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Article Citation - WoS: 7Citation - Scopus: 7A Generalized Class of Correlated Run Shock Models(de Gruyter Poland Sp Zoo, 2018) Yalcin, Femin; Eryilmaz, Serkan; Bozbulut, Ali RizaIn 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.Article Citation - WoS: 22Citation - Scopus: 24Reliability Analysis of Weighted-K System Consisting of Three-State Components(Sage Publications Ltd, 2019) Eryilmaz, Serkan; Bozbulut, Ali RizaThe reliability of a weighted-k-out-of-n system that consists of three-state components is studied. The system is assumed to comprise n three-state components, namely, perfect functioning, partial working, and complete failure and functions if the total weight of all the working components is at least k. Reliability expressions are presented when the times spent by components in perfect functioning and partial working states are dependent with a given joint distribution. Sufficient conditions are also provided to compare the expected total weights of two systems.
