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A system consists of components A and B connected in
Chapter 4, Problem 9E(choose chapter or problem)
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 \(\mu=1\) and \(\sigma=0.5\), and the lifetime in months of component
is lognormally distributed with \(\mu=2\) and \(\sigma=1\). 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?
Equation transcription:
Text transcription:
\mu=1
\sigma=0.5
\mu=2
\sigma=1
Questions & Answers
QUESTION:
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 \(\mu=1\) and \(\sigma=0.5\), and the lifetime in months of component
is lognormally distributed with \(\mu=2\) and \(\sigma=1\). 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?
Equation transcription:
Text transcription:
\mu=1
\sigma=0.5
\mu=2
\sigma=1
ANSWER:
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).