Circular consecutive k-out-of-r-from-n systems and circular multi-state sliding window systems

Previous research on consecutive systems focused on the model with linear consecutive connected elements. A circular consecutive k-out-of-r-from-n system is proposed in this paper as a generalization of circular consecutive k-out-of-n system. The model is further generalized to be a multi-state circular sliding window system. Two algorithms based on universal generating function technique are proposed to evaluate the system reliability of the two proposed models. The model and algorithms are illustrated through examples.