RELIABILITY

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RELIABILITY
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RELIABILITY

• A measure of the ability of a product, part, or
  system to perform its intended function under a
  prescribed set of conditions

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RELIABILITY AS A PROBABILITY

• The probability that the product or system will
  function on any given trial
• The probability that the product or system will
  function for a given length of time

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DEFINITION OF FAILURE

• A situation in which an item does not perform as
  intended----
• Does not perform at all
• Does not perform to standard (substandard
  performance)
• Performs in a way not intended

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NORMAL OPERATING CONDITIONS

• The set of conditions under which an items
  reliability is specified

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Customers Concept of Operating Conditions
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INDEPENDENT EVENTS

• Independent events have no relation to the
  occurrence or nonoccurrence of each other.

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RULE 1

• If two or more events are independent and
  success is defined as the probability that all
  of the events occur, then the probability of
  success is equal to the product of the
  probabilities of the events.
• Psuccess (R1)(R2)(R3)

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Rule 1 Components in a system
Determine the reliability of the system shown.
Psuccess (R1)(R2)(R3)
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RULE 2

• If two events are independent and success is
  defined as the probability that at least one of
  the events will occur, the probability of success
  is equal to the probability of either one plus
  1.00 minus the probability multiplied by the
  other probability.
• Psuccess R1 (1 - R1)(R2)

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Rule 2 Component with one backup
Determine the reliability of the component
with its individual backup.
Psuccess R1 (1 - R1)(R2)
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RULE 3

• If three events are involved and success is
  defined as the probability that at least one of
  them occurs, the probability of success is equal
  to the probability of the 1st (any of the
  events), plus the product of 1.00 minus that
  probability and the probability of the 2nd (any
  of the remaining events), plus the product of
  1.00 minus each of the first two probabilities
  and the probability of the 3rd, and so on.
• Psuccess R1 (1-R1)(R2) (1-R1)(1-R2)(R3)

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Rule 3 Component with two backups
Determine the reliability of the component
with its two backups.
Psuccess R1 (1-R1)(R2) (1-R1)(1-R2)(R3)
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FAILURE RATE
Infant mortality
Failures due to wear-out
Few (random) failures
Time, T
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Exponential Distribution
Reliability e -T/MTBF
1- e -T/MTBF
T
Time
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Normal Distribution
Reliability
0
z
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Availability

• The fraction of time a piece of equipment is
  expected to be available for operation

MTBF mean time between failures MTR mean
time to repair