Question 543895: 5. A component of a precision instrument is subject to random failure. The time to failure of the component, or its productive life, is normally distributed with a mean of 440 hours and a standard deviation of 25 hours. The production engineer would like to replace the component prior to failure after a certain number of productive hours. He is willing to take a 1% chance that the component fails prior to this scheduled replacement time.
(a) Should the replacement time be less than or greater than the mean time to failure?
(b) What replacement time should he select in this case?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A component of a precision instrument is subject to random failure. The time to failure of the component, or its productive life, is normally distributed with a mean of 440 hours and a standard deviation of 25 hours. The production engineer would like to replace the component prior to failure after a certain number of productive hours. He is willing to take a 1% chance that the component fails prior to this scheduled replacement time.
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(a) Should the replacement time be less than or greater than the mean time to failure?
Less than.
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(b) What replacement time should he select in this case?
Find the z-value with a left-tail of 1%
invNorm(0.01) = -2.3263
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Find the corresponding x-value:
x = zs+u
x = -2.3263**25+440 = 381.84 hours
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Cheers,
Stan H.
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