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[Moved]: n out of k system reliability

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jmvalks

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I have a system consisting of 4 identical components. The components are independent so that the probability of failure of each component is independent of the other.

I have a failure rate, lambda, of 4.60994 /10^6 hours.

I need to calculate the MTBF of the system assuming that 75% of the components must be operational, otherwise the system has failed. So 3 out of the 4 components must be operational.

I have been given a figure in the document I am working with of 4.8028x10^13 hours.

I have tried using a binomial distribution using the given failure rate and time (or mission length) t of 360 hours.
So the the exponentials in the binomial expansion become exp^(-lambda * t * i) and (1 - exp(^-lambda * t))^(4-k),
with k from 3 to 4.

I then take
1 - result to give the failure rate, F, which I then convert to MTBF as 1/F.

I cannot arrive anywhere near this figure. The best I have is 60748 hours.

Can anyone give me some guidance?

Thanks

JV
 

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