The Hazard Rate and the Reversed Hazard Rate Orders, with Applications to Order Statistics

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Ordering conditional lifetimes of coherent systems (2007, background): “If X1 rhY1 then −X1 hr −Y1; see, for example, Nanda and Shaked (2001).”
Conditional Ordering of k-out-of-n Systems with Independent But Nonidentical Components (2008, methodology): “The following lemma, due to Nanda and Shaked (2001), will be useful in the sequel.”
Entropy-based measure of uncertainty in past lifetime distributions (2002, background): “As pointed out by some authors (in particular, see [10]), its role is dual to that of r(t).”
On the Comparison of Reliability Experiments Based on the Convolution Order (2003, background): “Moshe Shaked is Professor, Department of Mathematics, University of Arizona, Tucson, AZ 85721 (E-mail: shaked@hedgehog.math.arizona.edu).”
Mean residual life functions of finite mixtures, order statistics and coherent systems (2008, background): “Remark 3 The path set satisfying (36) can be called the ‘leading path’ set of the coherent system T. If the components are independent, then the series systems X P = min(Xi : i ∈ P) is hazard rate (and hence, mean residual life) better than X Q = min(Xi : i ∈ Q) whenever P ⊂ Q (see Nanda and Shaked”