Eryılmaz, Serkan2023-06-162023-06-1620100895-7177https://doi.org/10.1016/j.mcm.2009.12.007https://hdl.handle.net/20.500.14365/1332In this paper, we obtain representations for the reliability of consecutive type systems as a mixture of the reliability of order statistics whenever the systems consist of exchangeable components. The representations enable us to compute the reliability of linear and circular consecutive systems in a simple way. Furthermore the limiting behaviour of these systems can be evaluated and stochastic ordering results can be established with the help of these mixture representations. (C) 2009 Elsevier Ltd. All rights reserved.eninfo:eu-repo/semantics/closedAccessConsecutive k-out-of-n systemConsecutive k-within-m-out-of-n systemMaximal signatureMinimal signatureOrder statisticsSystem reliabilitySystem signatureOut-Of-NF SystemCoherent SystemsDependent ComponentsExchangeable ComponentsSimulationSignaturesArticle10.1016/j.mcm.2009.12.0072-s2.0-74149086076