Importance measures for two semi-coherent systems with shared components

Importance measures are widely used for single components or pairs/groups of components in single reliability systems for evaluating their importance in the systems. In this paper, two semi-coherent systems with shared components are considered, and then the B-reliability importance and B-TDL (time-dependent-lifetime) importance measures are proposed for evaluating the importance of the shared components in both systems. Signature-based representations are presented next for facilitating the computation of the two proposed importance measures. The results established here are finally illustrated with some numerical examples involving consecutive- k systems with shared components. Applications of the results can be widely found for many practical systems in the field of reliability.