Optimal allocation of elements in a linear multi-state sliding window system

This paper proposes a new model that generalizes the consecutive k-out-of-r-from-n:F system to multi-state case. In this model (named linear multi-state sliding window system) the system consists of n linearly ordered multi-state elements. Each element can have different states: from complete failure up to perfect functioning. A performance rate is associated with each state. The system fails if the sum of the performance rates of any r consecutive elements is lower than a demand W. An algorithm is suggested that finds the order of elements with different characteristics within linear multi-state sliding window system, which provides the greatest possible system reliability. The algorithm is based on using a universal generating function technique for system reliability evaluation. A genetic algorithm is used as the optimization tool. Illustrative examples are presented.