode h ?p failure rate of component p
  t duration (period) used in analysis
  (e.g. year, month, etc.)
• Determination of corrective action Reliability
  design Maintenance design