a. Explanation Given info: The life of a roller bearing follows a Weibull distribution with the parameters β = 2 and δ = 10 , 000 . Calculation: If the random variable X follows a Weibull distribution. Then the probability density function is, f ( x ) = β δ ( x δ ) β − 1 exp ( − ( x δ ) β ) for x > 0 , δ > 0 and β > 0 with mean δ Γ ( 1 + 1 β ) The cumulative distributive function for Weibull distribution is, F ( x ) = 1 − e − ( x δ ) β , x > 0 , δ > 0 The probability of the event that a bearing lasts at least 8,000 hours: Let X be the lifetime of a bearing b. To determine Find the mean time until failure of a bearing. c. To determine Find the probability that all 10 bearings last at least 8,000 hours.

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118539712

Author: Douglas C. Montgomery

Publisher: WILEY

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Chapter 4.10, Problem 156E

To determine

Find the probability of the event that a bearing lasts at least 8,000 hours.

To determine

Find the mean time until failure of a bearing.

To determine

Find the probability that all 10 bearings last at least 8,000 hours.

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Chapter 4.10, Problem 155E

Chapter 4.10, Problem 157E

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