Situation Analysis: Tires

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Situation Analysis Tires

• My 1985 F250 has four independent and identical
  tires. If any tire fails, the vehicle cannot be
  driven. Assume the reliability of an individual
  tire is 0.9.
• What is the reliability of the F250 with respect
  to tires?

4WD, 460 V8, 375,000 miles
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Situation Analysis Tires

• Framing the question The truck works if
• tire1 works AND/OR
• tire2 works AND/OR
• tire3 works AND/OR
• tire4 works
• Is it AND or is it OR?

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Situation Analysis Tires

• The truck works if
• tire1 works AND
• tire2 works AND
• tire3 works AND
• tire4 works
• AND ? series equation
• Rs R1R2Rn (0.9)(0.9)(0.9)(0.9) 0.65

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Situation Analysis More Tires

• What is the reliability of an eighteen wheeler
  with tires of reliability equal to 0.9? Ignore
  dualies effect, assume if one tire fails, the
  truck fails.

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Situation Analysis More Tires

• What is the reliability of an eighteen wheeler
  with tires of reliability equal to 0.9? Ignore
  dualies effect, assume if one tire fails, the
  truck fails.
• Rs R1R2Rn (0.9)18 0.15

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Situation Analysis Flying

• You are flying on a Boeing 747 with four engines.
  The reliability of each engine is 0.9. The
  plane can fly with as few as one engine working.
• What is the probability of a failed flight?

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Situation Analysis Flying

• Framing the question The plane works if
• engine1 works AND/OR
• engine2 works AND/OR
• engine3 works AND/OR
• engine4 works
• Is it AND or is it OR?

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Situation Analysis Flying

• The plane works if
• engine1 works OR
• engine2 works OR
• engine3 works OR
• engine4 works
• OR ? parallel
• Reliability 1 (0.1)4 0.9999
• Probability of failure 1 - R .0001

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Reliability Situation Analysis

• Your favorite uncle has offered you two free
  tickets to the Hoobastank concert Saturday night
  in Salt Lake City.
• You have three choices for travelfly, drive, or
  train.
• Which one will get you there most reliably???

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Reliability getting to the Hoobastank concert

• Fly two serial flights, each with a reliability
  of 90 of getting you to each destination
• Drive Your car is 80 reliable, so your friend
  Megan offers to drive side-by-side with her car
  (to get the free ticket). Her car has a
  reliability of 80.
• Train Reliability of arrival on time of 80.

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Reliability getting to the Hoobastank concert

• Fly R (0.9)(0.9) 0.81 ? 81
• Drive R 1 (1-0.8)(1-0.8) 0.96 ? 96
• Train R 0.80 ? 80
• Drive, baby, drive!

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Situation Analysis Rock climbing

• Youve climbed up the backside of a cliff, 3,000
  feet off the valley floor. You and your partner
  each have one rope, each 1,800 feet long, and
  each with a reliability of not-breaking of 0.95.
  Theres a ledge halfway down, at 1,500 feet. You
  can get extra help at the top, but not at the
  ledge.
• What is the most reliable way to descend by rope,
  and what is the probability of a fall due to rope
  failure?

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Rock climbing Solution one

• Tie ropes together, drop them down, climb down
  all the way.
• You live if rope1 works AND rope2 works .series
  equation
• Reliability (0.95)2 0.90
• Probability of death 1 0.9 0.1 ? 10

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Rock climbing Solution two

• Drop two ropes down, climb half-way down drop
  ropes again, climb rest of way.
• Segment one You live if rope1 works OR rope2
  works . parallel equation
• RS1 1 (1-0.95)(1-0.95) 0.9975
• RS2 1 (1-0.95)(1-0.95) 0.9975
• You live if S1 AND S2 work
• R (0.9975)(0.9975) 0.995
• Probability of death 1 0.995 0.005 ? 0.5

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Situation Analysis Snowballs

• My two sons have a snowball hit-the-target
• reliability of 75, my two daughters 50.
• What is the reliability of one of them hitting me
  with a snowball, given that all four throw?

I get hit if Sue OR Greg OR Kim OR Sue hit
me. Reliability 1 (1-0.75)(1-0.75)(1-0.5)(1-0
.5) 1 - (0.25)(0.25)(0.5)(0.5)
0.984375 98
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Reliability Examples

• Item MTBF
• wood pencil 30 minutes
• PC (hardware) 10,000 hours 1 year
• Disk drive 150,000 hours 15 years
• Windows 98 8 hours
• Windows XP gt 40 hours (est.)
• Linux gt 1000 hours (est.)
• Automobile 500 hours (est.)

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Reliability Examples

• Item MTTR
• wood pencil 30 seconds (sharpen)
• PC (hardware) hours
• Disk drive hour or N/A
• Windows 98 minutes (reboot)
• Windows XP minutes (reboot)
• Linux minutes (reboot)
• Automobile hours