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Suppose that the lifetime of a component (in hours) is

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger ISBN: 9781118539712 55

Solution for problem 163E Chapter 4.10

Applied Statistics and Probability for Engineers | 6th Edition

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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

Applied Statistics and Probability for Engineers | 6th Edition

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Problem 163E

Problem 163E

Suppose that the lifetime of a component (in hours) is modeled with a Weibull distribution with β = 2 and δ = 4000. Determine the following in parts (a) and (b):

Step-by-Step Solution:

Answer

Step 1 of 3

(a)

Suppose that the lifetime of a component ( in hours) is modeled with a Weibull distribution with

We are asked to find the probability

The random variable  with probability density function

is a Weibull random variable with scale parameter  and shape parameter .

The cumulative distribution function of  is

………(1)

We can write  as,

Using equation (1), we can write,

Hence the probability  is


Step 2 of 3

Chapter 4.10, Problem 163E is Solved
Step 3 of 3

Textbook: Applied Statistics and Probability for Engineers
Edition: 6
Author: Douglas C. Montgomery, George C. Runger
ISBN: 9781118539712

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Suppose that the lifetime of a component (in hours) is