Chapter 11:Availability

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Chapter 11Availability

• Coverage
• Concepts and Definitions
• System Availability
• Inspection and Repair Availability Model
• Reference
• C.E. Ebeling. An Introduction to Reliability and
  Maintainability Engineering. McGraw-Hill, 1997

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Concepts and Definitions

• How to predict availability ?
• Availability is the probability that a system or
  component 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
• Point availability A(t) availability at time
  t
• Average availability over the interval 0,T
• Mission or interval availability general
  average availability

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Concepts and Definitions

• Steady-state or long-run equilibrium availability
• Inherent availability
• Achieved availability
• Where MTBM mean time between maintenance M
  mean system down time, Tpm PM interval, td
  design life, m(td) cumulative average number of
  failures over the design life, MPMT mean PM time

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Concepts and Definitions

• Operational availability
• Generalized Operational Availability
• Example A component has MTBF 200h, MTTR10h
  with both the failure and repair distributions
  exponential. Determine A(t), A(10), A10-0, A
  steady-state

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System Availability

• Series system n independent components
• Parallel system
• Standby system
• Setup Markov model for the system
• Determine the steady state probabilities ?A ?Pu
• Steady state availability from steady state
  equation constant failure and repair rate
• ?j(rate into state i from state j)Pj (rate
  out of state i) Pi
• Example A two-component active redundant system
  can be repaired only after both units have
  failed. Only one unit can then be repaired at a
  time. The units have constant failure rate ?1,
  ?2, and both repairs have MTTR.

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Inspection and Repair Availability Model

• Restorable systems inspection down time
  gtltdetection and restoration of failures
• Restore systems to as good as new
• Inspection not improve R(t) but improve A(t)
• The expected available time during a cycle T ?
• Where t1 inspection time, t2 repair time, T
  time between inspection, A(T) steady state
  availability

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Example

• A nuclear power plant has several sophisticated
  radiation detectors throughout the facility.
  These detectors historically have had a constant
  failure rate of 0.0002 failure per hour.
  Periodically, these detectors can be removed and
  brought into a lab for inspection. If found
  defective, they are replaced. If inspection time
  is 16h and it takes 48h to obtain a replacement
  for a failed unit. What is the optimum time
  between inspections?