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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi
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Refer to Example 4.81 (page 310). In order to increase the

Chapter 4, Problem 8E

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QUESTION:

Refer to Example 4.81 (page 310). In order to increase the lifetime of the system, the engineers have a choice between replacing component A with one whose lifetime is distributed Exp(1/2), or replacing component B with one whose lifetime is distributed Exp(1/3).

a. Generate, by simulation, a large number (at least 1000) of system lifetimes under the assumption that component A is replaced.

b. Generate, by simulation, a large number (at least 1000) of system lifetimes under the assumption that component B is replaced.

c. If the goal is to maximize the mean system lifetime, which is the better choice? Explain.

d. If the goal is to minimize the probability that the system fails within a month, which is the better choice? Explain.

e. If the goal is to maximize the 10th percentile of the system lifetimes, which is the better choice? Explain.

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QUESTION:

Refer to Example 4.81 (page 310). In order to increase the lifetime of the system, the engineers have a choice between replacing component A with one whose lifetime is distributed Exp(1/2), or replacing component B with one whose lifetime is distributed Exp(1/3).

a. Generate, by simulation, a large number (at least 1000) of system lifetimes under the assumption that component A is replaced.

b. Generate, by simulation, a large number (at least 1000) of system lifetimes under the assumption that component B is replaced.

c. If the goal is to maximize the mean system lifetime, which is the better choice? Explain.

d. If the goal is to minimize the probability that the system fails within a month, which is the better choice? Explain.

e. If the goal is to maximize the 10th percentile of the system lifetimes, which is the better choice? Explain.

ANSWER:

Solution:

Step 1 of 4:

In order to increase the lifetime of the system, there is two choices. Replacing component A ( with one whose lifetime is distributed exp(1/2) , or replacing component  ()with one whose lifetime is distributed exp(1/3). The system lifetime calculated as L= Max (,).

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