components. The 5. Consider an ensemble of three single-point-of-failure lifetime of the first component has an exponential distribution with parameter 0.001 failures per hour. The lifetime of the second component has a Weibull distribution with parameters 0.001 and 1.7, and the lifetime of the third component has a lognormal distribution with parameters 0.005 and 2.3. If the components are considered stochastically independent, what is the probability that the ensemble survives at least 40,000 hours? What information would be required to solve this problem if the components are not considered stochastically independent?

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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5. Consider an ensemble of three single-point-of-failure components. The
lifetime of the first component has an exponential distribution with
parameter 0.001 failures per hour. The lifetime of the second component
has a Weibull distribution with parameters 0.001 and 1.7, and the lifetime
of the third component has a lognormal distribution with parameters 0.005
and 2.3. If the components are considered stochastically independent,
what is the probability that the ensemble survives at least 40,000 hours?
What information would be required to solve this problem if the
components are not considered stochastically independent?
Transcribed Image Text:5. Consider an ensemble of three single-point-of-failure components. The lifetime of the first component has an exponential distribution with parameter 0.001 failures per hour. The lifetime of the second component has a Weibull distribution with parameters 0.001 and 1.7, and the lifetime of the third component has a lognormal distribution with parameters 0.005 and 2.3. If the components are considered stochastically independent, what is the probability that the ensemble survives at least 40,000 hours? What information would be required to solve this problem if the components are not considered stochastically independent?
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