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system reliability; unit reliability; unit importance; essential unit
The availability of a system with dependent units is obtained in the case where the system fails when one of the essential units fails. Markov model is assumed. The system considered consists of $n$ dependent units of which $r\leq n$ units are essential units. A unit is said to be essential if its failure causes the system to fail. The mean and variance of time to system failure are given. Unit reliability is also discussed.
[1] John G. Kemeny J. Laurie Snell: Finite Markov Chain. D. Van Nostrand Company Inc., New York (1960). MR 0115196
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