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Article Citation - WoS: 27Citation - Scopus: 31Generalized Extreme Shock Models and Their Applications(Taylor & Francis inc, 2020) Bozbulut, Ali Riza; Eryilmaz, SerkanIn the classical extreme shock model, the system fails due to a single catastrophic shock. In this paper, by assuming different arrival patterns of the shocks, two new types of extreme shock models are introduced. In these models, m possible sources may exert shocks on the system. Both models reduce to the classical extreme shock model when m = 1. Assuming phase-type distribution for times between successive shocks, we obtain survival functions and mean time to failure values of the system under new models. Two different optimization problems are also considered to determine the optimal number of sources.Article Citation - WoS: 29Citation - Scopus: 31Computing Marginal and Joint Birnbaum, and Barlow-Proschan Importances in Weighted-k-out-of-n< Systems(Pergamon-elsevier Science Ltd, 2014) Eryilmaz, Serkan; Bozbulut, Ali RizaA weighted-k-out-of-n:G system is a system that consists of n binary components, each with its own positive weight, and operates only when the total weight of working components is at least k. Such a structure is useful when the components have different contributions to the performance of the entire system. This paper is concerned with both marginal and joint Birnbaum, and Barlow-Proschan (BP) importances of the components in weighted- k-out-of-n:G systems. The method of universal generating function is used for computing marginal and joint Birnbaum importances. The method for computing BP-importance is based on a direct probabilistic approach. Extensive numerical calculations are presented. By the help of these calculations and illustrations, it is possible to observe how the marginal and joint importances change with respect to the weights of components. (C) 2014 Elsevier Ltd. All rights reserved.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.Article Citation - WoS: 36Citation - Scopus: 44An Algorithmic Approach for the Dynamic Reliability Analysis of Non-Repairable Multi-State Weighted k-out-of-n< System(Elsevier Sci Ltd, 2014) Eryilmaz, Serkan; Bozbulut, Ali RizaIn this paper, we study a multi-state weighted k-out-of-n:G system model in a dynamic setup. In particular, we study the random time spent by the system with a minimum performance level of k. Our method is based on ordering the lifetimes of the system's components in different state subsets. Using this ordering along with the Monte-Carlo simulation algorithm, we obtain estimates of the mean and survival function of the time spent by the system in state k or above. We present illustrative computational results when the degradation in the components follows a Markov process. (C) 2014 Elsevier Ltd. All rights reserved.
