New Developments on Stochastic Properties of Coherent Systems

We consider a coherent system consisting of n components where the component lifetimes are assumed to be random variables following a probabilistically exchangeable joint distribution function, where the probability distribution does not change with any permutation of the components. We study stochastic properties of the residual lifetime of live components of the system, under different conditions. The number of failed components of the system are explored, under the assumption that the system is operating at time t. We also study the probability that the ith component failure in the system causes the system failure, given that the system is operating at time t. The results of the paper extend some of the existing results in the literature.