ABSTRACT
Consecutive-k system is a general term for the systems, where a concentration of failed components causes the system failure. One of the consecutive-k systems is a consecutive-k-out-of-n system. It has been extensively studied since the early 1980s and was first studied by Kontoleon (1980). The consecutive-k-out-of-n:F (G) systems consist of n components and fail (work) if and only if at least k “consecutive” components fail (work). Based on this definition, we can see that a consecutive-1-out-of-n:F (G) system is equivalent to a series (parallel) system, while a consecutive-n-out-of-n:F (G) system is equivalent to a parallel (series) system.
