Comparisons of coherent systems under the time-transformed exponential model

Jorge Navarro () and Julio Mulero ()
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Jorge Navarro: Universidad de Murcia
Julio Mulero: Universidad de Alicante

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2020, vol. 29, issue 1, No 12, 255-281

Abstract: 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.

Keywords: Coherent system; TTE model; Archimedean copula; Frailty model; Stochastic orders; 60E15 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11749-019-00656-4

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