Importance measures for optimal structure in linear consecutive-k-out-of-n systems

•Definition of importance measures for optimal structure is given.•Relationships among importance measures are analyzed.•Characteristics of importance measures for optimal structure are discussed.•Numerical examples in linear consecutive-k-out-of-n systems are demonstrated.

Importance measures can describe which component reliability change is the most promising if the system structure can be easily changed. Recently, the Birnbaum importance for reconfigurable systems based on the constant reliability has been discussed. This importance shows that importance variation corresponds to the change in system optimal configuration. Traditionally, importance measures do not consider the possible change in a system structure throughout the system's lifetime. However, the possible optimal structural change and the system's lifetime should be considered in importance measures, which can describe the change of component importance with respect to the changes of the component sequencing in optimal system structure during the system lifetime. This paper studies the Birnbaum importance measure, integrated importance measure, and Mean Absolute Deviation with respect to the changes in optimal system structure throughout the system's lifetime. These measures provide useful information regarding the relationships between component reliability and importance measures with the changes in optimal system structure. Finally, examples of linear consecutive-k-out-of-n systems are used to illustrate the utilization of the proposed method.