Linear $m$ -Gap Sliding Window Systems

This paper proposes a new model that generalizes the linear multi-state sliding window system. In this model, the system consists of n linearly ordered multi-state elements. Each element can have different states spanning from complete failure up to perfectly functioning. A performance rate is associated with each state. The system fails if the gap between any pair of groups of r consecutive elements having the cumulative performance lower than a minimum allowable level W is less than m groups of r consecutive elements. An algorithm for system reliability evaluation is suggested which is based on an extended universal moment generating function. Examples of evaluating system reliability and elements´ reliability importance indices are presented.