**Naval Research Logistics (NRL)**

# Component importance for linear consecutive- *k* -Out-of- *n* and *m* -Consecutive- *k* -Out-of- *n* systems with exchangeable components

## Abstract

Measuring the relative importance of components in a mechanical system is useful for various purposes. In this article, we study Birnbaum and Barlow-Proschan importance measures for two frequently studied system designs: linear consecutive *k* -out-of- *n* and *m* -consecutive- *k* -out-of- *n* systems. We obtain explicit expressions for the component importance measures for systems consisting of exchangeable components. We illustrate the results for a system whose components have a Lomax type lifetime distribution. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013