Eryılmaz, SerkanTütüncü, Gözde Yazgı2023-06-162023-06-1620150932-50261613-9798https://doi.org/10.1007/s00362-014-0595-5https://hdl.handle.net/20.500.14365/865In this paper, two independent coherent systems with different structures, and different types of components are considered. The remaining lifetime and the remaining number of working components of system I after the failure of the system II when we know that the system II fails before the system I are studied. In particular, signature-based expressions are obtained for the distribution of these conditional random variables. Illustrative examples are provided.eninfo:eu-repo/semantics/closedAccessReliabilityResidual lifetimeSignatureMixture RepresentationsDependent ComponentsResidual LifeK SystemsReliabilitySignaturesLifetimesArticle10.1007/s00362-014-0595-52-s2.0-84939898345