The structural Birnbaum importance of consecutive-k systems

Abstract

This paper is concerned with three types of structural Birnbaum importance of components in a consecutive-k system. We accomplish the following three tasks: (i) Survey existing results, including pointing out results claimed but proofs are incomplete. (ii) Give some new results and useful lemmas. (iii) Observe what are still provable and what are not with the help of extensive computing.