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Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger
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The time between surface finish problems in a galvanizing

Chapter 5, Problem 20E

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QUESTION:

The time between surface finish problems in a galvanizing process is exponentially distributed with a mean of 40 hours. A single plant operates three galvanizing lines that are assumed to operate independently.

(a) What is the probability that none of the lines experiences a surface finish problem in 40 hours of operation?

(b) What is the probability that all three lines experience a surface finish problem between 20 and 40 hours of operation?

(c) Why is the joint probability density function not needed to answer the previous questions?

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QUESTION:

The time between surface finish problems in a galvanizing process is exponentially distributed with a mean of 40 hours. A single plant operates three galvanizing lines that are assumed to operate independently.

(a) What is the probability that none of the lines experiences a surface finish problem in 40 hours of operation?

(b) What is the probability that all three lines experience a surface finish problem between 20 and 40 hours of operation?

(c) Why is the joint probability density function not needed to answer the previous questions?

ANSWER:

Step 1 of 5

Consider the random variables as,

The problem time in line 1 = X

The problem time in line 2 = Y

The problem time in line 3 = Z

The exponentially distributed process with a mean of 40 hours is,

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