A reliability model for multivariate exponential distributions

In this paper, we consider a counting process approach for characterizing a system having dependent component failure rates. We study the transient state probabilities and related reliability properties based on a series of Poisson shocks. We also show that the proposed infinitesimal generator representation can be used to characterize the bivariate exponential distributions of Freund, Marshall–Olkin, Block–Basu and Friday–Patil.