Design and performance analysis of consecutive-k-out-of-n structure

A consecutive-k-out-of-n:F system consists of an ordered sequence of n components such that the system fails if and only if at least k consecutive components fail. This research summarizes the results available for the invariant optimal designs of consecutive-k-out-of-n systems, identifies invariant optimal designs of some consecutive-k-out-of-n systems, proves that there do not exist invariant optimal designs for other consecutive k-out-of-n systems, and thus completes the theories on invariant optimal designs of these systems. For those systems without invariant optimal designs, a heuristic method and a randomization method are presented to provide at least suboptimal designs.