Preservation of DMRL and IMRL aging classes under the formation of order statistics and coherent systems

If the random variable X represents the lifetime of a unit, the mean residual life (MRL) function m(t)=E(X−t|X>t) is a basic tool to study the aging process. The decreasing/increasing mean residual life (DMRL/IMRL) aging classes are defined by the corresponding monotonicity properties of function m. In this paper, sufficient properties are provided for the preservation of these aging classes under the formation of order statistics and coherent systems with identically distributed (ID) components. We consider both the cases of independent and dependent components. In the last case, the sufficient conditions are based on properties of the copula which determines the dependence structure.