Abstract
The coherent systems are basic concepts in reliability theory and survival analysis. They contain as particular cases the popular series, parallel and k-out-of-n systems (order statistics). Many results have been obtained for them by assuming that the component lifetimes are independent. In many practical cases, this assumption is unrealistic. In this paper, we study them by assuming a time-transformed exponential model for the joint distribution of the component lifetimes. This model is equivalent to the frailty model which assumes that they are conditionally independent given a common risk parameter (which represents the common environment risk). Under this model, we obtain explicit expressions for the system reliability function and comparison results for the main stochastic orders. We obtain both expressions from minimal path sets and those from minimal survival signatures. Some aging classes and the system residual lifetime (under different assumptions) are studied as well.
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Acknowledgements
We would like to thank the anonymous associated editor and reviewers for several helpful suggestions. In particular, we want to mention that Sects. 4 and 6 and Remark 1 are due to these suggestions. JN and JM acknowledge the support received from Ministerio de Economía, Industria y Competitividad of Spain under grant MTM2016-79943-P (AEI/ FEDER, UE). JM also acknowledges the support received from the Conselleria d’Educació, Investigació, Cultura i Esport (Generalitat de la Comunitat Valenciana) under grant GV/2017/015.
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Navarro, J., Mulero, J. Comparisons of coherent systems under the time-transformed exponential model. TEST 29, 255–281 (2020). https://doi.org/10.1007/s11749-019-00656-4
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DOI: https://doi.org/10.1007/s11749-019-00656-4