A hierarchy of importance indices

An importance index measures the relative importance of a component in comparison to other components with respect to the system reliability. We survey many importance indices proposed in the literature, and some new ones of our own, to show how they relate. Our results can be used in two situations: 1) When components are functionally interchangeable, then more reliable units should go to the more important components. 2) When there is a fixed budget to improve the system reliability, the more important components should get first attention if everything else is equal.