Linear $m$-Gap Sliding Window Systems

Abstract

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.