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# A system consists of components A and B connected in ISBN: 9780073401331 38

## Solution for problem 9E Chapter 4.12

Statistics for Engineers and Scientists | 4th Edition

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Problem 9E

A system consists of components A and B connected in series, as shown in the following schematic illustration. The lifetime in months of component A is lognormally distributed with µ = 1 and σ = 0.5, and the lifetime in months of component B is lognormally distributed with µ = 2 and σ = 1. The system will function only so long as A and B 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:

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:

We have to generate a sample of size 1000 of system lifetimes.

We can generate a sample of size 1000 of lifetimes of component A and component B by using minitab as

Calc- Random Data- Distribution(lognormal) - Parameters(mean,standard deviation(with sample size))- Ok (store data in column C1 and C2).

Find system lifetime L = Min( X,Y) (store it in column C3).

The generated sample may vary from ours. (b)  We have to estimate the mean system lifetime.

We can find the estimate of the mean lifetime in minitab as

Stat - Basic statistics - Descriptive statistics-  Assign variable - Statistics(mean) - ok. E(L) 2.7

Therefore the  estimate of the mean system lifetime is 2.7.

Step 3 of 4

Step 4 of 4

##### ISBN: 9780073401331

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A system consists of components A and B connected in

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