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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.
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Belzunce et al. (1999) studied this question.
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