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In the article “Parameter Estimation with Only One

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 9E Chapter 4.8

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 9E

Problem 9E

In the article “Parameter Estimation with Only One Complete Failure Observation” (W. Pang, P. Leung, et al., International Journal of Reliability, Quality, and Safety Engineering, 2001:109-122), the lifetime, in hours, of a certain type of bearing is modeled with the Weibull distribution with parameters  α=2.25 and β = 4.474 x 10-4.

a. Find the probability that a bearing lasts more than 1000 hours.

b. Find the probability that a bearing lasts less than 2000 hours.

c. Find the median lifetime of a bearing.

d. The hazard function is defined in Exercise 8. What is the hazard at t = 2000 hours?

Step-by-Step Solution:

Solution:

Step 1 of 3:

In an article the lifetime in hours of a certain type of bearing in modeled with the weibull distribution with parameters and .

We have to find

  1. The probability that a bearing lasts more than  1000 hours.
  2. Probability that bearing lasts less than 2000 hours.
  3. Median lifetime of a bearing.
  4. If the hazard function of T is  defined as h(t) = . Then what will be the hazard rate if t= 2000 hours.


Step 2 of 3

Chapter 4.8, Problem 9E is Solved
Step 3 of 3

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

Since the solution to 9E from 4.8 chapter was answered, more than 359 students have viewed the full step-by-step answer. The answer to “In the article “Parameter Estimation with Only One Complete Failure Observation” (W. Pang, P. Leung, et al., International Journal of Reliability, Quality, and Safety Engineering, 2001:109-122), the lifetime, in hours, of a certain type of bearing is modeled with the Weibull distribution with parameters ?=2.25 and ? = 4.474 x 10-4.a. Find the probability that a bearing lasts more than 1000 hours.________________b. Find the probability that a bearing lasts less than 2000 hours.________________c. Find the median lifetime of a bearing.________________d. The hazard function is defined in Exercise 8. What is the hazard at t = 2000 hours?” is broken down into a number of easy to follow steps, and 97 words. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This full solution covers the following key subjects: bearing, Find, lifetime, Probability, Hazard. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The full step-by-step solution to problem: 9E from chapter: 4.8 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4.

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In the article “Parameter Estimation with Only One