DETERMINING MEAN TIME BETWEEN FAILURES. Twenty air-conditioning systems designed for use by astronauts in Russia’s Soyuz spacecraft were operated for 1,000 hours at a Russian test facility. Two of the systems failed during the test—one after 200 hours and the other after 600 hours. APPROACH To

Question

DETERMINING MEAN TIME BETWEEN FAILURES. Twenty air-conditioning systems designed for use by astronauts in Russia’s Soyuz spacecraft were operated for 1,000 hours at a Russian test facility. Two of the systems failed during the test—one after 200 hours and the other after 600 hours.
APPROACH [latex]\blacktriangleright[/latex] To determine the percent of failures [FR(%)], the number of failures per unit of time [FR(N)], and the mean time between failures (MTBF), we use Equations (17-2), (17-3), and (17-4), respectively.

FR(%) = [latex]\frac{Number of failures}{Number of units tested} imes 100\%[/latex] (17-2)

FR(N ) = [latex]\frac{Number of failures}{Number of unit-hours of operating time}[/latex] (17-3)

MTBF = [latex]\frac{1}{FR(N)}[/latex] (17-4)

Accepted Answer

SOLUTION [latex]\blacktriangleright[/latex] Percentage of failures:

FR(%) = [latex]\frac{Number of failures}{Number of units tested} = \frac{2}{20} (100\%) = 10\%[/latex]

Number of failures per operating hour:

FR(N) = [latex]\frac{Number of failures}{Number of unit-hours of operating time}[/latex]

where Total time = (1,000 hr)(20 units)
= 20,000 unit-hour
Nonoperating time = 800 hr for 1st failure + 400 hr for 2nd failure
= 1,200 unit-hour
Number of unit-hours of operating time = Total time - Nonoperating time

FR(N) = [latex]\frac{2}{20,000 - 1,200} = \frac{2}{18,800} = .000106[/latex] failure/unit-hour

Because MTBF = [latex]\frac{1}{FR(N)}[/latex]:
MTBF = [latex]\frac{1}{.000106} = 9,434[/latex] hr

If the typical Soyuz shuttle trip to the International Space Station lasts 6 days, Russia may note that the failure rate per trip is:
Failure rate = (Failures/unit-hr)(24 hr/day)(6 days/trip)
= (.000106)(24)(6)
= .0153 failure/trip

INSIGHT [latex]\blacktriangleright[/latex] Mean time between failures (MTBF) is the standard means of stating reliability.
LEARNING EXERCISE [latex]\blacktriangleright[/latex] If nonoperating time drops to 800, what is the new MTBF? [Answer: 9,606 hr.]
RELATED PROBLEMS [latex]\blacktriangleright[/latex] 17.4, 17.5

Question 17.EX.2: DETERMINING MEAN TIME BETWEEN FAILURES. Twenty air-condition...

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