Computing Barlow-Proschan Importance in Combined Systems

This paper is concerned with the computation of the Barlow-Proschan importance measure for systems involving two common failure criteria, and consisting of statistically independent and identical components. The failure or survival of these systems generally depends on the number of consecutively failed or working components, or the total number of failed or working components in the whole system. The results are applied to $(n,f,k):{\rm F}$ and $ :{\rm F}$ systems.