Mixture Representations for the Joint Distribution of Lifetimes of two Coherent Systems with Shared Components

The signature of a system is defined as the vector whose i th element is the probability that the system fails concurrently with the i th component failure. The signature vector is known to be a distribution-free measure and a representation of the system's survival function has been developed in terms of the system's signature. The present work is devoted to the study of the joint distribution of lifetimes of pairs of systems with shared …