Some New Results About Shifted Hazard and Shifted Likelihood Ratio Orders

Shifted stochastic orders are a useful tool for establishing interesting inequalities. Two such stochastic orders are the up hazard rate order and the up likelihood ratio order. In this article, we give some results on the preservation of the above orderings between the components un-der the formation of coherent systems with different structures. Both the cases when components either identically distributed or not nec-essary identically distributed are discussed. Finally, we provide some applications to Poisson and non-homogeneous Poisson shock models