In this article, we give some results on the preservation of orderings between the components under the formation of coherent systems with different structures. We consider the stochastic, failure rate, reversed failure rate, and likelihood ratio orderings to compare two coherent structures formed from a set of components and from two sets of components, in both cases, when components are independent and either identically distributed or not necessarily identically distributed. As a consequence, we get new stochastic comparisons of systems with different k-out-of-n structures, and some results of partial orderings given by other authors may be also obtained from ours.

In this article, we establish stochastic comparisons between normalized spacings of generalized order statistics. These comparisons allow us to extend and unify some results obtained by other authors for ordinary order statistics and record values. Furthermore, we can compare spacings of different models (i.e., between ordinary order statistics and sequential order statistics, record values and Pfeifer's record values, and so forth).

In this paper, we give characterizations of nonparametric families of life distributions based on aging and variability orderings of the residual life of k-out-of-n systems. We obtain some results of increasing (decreasing) failure rate classes as well as of new classes decreasing (increasing) mean residual life of the system and new better (worse) than used in expectations of the system. Relationships among themselves and others such as new better (worse) than used, new better (worse) than used expectations, and decreasing (increasing) mean residual life are also given.