Eryilmaz, Serkan2026-04-032026-04-0320261573-77131387-584110.1007/s11009-026-10255-0https://hdl.handle.net/20.500.14411/11416https://doi.org/10.1007/s11009-026-10255-0This paper studies shock models by assuming a certain kind of dependence among shock magnitudes. In particular, discrete time extreme and run shock models are investigated when the shock magnitudes follow discrete autoregressive process of order 1. Exact expressions are obtained for the reliability functions and mean time to failure values under both models. The method for deriving the reliability characteristics is based on the use of probability generating functions. Numerical results are presented when the shocks arrive according to a Binomial process.eninfo:eu-repo/semantics/closedAccessDiscrete DistributionsProbability Generating FunctionDiscrete Autoregressive ModelShock ModelReliabilityArticle