Reliability Quiz: Selected solutions

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Reliability Quiz Selected solutions
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Laptop batteries

• Annas laptop battery is unreliable (R0.1), so
  she carries 2 additional batteries with her that
  can be used to replace a failing battery (each
  also with R0.1). What is the reliability of her
  laptop with all 3 batteries available?
• R 1 (1-0.1)(1-0.1)(1-0.1)
• R 1 (0.9)3
• R 1 0.729 0.271

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Getting to class on time

• In order for Bill to make it to class on time, he
  must leave on time (R0.9), his car must start
  (R0.8), and he must encounter low traffic
  (R0.5). What is the reliability of Bill making
  it to class on time?
• R (0.9)(0.8)(0.5)
• R 0.36

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iPod MTBF

• Bills new iPod has an advertised MTBF of 50,000
  hrs, but its battery failure rate is known to
  occur about every 1,000 hrs. What can you state
  about the iPod?
• Its advertised MTBF is in error
• Expect a failure about every 1,000 hours

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Calculator failures

• Youre about to take this quiz, but youre
  bothered that your calculator has a 50 chance of
  failing catastrophically during the quiz. If it
  does, Jim offers you the use of his 90 reliable
  calculator. What is the Reliability that you
  will have a working calculator for the quiz?
• R 1 (1-0.5)(1-0.9)
• R 1 (0.5)(0.1)
• R 1 0.05 0.95

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More calculator failures

• Another member in the class lets you use their
  calculators instead of Jims. You dont know the
  reliability of the loaned calculator, except to
  know that it is greater than zero. Between yours
  (R0.5) and your friends (R 0), what can you
  state about the Reliability that you will have a
  working calculator for the quiz?
• R 0.5

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System reliability

• You are responsible for a system that has four
  components shown below, three with R 0.99 and
  the fourth with R 0.50. Where would you place
  an additional component (A, B, or C) to maximize
  the overall systems reliability?

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Stoves, stoves, stoves
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Stoves, stoves, stoves

• Four burner stove The stove works
• (that is, you can heat something up)
• if burner1 OR burner2 OR burner3 OR burner4 work
• OR ? parallel equation
• R 1 (1-B)(1-B)(1-B)(1-B) 1 (1-B)4

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Stoves, stove, stoves

• Two burner stove The stove works
• if burner1 OR burner2 work
• OR ? parallel equation
• R 1 (1-B)2

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Stoves, stove, stoves

• Difference in Reliability equals
• 1 (1-B)4 - 1 (1-B)2
• 1 - (1-B)4 - 1 (1-B)2
• (1-B)2 - (1-B)4
• Pull out the common factor (1-B)2
• Difference (1-B)2 1 (1-B)2
• Simplify to getDifference B(1-B)2 (2-B)

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2 versus 4 burner Reliability
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2 versus 4 burner difference