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Assume that the life of a roller bearing follows a Weibull
Chapter 4, Problem 156E(choose chapter or problem)
Problem 156E
Assume that the life of a roller bearing follows a Weibull distribution with parameters β = 2 and δ = 10,000 hours.
(a) Determine the probability that a bearing lasts at least 8000 hours.
(b) Determine the mean time until failure of a bearing.
(c) If 10 bearings are in use and failures occur independently, what is the probability that all 10 bearings last at least 8000 hours?
Questions & Answers
QUESTION:
Problem 156E
Assume that the life of a roller bearing follows a Weibull distribution with parameters β = 2 and δ = 10,000 hours.
(a) Determine the probability that a bearing lasts at least 8000 hours.
(b) Determine the mean time until failure of a bearing.
(c) If 10 bearings are in use and failures occur independently, what is the probability that all 10 bearings last at least 8000 hours?
ANSWER:
Solution 156E
Step1 of 4:
Let us consider a random variable X it presents the lifetime of a bearing. And X follows weibull distribution with parameters and
Here our goal is:
a). We need to determine the probability that a bearing lasts at least 8000 hours.
b). We need to determine the mean time until failure of a bearing.
c). We need to find the probability that all 10 bearings last at least 8000 hours.
Step2 of 4:
a).
We know that cumulative distribution function of weibull distribution is:
Consider,