Comparing with the joint importance under consideration of consecutive-k-out-of-n system structure changes

For a multi-component system, the impact of the alteration of components on the system reliability often needs assessment. Existing importance measures, however, do not consider the impact of the possible change of the system structure during its life cycle. Therefore, relevant factors should be considered to better reflect the changes in system reliability. To this end, this paper proposes joint importance measures for the optimal component sequence of a consecutive-k-out-of-n system. Incorporating the generalized measures, the paper obtains the joint integrated importance measure and the joint differential importance measure for the optimal component sequence in the binary and multistate consecutive-k-out-of-n systems. Then some properties of the proposed joint importance measures for optimal component sequence are analyzed. Furthermore, this measure reveals the relationship between component reliability and joint importance measure under consideration of consecutive-k-out-of-n system structure changes. Finally, numerical examples are given to demonstrate the applicability of the proposed measures.