Abstract
The family of consecutive-type reliability systems is under investigation. More specifically, an up-to-date presentation of almost all generalizations of the well-known consecutive k-out-of-n: F system that have been proposed in the literature is displayed, while several recent and fundamental results for each member of the aforementioned family are stated.
Highlights
A linear consecutive k-out-of-n: F system consists of n components which are linearly arranged and the system fails if and only if at least k consecutive components fail
We present the main results appearing in the literature, such as recurrence relations and closed formulas for the evaluation of the reliability function and signature vector of m-consecutive-k-out-of-n: F systems
Beyond the results mentioned in the previous subsections, additional studies have appeared in the literature for the m-consecutive-k-out-of-n: F system
Summary
A linear (circular) consecutive k-out-of-n: F system consists of n components which are linearly (circularly) arranged and the system fails if and only if at least k consecutive components fail. Xn. It can be verified that, in the exchangeable case, the signature of a reliability system depends only on its structure and not on the specific underlying distribution of Xi. In other words, si(n) is the proportion of permutations, among the n! Eryilmaz and Bayramoglu [6] used the system signature in order to evaluate the extreme residual lifetimes of the remaining components after the complete failure of the system. Both reliability function and signature of a structure can be evaluated based on either recursive formulas or Journal of Quality and Reliability Engineering explicit expressions.
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