Consecutive k and related models—a survey

Abstract

As one of the most popular reliability models, the previous several decades have witnessed remarkable developments and extensive applications of consecutive k systems, and a number of related models have been developed. In the paper, a summary of the state of the arts in the field is provided. After a brief introduction of conventional consecutive k systems, we focus on variants of the consecutive k systems by considering failure criteria (single failure criterion and multiple failure criteria), geometric structure of the system, states of components and the system, weight of each component, dependency of components. Finally, several future challenges deserving further studies are highlighted.