In this paper the Barlow and Proschan (1975) measure of the importance of a component in a binary coherent system is revisited. This measure is for the case of components not undergoing repair equal to the probability of the component causing system failure. It is a useful guide during the system development phase as to which components should receive more urgent attention in achieving system reliability growth. Here we suggest some possible extensions of this measure both for nonrepairable and repairable systems, and a series of new results are proved, also on the Natvig (1979) measure. For repairable systems we especially consider taking a dual term into account based on the probability of the component causing system repair.