| This study introduces the concept of consecutive-k-out-of-n:G systems. Twelve theorems are derived to establish and support the basic theory of consecutive-k-out-of-n:G systems reliability.;Applying the theorems, one can evaluate the reliability of linear consecutive-k-out-of-n:G systems and the reliability of circular consecutive-k-out-of-n:G systems, respectively. One can determine the reliability importance of components that indicates which component deserves the most additional investigation and development to improve the overall system reliability at the minimum effort. The study also provides a way to apply the methods for consecutive-k-out-of-n:F systems to consecutive-k-out-of-n:G systems. There exist n!/2 possible designs for a linear consecutive-k-out-of-n system, and (n ;Reliability evaluations are mainly based on recursive approaches. If all components are equally reliable and the system size n is less than or equal to 3k, the closed formulas are provided to evaluate the system reliability directly for both linear and circular systems. Bounds on the reliability of consecutive-k-out-of-n systems are studied since it is, sometimes, sufficient to know the bounds on the system reliability. An approximation to the reliability of a large linear consecutive-k-out-of-n:G system with equally reliable components is proposed and a suggestion in this situation is given. |
