On preservation of some shifted and proportional orders by systems

In this paper, we establish some comparison results of two coherent structures formed from a set of components or from two sets of components with respect to some shifted and proportional stochastic orders. Both cases, independent and identically distributed and not necessarily identically distributed components, are considered. As a consequence of our results, we get new comparisons of systems with different k-out-of-n structures and some results on closure of aging classes.