The Barlow–Proschan importance and its generalizations with dependent components

AbstractFor a coherent system the Barlow–Proschan measure of importance of component i, defined when the components are independent to be the probability that i causes system failure, will here be generalized to the case where the component lifetimes are jointly absolutely continuous but not necessarily independent. When the system has a modular decomposition, properties analogous to that of the Barlow–Proschan measure are proved. Xie has generalized the Barlow–Proschan importance using the system yield function when all components are independent. This will be extended here to dependent components