Mean residual life functions of finite mixtures, order statistics and coherent systems

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Mixture Representations of Residual Lifetimes of Used Systems (2008, background): “they have the same law as t → ∞); see [7], [8], and [11] for analogous results based on the hazard rate and mean residual life functions.”
Parallel and k-out-of-n: G systems with nonidentical components and their mean residual life functions (2009, background): “Navarro and Hernandez [ 15 ] prove under some conditions that, (12) is a general property of the MRL functions of parallel systems.”
Signature-based representations for the reliability of systems with heterogeneous components (2011, result): “Hence, the asymptotic behavior (when t → ∞) of the ageing measures of T can be determined from the results established in [12], [13], and [16].”
Likelihood ratio ordering of order statistics, mixtures and systems (2008, result): “Block and Joe (1997) and Navarro and Shaked (2006) obtained similar results for the hazard rate function.”