Linear $m$ -Consecutive $k$ -out-of-$r$ -From- $n:{\rm F}$ Systems

This paper proposes a new model that generalizes the linear consecutive
k
-out-of-
r
-from-
n
system to the case of
m
consecutive runs of
r
elements. In this model, the system consists of
n
linearly ordered statistically independent elements, and fails iff in each of at least
m
consecutive overlapping groups of
r
consecutive elements at least
k
elements fail. This system model is motivated by a heating system for moving parts. An algorithm for system reliability evaluation is suggested which is based on an extended universal moment generating function. Examples of system reliability evaluation are presented.