Comparisons of coherent systems with non-identically distributed components

The signature-based mixture representations for coherent systems are a good way to obtain distribution-free comparisons of systems. Unfortunately, these representations only hold for systems whose component lifetimes are independent and identically distributed (IID) or exchangeable (i.e., their joint distribution is invariant under permutations). In this paper we obtain comparison results for generalized mixtures, that is, for reliability functions that can be written as linear combinations of some baseline reliability functions with positive and negative coefficients. These results are based on some concepts in Graph Theory. We apply these results to obtain new comparison results for coherent systems without the IID or exchangeability assumptions by using their generalized mixture representations based on the minimal path sets.