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Tail hazard rate ordering properties of order statistics and coherent systems. (English) Zbl 1136.62066

Summary: We study tail hazard rate ordering properties of coherent systems using the representation of the distribution of a coherent system as a mixture of the distributions of the series systems obtained from its path sets. Also some ordering properties are obtained for order statistics which, in this context, represent the lifetimes of \(k\)-out-of-\(n\) systems. We pay special attention to systems with components satisfying the proportional hazard rate model or with exponential, Weibull and Pareto type II distributions.

MSC:

62N05 Reliability and life testing
60E15 Inequalities; stochastic orderings
62G30 Order statistics; empirical distribution functions
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