Relayed consecutive-k lines.

A consecutive-k line is a system of components in sequence such that the system fails if and only if some k consecutive components all fail. Various relayed systems often quoted as examples of such systems differ from the definition by the fact that the first component must work to initiate the relay (in some cases the last component also must work). We differentiate such systems from ordinary consecutive-k lines by adding the word "relayed". We show that the main properties of the reliabilities of consecutive-k lines are preserved under this modification.