Dynamic Importance Measure for K-out-of-n System in Presence of Dependent Failure

Birnbaum importance measures the significance of a component to the system reliability. And it is widely applied in system reliability designs and risk assessments. Some studies have been made on Birnbaum importance for k-out-of-n systems, but most of them assumed that the failures of components are statistically independent of each other. In practice, component failures are usually statistically dependent and common cause failures (CCF) are almost ubiquitous in complex systems. Based on the system-level stress-strength interference (SSI) analysis, Birnbaum importance for k-out-of-n systems with same components and different components are extended. This approach can be applied to dependent systems to find weaknesses of systems in the presence of CCFs. Through two examples, we further illustrate the importance measure and discuss some attractive properties about the new importance measure: i) the extended importance measure is intuitive and simple to use; ii) importance of a component changes regularly with the variation of strength distribution parameters of the component; iii) failure dependence has a great influence on the importance evaluation and further may results in wrong importance ranking of all the components.