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Article Citation - WoS: 13Citation - Scopus: 13Reliability Assessment of a Discrete Time Cold Standby Repairable System(Springer, 2021) Kan, Cihangir; Eryilmaz, SerkanThis paper is concerned with the study of a discrete time repairable system consisting of one active and one standby component. The lifetime and repair time are assumed to have discrete phase-type distributions. The system's lifetime is represented as a compound random variable. A matrix-based expression for the probability generating function of the system's lifetime is obtained based on the phase characteristics of lifetime and repair time distributions. The probability generating function is then used to obtain the distribution of the system's lifetime. Reliability and hazard rate functions are computed and evaluated for some particular choices of lifetime and repair time distributions. The limiting behavior of the hazard rates is also investigated.Article Citation - WoS: 8Citation - Scopus: 12On the Mean Residual Lifetime of Consecutive K-Out Systems(Springer, 2012) Salehi, E. T.; Asadi, M.; Eryilmaz, S.In recent years, consecutive systems were shown to have many applications in various branches of science such as engineering. This paper is a study on the stochastic and aging properties of residual lifetime of consecutive k-out-of-n systems under the condition that n-r+1, ra parts per thousand currency signn, components of the system are working at time t. We consider the linear and circular consecutive k-out-of-n systems and propose a mean residual lifetime (MRL) for such systems. Several properties of the proposed MRL is investigated. The mixture representation of the MRL of the systems with respect to the vector of signatures of the system is also studied.Article Citation - WoS: 11Citation - Scopus: 15Optimal Age Replacement Policy for Discrete Time Parallel Systems(Springer, 2023) Eryilmaz, Serkan; Tank, FatihIn the case of discrete age replacement policy, a system whose lifetime is measured by the number cycles is replaced preventively after a specific number of cycles or correctively at failure, whichever occurs first. Under the discrete setup, the policy has been mostly considered for single unit systems. In this paper, a discrete time age replacement policy is studied for a parallel system that consists of components having discretely distributed lifetimes. In particular, the necessary conditions for the unique and finite replacement cycle that minimize the expected cost rate are obtained. The theoretical results are illustrated with numerical examples to observe the effect of the cost values and the mean lifetime of the components on the optimal replacement cycle.
