The study of stochastic comparisons of coherent systems with different structures is a relevant topic in reliability theory. Several results have been obtained for specific distributions. The present paper is focused on distribution-free comparisons, that is, orderings which do not depend on the component distributions. Different assumptions for the component lifetimes are considered which lead us to different comparison techniques. Thus, if the components are independent and identically distributed (IID) or exchangeable, the orderings are obtained by using signatures. If they are just ID (homogeneous components), then ordering results for distorted distributions are used. In the general case or in the case of independent (heterogeneous) components, a similar technique based on generalized distorted distributions is applied. In these cases, the ordering results may depend on the copula used to model the dependence between the component lifetimes. Some illustrative examples are included in each case.
Coherent systems Signature Stochastic comparisons Copula Distorted distributions
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I would like to thank an anonymous reviewer for several helpful suggestions. This work is supported in part by Ministerio de Economía, Industria y Competitividad of Spain under grant MTM2016-79943-P. A preliminary version of this work was presented at the 10th International Conference on Mathematical Methods in Reliability (MMR 2017), in Grenoble, France (July 3–6, 2017).
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