In this talk we consider lifetime of coherent systems as a generalized finite mixture model, which formed by dependent and identically distributed (d.i.d) components. We then establish some general results for the comparisons of two such generalized finite mixture models in two different cases: (i) when two mixture models are formed from two random vectors ${\bm X}$ and ${\bm Y}$ and having same weights, (ii) when two mixture models are formed with the same random vectors and having different weights. Because the lifetimes of $k$-out-of-$n$ systems and coherent systems are special cases of the considered mixture model, we established results and then used to compare the lifetimes $k$-out-of-$n$ systems and of coherent systems with respect to various stochastic orderings.
