STOCHASTIC ORDERING OF LIFETIMES OF PARALLEL AND SERIES SYSTEMS COMPRISING HETEROGENEOUS DEPENDENT COMPONENTS WITH GENERALIZED BIRNBAUM-SAUNDERS DISTRIBUTIONS

In this paper, we discuss stochastic orderings of lifetimes of two heterogeneous parallel and series systems with heterogeneous dependent components having generalized Birnbaum-Saunders distributions. The comparisons presented here are based on the vector majorization of parameters. The ordering results are established in some special cases for the generalized Birnbaum-Saunders distribution based on the multivariate elliptical, normal, t, logistic, and skew-normal kernels. Further, we use these results by considering Archimedean copulas to model the dependence structure among systems with generalized Birnbaum-Saunders components. These results have been used to derive some upper and lower bounds for survival functions of lifetimes of parallel and series systems.