The literature on "weighted k-out-of-n" systems is briefly reviewed. The concept may result in systems with quite a broad array of possible structures and thus seems more aptly described by the phrase "systems with weighted components (SWCs)". It is observed that a system with weighted components of order n is equivalent to a coherent system of order no greater than n. We describe how to obtain the equivalent coherent system. While not every coherent system is equivalent to an SWC, necessary and sufficient conditions on the parameters of an SWC are identified for the two systems to be equivalent. We then examine how the component weights influence the lifetime of the SWC and the reliability importance and structural importance of its components. Consecutive linear SWCs are also studied. We conclude with a general summary and discussion and some commentary on the calculation of the reliability of an SWC.
Coherent systems Cut and path sets Failure profiles Reliability importance Structural importance Consecutive SWCs Signature Inclusion-exclusion formula Domination Stochastic order
