Linear $m$ -Consecutive $k$ -out-of-

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.