Abstract
In this paper a general procedure is proposed to get stochastic comparisons of residual lifetimes of coherent systems. The comparison results obtained are based on the structure of the system and on properties of the copula used to describe the dependence between the component lifetimes. They are distribution-free with respect to the component lifetime distributions. We consider two system residual lifetimes at a given time \(t>0\). In the first one, we just assume that the system is working at time t while, in the second one, we assume that all the components are working at time t. We study the main stochastic orderings: hazard rate, stochastic, mean residual life and likelihood ratio orders. Specific results are obtained in the particular case of independent components and in the case of identically distributed components. Some illustrative examples are included. They prove that, in some cases, these system residual lifetimes are not ordered. Even more, surprisingly, sometimes the first residual lifetime is greater (in some stochastic sense) than the second one under a given dependence model.
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I would like to thank an anonymous reviewer for his/her helpful suggestions.
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Partially supported by Ministerio de Economía y Competitividad under grant MTM2012-34023-FEDER.
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Navarro, J. Distribution-free comparisons of residual lifetimes of coherent systems based on copula properties. Stat Papers 59, 781–800 (2018). https://doi.org/10.1007/s00362-016-0789-0
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DOI: https://doi.org/10.1007/s00362-016-0789-0