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Get Full Access to Applied Statistics And Probability For Engineers - 6 Edition - Chapter 4.10 - Problem 156e
Get Full Access to Applied Statistics And Probability For Engineers - 6 Edition - Chapter 4.10 - Problem 156e

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# Assume that the life of a roller bearing follows a Weibull ISBN: 9781118539712 55

## Solution for problem 156E Chapter 4.10

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 156E

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?

Step-by-Step Solution:
Step 1 of 3

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,      Therefore, P(X > 8000) = 0.5273.

Step3 of 4:

b).

The mean of the weibull distribution is:      [therefore ] Therefore, The mean of the weibull distribution is 8862.3.

Step4 of 4:

c).

Here we have n = 10 and from part (a) we have p = 0.5273.

Now,    Therefore, P(X = 10) = 0.00166.

Step 2 of 3

Step 3 of 3

##### ISBN: 9781118539712

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