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A system consists of components A and B connected in

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

Solution for problem 9E Chapter 4.12

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

A system consists of components  and  connected in series, as shown in the following schematic illustration. The lifetime in months of component  is lognormally distributed with  and , and the lifetime in months of component  is lognormally distributed with  and . The system will function only so long as  and  both function.

a. Generate, by simulation, a large number (at least 1000) of system lifetimes.

b. Estimate the mean system lifetime.

c. Estimate the probability that the system fails within 2 months.

d. Estimate the 20th percentile of system lifetimes.

e. Construct a normal probability plot of system lifetimes. Is the system lifetime approximately normally distributed?

f. Construct a histogram of the system lifetimes. Is it skewed to the left, skewed to the right, or approximately symmetric?

Step-by-Step Solution:

Solution:

Step 1of 4:

A system consist of components A and B connected in series. The lifetime of component A in months is lognormally distributed with mean =1, and standard deviation =0.5. Similarly the lifetime of component B is lognormally distributed with =2 and =1.

                 

The system will function as long as the both will functions. Let x denote the lifetime of system A and Y denote the lifetime of system B.

Which means the system lifetime can be defined as L= Min (X,Y).


Step 2 of 4

Chapter 4.12, Problem 9E is Solved
Step 3 of 4

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

Since the solution to 9E from 4.12 chapter was answered, more than 481 students have viewed the full step-by-step answer. The answer to “?A system consists of components and connected in series, as shown in the following schematic illustration. The lifetime in months of component is lognormally distributed with and , and the lifetime in months of component is lognormally distributed with and . The system will function only so long as and both function. a. Generate, by simulation, a large number (at least 1000) of system lifetimes.b. Estimate the mean system lifetime.c. Estimate the probability that the system fails within 2 months.d. Estimate the 20th percentile of system lifetimes.e. Construct a normal probability plot of system lifetimes. Is the system lifetime approximately normally distributed?f. Construct a histogram of the system lifetimes. Is it skewed to the left, skewed to the right, or approximately symmetric?” is broken down into a number of easy to follow steps, and 122 words. This full solution covers the following key subjects: system, lifetimes, lifetime, Months, estimate. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The full step-by-step solution to problem: 9E from chapter: 4.12 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4.

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