Yalcin, FeminEryilmaz, SerkanBozbulut, Ali RizaIndustrial Engineering2024-07-052024-07-0520182300-229810.1515/demo-2018-00082-s2.0-85050892001https://doi.org/10.1515/demo-2018-0008https://hdl.handle.net/20.500.14411/2695Yalcin, Femin/0000-0003-0602-9392; Eryilmaz, Serkan/0000-0002-2108-1781In this paper, a generalized class of run shock models associated with a bivariate sequence {(X-i, Y-i)}(i >= 1) of correlated random variables is defined and studied. For a system that is subject to shocks of random magnitudes X-1, X-2, ... over time, let the random variables Y-1, Y-2, ... denote times between arrivals of successive shocks. The lifetime of the system under this class is defined through a compound random variable T = Sigma(N)(t=1) Y-t, where N is a stopping time for the sequence {Xi}(i >= 1) and represents the number of shocks that causes failure of the system. Another random variable of interest is the maximum shock size up to N, i.e. M = max {X-i, 1 <= i <= N}Distributions of T and M are investigated when N has a phase-type distribution.eninfo:eu-repo/semantics/openAccessCompound distributionsDependenceLaplace transformPhase-type distributionsShock modelsArticle61131138WOS:0004506849000024