On Consecutive-k-Out-of-n: F Systems.
STANFORD UNIV CA DEPT OF STATISTICS
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A consecutive-k-out-of-n F system consists of n lineraly ordered components and th system fails if and only if at least k consecutive components fail. This type of system has attracted considerable attention since 1980. In this paper first a brief survey of the literature is given. Then the system is studied in the general case when the n components are statistically independent, but may not have the same reliability. Most of the papers in the literature use traditional combinatorial or conditional probability approaches to derive the formulae for the system reliability. Here the authors show that using the elegant and concise algebraic approach and network diagram representation given in Chapters 1 and 2 of Barlow and Proschan 1975, one can easily obtain the exact formula for the system reliability. Futhermore, they are able to obtain algorithms for finding all the minimal path sets and cut sets of the system, and hence the upper and lower bounds of the system reliability. A simplified upper bound is also proposed.
- Statistics and Probability