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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 blade and the bearings are important parts of a lathe.

Chapter 5, Problem 22E

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QUESTION:

The blade and the bearings are important parts of a lathe. The lathe can operate only when both of them work properly. The lifetime of the blade is exponentially distributed with the mean three years; the lifetime of the bearings is also exponentially distributed with the mean four years. Assume that each lifetime is independent.

(a) What is the probability that the lathe will operate for at least five years?

(b) The lifetime of the lathe exceeds what time with 95% probability?

Questions & Answers

QUESTION:

The blade and the bearings are important parts of a lathe. The lathe can operate only when both of them work properly. The lifetime of the blade is exponentially distributed with the mean three years; the lifetime of the bearings is also exponentially distributed with the mean four years. Assume that each lifetime is independent.

(a) What is the probability that the lathe will operate for at least five years?

(b) The lifetime of the lathe exceeds what time with 95% probability?

ANSWER:

Solution

Step 1 of 3

Let  be the lifetime of the blade

And it is exponentially distributed with mean 3 years

Let  be the lifetime of the bearings

And it is exponentially distributed with mean 4 years

The pmf of exponential distribution is

Then

And

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